A Blast from the Past and  a Message for Today

With the large volumes of football data now being mined by armies of analysts looking for hidden nuggets of knowledge, we can easily overlook some of the ground-breaking work from the past, which is in danger of being forgotten, yet still has something to tell us today. One such piece of work that I recently came across is John Cohen’s study of football decision-making dating from the 1960’s.  It was published in the British Journal of Psychology in 1962 under the title Skill and Judgement of Footballers in Attempting to Score Goals: A Study of Psychological Probability.

Of course, football has changed out of all recognition since the 1960’s, and modern footballers are quite different from their counterparts of 50 years ago. But I thought it would still be worthwhile bringing some attention to this work because it asks questions about football that we are still struggling to answer today.  And in a sport where the importance of mental factors and psychology are becoming more mainstream, Cohen’s work offers some innovative avenues for improving performance.

John Cohen was a pioneer. A professor of psychology at the University of Manchester, and the author of over 20 books, the focus of his research was human decision-making, risk-taking and doubt. In his 1960 book Chance, Skill and Luck: The Psychology of Guessing and Gambling, Cohen discussed his work on the differences between psychological and statistical probability.  (He notes in the abstract that “Some of the experimental work includes risk-taking in hazardous circumstances under the influence of alcohol.”  - the mind boggles.)  Half a century later, Daniel Kahneman brought his own studies on psychological probability to public notice in his widely acclaimed best-seller Thinking Fast and Slow.

Cohen’s 1962 paper asked when a football player would attempt to shoot, and whether his decisions were based on accurate assessments of his shooting prowess. To answer these questions, Cohen conducted an ingenious set of experiments on four groups of players; first team players from Manchester United and West Bromwich Albion (both then in the First Division), university students and schoolboys.  In this post I will select a couple of experiments from the paper and highlight their main points, and then consider their implications.

Experiment 1.

Cohen’s experiments were carried out on the team’s own football grounds. In Experiment 1, the player stood in his own half of the field, at a distance from the goal at which he thought he had no chance of scoring, and facing the goalkeeper who stood on his goal line.  With the ball at his feet, each player was then asked to approach his opponents’ goal down the centre of the field. He was instructed to stop when he first felt that he had a chance of scoring once in a hundred attempts. The distance to goal was measured. The player then continued to approach the goal while indicating the different points where he felt he could score once, twice, three times, and four times in five attempts (i.e. 20%, 40%, 60%, 80% of the time) and finally the point at which he first felt he could score ninety-nine times in a hundred attempts. These distances were also measured.

The players were then asked to take five shots from each of the measured positions. The results are summarized in Table 1.


Estimated chance of success
Team 1% 20% 40% 60% 80%
Man. United


Distance (feet)

106 67 39 29 29
West Brom. 96 68 46 36 36
Students 96 59 36 28 28
Schoolboys 116 71 45 33 33
Man. United


Actual Success



6% 30% 50% 84%
West Brom. 22% 42% 62% 68%
Students 20% 48% 60% 72%
Schoolboys 8% 22% 46% 76%

The top half of the table shows the distances for each decision point. (The 99/100 distance is described later.) The bottom half of the table shows the percentage of shots that scored. Green text shows where players scored more than they expected, and the red text where they performed worse. As we might have guessed, the schoolboys are consistently optimistic, and overestimated their ability to score at all four data points.  Surprisingly however, the professional players didn’t seem any better than the students at accurately estimating their shooting ability.

In a second part of the experiment, the experimenter determined the furthest distance from the goal at which the player could score 5 out 5 times (unless this was already known from the previous test). This was compared to the 99/100 distance measured previously.  Thus he could compare the actual distance at which players could score with 100% certainty with their estimated distance for virtual (i.e. 99%) certainty.


We can see from the chart that players consistently underestimate their ability.  On average they can score with virtually 100% certainty (blue bars) from five feet further out than they think they can.  And once again, the professional players seem no better than the amateurs at estimating their own abilities.

Experiment 2

In a second experiment, the player, with the ball at his feet, ran towards the opponent’s goal. He was asked to imagine that in an important match, he had beaten the defence and was being chased, with only the goalkeeper to beat. He was to shoot at the first appropriate moment,  and the distance he chose was called the “longest shot attempted”.

Longest Shot ATTEMPTED (ft.) Maximum risk taking level
Manchester United 59 29%
West Bromwich Albion 83 8%
University students 51 33%
Schoolboys 68 27%

The maximum risk-taking level in Table 2 is defined as the most uncertain risk a player is prepared to undertake.  It is calculated by interpolating the longest shot distance from Table 2 into the distance measurements in Table 1. For example, Manchester United’s longest shot distance is 59 feet. From Table 1 we see this corresponds to an expectation of scoring about mid-way between 20% and 40%.  In other words, a Manchester United player through on goal holds off from shooting until his subjective probability of scoring reaches 29%, and then shoots.  The typical West Bromwich Albion player however is much more impetuous, and only needs to an 8% chance of success before deciding to shoot.

Potential for Improving Performance

I found these results intriguing in their own right, but I also think they suggest ways of improving the performance of footballers today.

Cohen found that the country’s best footballers were no better at assessing their own abilities than amateurs. Of course, his experiments date to an earlier era, and we don’t know how far this result holds true today. But to the extent it does, it suggests there is room for top players to improve the assessments of their own performance.

Now, I know next to nothing about coaching footballers - so what I’m saying here might be completely off the wall.  But as far as I am aware, the development of football players focuses very largely on honing individual skills, and cultivating the physical abilities to execute those skills at speed and under pressure.  However, a skill that is not correctly understood is a skill whose effectiveness is limited.  If a player can score reliably from 30 feet out, but thinks he needs to get closer than that, some of his hard-won skill is being squandered. And recognizing this inefficiency is an opportunity to create an edge.  When two players have the same level of ability, the one who knows his true level of ability - and can therefore make decisions in accordance with reality - will appear to be more talented than the one who does not.

The key question I have is whether coaching and education could help players to align their perceived skills more closely with their actual skills.  Perhaps Cohen’s experimental paradigm, or something a bit more realistic, could be used to demonstrate where individual players are either too optimistic or too pessimistic about their ability to score. At a time when clubs are looking for marginal gains, helping players develop accurate assessments of their own abilities might be a low-cost route to increasing player effectiveness. It would be interesting to have the views of some experienced coaches on this.