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The Problem with Teddy – A Short Story

The Problem with Teddy – A Short Story

By Leighton Vaughan Williams

It was difficult to argue with Teddy. Whether he was right or wrong, I could never be sure. But I was sure of one thing, that if he said something was going to happen, it did. That was the problem with Teddy. He never got it wrong. And soon that would become a problem for me.


Chapter 1
The problem with language

A dog can expect its master. That is certainly true. But it can’t expect its master next Tuesday,” said Teddy. “Why not?” I asked. “Because a dog has no concept of time?” “No,” responded Teddy, “it is because a dog has no concept of language.” “So can a lion expect a meal when it sees its wounded prey?” I enquired. “You could ask it,” he said, “but you would never understand the answer. Because even if a lion had language, it would be no language we could ever understand.”

“You see,” said Teddy, “language is how we experience the world, as well as the way that we choose to represent it.”

“So language represents the boundaries of what we can know?”, I asked. “You have said it,” he exclaimed. “In clear, plain language.” “This doesn’t mean that nothing exists that can’t be expressed in language, only that it is outside the limits of our philosophy. “There are more things in heaven and earth than are dreamt of in your philosophy,” I offered. “Yes, than in all our philosophies”, he assured me. “But we can never use philosophy to find or explain them.”

“Can you be sure of that?”, I asked. “There is no way to verify that. And if a statement can’t be verified it is meaningless. That’s the test of a meaningful statement.” For a brief moment I felt clever.

“Why do you say that an unverifiable statement is meaningless?’” Teddy asked me. “In that case your own statement is meaningless.”

It was difficult to argue with Teddy. Whether he was right or wrong, I could never be sure. But I was sure of one thing, that I had never shown him to be wrong. Not to myself or to anyone else. That was the genius of Teddy, but it was also the problem.


Chapter 2
The problem with probability

“Even a double-headed coin can come down tails,” said Teddy when he entered our shared workspace, displaying his particularly sprightly gait. And his tap, tap, tap of ebony stick. Now, he didn’t need the walking stick. But he did like to tap, tap, tap it along the floor. That was another problem with Teddy.

“I don’t see how a double-headed coin can come down tails,” came my instant riposte. “It’s all about probability,” he said. “It’s a very low probability, but in the quantum universe, a double-headed coin can definitely come down tails.” I assumed he was right, but I couldn’t see how.

He read a lot, and was proud of what he’d learned. “The man who DOES NOT read the great thinkers has no advantage over the man who CAN NOT read them,” Teddy once told me. “The same goes for a woman,” I said, trying to sound enlightened. I liked to sound enlightened in front of Teddy. I don’t know why. I never did. Even when I said something that I thought made some kind of sense. A glance from Teddy always made that abundantly clear.

But I did admire Teddy’s uncanny ability to distinguish what was going to happen from what was not. He had the gift of what some call prescient foresight but what others might call knowing a sure thing.

You see, when Teddy said something would happen, it happened. Like when he called double-six on the pair of dice I had brought from home. That’s a 35 to 1 chance, logic told me, but in my belly I knew it would happen. I knew that as soon as Teddy said six-six. And six-six it was. I guess you could call it a trick, or you could call it magic. I don’t know about that, but I did now something for sure. If Teddy said it would happen, it would. Never bet against Teddy. That was my watchword. Until I did.


Chapter 3
The problem with wagers

“It’s usually best to back the favourite”, I told Teddy. “I had read it in a book. A book by an expert.” “That’s true if you’re talking probabilities,” said Teddy. So now I knew it was true. “But if you know something is going to happen, that doesn’t apply,” he said.

And so we went on Sunday night to the casino, at the insistence of the man who knew when things would happen. We never met at the weekend, but today there was a reason, said Teddy. He knew I would win.

“Let’s play roulette,” he said. And produced a wad of notes, a very big wad of notes. “”Red or black,” he asked. “You choose.”

I chose black. “I would choose red,” he said. “It’s your money,” I said. “No, it’s not,” he replied. “It’s yours now, a thousand pounds, to lose, to double, or to keep.”

“Can I just keep the thousand pounds?” I asked, and not risk it on red, or black. It was a joke, of a kind. Teddy was not a generous man, and certainly not generous enough to gift me a grand. And to me it was a lot of money, money I needed to live.

“You’ve struck lucky in the quantum world,” said Teddy. “The thousand is yours. To keep or to spin. I say red, and I say it’s a sure thing.”

“One spin of the wheel, for the lot, or take it home. Your choice.”

Now, when Teddy said something would happen, it did. And he was saying it was going to be red. But my common sense told me that Teddy could not know. The wheel had not yet even started to spin.

“I’ll keep it,” I declared. A thousand pounds. “OK, cash it in,” he said. “It’s yours.” I protested – what if we share it, I said? But he declined. Teddy didn’t need the money. Knowing what would happen had already made him a rich man. And he was not the kind to share. “Good night,” he said, and tap, tap, tapped off into the gathering twilight.

So to the next day, and I asked him how he knew the ball would have landed on red. “I knew we’d never find out,” said Teddy. “Because I knew you’d never wager a thousand pounds on the spin of the wheel.” “But what if I had spun the wheel?” I asked. “Then you would have won,” he said. “A universe in which you would spin that wheel is a universe in which you would be sure to win.” I thought I understood what he meant.


Chapter 4
The problem with money

“Does it make you happy, knowing what’s going to happen?” I asked. “Isn’t it a burden?” “I don’t always know what’s going to happen,” he corrected me. “But when I know for sure that something will happen, it does,” he said. “It’s not at all the same thing.”

“But that’s enough to make you a lot of money,” I said. “Knowing some things for sure that others think are unsure has made you so much money.”

And so he told me the tale of Thales, the Greek philosopher, who made his fortune by the application of modern day principles of analysis to ancient day Greece. The story involved forecasts and finance and options on olive presses. I honestly can’t recall all the details. But Teddy could. “Which shows,” he concluded, “that it is much easier for a philosopher to become rich than for a rich man to become a philosopher. But the ambitions of philosophers are of another kind.” It was clear he was talking about himself.

As for me, I just wanted to be rich like Teddy. I knew I would never be as wise.

But all of his great knowledge, great insight, great wisdom – was a burden to him? He seemed to read my mind.

“Great wisdom does not necessarily bring great happiness,” was his now detached observation. “Nor does great riches.”

“So maybe I’m better off being ignorant old me,” I said. “Just seeking the simple things in life, and enough money to enjoy them.”

He shook his head now, disapprovingly.

“Which is better?”, he asked me, “to be a human being dissatisfied or a pig satisfied, to be Socrates dissatisfied or a fool satisfied?” He was quoting one of the great philosophers again. I could tell that by the way he spoke his syllables. But I didn’t really understand the question, let alone the answer. That, I am afraid, was the problem with me.


Chapter 5
The problem with cars

We shared coffee and lunch that day, accompanied by the walking stick, the shiny ebony walking stick. I plucked up courage to ask him about the walking stick, why it accompanied him wherever he walked. “This is not a walking stick,” he replied. I did not ask again.

“So what if I told you that I am sure you will be knocked down by a car tomorrow?”, he now asked me.

“You can’t be sure of that,” I said. “I might not go anywhere near a car.” I suspected he was joking. Not a pretty joke, but Teddy and good taste didn’t always see eye to eye.

He reminded me that there was no way of reaching the office without crossing a road. “I’ll be extra careful,” I said.

“You will be knocked down by a car tomorrow,” he repeated, ” and you will be crippled for life.”

He was deadly serious and now I was scared, because when Teddy knew that something was going to happen, it always did.

“It can’t be inevitable,” I said. “What if I don’t even step outside my front door?” “You won’t do that,” he replied. “You are too curious to see if I’m right.” “Nobody’s that curious,” was my instant response. But I was, because I couldn’t see how he could know this. It was like predicting where the roulette ball would land before the wheel even started spinning. I told him so. “Or like predicting six-six on the dice,” he said. I shuddered – and suddenly felt cold.

How could he know? Had he heard of a plot to harm me? Did he know people who knew? Or was he planning to harm me himself. But if so, why warn me? I could make no sense of the problem, no way through the maze. What would Socrates make of this, I wondered. And what advice would he have for the fool?

I asked Teddy for evidence, for proof. He offered none. He said he knew but said he could not explain. Not to me. He gave no reason, but this told me nothing, because he never did. He never told me how he knew that something would happen, but I knew that it always did.

I turned to close friends, close family. Ignore it. Play safe. He’s just trying to frighten you. Maybe he knows something. A mix of opinions, but nothing to help. Not one of them knew Teddy, nor his ebony stick. And not one of them knew that when Teddy knew something, he knew it for sure.

That was the problem with Teddy. And now it had become a very real problem for me.

Chapter 6
The problem with fate

The day wore on and soon a decision had to be made. A choice to make. A choice between the evidence of my experience, that Teddy was never wrong, or my experience of the evidence, of which there was none. I asked Teddy one last time before we retired to our separate homes. Should I stay home all the next day, or should I brave life’s fate? Could I change destiny?

“All fates are possible,” said Teddy, “but the universe where you will come to no harm is not the universe in which you currently live.” I was thinking back now to that spin of the roulette wheel. In a universe where I spun the wheel, I felt sure I would have won. I chose not to. But I could have done. Surely this meant that life’s events were not pre-destined, written in stone and waiting to simply unfold. I could do something about it. I could have spun that wheel. But that would have been a different universe, where everything would be different. Would it even be me on that universe? I wanted to go back, to ask myself to spin that wheel. But I could never meet myself, because yesterday I was a different person, as are we all. We can never go back and meet ourselves, only meet ghostly shadows of who we were, shadows that made us what we are and who we might have been.

I no longer saw things as they were, asking why. I saw things now as they might be, asking why not.

“I can change the world,” I told Teddy. “I can spin that wheel.”

“Yes, we can change our destinies,” he said. “We have the freedom of will to choose.”

It was approaching six and the caretakers came to shut up the building. It was not the perfect arrangement, but it suited us.

He picked up his ebony stick and set off, with his usual jaunty gait. “You are quite the philosopher now,” he called back, “I’ll see you the day after tomorrow.”

“But …” I started to say. He was gone already. That was the problem with Teddy. Always too quick on that stick.

Chapter 7
The problem with thinking

I woke up at dawn next morning and thought of the double-headed coin that might come down tails. But I knew that I could do nothing about that. The quantum world was out of my control.

But some things were within my control, and one was the choice of whether to change life’s plan, to spin the wheel, to change the course of fate.

This could mean staying home, behind closed doors, away from the rush of traffic. This is what it meant to Teddy. But this is not what it meant to me.

Teddy saw things as they were, and he saw things that would be. I now saw things differently. I saw a world as it might be. Where I had the choice to use reason and faith and hope. To conquer fear, on my own terms.

But reason told me that Teddy’s foresight of my fate was not to be overlooked lightly. Teddy didn’t make that kind of mistake.

But Teddy’s universe wasn’t the one I had to inhabit. I could change my destiny. I could stay home, shuttering out the summer day. But I was becoming a philosopher. And the ambitions of philosophers are of another kind.

“A dog can expect its master, but it cannot expect its master next Tuesday,” Teddy had once explained. I thought of that now as I realised that Teddy was not expecting me today. I had become a philosopher, a thinker. Teddy would soon see.

So I called a taxi, all the way to my front door, and asked to be dropped off at the back entrance to our shared workplace. No cars to knock me down. I would be straight into that taxi, approached from the back. I would ask for the back door of the taxi to adjoin the back door of the workplace. I would give an excuse. Security. And the same when I returned home. Reason over fear. No room for error.

Until the taxi, en route from home to work, came to a halt. On the busy dual carriageway. Something rattling. So Teddy was right. Terrifyingly right. Could I get out and help him identify the noise, asked the driver. No, no, no, I screamed! He looked at me as if I was slightly mad. But this madness had method. To spin the wheel, to save life and limb.

And soon we got going again, me firmly in back seat.

So it was with some surprise, and my almost crazed relief, that we arrived at the door. To park with back door adjoining back door came as a curiosity to the driver. But he nodded sympathetically and I tipped him in thanks.

I skipped up the steps to our plush interconnecting offices, where Teddy wrote software, and I helped him do it. He heard my steps and tried to shut the door, but I was through first. “How are you here?” he shouted. “You’re at home!” Evidently not, I might have replied. Instead, I just stood there, in openmouthed shock at the scene that unfolded before me.


Chapter 8
The problem with Teddy

Every drawer had been emptied, every cupboard laid bare, ornaments and accessories opened or turned upside down. If something had been hidden, it would by now have been found. “What is happening?” I would have sat down, but the seats were upturned, and I had no stomach to right them.

“A burglary,” he said. But I didn’t believe him. “Why would burglars turn everything upside down and take nothing?” I asked. “That beggars belief.”

“I disturbed them,” he said, “took about them with my stick. They fled.”

“Let’s call the police,” I insisted, “Check the CCTV.” “No,” he said sharply. “Let’s not.”

A short pause. “Is it safe?” he asked. “Is it safe?”

“Is what safe, Teddy, is what safe?”

He seemed unsure now, what to say or do. “They were my numbers,” he said, “I suggested the numbers. They came up on Saturday night. I know that you keep it here, you always keep your ticket here until you check the numbers on a Wednesday. And I know you never sign it. Be fair, Charlie, let’s share it.”

He looked at me menacingly. Teddy, I knew, was not the sort of man who shared anything. It was all about Teddy. The gift of the thousand pounds now made sense. He had made his case, that I should spin the wheel, that I could re-arrange fate. But a gift so generous. Now I saw. It was his back-up plan.

“No, Teddy, it isn’t safe. I didn’t buy a ticket last week. There’s nothing to share.”

Teddy lunged at me, screaming, before collapsing to the floor, thrashing around. Yet still looking up at me, the look of sheer menace still etched on his face.

I was relieved that I hadn’t bought a ticket. He would have found it, signed it, cashed it, if it had existed. I would not have seen a penny. He had suggested some numbers, but for once this was blind chance. He had not seen the future, the future had grasped him invitingly by the hand. Or so he had thought. And now he sought control, control of what was to come.

I peered now yet further into his soul, and saw it for what it was. I had glimpsed it before. But what I saw now was yet darker. Consciousness without conscience. A man with no love for anything higher or other than himself.

And I saw now how the things he forecast always came true. Because he made them come true. Until now. He was the sort of man who would sell shares in cruise liners and then plant an iceberg, if he could.

“But you would have been rich too!” cried the man who was already rich. The man who lived in a mansion and looked down on the homeless. The man who liked to rip up the charity envelope.

“What shall it profit a man if he should gain the whole world, and lose his own soul?” I asked him now. “Answer me, Teddy!” But no answer came from the man who knew when bad things were going to happen, who knew because he made those things so.

I picked up his stick. I wanted to hit him, to beat him with that shiny, ebony stick. He cowered. A coward, infused with consciousness, but devoid of conscience. I put it down again. It would have given me satisfaction. But it would have made me more like Teddy. For Teddy, his own personal satisfaction was all that mattered.

That was the problem with Teddy. I didn’t want it to be the problem with me.

I sat on the floor, and considered my options.

“I have something to report,” I told the operator. About some bad things that have happened, some things unexplained. Can I speak to the police?”

Bertie’s Big Idea – A Short Story

Bertie’s Big Idea – A Short Story

By Leighton Vaughan Williams


Albert ‘Bertie’ Simpson Sinclair was a man who in earlier days might have been described as a bounder and a cad, albeit an immensely likeable and charming member of that sub-species. The problem for Bertie was that he was, as such, a hopeless, if heroic, failure. But Bertie was an optimist, a man who believed in the philosophy of ‘one more push’, of the sure triumph of unsound hope over all too sound experience. And he had an idea which he believed would make him rich. This is the story of Bertie and his magnificent idea.


Bertie’s Dream

Mr. Bertie Simpson Sinclair liked to think of himself as an ideas man. And an ideas man he certainly was. He had plenty of ideas, albeit none of them good. But his latest idea was going to be different. Of that he was sure. He had envisaged, in one giant midsummer night’s dream, a scheme to make himself rich, without making others commensurately poor. To this extent, it was an unusual idea for Bertie, for whom all previous schemes consisted of persuading others to part with their money in pursuit of an apparent though negative actual benefit. Bertie called such schemes win-win. By this he meant that he would win twice, first by taking their money, then by virtue of the scheme into which they had invested. The problem for Bertie was that every such scheme remained a dream, for all his boundless wit and charm. Even his plan to sell tips on the horses, then persuade his followers to place their own money on these gems of advice and share with him half the winnings, but none of the losses, failed when faced with the cold light of reality. There were so many others, including Bertie’s ‘Grow rich while you sleep’ manual, his ‘Learn while you doze’ method, his ‘Snooze yourself slim’ prospectus, his ‘Succeed while you slumber’ pamphlet. Bertie reasoned that alert, wakeful people were out of his reach, which left the more reposed segment of the population as his natural target audience. It was not just the fact that he himself was neither rich, learned, successful nor svelte. The real problem for Bertie was that he had singularly failed to convince even one other member of the human race that he could help them become what he so evidently was not. But that, decided Bertie, was about to change. Because of his midsummer night’s dream.


Bertie’s Idea

Bertie liked to think of himself as a clubbable man, a sociable ‘bon viveur’ who could mix with natural ease and grace with ladies and gentlemen of refinement. To this end he sought membership of tennis clubs, golf clubs, health clubs, focusing on the most exclusive of each. But Bertie had not grown rich while he slept. On the contrary, he had grown increasingly poor even as he dreamed of growing rich. As such, he was unable to actually gain entry to any of these clubs of the clubbable, as he thought of them. It was all an unrequited dream. But then came the big dream, that midsummer night, the night that inspired Bertie’s big idea. He had dreamed that he was at the door of one of these desirable clubs of the clubbable, begging inwardly to be allowed in, when an elegantly attired gentleman, upon exiting, had spotted the less than svelte figure of the unlearned though charming Bertie, and spoken to him, softly.  “Sir,” he had quietly ventured, “what are you doing waiting at the door? Did you not know that this is a club reserved only for the clubbable?” Taking immediate offence, Bertie’s dreamworld person had risen quickly to his own defence. “I AM a clubbable man,” he had expostulated, invoking his own claims to that most cherished status in society. But something within him had turned, something that was stirred by the well-dressed accuser. And so awoke Bertie, with his brand new big idea, an idea which he had instantly concluded would make him rich.


Bertie’s plan

A club for the unclubbable! That’s what he would create. He would create the world’s first club which would only accept members who didn’t want to join, members who were truly unclubbable. He would in other words create a club for those unwilling to join any club that would accept them as a member. The idea was one thing, turning it into a practical scheme was quite another. But that, for Bertie, was the challenge. And the rewards beckoned for Bertie like a shining beacon on a golden hilltop. At least that’s the way that Bertie visualized things. But he knew he was at base camp and the climb that lay ahead was steep and possibly long.

He was not a gifted thinker, but he did have thoughts, and the first of these was to place an advertisement in the local newspaper. Although a man of strictly limited means, it was his only hope of starting the climb which would take him to that shining beacon atop the golden hilltop. The advert was quite simply stated. “Would you join any club that would accept you as a member? If so, we’re wrong for you. We are the world’s only club for the unclubbable. We accept all and only those who don’t wish to join us.”

It was more words than Bertie could really afford, but he had seen that beacon atop the glittering hill and this was his one-time chance to glimpse its light. In the face of that shining lamp, he was steadfast. He would not blink. He waited. For the first response. It arrived by mail the very next day. Addressed to Mr. A. Sinclair, the envelope contained one sheet of blue vellum notepaper. In neat lettering, it was from a Mr. Charles Bone, who simply enquired whether there was an active membership of the club. If so, he was not interested. If not, he might be. Bertie replied with alacrity.  “There is no active membership, so we do not wish to accept you as a member.” By return of post, Mr. Bone accepted membership of this club that didn’t wish to accept him as a member, on one condition. “I am not an active man, and have no wish to be involved with active people. I will join on this condition,” wrote the first and thus far only member of the world’s first club for the unclubbable.

By the same post came an enquiry from a Miss Edith Spratt, who declared herself unwilling to join the club because, while she had been told of the advert, she was not from the local area. As such, she could not make use of its services, even if she wished to, which she did not. Bertie was delighted to accept her as a member, because she was so clearly unable and unwilling to benefit from membership. He wrote to tell her so. On this basis, Miss Spratt became the second member of Sinclair’s club for the unclubbable.

No fee was asked, and none given, by either Mr. Bone or Miss Spratt. But they served their purpose. Neither could in any way reasonably be classed as active members of the fledgling club, but there was now at least a club in existence, and in their different ways both of its members were of the unclubbable kind. There were no further replies to the advertisement, but Bertie was not discouraged. He had left base camp and set forth up the golden hill. He would not turn back.

And so came to Bertie his next idea. If he could introduce Mr. Bone to Miss Spratt, they might help him spread the word through what he conceived as some form of human chain letter that would spread forth and gather together the great unclubbable hordes, brought together into one vast club composed of only those unable and unwilling to join a club.

“Do you possess transport?” Bertie now wrote to Miss Spratt. “Yes”, came the one word reply. Seizing upon this positive news, Bertie devised a plan to bring together the only members of his brand new club. He offered, though he could ill afford it, to pay the cost of fuel for what would be a 70 mile journey for Miss Spratt. The response from Miss Spratt was quick in coming and even quicker in its message. “Dear Mr. Sinclair, my transport is an electric wheelchair. Yours sincerely, Miss E. Spratt”.

To Bertie, that hilltop was starting to look further away than ever.


Bertie’s vision

Was Bertie’s vision turning into a mirage? It was a question that might have deterred many, but not a question that deterred Bertie. If Miss Spratt could not come to Mr. Bone, then Mr. Bone must be brought to Miss Spratt, reasoned Bertie with impeccable rigour. Without further ado, he grabbed his quill-like pen, and rushed off a letter. “Dear Mr. Bone, I would like you to meet Miss Edith Spratt.  Like you, she is totally unsuited to the life of a club. In short, she is totally unclubbable. Yet she is a member of the club to which you belong. I think this remarkable coincidence is too great to be overlooked. For that reason, I would like you to meet Miss Spratt. She lives some distance away, but this has the advantage of offering you a pleasant journey even if the meeting is less pleasant than might reasonably be hoped. I hope you reply affirmatively. Yours sincerely, Albert Simpson Sinclair.”

Mr. Bone responded immediately, posing just one short question. “Is Miss Spratt an active member of the club?” Bertie was eager to re-assure. “No, Miss Spratt is not an active member of the club. I trust this reassures you.” It did. The following day, Bertie received the acceptance of his invitation. All that remained was to persuade Edith Spratt to accept the same invitation to meet Mr. Bone. “Dear Miss Spratt,” wrote Bertie, “I would like you to meet Mr. Charles Bone. He is not a clubbable man, and by natural inclination not an active man, but he shares with you membership of the club which I am proud to manage. I trust this remarkable coincidence offers sufficient grounds for you to accept this invitation. Yours sincerely, Albert ‘Please call me Bertie’ Simpson Sinclair.

The letter of response arrived by return of post. Addressed to Mr. Bertie Sinclair, and written in exquisite script, it was simply expressed. “Dear Bertie, I accept your invitation. Please be so kind as to bring Mr. Bone to me. Yours truly, Edith.”

And so was arranged the meeting between Mr. Charles Bone, retired undertaker, and Miss Edith Spratt, lady of leisure, to take place the following Wednesday at the home of Edith Spratt. Thursday and Friday came and went, as did the weekend, but no news leaked out. For several more days, Bertie rushed each morning to pick up the morning mail. But no letter arrived from either Mr. Bone or Miss Spratt. After two weeks had elapsed, which seemed like three months, Bertie reached for his pen and wrote to Mr. Bone. “Dear Mr. Bone, I hope and trust that your meeting with Miss Edith Spratt went well. Perhaps your meeting went so well that you have had little time to write letters. If so, I would be delighted to hear of this happy news, which you might perhaps share much more widely. Yours expectantly, Albert Simpson Sinclair”.

Sooner rather than later a letter arrived, addressed to Mr. A. S. Sinclair.

“Dear Mr. Sinclair,” it read, “Thank you for arranging the meeting between myself and Miss Spratt. You assured me, however, that the lady was not an active member of the club. I cannot agree with your assessment. Could you in future introduce me to one of your less active members? Yours sincerely, Mr. Charles Bone.”

The human chain letter, it seemed, had come apart at the first link.

Bertie took pen to fresh paper, addressed to Miss Edith Spratt.

“Dear Miss Spratt, I understand that no developments arose out of your rendezvous with Mr. Charles Bone, and that you are no longer in contact. Can you confirm my impression? With sincere regards, Albert (Bertie to you) Simpson Sinclair.”

Two days passed, while Bertie fretted. And then it came. The envelope was coloured pink and addressed to Bertie Sinclair. On matching pink notepaper, it simply stated. “Apparently I was too active for the liking of Mr. Bone, or so he told me. Please do, however, feel free to introduce me to someone from your club rather more active than Mr. Bone. Hoping to hear further. Yours in anticipation, Edie.”


Bertie’s day

Bertie had lost interest in Mr. Bone, but not in his project. He still possessed the vision of a network of clubs composed entirely of unclubbable people. But the vision was starting, even to Bertie, to flicker a little. His only hope now, he reasoned, lay with Miss Edith Spratt. But he had nobody else to introduce her to, active, inactive or semi-active. Except himself. And so he resolved to visit Miss Spratt at her residence, disguised as a member of his club for the unclubbable. He wrote as follows.

“Dear Edie (if I may), I am sorry to hear that you were too active a member for Mr. Bone. I prefer to see it from a different perspective – that he was not active enough for you. That can easily be remedied. I have on my books a very unclubbable man, who likes his own company, but who I can assure you is a very active member of the club. I will send him to you next Wednesday, if that is convenient. Kindest regards, Bertie.”

Wednesday did prove convenient, and soon a disguised Albert Sinclair, replete with flowing beard, heavy horn-rimmed spectacles and extravagant moustache, was entering the country residence of the wealthy widow newly self-described as Miss Edith Spratt. Introducing himself as Archibald Henry, former solo arctic explorer, he was at once able to tick two boxes, as both a private man and an active man. Miss Spratt was impressed to meet an explorer, less so a former explorer, and even less so a man who had clearly given up the athletic lifestyle at some distant corner in time. They had little in common, so she asked him whether it was cold in the Arctic. Yes, very cold, he said, and there the discussion of his days as an explorer froze. It was only when he spoke of the club that she lit up, asking him whether he had ever met Mr. Bertie Sinclair. She was disappointed to hear he had not, sharing with him her secret crush on this exciting innovator who had created a wonderful club for the unclubbable, and whose charm and good manners flowed out of every word he committed to paper in his delightful letters. She confided in the former explorer how she secretly wished Bertie would visit.

What had he done? This lady of wealth and refinement wanted him, Bertie, and he had entered her life disguised as a hairy arctic explorer. What should he do? Should he discard the disguise and reveal himself, like some sort of superhero, to be the witty, charming man of her dreams? He thought better of it, if only because he wanted more time to think. He bid her farewell and returned the 70 miles to his small suburban bedsit.

He had not spotted the electric wheelchair she had spoken of, but he had been dazzled by the vintage Mercedes sports car gracing her ample driveway. It somehow made her all the more attractive. He slept fitfully that night, rising at dawn to do what he had to.

Drawing from his battered desk the fine stationary he used for only the most important of communications, he applied modern quill to traditional vellum. “Dear Edie,” he wrote, “Mr. Henry, who visited you at my invitation, has contacted me to express his great pleasure at the making of your acquaintance. He tells me, however, that he is not worthy of your notice, and has asked me to convey his great good wishes to you in all you do. Although I am persuaded that I also am not worthy of your notice, I would be happy to follow in the estimable footsteps of our arctic adventurer in order to make your personal acquaintance, should that be your wish. I remain, with the greatest respect, your humble servant. Bertie.”

The next day dragged heavily on Albert Sinclair, as he waited and hoped for a positive reply. He was waiting at the door next day for the arrival of the postman. A quick reply should mean good news, a slow reply worse news, and no reply the worst news of all. The pink envelope arrived at the first opportunity. He opened it gently, hardly daring to read it. “Dear Bertie. I did have some regard for Mr. Archibald Henry, and believed that under his hirsute exterior probably lurked a fine, attractive gentleman. Still, I expect the excess of hair served him well in the cold arctic climate, and he has now grown well accustomed to it. Yes, I would indeed welcome a visit from your fine self. For a man of your considerable talents as gifted entrepreneur, your humility is a further charming sign of the true gentleman that you so clearly show yourself to be. With regards from your friend, Edie.

Bertie could not contain all the excitement shooting through his body. All that stood between him and the wealthy, attractive widow, it appeared, was the removal of his pencil moustache. As such, he would turn up at the elegant doorway, and introduce himself, Albert Simpson Sinclair, to the lady who would clearly not be able to resist his very considerable charms. Wednesday at noon was the agreed time.


Bertie’s meeting

She was waiting for him at the door, and extended her hand to him in such a way that he was not sure whether she was expecting him to shake it or kiss it. He shook it. “It is a pleasure and a delight to make your acquaintance in person,” he opened. “Tea or coffee,” she asked. “Coffee, please”. “White or black?” As a man who had not had either tea or coffee made for him for quite some time, he was not used to being questioned about his preferences in such detail. “Black, please, with milk,” he said. She looked at him quizzically. “Yes, plenty of milk,” he confirmed. Decaffeinated, please.

There was no conversation while the coffee was prepared, and after it was served, little more. The series of awkward silences, interrupted by sips of caffeinated coffee, was eventually interrupted by the chime of the grandfather clock standing in the corner of the room, alerting them to the fact that it was 12.30. It presented a much-needed natural break.

“I must take my leave,” said Bertie, “I have so much business to attend to.” There was a further moment of silence, while Miss Spratt rose to her feet, pointing accusingly at him. “What have you done with Bertie?” she asked. “Tell me NOW, what have you done with Bertie?” He was sure he had misheard her. “What have I done with WHAT?” he asked.

“What have you done with Bertie?” she persisted, in an increasingly strident tone. “But I AM Bertie!” “You, Sir, are NOT. You are Mr. Archibald Henry, former arctic explorer. Do you really think you could trick me into thinking you were my Bertie by shaving off your formerly abundant facial hair.” “No,” she continued, “Mr. Archibald Henry minus beard, moustache and large-rimmed spectacles is still Mr. Archibald Henry. Now tell me what you have done with Bertie, or I shall call the police to have you arrested.”

“I AM Albert Simpson Sinclair,” he insisted, “Archibald Henry does not exist.” At these words, Edith Spratt reached urgently for the telephone. “So you are now saying that you, Archibald Henry, do not exist, even though you stand right before me. Is this your defence to the charge of abducting Mr. Sinclair, or worse? A defence of insanity.”

Bertie could see his Big Idea unravelling before his eyes, the dream giving way to stone cold reality. Maybe he was insane, to hope that any idea of his could come true, maybe he was insane to still dream that one day he could persuade people that they could grow rich while they slept, succeed while they slumbered, learn while they dozed, slim while they snoozed. Maybe he was insane to believe that he could create a club for the unclubbable. But he was not insane in the way that Edith Spratt thought he was, and certainly not criminally insane.

For perhaps the first time in many years, he now decided upon a plan at odds with every instinct in his bones, a plan to tell the truth.

“It was I, Albert Simpson Sinclair, who came to your home last week disguised as the fictional arctic explorer, Archibald Henry. It is I, Archibald Simpson Sinclair, who stand before you now. I throw myself upon your good graces. I can do no more.” He paused. “Edie,” he half sobbed now, “I am Bertie.”

Edith Spratt said nothing but put down the telephone she had been wielding with increasing menace. “Mr. Sinclair,” she said quietly. “I am not sure whether you are a good man or a bad man, a sound man or an unsound man, and I am not really concerned to find out.” Bertie winced. “But”, she continued, “I do know the difference between a good idea and a bad idea, a sound idea and an unsound idea. And I am rather attracted to your big idea.” “A club for the unclubbable?” piped up Bertie, excitedly. “Quite so,” declared Miss Edith Spratt. “I shall turn this idea into reality, and because I am a lady of honour and refinement, you shall be rewarded with a respectable share in its fortunes. But be assured, Mr. Sinclair, this shall become my vision, the vision of Edith Evadne Spratt.

And so began a new dawn for Mr. Bertie Sinclair. Employed to use his considerable wit and charm to help expand the Spratt chain of clubs for the unclubbable, his big idea had become reality. He knew now that he would never grow rich while he slept, nor succeed while he slumbered, but he would indeed grow rich, by working hard while awake, and he would succeed. But much more importantly, Mr. Archibald Simpson Sinclair had now achieved a station in life which neither money nor worldly success could alone bestow. Bertie Sinclair, one-time conman, cad and bounder, had been transformed. Eminently clubbable, he had finally become a gentleman.

The Tenth Hole – A Short Story

The Tenth Hole
A short story – based on a real event

By Leighton Vaughan Williams

Based closely on a meeting with a stranger on a golf course, it is a meeting
that has inspired me to write this story. It is a story that I didn’t expect to
need to tell, but have needed to tell. If nobody reads it, no matter. But I
hope people do read it. Especially the people who have lessons still to
learn and dreams still to dream. Especially the people who want to play the
tenth hole! Especially those people. But it is a story for everyone.

It all started on the first green when a little white ball mysteriously appeared over our heads, landing next to the pin. Enter nobody! Then a stranger! The journey had not yet begun but would soon do so. As we parted company at the final green with a firm handshake and a salutary farewell, we realised that we had been part of one of those experiences which challenges one’s fundamental perceptions and pre-conceptions, illuminating us without dazzling us, humbling us without diminishing us. Yet we know not the stranger’s name nor philosophy. We did not ask, nor did we desire to know. We had learned enough without needing to seek further. As I placed my trusty white putter into the bag for the final time in the round, I realised I would never reach for it again in quite the same way. I realised also that our journey could only really be experienced, not told. Yet at the same time I knew that our journey offers a tale that needs to be told and re-told, for as long as there remain in golf, and life, lessons to be learned, dreams to be dreamed. Steve knew so too. He knew so because of what had happened the night before.

Chapter 1
The Third Hole
“Sorry about the shot back there. I didn’t know there was anyone on the green. I should have checked.” In truth, the apologised-for strike up the demanding uphill first hole was not a shot many would have expected to reach the skirts of the putting surface, let alone come to rest blowing a six inch kiss to the flag. I brushed it off with a dismissive wave. It is part of the happenstance that populates any game of golf, and especially one in which the opening challenge is played blind over the brink of a hill peering barely 60 yards to the front edge of the polestick’s personal domain. It was not until we were standing astride the third tee that the stranger had made his presence known, in the guise of one of the series of sauntering singleton players who increasingly grace the summer weekday afternoons with their individual displays of personal golfing panache.

A stranger, a singleton, that much we established on sight. A player of the game whose pace, and possibly skill, somewhat outstripped ours, we now established by simple deduction. “Go ahead of us. Play through.” Steve made the offer, as if in response to the words of apology, though it came out more like a barked command. “But I have all the time in the world.” The stranger’s words could have been spoken with weary regret or mock ribaldry or simply matter-of-factly, but there was no flicker of any of these sentiments. None. They were spoken instead with an inflection of what might be described as detached satisfaction lightly brushed with a hint of passion. Such a vocal inflection was strange, but only because it was unexpected. But it somehow sounded neither odd nor unusual. Nor was it discomforting. Yet we were discomforted, for another reason. That offer to go ahead of us, such a superficially selfless act of generosity, was in fact neither selfless nor generous. It was born rather out of a simple desire to see the stranger proceed on his way. And to free us from the burden of a pressing presence to our rear. As well as potential exposure to a dimpled projectile rising bullet-like in undetected flight toward our unprotected frames. And to free us from the burden of unbidden external inspection and inner judgement. We played on, in the quiet hope, even expectation, that a couple of wayward and horizontally challenged strikes off the tee would achieve the result which invitation had regrettably failed to achieve. The concept of limitless time would be put to the test of the real ticking clock.

I struck the ball first, to see it simply disappear from sight. In my experience this always means one thing – that the ball, while technically still in its own existence, would never again be part of mine. It was lost. Steve kept track of his own ball, but only because it had travelled a bare 30 yards towards its destination roughly a quarter of a mile away. We looked to the stranger. “Bad luck” , he intoned. “It happens to us all.” “Play through?”, I enquired. The stranger seemed to consider for an extended moment. “I know where your ball is. I’ll show you.” The ball was soon retrieved, from some of the rough grass designed to challenge players on the adjacent hole. Meanwhile, Steve had played his second shot. Eventually we reached the putting green. As we considered line and length, a ball could be seen descending from its high trajectory. Struck from the third tee, it landed short of our feet but long of reason. An obvious fluke, this was a ball delivered to its flight path as if by mechanical, not human, means. Inspired, we sank our putts. We bagged our respective putters, one made for the left handed and one for the right, and turned, a little lighter of foot, to tee off at the short fourth. Our path meandered edgingly close to the little white missile which awaited the stranger’s next smack. We paused as he came closer. “That was a big hit”, I ventured. “It achieved its purpose,” he smiled. “After all, you sunk your putts.” I considered how he knew our green play from so afar, but set the thought aside. “By the way, thanks for finding my ball. I was sure it was lost.” He looked at me quizzically. “If you know where something is, can it be lost?” He paused for a moment. “I’m not just talking about golf, you know. I’m really not!”

Chapter 2
The Fourth Hole
It is a relatively short hole, so the course designers had felt the need to compensate. They dug a deep bunker to the front side of the green, another to the right side and a steep grassy bank running down its back side. But we were confident. That’s what a hole-dropping long putt does for you. But the tee is set atop a flight of short steps, offering a balcony view to any short strike to the third. So we viewed. The stranger obliged. He knew where the hole was. And he knew how to reach it. Two feet from the hole. Now a simple tap-in, he marked the ball, cleaned it, set it down again. He tapped but it stayed out. He turned and looked up to us atop our temporary perch. He was smiling broadly. He was happy. Now it was my turn. To be happy. To sidestep or overfly sandy trap, to shy short of flirtation with treacherous back side.

I visualised. I swung golf’s version of bat at ball. I succeeded. In my own way. I was satisfied. But I was not happy. Not happy like the stranger. As Steve stepped up, the happy face, now muted, stood with him, still, close yet distant. Club hit ball, ball responded. Then misbehaved. “Difficult hole.” Steve and I were silent, then Steve spoke. “We’re not on song today. You go ahead. Please proceed.” Proceed he did, to place tee in ground, ball on tee, administer smart blow of short club to small ball. Perfect shot, perfect line, perfect distance, if aimed at the deep forward sandy trap. “Beached!”, he noted. It was a simple statement of fact. “I could be quite some time. You two play ahead.” We did.

Steve withdrew a club of middling length and swung freely at the ball. A pleasing crack. It was well timed. We all knew it. It found the green, albeit the right edge, opposite end to the stick. But nice enough. This was a turnaround. Both Steve and I with at least a chance of potting the hole in three, and the stranger’s ball buried deep below a gaping, uninviting, curling upper lip. This was an unequal contest between skill and natural sand, tipped heavily in favour of nature. And tipped in favour of us. I had clear sight of the pin, about 40 feet away, angled just forward of my left shoulder. Maybe 12 feet to the relatively smooth surface which surrounded the flag. I was furthest from the hole, if measured by distance. I locked my wrists and applied blade to ball. Ball bounced away to order. Slow surface. Good for once. Just short and below the hole. Steve was on the green. Still separated, ball to cup, by more than the stranger. But Steve’s ball had the advantage. It could see the objective. So could Steve. He took his time. He took his time on that putt as if he had all the time in the world. He had the line. He sort of had the length. Came up a nose short, queried its options, then decided to drop. Three. Par. He seemed to wave. Almost imperceptibly, but he seemed to wave. He seemed to wave to the stranger.

Now it was my turn. A five footer to share the hole. Don’t leave it short. Don’t leave it short. I didn’t. Hole shared. Move on or wait for splash of grainy sand. We waited and got a shower, and a show, as the flecked sphere soared from its tomb aloft a chariot of spray. It was long of the pin, before the backspin, and less long after, but still the length of a longshot. “You go ahead,” he shouted. “I might be quite some time.”

Chapter 3
The Fifth Hole
We walked on to the difficult fifth. My honour again to tee off first. 480 yards to the middle of the green. No need to guess. Modern technology has seen to that. Smooth swing. This time it flew straight, but not particularly long, and so tracked by eye through its entire flight. “I’m happy enough with that”. Could have been longer but a shot to make you happy. Now Steve inserted his tee into the sloping ground, placed his ball on it and prepared to play. “Same action, using a higher tee, and you would get the same result and a lot more length.” The stranger spoke softly but it interrupted Steve’s pre-shot ritual. Steve stopped and took a few steps backward. Hesitant now, where he had been confident, he sort of tiptoed to tee, imparted a dull thwack to ball and stood back to inspect the damage. He had topped it, had hit just its very top. It had at least gone straight.

It was in the short grass, that much could be said for it. But if only he had cradled the ball upon a higher tee. He remembered the stranger’s words. He looked at the stranger. The stranger said nothing. He had no need to. Steve was still a good 400 yards short of the green, I a little closer, but there was someone with us who placed his ball on a somewhat higher tee than either of us. I saw an opportunity. “Why don’t you show us how you tee up your ball, and show us the result?” He obliged, propelling the ball into an unusually steep trajectory, unusual by our standards.

“How did you do that?”, I asked. “Practice,” he murmured. “And belief.”
“So you can do it every time?” I was curious. “Not at all,” he replied.”You saw. I just missed a simple putt back there. It happens.” He paused. “Acceptance. When we fail we need acceptance. It’s about belief and acceptance. And practice.”
“Easier when the putts are dropping, and you’re hitting the greens. It’s when they’re not that the doubt creeps in.” I looked at Steve, still mulling over his mishit.
The stranger smiled, as if he’d heard it all before. “That, of course, is when your belief in your game is most important of all. Trust me!”

I did trust in something. I trusted in his own belief in his game. I shared his belief in his game. It was my game that I didn’t trust, that I didn’t believe in. I told him just that. “Well, it’s a start,” he said. “It’s a good start.” And he was off. “See you!” We bid the stranger well as he strode off over the artificial horizon created by the dip down the hill. “Try transferring some weight onto your back foot if you want lift.” He was calling back to us. “But don’t expect miracles. Genuine miracles are rare.”

Soon out of sight, he was not out of mind. We played on. To play safe or straddle the lake? Doubt or belief? We both chose the middle path, left of lake and far short of target. And found, in each case, the creek. Doubt played no further part. Lost ball, dropped ball, lose a shot, carry on. Lost ball? “It’s not lost if you know where to find it!” It was the same voice, of the stranger. “But I don’t know where to find it.” “Nor I”, echoed Steve. “Here they are!” Balls both found, thanks to stranger. We could barely see them, but there they were, buried treacherously, all but invisibly deep. How did he spot them? Why was he looking? Questions soon rendered academic. We could not retrieve them. Thank you stranger, we thought, you have shown us what we looked for. We know more but have gained nothing. But we were thinking of golf. We were only thinking of golf. We had learned nothing. But the stranger, he wasn’t just talking about golf, you know. He really wasn’t! We didn’t mind that. Get a new ball out of our bags. Time to play our shots. So we did. We were playing golf. And the game, to win or lose,was on. So to the green.

Preparing to putt for the hole. I’m confident. I bring the putter head straight back. Now don’t decelerate on the shot! A cry from the direction of adjacent tee. ‘Fore!’ “Watch out!” I react, instinctively, and miss. In truth, the rocketing wayward ball missed my person by all of six feet. “Unlucky,” Steve commiserated. But he was happy really. He shared the hole. I was lucky in another sense. Six feet to the left and I might have played my last shot. I hadn’t prepared for that. You never do. You’re concentrating too much on playing the game.

Chapter 4
The Sixth Hole
I like the sixth hole, except for the tree, the tree that always grabs my ball out of its soaring greenward flight. A neighbouring golf club had taken a vote on whether to demolish a tree. Their golfers had the same problem. It stopped the ball going where it was hit. It was a hazard, like a sand trap, only taller and more explicitly menacing. They voted to chop it down. Ours is much the same, but there’s no plan for a vote. One of my balls is still up it, trapped for posterity. I guess it will still be there when I am gone. I think about that every time I pass that tree. It was there as I considered my second shot. We had both hit pretty standard drives up the hill, off the tee. If the ball flies far enough that it disappears over the brow of the hill, I always jump a little. I don’t actually leave the ground, but I jump inside, if you understand. I suppose Steve does too, though not when I do it. Then he has the opposite feeling. There’s not much room for empathy on the golf course. Maybe there should be. It’s only a game, they say. But they’re wrong. Games are important. They teach you things. About yourself. And about others.

Standing atop the crest of the hill, and a few strides beyond, I prepare to avoid the tree. It’s to my left, about 100 yards, maybe a bit more. Should be able to avoid it this time. Hit straight or perhaps a little right. Then it’s a safe, controlled punch to the middle of the green. I can dream. That’s part of the game. But do I believe? I think I do. Then I see the branches. I always see the branches. I try to see the smooth, even grass of the fairway beyond the tree. I believe I will reach it. I’m sure I will reach it. But what about the branches? It’s always about the branches. There are so many branches. I prepare to play. A shout to me, this time heralding advice not danger. “It’s not about the tree!” It was the stranger. “It really isn’t about the tree. It’s about the fairway. Focus on that and you’ll be safe.” Easy for him to say that, I thought. He knows the game. He may as well have invented it. But I didn’t know the game. Well, I knew the rules, at least the ones that let me play the game, but I didn’t really know the game. Not like the stranger. “Trust me!” I looked at him, bag of clubs slung over his right shoulder, left hand propped against tree. “Keep standing there and it’s you who’ll be needing to trust,” I shouted back. Addressing the ball, I took aim. He didn’t take cover. He seemed to know. As did I. I simply knew that I wasn’t going to hit that tree. I trusted him. Despite the branches.

As I walked past the tree toward the pleasant fairway lie, I thanked him. I didn’t even ask him why he had waited, and not moved on to the next hole. I didn’t need to. And I didn’t want to. He returned the thanks. “You won’t always miss that tree,” he said. “But you will always know that you can.” He walked on to the next hole. My next shot found the deep rough, then the sand, then three more shots. Steve raised his hand. But he didn’t jump. Not in the air. Just inside. So did I. For a different reason, so did I.

Chapter 5
The Seventh Hole
Hit it down the fairway. Straight as you can. Easy shot to the green. One putt. In the hole. Shout of ‘Birdie.’ Job done. Before we hit the ball, we can all dream. I had the dream that day. Until I swung the club. The ball bore no blame. It had no will, no self-control. It simply obeyed instructions. But I had will, I had the freedom to instruct it as I liked. And I had the dream. So why was the ball buried deep in the bushes? I had teed it up high as I should, swung club with smoothness of action, completed follow through with self-referenced elegance. So why? I could have asked the stranger, had he been there. Steve was there, but he didn’t know the answer, even if it had been a real question.

Then I saw a dog. Looked like a nice dog, a spaniel, I think. I don’t know a lot about dogs so I can’t be sure. I just know that there are nice dogs and nasty dogs. This one looked nice. The one that bit Steve a few weeks back was the other kind. That dog wasn’t on a lead. It was free to bite and it bit. It bit Steve on the belly. But he didn’t tell anyone, not anyone in authority. That was his choice. He chose to hope it wouldn’t do it again. Steve wasn’t doing anything wrong, not when he was bit. He had no choice about that. The choice came later. I had a choice. I could have chosen to give the ball better instructions. But it was not a real choice. I did try. But now I had a real choice. To forget the fluffed shot, drop another ball, lose a shot, address the ball, play as if this was the ball’s natural resting place. Or to continue asking ‘why’ in plaintive cry. I knew what the stranger would do. So I played the ball, as best I could. Not in anger but in thanks. Thanks to the stranger. And now to the lady with the dog, who shouts “Well played!” The kindness of strangers. Quite pleased with the outcome. Not as pleased as Steve who will soon be at the flag. Or at least near enough to ensure the hole. But I was playing against the course. When Steve plays well, I play against the course. When Steve plays badly, I play against Steve. Confident now, unhurried, undisturbed. I dream of holing it in one from here. Hit the flag. That’ll do. I’ll be happy with that. I look around. Nobody to impress this time.

The lady has moved on, taking her nice dog with her. It had no choice. It was on a lead. The man in the motorised grass-cutter does have a choice. He can choose to buzz around when you are trying to play, or buzz off until you’ve played. He chooses to buzz around. He always does. It stops him getting bored. He’s near enough now that the ball might hit him if you take your shot quickly. The stranger could definitely hit him. He has the skill. But you’d have to be lucky. He’s not even wearing a helmet. His own silly fault if I hit him. I feel lucky. Then I see him. Back of the green. Watching. I see the stranger. Embarrassed, I aim for the green, and almost hit the flag. I’m playing the game now. That’s why games are important. They teach you things. Steve wins the hole, but I’ve won too. The man in the machine has moved on. So has the stranger. And so, I feel, have I.

Chapter 6
The Eighth Hole
The weather forecast had said heavy showers. But I didn’t believe the forecast. They say bad things and if they’re wrong, you will be happy anyway. And forget their mistake. But if they say good weather, and you are drenched, you will not easily forgive them. Clever strategy. But no good if you want to know how the weather will be. So I didn’t believe, and persuaded Steve I was right. He believed me. Now he was wet. I saw the lady with the dog in the distance. She had opened an umbrella. I wondered about the stranger. Now we had a decision to make. We could take whatever partial shelter we could or play on and be fully sheltered sooner. We played on.

The weather did its worst but only served to help us focus. Two shots. Straight off the tee. Both off the putting green. But neither by much. Then a flash. Count to three and the crash of thunder. Not far away now. I know someone who knew someone who was struck by lightning. The girl she knew was on a golf course when it happened. Did everything right. Made all the right choices once she saw the electric fork. But she hadn’t believed the forecast. Clever strategy, she had said, to forecast storms. You’d forgive and forget if the weather was good. This time it wasn’t. The forecasters were right. She was wrong. She paid the price. A high price for getting it wrong, but life is like that sometimes. This was on my mind as I lined up my shot, designed as a little chip to the flag. Maybe my wrist quivered. I suppose the ball obeyed my instructions, it always does, but not my intent. Short, very short of the pin. Steve wasn’t scared like me. He said that it was very long odds to be struck dead. But he didn’t know someone who knew someone who succumbed despite the odds. I think it makes a difference. At least it made a difference that day. He holed it. And would probably live to tell the tale. Very probably, according to the odds. We move on to the closing hole of this nine hole course. You can play eighteen holes if you like, but not eighteen different holes. You just play the nine holes twice. We play them just once. For us, there is no tenth hole.

Chapter 7
The Ninth Hole
The heavens continued to flash, almost in time now with thunderous clash, but Steve was unconcerned. He was chatting with someone in what the British call a golf buggy and the Americans call a cart. Steve climbed in. Then climbed out. “Safer in there”, he said. But he was wrong. First advice is to get clear of open frame vehicles. I told him. “But they’re earthed, grounded. Look at those rubber tyres.” Steve was sure of his physics. I didn’t know the physics but I knew the advice. Get clear, it said. “Anyway, meet Chris, who knows about these things.” My heart sank. The stranger, in whom I’d placed so much trust. Sitting in the nippy four-wheeler. So sure of himself. Placing his trust in a death trap. Now it made sense. I thought as we left the fourth green that I’d seen Steve wave at him. Almost imperceptibly, but definitely an acknowledgment. I had put it out of my mind, put it down to courtesy, but now it all came together. He was not a stranger, not to Steve. I went over to Chris, back turned but obviously impervious to danger. Blissful in ignorance. I tapped on the shoulder of the white collared shirt. Chris turned. She turned and looked at me. “Always best to hire the car when there’s a chance of thunder”. It was one of the local lady golfers, good player, better than us, at golf, but no better at physics. I laughed. Out of relief, really. The stranger would never sit in an open vehicle in a thunderstorm. We were free to do what we wanted, but not the stranger. He would only do what was right. I trusted in him. Then I saw him, at the crest of the hill, over which we hoped to propel our first volleys.

He was calling us on. I felt safe now. And Steve seemed to wave. He seemed to wave to the stranger. We cleared the hill, first bounce I prefer to recall, and took good advantage of the downward sloping smooth grassed fairway. Two further blows apiece, of club on ball, and we were on the green. Then two putts from Steve, one from me. “Well played, Sirs!” He joined us on the green, shook our hands firmly. “The game is important,” he said. It teaches us things, about ourselves, and about others. The question is how we play it.” We wanted to play it like him.

On to the tenth hole?” he asked. “There is no tenth hole,” we said, almost in unison. “There are only the ones you see. You keep going round and round. Until you stop. That’s all there is. Didn’t you know?” The stranger smiled. He knew that we were still talking about golf. “There is a tenth hole,” he said. But you need to look for it. And to believe in it.” He proceeded to hand each of us a little white ball. They were the same two balls, with their distinctive markings, that we had lost in the creek. I was momentarily staggered. “But how? They were lost, unreachable.” “Yes, those balls truly were lost, they were unreachable,”‘said the stranger. “But on the tenth hole, there are no lost balls. Nothing is lost on the tenth. Trust me.”

We did trust him now. We had seen and we believed. “You remember that shot off the tee, the one that soared so high, over the very tall pines. I saw you watching. Well, you can do that too. You can do that, when you reach the tenth hole.”
Then, with a wave, he started to walk away. “It’s about belief and acceptance”, he called back, “and practice. So, practise these things.” The stranger now out of sight, Steve turned to me. “He gave me a lift home last night,” he said, “when I missed the last bus, and was caught three miles from home in that terrible storm. He stopped his car and offered me a lift. Went totally out of his way, took me to my front door, then he was gone. I didn’t even have chance to thank him.”

“So why didn’t you say anything before?” I was perplexed. “Because I didn’t recognise him at first, though I did feel that I knew him. I didn’t recognise him until he called us on in the storm.” “Steve, are you absolutely sure it was him?” “Not for certain,” he said, “But that doesn’t really matter, does it?” “I suppose not,” I agreed. “I suppose not.” The kindness of strangers. What a wonderful thing. We looked to the sky. The clouds were slowly parting. We knew where we were now. We knew now that there was a tenth hole!

Strictly Come Dancing: the luck of the draw really does matter!

A viscountess, a radio DJ, a reality star, a vlogger, a comedian, several sportspeople and an assortment of actors and presenters. These, more or less, are the celebrities lined up to compete in the 2019 season of Strictly Come Dancing.

Outside their day jobs, few people know much about them yet. But over the 13 weeks or so of shows up until Christmas, viewers will at least learn how well the contestants can dance. But how much will their success in the competition have to do with their foxtrot and to what extent will it be, literally, the luck of the draw that sees the victors lift the trophy in December?

seminal study published in 2010 looked at public voting at the end of episodes of the various Idol television pop singing contests and found that singers who were later on in the bill got a disproportionately higher share of the public vote than those who had preceded them.

This was explained as a “recency effect” – meaning that those performing later are more recent in the memory of people who were judging or voting. Interestingly, a different study, of wine tasting, suggested that there is also a significant “primacy effect” which favours the wines that people taste first (as well, to some extent, as last).

A little bias is in order

What would happen if the evaluation of each performance was carried out immediately after each performance instead of at the end – surely this would eliminate the benefit of going last as there would be equal recency in each case? The problem in implementing this is that the public need to see all the performers before they can choose which of them deserves their vote.

Dress rehearsal for Strictly Come Dancing, August 2019. madathanu /

You might think the solution is to award a vote to each performer immediately after each performance – by complementing the public vote with the scores of a panel of expert judges. And, of course, Strictly Come Dancing (or Dancing with the Stars if you are in the US) does just this. So there should be no “recency effect” in the expert voting – because the next performer does not take to the stage until the previous performer has been scored.

We might expect in this case that the later performers taking to the dance floor should have no advantage over earlier performing contestants in the expert evaluations – and, in particular, there should be no “last dance” advantage.

We decided to test this out using a large data set of every performance ever danced on the UK and US versions of the show – going right back to the debut show in 2004. Our findings, published in Economics Letters, proved not only surprising, but almost a bit shocking.

Last shall be first

Contrary to expectations, we found the same sequence order bias by the expert panel judges – who voted after each act – as by the general public, voting after all performances had concluded.

We applied a range of statistical tests to allow for the difference in quality of the various performers and as a result we were able to exclude quality as a reason for getting high marks. This worked for all but the opening spot of the night, which we found was generally filled by one of the better performers.

So the findings matched the Idol study in demonstrating that the last dance slot should be most coveted, but that the first to perform also scored better than expected. This resembles a J-curve where there are sequence order effects such that the first and later performing contestants disproportionately gained higher expert panel scores.

Although we believe the production team’s choice of opening performance may play a role in this, our best explanation of the key sequence biases is as a type of “grade inflation” in the expert panel’s scoring. In particular, we interpret the “order” effect as deriving from studio audience pressure – a little like the published evidence of unconscious bias exhibited by referees in response to spectator pressure. The influence on the judges of increasing studio acclaim and euphoria as the contest progresses to a conclusion is likely to be further exacerbated by the proximity of the judges to the audience.

When the votes from the general public augment the expert panel scores – as is the case in Strictly Come Dancing – the biases observed in the expert panel scores are amplified.

All of which means that, based on past series, the best place to perform is last and second is the least successful place to perform.

The implications of this are worrying if they spill over into the real world. Is there an advantage in going last (or first) into the interview room for a job – even if the applicants are evaluated between interviews? The same effects could have implications in so many situations, such as sitting down in a dentist’s chair or doctor’s surgery, appearing in front of a magistrate or having your examination script marked by someone with a huge pile of work to get through.

One study, reported in the New York Times in 2011, found that experienced parole judges granted freedom about 65% of the time to the first prisoner to appear before them on a given day, and the first after lunch – but to almost nobody by the end of a morning session.

So our research confirms what has long been suspected – that the order in which performers (and quite possibly interviewees) appear can make a big difference. So it’s now time to look more carefully at the potential dangers this can pose more generally for people’s daily lives – and what we can do to best address the problem.

Prediction markets and political forecasting – evidence to House of Lords

Professor Leighton Vaughan Williams – Written evidence (PPD0024)

Available at:

1. In this evidence, I consider the relationship between political betting and political opinion polls, and highlight peer-reviewed research I have undertaken into this. I also reference some other published work of mine on opinion polling and political forecasting more generally. Research I have undertaken into the impact of the dissemination of information via social media is also highlighted.
2. The recorded history of election betting markets can be traced as far back as 1868 for US presidential elections (Rhode and Strumpf, 2013) and 1503 for papal conclaves. Between 1868 and 2012, no clear favourite for the White House had lost the presidential election other than in 1948, when longshot Harry Truman defeated his Republican rival, Thomas Dewey. 2016 can be added to that list, following the defeat of strong favourite Hillary Clinton in the Electoral College.
3. The record of the betting markets in predicting the outcome of papal conclaves is somewhat more chequered and is considered in Vaughan Williams and Paton (2015) in which I examine, with my co-author Professor David Paton, the success of papal betting markets historically.
4. The potential of the betting markets and prediction markets (markets created specifically to provide forecasts) to assimilate collective knowledge and wisdom has increased in recent years as the volume of money wagered and number of market participants has soared. Betting exchanges alone now see tens of millions of pounds trading on a single election.
5. An argument made for the value of betting markets in predicting the probable outcome of elections is that the collective wisdom of many people is greater than that of the few. We might also expect that those who know more, and are better able to process the available information, would on average tend to bet more.
6. The lower the transaction costs (the betting public have not paid tax on their bets in the UK since 2001, and margins have fallen since the advent of betting exchanges) and the lower the costs of accessing and processing information (through the development of the Internet and search engines), the more efficient we might expect betting markets to become in translating information into forecasts. Modern betting markets might be expected for these reasons to provide better forecasts than ever.
7. There is plenty of anecdotal evidence about the accuracy of political betting markets, especially compared to the polls. The 1985 by-election in Brecon and Radnor is a classic example. On Election Day, July 4th, an opinion poll undertaken by the Mori polling organisation was published which gave Labour a commanding lead of 18 percent over the Liberal Alliance candidate. Ladbrokes simultaneously made the Liberal the 4/7 favourite. The Liberal won.
8. Forward 20 years to a BBC World Service live radio debate in 2005, in the run-up to the UK general election, when forecasts were swapped between the Mori representative and myself on the likely outcome of the election. I predicted a Labour majority of about 60, as I had done a few days earlier in the Economist magazine (Economist, April 14th, 2005) and on BBC Radio 4 Today (April, 18th, 2005), based on the betting at the time. The Mori representative predicted a Labour majority of over 100 based on their polling. The actual majority was 66.
9. More recent anecdotal evidence comes from the 2012 US presidential election. Barack Obama was the heavy favourite to win, while the average of the pollsters had the popular vote within 0.7%, and two leading polling organisations, Gallup and Rasmussen, had Mitt Romney ahead in final polls. Obama won by 3.9%.
10. During the later stages of the 2014 Scottish referendum campaign, the polling average had it relatively close (especially compared with the actual result), with more than one poll calling it for independence (one by 7%). The betting odds were always very strongly in favour of Scotland staying in the UK. The result echoed the 1995 Quebec separation referendum in Canada. There the final polling showed ‘Yes to separation’ with a six point lead. In the event, ‘No to separation’ won by one point. This late swing to the ‘status quo’ is credited by some with the confidence in the betting markets about a ‘NO’ outcome in Scotland.
11. In the 2015 general election in Israel, final polls showed Netanyahu’s Likud party trailing the main opposition party by 4% (Channel 2, Channel 10, Jerusalem Post), by 3% (Channel 1) and by 2% (Teleseker/Walla). Meanwhile, Israel’s Channel 2 television news on Election Day featured the odds on the online prediction market site, Predictwise. This gave Netanyahu an 80% chance of winning. The next day, Netanyahu declared that he had won “against the odds.” He actually won against the polls.
12. Polling averages during the 2015 UK general election campaign often showed Conservatives and Labour very close in terms of vote share. Meanwhile, the betting odds always had Conservative most seats as short odds-on. On the Monday before polling day, for example, the polling average had it essentially tied in terms of vote share, while Conservatives to win most seats was trading on the markets as short as 1/6.

13. For the 2015 Irish same-sex marriage referendum, the spread betting markets were offering a mid-point of 60% for YES to same-sex marriage, and 40% for NO. The average of the final opinion polls had YES on 71% and NO on 29%. The final result was 62%-38% for YES, much closer to the projection from the markets.
14. If this anecdotal evidence is correct, it is natural to ask why the betting markets outperform the opinion polls in terms of forecast accuracy. One obvious reason is that there is an asymmetry. People who bet in significant sums on an election outcome will usually have access to the polling evidence, while opinion polls do not take account of information contained in the betting odds (though the opinions expressed might). Sophisticated political bettors also take into account the past experience of how good different pollsters are, what tends to happen to those who are undecided when they actually vote, differential turnout of voters, what might drive the agenda between the dates of the polling surveys and election day itself, and so on. All of this can in principle be captured in the markets.
15. Pollsters, except perhaps with their final polls, tend to claim that they are not producing a forecast, but a snapshot of opinion. In contrast, the betting markets are generating odds about the final result. Moreover, the polls are used by those trading the markets to improve their forecasts, so they are a valuable input. But they are only one input. Those betting in the markets have access to much other information as well including, for example, informed political analysis, statistical modelling, focus groups and on-the-ground information including local canvass returns.
16. To test the reliability of the anecdotal evidence pointing to the superior forecasting performance of the betting markets over the polls, I collected vast data sets of every matched contract placed on two leading betting exchanges and from a dedicated prediction market for US elections since 2000. This was collected over 900 days before the 2008 election alone, and to indicate the size, a single data set was made up of 411,858 observations from one exchange alone for that year. Data was derived notably from presidential elections at national and state level, Senate elections, House elections and elections for Governor and Mayor. Democrat and Republican selection primaries were also included. Information was collected on the polling company, the length of time over which the poll was conducted, and the type of poll.
17. My co-author, Dr. James Reade, and I compared the betting over the entire period with the opinion polls published over that period, and also with expert opinion and a statistical model.
18. In a paper, titled ‘Forecasting Elections’ (Vaughan Williams and Reade, 2016b), published in the ‘Journal of Forecasting’ – see also Vaughan Williams and Reade, 2017, 2015), we specifically assessed opinion polls, prediction and betting markets, expert opinion and statistical modelling over this vast data set of elections in order to determine which performed better in terms of forecasting outcomes. We

considered accuracy, bias and precision over different time horizons before an election.
19. A very simple measure of accuracy is the percentage of correct forecasts, i.e. how often a forecast correctly predicts the election outcome.
20. A related but distinctly different concept to accuracy is unbiasedness. An unbiased vote share forecast is, on average, equal to the true vote share outcome. An unbiased probability forecast is also, on average, equal to the true probability that the candidate wins the election. Forecasts that are accurate can also be biased, provided the bias is in the correct direction. If polls are consistently upward biased for candidates that eventually win, then despite being biased they will be very accurate in predicting the outcome, whereas polls that are consistently downward biased for candidates that eventually win will be very inaccurate as well as biased
21. We also identified the precision of the forecasts, which relates to the spread of the forecasts.
22. We considered accuracy, bias and precision over different time horizons before an election. We found that the betting/prediction markets provided the most accurate and precise forecasts and were similar in terms of bias to opinion polls. We found that betting/prediction market forecasts also tended to improve as the elections approached, while we found evidence of opinion polls tending to perform worse.
23. In Brown, Reade and Vaughan Williams (2017), we examine the precise impact of the release of information from a leading opinion polling company on the political betting markets. To do this, we use an extensive data set of over 25 million contracts that records (anonymised) individual trader IDs for the buyers and sellers of the contracts and align this to the exact time of release of this information. We find that polling releases by this prominent opinion pollster quickly influences trading volumes and market prices, but that experienced and more aggressive liquidity-taking traders bide their time before entering the market after such news events. We find that the market prices are not at their most informative in the immediate aftermath of a poll release.
24. We also conducted research into the impact of breaking news on the markets, notably via social media and live blogging. In Vaughan Williams and Paton (2015) we use an extensive data set of contracts matched on a leading betting exchange specifically regarding the outcome of the 2013 papal election. We found that genuine information released on Twitter was not reflected in the betting markets, and was only very partially incorporated when published later on the live blog of a major British newspaper. One possible explanation is that the information was not believed as it related to a closed-door conclave (Vaughan Williams, 2015a, considers

closed door forecasting in another context). However, this finding was consistent in some respects with evidence in Vaughan Williams and Reade (2016a) about the limited impact on a leading betting exchange of major breaking news in a UK general election when released on Twitter, at least until the news was validated by traditional media.
25. In summary, the overwhelming consensus of evidence prior to the 2015 UK General Election pointed to the success of political betting markets in predicting the outcome of elections. In contrast, the 2015 UK General Election, the 2016 EU referendum in the UK, the 2016 US presidential election and the 2017 UK election, all produced results that were a shock to the great majority of pollsters as well as to the betting markets. In each case, the longshot outcome (Conservative overall majority, Brexit, Trump, No overall majority) prevailed.
26. There are various theories as to why the polls and markets broke down in these recent big votes. One theory is based on the simple laws of probability. An 80% favourite can be expected to lose one time in five, if the odds are correct. In the long run, according to this explanation, things should balance out.
27. A second theory to explain recent surprise results is that something fundamental has changed in the way that information contained in political betting markets is perceived and processed. One interpretation is that the widespread success of the betting markets in forecasting election outcomes, and the publicity that was given to this, turned them into an accepted measure of the state of a race, creating a perception which was difficult to shift in response to new information. To this extent, the market prices to some extent led opinion rather than simply reflecting it. From this perspective, the prices in the markets became somewhat sticky.
28. A third theory is that conventional patterns of voting broke down in 2015 and subsequently, primarily due to unprecedented differential voter turnout patterns across key demographics, which were not correctly modelled in most of the polling and which were not picked up by those trading the betting markets.
29. There are other theories, which may be linked to the above, including the impact of social media, and manipulation of this, on voter perceptions and voting patterns.
30. I explore how well the pollsters, ‘expert opinion’, modellers, prediction and betting markets performed in the 2017 UK general election in Vaughan Williams (2017a) – “Report card: how well did UK election forecasters perform this time?” and explore the polling failure in the 2015 UK general election in Vaughan Williams (2015b) – “Why the polls got it so wrong in the British election”, and some implications in a follow-up article (Vaughan Williams, 2015c).

31. I explore how well the pollsters, ‘expert opinion’, modellers, prediction and betting markets performed in the 2016 US presidential election in Vaughan Williams (2016) – “The madness of crowds, polls and experts confirmed by Trump victory”, and the implications of turnout projections for opinion polling in Vaughan Williams, 2017b – “Election pollsters put their methods to the test – and turnout is the key.”
BBC Radio 4 Today, Are betting markets a better guide to election results than opinion polls? April 18th, 2005, 0740.
Brown, A., Reade, J.J. and Vaughan Williams, L. (2017), ‘When are Prediction Market Prices Most Informative?’ Working Paper.
Economist, Punters v pollsters. Are betting markets a better guide to election results than opinion polls? April 14th, 2005.
Rhode, P.W. and Strumpf, K. (2013), ‘The Long History of Political Betting Markets: An International Perspective’, in: The Oxford Handbook of the Economics of Gambling, ed. L. Vaughan Williams and D. Siegel, 560-588.
Vaughan Williams, L. (2017a), ‘Report card: how well did UK election forecasters perform this time?’ The Conversation, June 10. did-uk-election-forecasters-perform-this-time-79237
Vaughan Williams, L. (2017b), ‘Election pollsters put their methods to the test – and turnout is the key’, The Conversation, June 2. their-methods-to-the-test-and-turnout-is-the-key-78778
Vaughan Williams, L. (2016), ‘The madness of crowds, polls and experts confirmed by Trump victory’, The Conversation, November 9. crowds-polls-and-experts-confirmed-by-trump-victory-68547
Vaughan Williams, L. (2015a), ‘Forecasting the decisions of the US Supreme Court: lessons from the ‘affordable care act’ judgment,’ The Journal of Prediction Markets, 9 (2), 64-78.
Vaughan Williams, L. (2015b), ‘Why the polls got it so wrong in the British election’, The Conversation, May 8. british-election-41530
Vaughan Williams, L. (2015c), ‘How looking at bad polls can show Labour how to win the next election’, The Conversation, May 20. polls-can-show-labour-how-to-win-the-next-election-42065
Vaughan Williams, L. and Paton, D. (2015), ‘Forecasting the Outcome of Closed-Door Decisions: Evidence from 500 Years of Betting on Papal Conclaves’, Journal of Forecasting, 34 (5), 391-404.

Vaughan Williams, L. and Reade, J.J. (2016a), ‘Prediction Markets, Social Media and Information Efficiency’, Kyklos, 69 (3), 518-556.
Vaughan Williams, L. and Reade, J.J. (2016b), ‘Forecasting Elections’, Journal of Forecasting, 35 (4), 308-328.
Vaughan Williams, L. and Reade, J.J. (2017), ‘Polls to Probabilities: Prediction Markets and Opinion Polls’, Working Paper.
Vaughan Williams, L. and Reade, J.J. (2015), ‘Prediction Markets and Polls as Election Forecasts’, Working Paper.
31 October 2017

Home Advantage Bias – Guide Notes.

There are five influential articles that have been published since 1982 on the key source of home advantage. All are agreed.

Jack Dowie’s article in New Scientist was a seminal piece. Dowie distinguishes the three Fs  – fatigue, familiarity and fans, each of which might have contributed to home advantage.

Fatigue: In a sample of 40 years of data, Dowie looked for evidence that away teams’ performances drop off relative to home teams as the game progresses, as measured by the likelihood of scoring a goal at any given point during the course of the match. Away teams did score fewer goals, on average, than home teams, but this disparity got no worse as the game developed.

Familiarity: Is familiarity with the pitch a bonus for the home team? If this is a key factor, teams who are travelling from a similar pitch to the home team should be less disadvantaged than those who are travelling to a very different sort of pitch. One obvious way to test this is ask whether teams who play on relatively big pitches have a particular statistical advantage when laying host to visitors whose own home ground boasts a small pitch, and vice versa. In fact, home advantage seemed to remain constant whatever the relative pitch sizes of hosts and visitors.

Fans: Is it the absolute number of fans, or is it the relative number of home and away fans? The data showed that the advantage conferred by playing at home was significantly greater for games played in the lower divisions than in the top division, even though the absolute number of supporters was much smaller in these games. Moreover, the advantage was much less in ‘local derbies.’ The conclusion is that the balance of support is what matters at the ground.

Nevill, Balmer and Williams looked into this further in 2002, showing 40 qualified referees video footage of 47 tackles from a Premiership match. The referees were divided into two groups, half of whom were exposed to the original soundtrack, while the other half listened to a silent version of the match. Neither group had access to the original referee’s decision. In actual matches, about 60% of bookings points (10 for a yellow, 25 for a red) are awarded to the visiting team. Those referees who watched the original soundtrack were reluctant to penalise the home team, judging 15% fewer of the tackles by home players to be fouls as compared to those referees who watched the silent footage. So in the absence of crowd noise the officials were more even-handed between the home and away sides. The original referees’ decisions, however, more accurately mirrored the behaviour of those armchair referees who had access to sound. It is as if, to get the crowd off their back, they wave play on.

In ‘Scorecasting’, Moskowitz and Wertheim (2011) compile further data to test a variety of popular theories explaining home advantage. They argue that when athletes play at home, they don’t seem to hit or pitch better in baseball … or pass better in football. The crowd doesn’t appear to be helping the home team or harming the visitors. They also checked scheduling bias against the away team, concluding that while this explains some of the home-field advantage, particularly in college sports, it’s irrelevant in many sports.

Thomas Dohmen looked at home advantage in the Bundesliga, the premier football league in Germany. Dohmen found that home advantage was smaller in stadiums that happened to have a running track surrounding the soccer pitch, and larger in stadiums without a track. Why? Apparently, when the crowd sits closer to the field, the officials are more susceptible to getting caught up in the home-crowd emotion. The social atmosphere in the stadium, he argues, leads referees into favouritism despite the fact that being impartial is optimal for them in career terms.

Here is the take of Steven Levitt and Stephen Dubner. “It’s worth noting that a soccer referee has more latitude to influence a game’s outcome than officials in other sports, which helps explain why the home-field advantage is greater in soccer, around the world, than in any other pro sport … officials don’t consciously decide to give the home team an advantage – but rather, being social creatures (and human beings) like the rest of us, they assimilate the emotion of the home crowd and, once in a while, make a call that makes a whole lot of close-by, noisy people very happy.”

References and Links

Dohmen, T.J. (2008). The Influence of Social Forces: Evidence from the Behavior of Soccer Referees. Economic Inquiry, 46, 3, 411-424.

Dowie, J. Why Spain Should Win the World Cup, New Scientist, 1982, 94 (10), 693-695.

Nevill, A.M., Balmer, N.J. and Williams, A.M. (2002), The influence of crowd noise and experience upon refereeing decisions in football, Psychology of Sport  and Exercise, 3 (4), 261-272.

Moskowitz, T.J. and Wertheim, L.J. (2011), Scorecasting. Random House.

Levitt, S.D. and Dubner, S.J. (2015), ‘When to Rob a Bank’, Penguin Books, pp. 211-12.

The Strange Case of Sunrise, Sunset and the Shortest Day of the Year.

December 21st, 2018 is the shortest day of the year, at least in the UK, located in the Northern hemisphere of our planet.

So does that mean that the mornings should start to get lighter after today (earlier sunrise), as well as the evenings (later sunset). Not so, and there’s a simple reason for that. The length of a solar day, i.e. the period of time between the solar noon (the time when the sun is at its highest elevation in the sky) on one day and the next, is not 24 hours in December, but about 30 seconds longer than that.

For this reason, the days get progressively about 30 seconds longer throughout December, so that by the end of the month a standard 24-hour clock is lagging roughly 15 minutes behind real solar time.

Let’s say just for a moment that the hours of sunlight (the time difference between sunrise and sunset) stayed constant through December. This means that a 24-hour clock which timed sunset at 3.50pm one day would be 30 seconds slow by 3.50pm the next day. The solar day would be 30 seconds longer than this, so the sun would not set the next day till 3.50pm and 30 seconds. After ten days the sun would not set till 3.55pm according to the 24-hour clock. So the sunset would actually get later through all of December. For the same reason, the sunrise would get later through the whole of December.

In fact, the sunset doesn’t get progressively later through all of December because the hours of sunlight shorten for about the first three weeks. The effect of this is that the sun would set earlier and rise later.

These two things (the shortening hours of sunlight and the extended solar day) work in the opposite direction. The overall effect is that the sun starts to set later from a week or so before the shortest day, but doesn’t start to rise earlier till about a week or so after the shortest day.

So the old adage that that the evenings will start to draw out after the end of the third week of December or so, and the mornings will get lighter, is false. The evenings have already been drawing out for several days before the shortest day, and the mornings will continue to grow darker for several days more.

There’s one other curious thing. The solar noon coincides with noon on our 24-hour clocks just four times a year. One of those days is Christmas Day! So set your clock to noon on December 25th, look up to the sky and you will see the sun at its highest point. Just perfect!



The US mid-term elections: a triumph for political forecasting.

The results of the US midterm elections are now largely in and they came as a shock to many seasoned forecasters.

This wasn’t the kind of shock that occurred in 2016, when the EU referendum tipped to Brexit and the US presidential election to Donald Trump. Nor the type that followed the 2015 and 2017 UK general elections, which produced a widely unexpected Conservative majority and a hung parliament respectively.

On those occasions, the polls, pundits and prediction markets got it, for the most part, very wrong, and confidence in political forecasting took a major hit. The shock on this occasion was of a different sort – surprise related to just how right most of the forecasts were.

Take the FiveThirtyEight political forecasting methodology, most closely associated with Nate Silver, famed for the success of his 2008 and 2012 US presidential election forecasts.

In 2016, even that trusted methodology failed to predict Trump’s narrow triumph in some of the key swing states. This was reflected widely across other forecasting methodologies, too, causing a crisis of confidence in political forecasting. And things only got worse when much academic modelling of the 2017 UK general election was even further off targetthan it had been in 2015.

How did it go so right?

So what happened in the 2018 US midterm elections? This time, the FiveThirtyEight “Lite” forecast, based solely on local and national polls weighted by past performance, predicted that the Democrats would pick up a net 38 seats in the House of Representatives. The “Classic” forecast, which also includes fundraising, past voting and historical trends, predicted that they would pick up a net 39 seats. They needed 23 to take control.

Read more: Women candidates break records in the 2018 US midterm elections

With almost all results now declared, it seems that those forecasts are pretty near spot on the projected tally of a net gain of 40 seats by the Democrats. In the Senate, meanwhile, the Republicans were forecast to hold the Senate by 52 seats to 48. The final count is likely to be 53-47. There is also an argument that the small error in the Senate forecast can be accounted for by poor ballot design in Florida, which disadvantaged the Democrat in a very close race.

Some analysts currently advocate looking at the turnout of “early voters”, broken down by party affiliation, who cast their ballot before polling day. They argue this can be used as an alternative or supplementary forecasting methodology. This year, a prominent advocate of this methodology went with the Republican Senate candidate in Arizona, while FiveThirtyEight chose the Democrat. The Democrat won. Despite this, the jury is still out over whether “early vote” analysis can add any value.

There has also been research into the forecasting efficiency of betting/prediction markets compared to polls. This tends to show that the markets have the edge over polls in key respects, although they can themselves be influenced by and overreact to new poll results.

There are a number of theories to explain what went wrong with much of the forecasting prior to the Trump and Brexit votes. But looking at the bigger picture, which stretches back to the US presidential election of 1868 (in which Republican Ulysses S Grant defeated Democrat Horatio Seymour), forecasts based on markets (with one notable exception, in 1948) have proved remarkably accurate, as have other forecasting methodologies. To this extent, the accurate forecasting of the 2018 midterms is a return to the norm.

And the next president is …

But what do the results mean for politics in the US more generally? The bottom line is that there was a considerable swing to the Democrats across most of the country, especially among women and in the suburbs, such that the Republican advantage of almost 1% in the House popular vote in 2016 was turned into a Democrat advantage of about 8% this time. If reproduced in a presidential election, it would be enough to provide a handsome victory for the candidate of the Democratic Party.

The size of this swing, and the demographics underpinning it, were identified with a good deal of accuracy by the main forecasting methodologies. This success has clearly restored some confidence in them, and they will now be used to look forward to 2020. Useful current forecasts for the 2020 election include PredictIt, OddsChecker, Betfairand PredictWise.

Taken together, they indicate that the Democratic candidate for the presidency will most likely come from a field including Senators Kamala Harris (the overall favourite), Bernie Sanders, Elizabeth Warren, Amy Klobuchar, Kirsten Gillibrand and Cory Booker. Outside the Senate, the frontrunners are former vice-president, Joe Biden, and the recent (unsuccessful) candidate for the Texas Senate, Beto O’Rourke.

Whoever prevails is most likely to face sitting president, Donald Trump, who is close to even money to face impeachment during his current term of office. If Trump isn’t the Republican nominee, the vice-president, Mike Pence, and former UN ambassador Nikki Haley are attracting the most support in the markets. The Democrats are currently about 57% to 43% favourites over the Republicans to win the presidency.

With the midterms over, our faith in political forecasting, at least in the US, has been somewhat restored. The focus now turns to 2020 – and whether they’ll accurately predict the next leader of the free world, or be left floundering by the unpredictable forces of a new world politics.

Is the simpler explanation usually the better one?

William of Occam (also spelled William of Ockham) was a 14th century English philosopher. At the heart of Occam’s philosophy is the principle of simplicity, and Occam’s Razor has come to embody the method of eliminating unnecessary hypotheses. Essentially, Occam’s Razor holds that the theory which explains all (or the most) while assuming the least is the most likely to be correct. This is the principle of parsimony – explain more, assume less. Put more elegantly, it is the principle of ‘pluritas non est ponenda sine necessitate’ (plurality must never be posited beyond necessity).

Empirical support for the Razor can be drawn from the principle of ‘overfitting.’ In statistics, ‘overfitting’ occurs when a statistical model describes random error or noise instead of the underlying relationship. Overfitting generally occurs when a model is excessively complex, such as having too many parameters relative to the number of observations. Critically, a model that has been overfit will generally have poor predictive performance, as it can exaggerate minor fluctuations in the data. For example, a complex polynomial function might after the fact be used to pass through each data point, including those generated by noise, but a linear function might be a better fit to the signal in the data. By this we mean that the linear function would predict new and unseen data points better than the polynomial function, although the polynomial which has been devised to capture signal and noise would describe/fit the existing data better.

We can also look at it through the lens of what is known as Solomonoff Induction. Whether a detective trying to solve a crime, a physicist trying to discover a new universal law, or an entrepreneur seeking to interpret some latest sales figures, all are involved in collecting information and trying to infer the underlying causes. The problem of induction is this: We have a set of observations (or data), and want to find the underlying causes of those observations, i.e. to find hypotheses that explain our data. We’d like to know which hypothesis is correct, so we can use that knowledge to predict future events. In doing so, we need to create a set of defined steps to arrive at the truth, a so-called algorithm for truth.

Ray Solomonoff’s algorithmic approach takes in data (observations) and outputs the rule by which the data was created. That is, it will give us an explanation of the observations; the causes. Suppose there are many hypotheses that could explain the data. All of the hypotheses are possible but some are more likely than others. How do you weight the various hypotheses? This depends on prior knowledge. But what if you have no prior knowledge of which hypothesis is likely to be better than another. This is where Occam’s Razor comes in. Solomonoff’s theory is one of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is as such a mathematical formalisation of Occam’s Razor.

All computable theories which perfectly describe previous observations are used to calculate the probability of the next observation, with more weight put on the shorter computable theories. Shorter computable theories have more weight when calculating the expected reward to an action across all computable theories which perfectly describe previous observations. At any time, given the limited observation sequence so far, what is the optimal way of selecting the next action? The answer is to use Solomonoff’s method of calculating the prior probabilities in order to predict the probability of each possible future, and to execute the policy which, on a weighted average of all possible futures, maximises the predicted reward up to the horizon. This requires a way, however, of measuring the complexity of a theory.

Here we can turn to methods discovered to digitalise communication into a series of 0s and 1s. These series of bits of binary information can be termed strings, of a given length, say y, for a given language, the length of which will differ depending on the complexity of what is being communicated. This is where the idea of so-called Kolomogorov complexity, K(y), comes in. K(y) is the shortest possible description of string y for a given language. The upper bounds on the Kolomogorov complexity can be simple. Consider, for example, the two 32 character sequences:



The first can be written “ab 16 times”. The second probably cannot be simplified further.

Now consider the following inductive problem. A computer program outputs the following sequence of numbers: 1, 3, 5, 7.

What rule gives rise to the number sequence 1,3,5,7? If we know this, it will help us to predict what the next number in the sequence is likely to be, if there is one. Two hypotheses spring instantly to mind. It could be: 2n-1, where n is the step in the sequence. So the third step, for example, gives 2×3-1 = 5. If this is the correct rule generating the observations, the next step in the sequence will be 9 (5×2-1).

But it’s possible that the rule generating the number sequence is: 2n-1 + (n-1)(n-2)(n-3)(n-4). So the third step, for example, gives 2×3-1 + (3-1)(3-2)(3-3)(3-4) = 7. In this case, however, the next step in the sequence will be 33.

But doesn’t the first hypothesis seem more likely? Occam’s Razor is the principle behind this intuition. “Among all hypotheses consistent with the observations, the simplest is the most likely.” This sounds right, but can it be made more precise, and can it be justified? How do we find all consistent hypotheses, and how do we judge their simplicity?

Probability theory is the mathematics of reasoning with uncertainty. The keystone of this subject is Bayes’ Theorem. This tells you how likely something is given some other knowledge. Bayes’ Theorem can tell us how likely a hypothesis is, given evidence (or data, or observations). This is helpful because we want to know which model of the world is correct so that we can successfully predict the future.

It calculates this probability based on the prior probability of the hypothesis alone, the probability of the evidence alone, and the probability of the evidence given the hypothesis. It is just a matter of plugging the numbers in, although it is not always easy to identify these. But you can do your best. With enough evidence, it should become clear which hypothesis is correct. But guesses are not well-suited to an exact algorithm, so how can we construct this algorithm? Most situations in real life are complex, so that your “priors” (as used in Bayes’ Theorem) are actually probabilities that have been updated several times with past evidence.

But what would our ideal reasoning computer do before it knew anything? What would the probabilities be set to before we turned it on? How can we determine the probability of a hypothesis before seeing any data?

The answer is Occam’s Razor; simpler hypotheses more likely. But how rigorous is this? It’s usually difficult to find a measure of complexity, even for mathematical hypotheses. Is a normal curve simpler than an exponential curve, for example? Bayesian probability theory doesn’t have anything to say about choosing priors. Thus, the same probability is often assigned to each of the various hypotheses that might explain the observations. Of course this is a good approach if all the hypotheses actually are equally likely. But some hypotheses are more complex than others, and this makes them less likely than the other hypotheses. So when distributing your probability across several hypotheses, you shouldn’t necessarily distribute it evenly.

But we need a method that all can agree provides the correct priors in all situations. This helps us perform induction correctly and instils more honesty into the process. Since priors partly determine what people believe, they can sometimes choose priors that help “prove” what they want to prove, intentionally or unintentionally. To solve the problem of priors once and for all, we’d like to have an acceptable, universal prior distribution, so that there’s no vagueness in the process of induction. We need a recipe, an algorithm, for selecting our priors. For that we turn to the subject of binary sequences.

So if this is all the information we have, we have two different hypotheses about the rule generating the data. How do we decide which is more likely to be true? In general, when we have more than one hypothesis, each of which could be true, how can we decide which one actually is true? To start, is there a language in which we can express all problems, all data, all hypotheses? Let’s look at binary data. This is the name for representing information using only the characters ‘0’ and ‘1’. In a sense, binary is the simplest possible alphabet. With these two characters we can encode information. Each 0 or 1 in a binary sequence (e. g. 01001011) can be considered the answer to a yes-or-no question. And in principle, all information can be represented in binary sequences. Indeed, being able to do everything in the language of binary sequences simplifies things greatly, and gives us great power. We can treat everything contained in the data in the same way. Now, which of the three is more likely to be the true hypothesis that generated the data in the first place? How do we decide what the probability is of each of these hypotheses being true?

Now that we have a simple way to deal with all types of data, we need to look at the hypotheses, in particular how to assign prior probabilities to the hypotheses. When we encounter new data, we can then use Bayes’ Theorem to update these probabilities. To be complete, to guarantee we find the real explanation for our data, we have to consider all possible hypotheses. But how could we ever find all possible explanations for our data? By using the language of binary, we can do so.

Here we look to the concept of Solomonoff induction, in which the assumption we make about our data is that it was generated by some algorithm, i.e. the hypothesis that explains the data is an algorithm. Now we can find all the hypotheses that would predict the data we have observed. Given our data, we find potential hypotheses to explain it by running every hypothesis, one at a time. If the output matches our data, we keep it. Otherwise, we discard it. We now have a methodology, at least in theory, to examine the whole list of hypotheses that might be the true cause behind our observations.

Since they are algorithms, these hypotheses look like binary sequences. For example, the first few might be 01001101, 0011010110000110100100110, and 100011111011111110001110100101000001.

That is, for each of these three, when you give them as input, the output is our data. But which of the three is more likely to be the true hypothesis that generated the data in the first place? The first thing is to imagine that the true algorithm is produced in an unbiased way, by tossing a coin. For each bit of the hypothesis, we toss a coin. Heads will be 0, and tails will be 1. In the previous example, 01001101, the coin landed heads, tails, heads, tails and so on. Because each toss of the coin has a 50% probability, each bit contributes ½ to the final probability. Therefore, an algorithm that is one bit longer is half as likely to be the true algorithm. This intuitively fits with Occam’s Razor: a hypothesis that is 8 bits long is much more likely than a hypothesis that is 34 bits long. Why bother with extra bits? We’d need evidence to show that they were necessary. So why not take the shortest hypothesis and call that the truth? Because all of the hypotheses predict the data we have so far, and in the future we might get data to rule out the shortest one. The more data we get, the easier it is likely to become to pare down the number of competing hypotheses which fit the data.

With the data we have, we keep all consistent hypotheses, but weight the shorter ones with higher probability. So in our eight-bit example, the probability of 01001101 being the true algorithm is 1/256, although this isn’t a probability in the normal sense, since the sum of the probabilities have not been normalised to add to one. But these probabilities can still be used to compare how likely different hypotheses are. Solomonoff induction is the process that describes the scientific method made into an algorithm.

To summarize, Solomonoff induction works by starting with all possible hypotheses (sequences) as represented by computer programs (that generate those sequences), weighted by their simplicity (2n, where n is the program length), and discarding those hypotheses that are inconsistent with the data. Weighting hypotheses by simplicity, the system automatically incorporates a form of Occam’s Razor.

Turning now to ‘ad hoc’ hypotheses and the Razor. In science and philosophy, an ‘ad hoc hypothesis’ is a hypothesis added to a theory in order to save it from being falsified. Ad hoc hypothesising is compensating for anomalies not anticipated by the theory in its unmodified form. For example, you say that there is a leprechaun in your garden shed. A visitor to the shed sees no leprechaun. This is because he is invisible, you say. He spreads flour on the ground to see the footprints. He floats, you declare. He wants you to ask him to speak. He has no voice, you say. More generally, for each accepted explanation of a phenomenon, there is generally an infinite number of possible, more complex alternatives. Each true explanation may therefore have had many alternatives that were simpler and false, but also approaching an infinite number of alternatives that are more complex and false.

This leads us the idea of what I term ‘Occam’s Leprechaun.’ Any new and more complex theory can always be possibly true. For example, if an individual claims that leprechauns were responsible for breaking a vase that he is suspected of breaking, the simpler explanation is that he is not telling the truth, but ongoing ad hoc explanations (e.g. “That’s not me on the CCTV, it’s a leprechaun disguised as me) prevent outright falsification. An endless supply of elaborate competing explanations, called ‘saving hypotheses’, prevent ultimate falsification of the leprechaun hypothesis, but appeal to Occam’s Razor helps steer us toward the probable truth. Another way of looking at this is that simpler theories are more easily falsifiable, and hence possess more empirical content.

All assumptions introduce possibilities for error; if an assumption does not improve the accuracy of a theory, its only effect is to increase the probability that the overall theory is wrong. It can also be looked at this way. The prior probability that a theory based on n+1 assumptions is true must be less than a theory based on n assumptions, unless the additional assumption is a consequence of the previous assumptions. For example, the prior probability that Jack is a train driver must be less than the prior probability that Jack is a train driver AND that he owns a Mini Cooper, unless all train drivers own Mini Coopers, in which case the prior probabilities are identical.

Again, the prior probability that Jack is a train driver and a Mini Cooper owner and a ballet dancer is less than the prior probability that he is just the first two, unless all train drivers are not only Mini Cooper owners but also ballet dancers. In the latter case, the prior probabilities of the n and n+1 assumptions are the same.

From Bayes’ Theorem, we know that reducing the prior probability will reduce the posterior probability, i.e. the probability that a proposition is true after new evidence arises. Science prefers the simplest explanation that is consistent with the data available at a given time, but even so the simplest explanation may be ruled out as new data become available. This does not invalidate the Razor, which does not state that simpler theories are necessarily more true than more complex theories, but that when more than one theory explains the same data, the simpler should be accorded more probabilistic weight. The theory which explains all (or the most) and assumes the least is most likely. So Occam’s Razor advises us to keep explanations simple. But it is also consistent with multiplying entities necessary to explain a phenomenon. A simpler explanation which fails to explain as much as another more complex explanation is not necessarily the better one. So if leprechauns don’t explain anything they cannot be used as proxies for something else which can explain something.

More generally, we can now unify Epicurus and Occam. From Epicurus’ Principle we need to keep open all hypotheses consistent with the known evidence which are true with a probability of more than zero. From Occam’s Razor we prefer from among all hypotheses that are consistent with the known evidence, the simplest. In terms of a prior distribution over hypotheses, this is the same as giving simpler hypotheses higher ‘a priori’ probability, and more complex ones lower probability.

From here we can move to the wider problem of induction about the unknown by extrapolating a pattern from the known. Specifically, the problem of induction is how we can justify inductive inference. According to Hume’s ‘Enquiry Concerning Human Understanding’ (1748), if we justify induction on the basis that it has worked in the past, then we have to use induction to justify why it will continue to work in the future. This is circular reasoning. This is faulty theory. “Induction is just a mental habit, and necessity is something in the mind and not in the events.” Yet in practice we cannot help but rely on induction. We are working from the idea that it works in practice if not in theory – so far. Induction is thus related to an assumption about the uniformity of nature. Of course, induction can be turned into deduction by adding principles about the world (such as ‘the future resembles the past’, or ‘space-time is homogeneous.’) We can also assign to inductive generalisations probabilities that increase as the generalisations are supported by more and more independent events. This is the Bayesian approach, and it is a response to the perspective pioneered by Karl Popper. From the Popperian perspective, a single observational event may prove hypotheses wrong, but no finite sequence of events can verify them correct. Induction is from this perspective theoretically unjustifiable and becomes in practice the choice of the simplest generalisation that resists falsification. The simpler a hypothesis, the easier it is to be falsified. Induction and falsifiability are in practice, from this viewpoint, as good as it gets in science. Take an inductive inference problem where there is some observed data and a set of hypotheses, one of which may be the true hypothesis generating the data. The task then is to decide which hypothesis, or hypotheses, are the most likely to be responsible for the observations.

A better way of looking at this seems to be to abandon certainties and think probabilistically. Entropy is the tendency of isolated systems to move toward disorder and a quantification of that disorder, e.g. assembling a deck of cards in a defined order requires introducing some energy to the system. If you drop the deck, they become disorganised and won’t re-organise themselves automatically. This is the tendency in all systems to disorder. This is the Second Law of Thermodynamics, which implies that time is asymmetrical with respect to the amount of order: as the system, advances through time, it will statistically become more disordered. By ‘Order’ and ‘Disorder’ we mean how compressed the information is that is describing the system. So if all your papers are in one neat pile, then the description is “All paper in one neat pile.” If you drop them, the description becomes ‘One paper to the right, another to the left, one above, one below, etc. etc.” The longer the description, the higher the entropy. According to Occam’s Razor, we want a theory with low entropy, i.e. low disorder, high simplicity. The lower the entropy, the more likely it is that the theory is the true explanation of the data, and hence that theory should be assigned a higher probability.

More generally, whatever theory we develop, say to explain the origin of the universe, or consciousness, or non-material morality, must itself be based on some theory, which is based on some other theory, and so on. At some point we need to rely on some statement which is true but not provable, and so we think may be false, although it is actually true. We can never solve the ultimate problem of induction, but Occam’s Razor combined with Epicurus, Bayes and Popper is as good as it gets if we accept that. So Epicurus, Occam, Bayes and Popper help us pose the right questions, and help us to establish a good framework for thinking about the answers.

At least that applies to the realm of established scientific enquiry and the pursuit of scientific truth. How far it can properly be extended beyond that is a subject of intense and continuing debate.

Forecasting Elections and Other Things – Where did it all go wrong?

There are a number of ways that have been used over the years to forecast the outcome of elections. These include betting markets, opinion polls, expert analysis, crystal balls, tea leaves, Tarot cards and astrology! Let’s start by looking at the historical performance of betting markets in forecasting elections.

The recorded history of election betting markets can be traced as far back as 1868 for US presidential elections and 1503 for papal conclaves. In both years, the betting favourite won (Ulysses S. Grant, 1868 elected President; 1503 Cardinal Francesco Piccolomini elected Pope Pius III). From 1868 up to 2016, no clear favourite for the White House had lost the presidential election other than in 1948, when longshot Harry Truman defeated his Republican rival, Thomas Dewey. The record of the betting markets in predicting the outcome of papal conclaves since 1503 is less complete, however, and a little more chequered. The potential of the betting markets and prediction markets (markets created to provide forecasts) to assimilate collective knowledge and wisdom has increased in recent years as the volume of money wagered and number of market participants has soared. Betting exchanges (where people offer and take bets directly, person-to-person) now see tens of millions of pounds trading on a single election. An argument made for the value of betting markets in predicting the probable outcome of elections is that the collective wisdom of many people is greater than that of the few. We might also expect that those who know more, and are better able to process the available information, would on average tend to bet more. Moreover, the lower the transactions costs of betting and the lower the cost of accessing and processing information, the more efficient we might expect betting markets to become in translating information into forecasts. In fact, the betting public have not paid tax on their bets in the UK since 2001, and margins have fallen significantly since the advent of person-to-person betting exchanges which cut out the middleman bookmaker. Information costs have also plummeted as we have witnessed the development of the Internet and search engines. Modern betting markets might be expected for these reasons to provide better forecasts than ever.

There is indeed plenty of solid anecdotal evidence about the accuracy of betting markets, especially compared to the opinion polls. The 1985 by-election for the vacant parliamentary seat of Brecon and Radnor in Wales offers a classic example. Mori, the polling organisation, had the Labour candidate on the eve of poll leading by a massive 18%, while Ladbrokes, the bookmaker, simultaneously quoted the Liberal Alliance candidate as odds-on 4/7 favourite. When the result was declared, there were  two winners – the Liberal candidate and the bookmaker.

In the 2000 US presidential election, IG Index, the spread betting company, offered a spread on the day of 265 to 275 electoral college votes about both Bush and Gore. Meanwhile, Rasmussen, the polling company, had Bush leading Gore by 9% in the popular vote. In the event, the electoral college (courtesy of a controversial US Supreme Court judgment) split 271 to 266 in favour of Bush, both within the quoted spreads. Gore also won the popular vote, putting the pollster out by almost 10 percentage points.

In the 2004 US presidential election, the polls were mixed. Fox had Kerry up by 2 per cent, for example, while GW/Battleground had Bush up 4. There was no consensus nationally, much less state by state. Meanwhile, the favourite on the Intrade prediction market for each state won every single one of those states.

In 2005, I was asked on to a BBC World Service live radio debate in the immediate run-up to the UK general election, where I swapped forecasts with Sir Robert Worcester, Head of the Mori polling organisation. I predicted a Labour majority of about 60, as I had done a few days earlier in the Economist magazine and on BBC Radio 4 Today, based on the betting at the time. Mori had Labour on a projected majority of over 100 based on their polling. The majority was 66.

In the 2008 US presidential election, the Betfair exchange market’s state-by-state predictions called 49 out of 50 states correctly. Only Indiana was called wrong.  While the betting markets always had Obama as firm favourite, the polls had shown different candidates winning at different times in the run-up to the election. On polling day, Obama was as short as 1 to 20 to win on the betting exchanges, but some polls still had it well within the margin of error. He won by 7.2%. By 365 Electoral Votes to 173.

In the 2012 US presidential election, the RealClearPolitics average of national polls on election day showed Obama and Romney essentially tied. Gallup and Rasmussen had Romney leading, others had Obama narrowly ahead. To be precise, the average of all polls had Obama up 0.7%. Obama won by 4% and by 332 electoral votes to 206.

In the week running up to polling day in the 2014 Scottish referendum, polls had No to independence with leads of between 1% (Panelbase and TNS BMRB) to, at the very top end, Survation (7%), and YES to independence with leads of between 2% (YouGov) and 7% (ICM/Sunday Telegraph). The final polls had No to independence between 2% and 5% ahead. The actual result was No by 10.6%. The result had been reflected in the betting markets throughout, with No to independence always a short odds-on favourite. To give an example of the general bookmaker prices, one client of William Hill staked a total of £900,000 to win £193,000 which works out at an average price of about 1 to 5.

In the 2015 Irish referendum on same-sex marriage, the final polls broke down as a vote share of 70% for Yes to 30% for No. In the spread betting markets, the vote share was being quoted with mid-points of 60% Yes  and 40% No. The final result was 62% Yes, 38% No, almost exactly in line with the betting markets.

In the Israeli election of 2015, the final polls showed Netanyahu’s Likud party trailing the main opposition party by 4% (Cannel 2, Channel 10, Jerusalem Post, by 2% (Teleseker/Walla) and by 3% (Channel 1). Meanwhile, Israel’s Channel 2 television news on election day featured the betting odds on the online prediction market service, Predictwise. PredictWise had Netanyahu as 80% favourite. The next day, Netanyahu declared that he won “against the odds.” In fact, he did not. He won against the polls.

In the 2015 UK general election, the polling averages throughout the campaign had the Conservatives and Labour neck and neck, within a percentage point or so of each other. Meanwhile, the betting odds always had Tory most seats at very short odds-on. To compare at a point in time, three days before polling, the polling average had it tied. Simultaneously, Conservatives most seats was trading on the markets as short as 1 to 6.

If this anecdotal evidence is correct, it is natural to ask why the betting markets outperform the opinion polls in terms of forecasting accuracy. One obvious reason is that there is an asymmetry. People who bet in significant sums on an election outcome will usually have access to the polling evidence, while opinion polls do not take account of information contained in the betting odds (though the opinions expressed might, if voters are influenced by the betting odds). Sophisticated political bettors also take account of how good different pollsters are, what tends to happen to those who are undecided when they actually vote, differential turnout of voters, what might drive the agenda between the dates of the polling surveys and election day itself, and so on. All of this can in principle be captured in the markets.

Pollsters, except perhaps with their final polls (and sometimes even then) tend to claim that they are not producing a forecast, but a snapshot of opinion. This is the classic ‘snapshot defence’ wheeled out by the pollsters when things go badly wrong. In contrast, the betting markets are generating odds about the final result, so can’t use this questionable defence. In any case, polls are used by those trading the markets to improve their forecasts, so they are (or should be) a valuable input. But they are only one input. Those betting in the markets have access to much other information as well including, for example, informed political analysis, statistical modelling, focus groups and on-the-ground information including local canvass returns.

Does Big Data back up the anecdotal evidence? To test the reliability of the anecdotal evidence pointing to the superior forecasting performance of the betting markets over the polls, we collected vast data sets for a paper published in the Journal of Forecasting (‘Forecasting Elections’, 2016, by Vaughan Williams and Reade) of every matched contract placed on two leading betting exchanges and from a dedicated prediction market for US elections, since 2000. This was collected over 900 days before the 2008 election alone, and to indicate the size, a single data set was made up of 411,858 observations from one exchange alone for that year. Data was derived notably from presidential elections at national and state level, Senate elections, House elections, and elections for Governor and Mayor. Democrat and Republican selection primaries were also included. Information was collected on the polling company, the length of time over which the poll was conducted, and the type of poll. The betting was compared over the entire period with the opinion polls published over that period, and also with expert opinion and a statistical model. In this paper, as well as in Vaughan Williams and Reade – ‘Polls and Probabilities: Prediction Markets and Opinion Polls’, we specifically assessed opinion polls, prediction and betting markets, expert opinion and statistical modelling over this vast data set of elections in order to determine which performed better in term of forecasting outcomes. We considered accuracy, bias and precision over different time horizons before an election.

A very simple measure of accuracy is the percentage of correct forecasts, i.e. how often a forecast correctly predicts the election outcome. We also identified the precision of the forecasts, which relates to the spread of the forecasts. A related but distinctly different concept to accuracy is unbiasedness. An unbiased probability forecast is also, on average, equal to the probability that the candidate wins the election. Forecasts that are accurate can also be biased, provided the bias is in the correct direction. If polls are consistently upward biased for candidates that eventually win, then despite being biased they will be vey accurate in predicting the outcome, whereas polls that are consistently downward biased for candidates that eventually win will be very inaccurate as well as biased.

We considered accuracy, precision and bias over different time horizons before an election. We found that the betting/prediction market forecasts provided the most accurate and precise forecasts and were similar in terms of bias to opinion polls. We found that betting/prediction market forecasts also tended to improve as the elections approached, while we found evidence of opinion polls tending to perform worse.

In summary, we concluded that betting and prediction markets provide the most accurate and precise forecasts. We noted that forecast horizon matters: whereas betting/prediction market forecasts tend to improve nearer an election, opinion polls tend to perform worse, while expert opinion performs consistently throughout, though not as well as betting markets. There was also a systematic small bias against favourites, so that most likely outcome is actually usually a little more likely than suggested in the odds. Finally, if the polls and betting markets say different things, it is normally advisable to look to the betting markets.

So let’s turn again to why might we expect the betting markets to beat the polls. Most fundamentally, opinion polls, like all market research, provide a valuable source of information, but they are only one source of information, and some polls have historically been more accurate than others. Traders in the markets consider such things as what tends to happen to ‘undecideds’. Is there a late swing to incumbents or ‘status quo’? What is the likely impact of late endorsements by press or potential late announcements? Late on-the-day ‘tabloid press effect’, esp. on emotions. Influences undecideds, drives turnout to chosen editorial line. What is the likely turnout? What is the impact of differential turnout. Finally, sophisticated bettors take account of the relative accuracy of different polls and look behind the headline results to the detailed breakdown and the methodology used the poll. Betting markets should aggregate all the available information and analysis.

Moreover, people who know the most, and are best able to process the information, will tend to bet the most, but people who know only a little tend to bet only a little. The more money involved, or the greater the incentives, the more efficient and accurate will the market tend to be. It really is in this sense a case of “follow the money”.

Sometimes it is even possible to follow the money all the way to the future. To capture tomorrow’s news today. A classic example is the ‘Will Saddam Hussein be captured or neutralised by the end of the month’ Intrade exchange market? Early on 13 December, 2003, the market moved from 20 (per cent chance) to 100. The capture was announced early on 14 December, 2003, and officially took place at 20:30 hours Iraqi time, several hours after the Intrade market moved to 100. I call these, with due deference to Star Trek,  ‘Warp speed markets’.

But we need to be cautious. With rare exceptions, betting markets don’t tell us what the future will be. They tell us at best what the probable future will be. They are, in general, not a crystal ball. And we need to be very aware of this. Even so, the overwhelming consensus of evidence prior to the 2015 UK General Election pointed to the success of political betting markets in predicting the outcome of elections.

And then the tide turned.

The 2016 EU referendum in the UK (Brexit), the 2016 US presidential election (Trump) and the 2017 UK General Election (No overall majority) produced results that were a shock to the great majority of pollsters as well as to the betting markets. The turning of the tide could be traced, however, to the Conservative overall majority in 2015, which came as a shock to the markets and pollsters alike. After broadly 150 years of unparalleled success for the betting markets, questions were being asked. The polls were equally unsuccessful, as were most expert analysts and statistical models.

The Meltdown could be summarised in two short words. Brexit and Trump. Both broadly unforeseen by the pollsters, pundits, political scientists or prediction markets. But two big events in need of a big explanation. So where did it all go wrong?  There are various theories to explain why the markets broke down in these recent big votes.

Theory 1: The simple laws of probability. An 80% favourite can be expected to lose one time in five, if the odds are correct. In the long run, according to this explanation, things should balance out. It’s like there are five parallel universes. The UK on four of the parallel universes votes to Remain in the EU, but not in the fifth.Hillary Clinton wins in four of the parallel universes but not in the fifth. In other words, it’s just chance, no more strange than a racehorse starting at 4/1 winning the race. But for that to be a convincing explanation, it would need to assume that 2015 election, Brexit, Trump and 2017 election were totally correlated. Even if there is some correlation of outcome, the markets were aware of each of the predictive failures in the previous votes and still favoured the losing outcome by a factor of 4 or 5 to 1. That means we can multiply the probabilities. 1/5×1/5×1/5×1/5 = 1/625.   1/6×1/6×1/6×1/6 = 1/1296. Either way, its starting to look unlikely.

Theory 2: A second theory to explain recent surprise results is that something fundamental has changed in the way that information contained in political betting markets is perceived and processed. One interpretation is that the hitherto widespread success of the betting markets in forecasting election outcomes, and the publicity that was given to this, turned them into an accepted measure of the state of a race, creating a perception which was difficult to shift in response to new information. This is a form of ‘anchoring’. To this extent, market prices to some extent led opinion rather than simply reflecting it. From this perspective, the prices in the markets became a yardstick of the true probabilities and thus somewhat inflexible in response to the weight of new information.This leads to the herding hypothesis. Because the prediction markets had by 2015 become so firmly entrenched in conventional wisdom as an accurate forecasting tool, people herded around the forecasts, propelling the implied probabilities of existing forecasts upwards. So a 55% probability of victory, for example, became transformed into something much higher. In consequence, a prediction market implied probability of 70%, say, might be properly adjusted to a true probability of, say, 55%. In principle, it is possible to de-bias (or de-herd) each prediction market probability into a more accurate adjusted probability. We also need to look at the idea of self-reinforcing feedback loops. City traders look to the betting exchanges and the fixed-odds and spread bookmakers’ odds for evidence of what is the true state of play in each race. That influences the futures markets, which in turn influences perceptions among bettors. A sort of prediction market loop, in which expectations become self-reinforcing. This is a form of ‘groupthink’ in which those trading the futures and prediction markets are taking the position they are simply because others are doing so. This is further reinforced by the key arbitrating divide which more than anything acts as a distinguishing marker between Brexit supporters and Remain supporters, between Trump voters and Hillary Clinton voters – educational level. More than any other factor, it is the ‘University education’ marker that identifies the Remain voter, the Clinton voter. Also, the vast majority of City traders as well as betting exchange traders are University-educated, and tend to mix with similar, which may have reinforced the perception that Trump and Brexit were losing tickets. Indeed, more than ever before, as the volume of information increases, and people’s ability to sort between and navigate and share these information sources increases, there is a growing disjoint between the information being seen and processed by different population silos. This is making it increasingly difficult for those inhabiting these different information universes to make any sense of what is driving the preferences of those in alternative information universes, and therefore engaging with them and forming accurate expectations of their likely voting behaviour and likelihood of voting. The divide is increasingly linked to age and educational profile, reducing the diversity of opinion which is conventionally critical in driving the crowd wisdom aspect of prediction markets. It also helps explain the broad cluelessness of the political and political commentating classes in understanding and forecasting these event outcomes. Of course, the pollsters, pundits, political scientists and politicians were broadly speaking just as clueless. So why?

Theory 3: Conventional patterns of voting broke down in 2015 and subsequently, primarily due to unprecedented differential voter turnout patterns across key demographics, which were not correctly modelled in most of the polling and which were missed by political pundits, political scientists, politicians and those trading the betting markets. In particular, there was unprecedented turnout in favour of Brexit and Trump by demographics that usually voted in relatively low numbers, notably the more educationally disadvantaged sections of society. And this may be linked to a breakdown of the conventional political wisdom. This wisdom holds that campaigns don’t matter, that swings of support between parties are broadly similar across the country, that elections can only be won from the centre, and that the so-called ‘Overton window’ must be observed. This idea, conceived by political scientist Joseph Overton, is that for any political issue there’s a range of socially acceptable and broadly tolerated positions (the ‘Overton window’) that’s narrower than the range of possible positions. It’s an idea which in a Brexit/Trump age seems to have gone very much out of the window.

Theory 4: Manipulation. Robin Hanson and Ryan Oprea co-authored a paper titled, ‘A Manipulator Can Aid Prediction Market Accuracy‘, in a special issue of Economica in 2009 which I co-edited. Manipulation can actually improve prediction markets, they argue, for the simple reason that manipulation offers informed investors a proverbial ‘free lunch.’ In a stock market, a manipulator sells and buys based on reasons other than expectations and so offers other investors a greater than normal return. The more manipulation, therefore, the greater the expected profit from betting. For this reason, investors should soon move to take advantage of any price discrepancies thus created within and between markets, as well as to take advantage of any perceived mispricing relative to fundamentals. Thus the expected value of the trading is a loss for the manipulator and a profit for the investors who exploit the mispricing. Manipulation creates liquidity, which draws in informed investors and provides the incentive to acquire and process further information, which makes the market ever more efficient.

Theory 5: Fake News. There are other theories, which may be linked to the demographic turnout theory, including notably the impact of misinformation (fake news stories), of hacked campaign email accounts, and direct manipulation of social media accounts. In fact, we know when it all started to go wrong. That was 7th May, 2015, when the Conservatives won an unforeseen overall majority in the General Election. That result led to Brexit. That in turn arguably helped propel Trump to power. And it led to the shock 2017 UK election result. Common to all these unexpected outcomes is the existence of a post-truth misinformation age of ‘fake news’ and the potential to exploit our exposure to social media platforms by those with the money, power and motivation to do so. The weaponisation of fake news might explain the breakdown in the forecasting power of the betting markets and pollsters, commencing in 2015, as well as the breakdown of the traditional forecasting methodologies in predicting Brexit and Trump. This has in large part been driven by the power of fake news distribution and the targeting of such via social media platforms, to alter traditional demographic turnout patterns. This is by boosting turnout among certain demographics and suppressing it among others. The weaponisation of fake news by the tabloid press is of course nothing new but it has become increasingly virulent and sophisticated and its online presence amplifies its reach and influence. The weaponisation of fake news by the tabloid press can also help explain on-the-day shifts in turnout patterns.

What it does not explain is some very odd happenings in recent times. Besides Brexit and Trump, Leicester City became 5.000/1 winners of the English Premier League. The makers and cast of La La Land had accepted the Oscar for Best Picture before it was snatched away in front of billions to be handed to Moonlight. This only echoed the exact same thing happening to Miss Venezuela when her Miss Universe crown was snatched away after her ceremonial walk to be awarded to Miss Philippines.  And did the Atlanta Falcons really lose the SuperBowl after building an unassailable lead? And did the BBC Sports Personality of the Year Award go to someone whose chance of winning was so small he didn’t even turn up to the ceremony, while the 1/10 favourite was beaten by a little-known motorcyclist and didn’t even make the podium.  Which leads us to Theory 6.

Theory 6: We live in a simulation. In the words of a New Yorker columnist in February 2017: “Whether we are at the mercy of an omniscient adolescent prankster or suddenly the subjects of a more harrowing experiment than any we have been subject to before … we can now expect nothing remotely normal to take place for a long time to come. They’re fiddling with our knobs, and nobody knows the end.”

So maybe the aliens are in control in which case all bets are off. Or have we simply been buffeted as never before by media manipulation and fake news? Or is it something else? Whatever the truth, we seem to be at the cusp of a new age. We know not yet which way that will lead us. Hopefully, the choice is still in our hands.