How Can We Improve Our Game?

Performance, Putts, and Parables

A version of this article appears in my book, Twisted Logic: Puzzles, Paradoxes, and Big Questions (Chapman and Hall/CRC Press, 2024). 

THE PROBLEM OF LOSS AVERSION

Loss aversion, a key concept in behavioural economics, explains our tendency to prefer avoiding losses over acquiring equivalent gains. This principle is illustrated in diverse settings, from biblical parables to professional sports.

LOSS AVERSION IN THE VINEYARD

The Gospel of Matthew in the New Testament of the Bible relates the Parable of the Workers in the Vineyard. Here’s a breakdown of the parable:

Setting: A landowner goes out early in the morning to hire workers for his vineyard.

Early Morning Hiring: The landowner hires the first group of workers at daybreak, agreeing to pay them a denarius for the day’s work, which was a typical day’s wage at the time.

Subsequent Hirings: Throughout the day, the landowner hires additional groups of workers. He goes out again at the third hour (around 9 a.m.), the sixth hour (noon), the ninth hour (3 p.m.), and even the 11th hour (5 p.m.) to hire more workers. With these groups, he doesn’t specify an exact wage, but promises to pay them ‘whatever is right’.

End of the Day—Payment Time: When evening comes, the workers line up to receive their wages, starting with those who were hired last. To everyone’s surprise, the workers hired at the 11th hour receive a full day’s wage (a denarius).

Discontent among the First Hired: Seeing this, the workers who were hired first expect to receive more than their agreed-upon denarius. However, they too receive the same wage. This leads to grumbling against the landowner. They feel it’s unfair that they worked the whole day, bearing the heat, and yet received the same as those who worked just an hour.

Landowner’s Response: The landowner points out that he did not cheat the first workers; he paid them the agreed-upon wage.

Reference Points and Relative Outcomes: The workers who commenced early had a clear reference point; a denarius for a day’s toil. Despite receiving the agreed wage, they perceived receiving the same pay as those who worked less as a loss. Observing others receiving equivalent wages for fewer hours of work framed their wages in this way. This episode underlines the significance of reference points in human decisions, emphasising the relational aspect of outcome evaluations, surpassing absolutes. The dissatisfaction emanating from the early workers is a classic example of loss aversion. It is a central feature of modern Prospect Theory, albeit some 2,000 years ahead of its time.

BENCHMARKS AND BEHAVIOUR

An intriguing study on the behaviour of New York City cab drivers focused on how they decided the duration of their work shifts in relation to their daily earnings. Contrary to the expectations set by traditional economic theories, which suggest workers would maximise their hours on days with higher demand (and thus potential earnings), the study discovered that cab drivers tended to work fewer hours on days where they were earning more per hour and worked longer hours on less lucrative days. This behaviour aligns more closely with the concept of setting earning targets—drivers tended to end their shifts once they reached a certain income goal, regardless of how quickly they achieved it. This finding, led by Colin Camerer and Linda Babcock, challenged the rational agent model in economics, suggesting that real-world decisions are influenced more by psychological factors and personal benchmarks than traditional economics would expect.

BENCHMARKS ON THE GOLF COURSE

In the game of professional golf, the reference point takes on a very different aspect. This time the problem does not arise because those playing for just a couple of holes earn the same as those who complete four rounds. Instead, the problem arises from the so-called ‘Par’ assigned to each hole, which is a benchmark indicating the number of strokes that a skilled golfer, typically a ‘scratch golfer’ – who plays without any handicap – is expected to take to complete that particular hole under standard playing conditions. While the total number of shots should be the player’s real concern in most competitions, regardless of the assigned ‘par’ scores, the fear of failing to achieve par on individual holes may trigger the influence of loss aversion. In this case, the aversion is to underperforming expectations.

FINDING EVIDENCE OF LOSS AVERSION

Contrary to what might seem rational, analysis of more than 2.5 million putts, with detailed measurements of initial and final ball placement, reveals that professional golfers are indeed significantly influenced by the artificial par reference point. Specifically, it can be shown from the data that golfers are less accurate when putting to score better than par on a hole than when aiming for par. The data suggests, as such, that professional golfers exert more effort to avoid missing par on a hole than in scoring better than par. But why? Their only true objective in most competitions should be to minimise the number of shots taken, regardless of the ‘par’ assigned to each hole.

A paper published by Devon Pope and Maurice Schweitzer in the American Economic Review in 2011 examines a range of possible explanations, systematically eliminating them one by one until the true cause becomes evident. They conclude that golfers view par as their ‘reference’ score. Therefore, a missed par putt is perceived by golfers, perhaps subconsciously, as a more significant loss than a missed ‘birdie’ putt, i.e. one shot better than par. The reality is that par is an artificial construct; all that really matters in strokeplay competitions is the total number of shots taken. This implicit mental bias, however, leads to irrational behaviour during the game, with golfers unable to adjust their strategy even when made aware of this bias.

Interestingly, the researchers also observed a tendency for equivalent ‘birdie’ putts to come up slightly short of the hole in comparison to par putts, further confirming the hypothesis that a fear of a loss to par impacts the players’ putting strategies.

EXPLORING ALTERNATIVE EXPLANATIONS

Despite the compelling evidence for loss aversion, alternative explanations were considered. The possibility that birdie putts might originate from more precarious positions, for example, was explored. However, comprehensive data and rigorous analysis ruled out competing theories.

DYNAMICS OF LOSS AVERSION ACROSS TOURNAMENT ROUNDS

Interestingly, the accuracy gap between par and birdie putts varied across the tournament rounds. It was largest during the initial round and decreased significantly by the fourth round. This fluctuation suggests that the influence of loss aversion and the salience of the par reference point are neither automatic nor immutable and may be affected by factors such as competitor scores later in the tournament.

IMPLICATIONS: BENEFICIAL KNOWLEDGE FOR FORECASTERS AND PSYCHOLOGISTS

This unique insight into professional golfer behaviour has profound implications. It provides valuable information for sports forecasters or even those betting on the match in-play. Moreover, it serves as critical knowledge for sports psychologists working with professional golfers. If these psychologists could find a way to subtly reframe a golfer’s perception of a birdie putt, they could significantly improve a golfer’s performance and earnings over time.

CONCLUSION: PERSISTENCE OF BENCHMARKS AND LOSS AVERSION

This analysis demonstrates that even in a high-stakes, competitive market setting, loss aversion persists among experienced agents. Even top-performing golfers in the study displayed signs of this enduring bias, highlighting its pervasive influence in decision-making scenarios.

The concept has, of course, much broader significance than in competitive sports or even at the workplace. It has been shown to exist in so many of our personal choices and perceptions. By considering how we respond in our own lives to artificial benchmarks and reference points, it has the potential to significantly improve our everyday decisions and actions for the better.