In 1985, Amos Tversky and Thomas Gilovich conducted a study into whether players are more likely to score successful shots based on previous success rates. Titled the “Hot Hand Fallacy: On the Misperception of Random Sequences” [PDF], the two scientists discovered there was no relationship between previous successful shots and future success rates, and that correcting for the basic underlying skill of professional basketball players able to hit 50% of their shots, the success rate of shots reflects a random sequence. In layman’s terms, “streaks” in basketball are just statistical noise, not signal.
Determining whether there is truly a “hot hand” in basketball is relatively easy. As the study authors indicate, despite the relative difficulty of a shot depending on where on the court it’s taken and the strength of the opposition, the free throw data provides a sample free from those “contaminating effects.”
These effects are a little harder to isolate in football, beyond penalty kicks of course. But the basic parameters of Tversky and Gilovich’s work is still reproducible in a football setting (although it would arguably need a larger sample of games): is a player who scores in several games in a row statistically more likely to score on subsequent chances, at a rate exceeding 50%?
This question came up on Twitter yesterday involving Robin van Persie. The Manchester United star forward failed to score against Chelsea. This was, we discovered, the ninth game in a row for Man United in which the Dutch player failed to score (he did score for Holland during the last international break, including a brace against Romania saw him break Johann Cruyff’s national scoring record).
Almost immediately, theories emerged about some sort of player slump. Robin van Persie was clearly losing confidence.
This is quite an empirical leap. For one, drawing this conclusion would require a lot of statistical ground work. Has Robin van Persie had the same number of chances to score from the same advantageous areas of the pitch since he last scored on Everton in February? What was the quality of competition among Man United’s opponents in those games? Was van Persie able to get into good positions to score based on United’s formation? Or the opposition’s formation? Did scoring effects distort the persistence of Man United’s attack?
Once we’ve isolated for individual game effects, we then have to move into probable causes for Robin van Persie’s alleged “slump.” Is van Persie recovering from an injury? Has he lost a measure of pace? Have his teammates lost confidence in him and are passing to him less?
After dismissing those possibilities, we’d have to do some work on establishing a real relationship between personal confidence and shooting accuracy and chance creation. Do we know for a fact that Robin van Persie’s failure to score has had an effect on his personal mood? Is there a demonstrable correlation between personal confidence and scoring that would have an effect over a relatively small number of matches?
This is not to discount the possible effect of psychology on athlete performance. But the burden of proof rests on those who would blithely state that Robin van Persie’s “goal drought” is somehow a crisis of confidence and not a random sequence possibly augmented by a series of opponents that included Real Madrid twice and Chelsea twice, and four games in which he did not play more than 70 minutes.
In any case, we do know a little of Robin Van Persie’s overall historical performance record in the Premier League over the past four seasons (the EPL is a good source too, with its spread of competition and number of games). This season his shooting percentage is currently 17%. Last season it was 17%. The season before it was 19%, although he played fewer matches. Moreover, he has maintained a shot-on-target rate of 21% in the last three seasons. This is not the most ideal indicator of underlying performance, but it is at least consistent. This would suggest it’s not completely out of the realm of possibility that both Robin van Persie’s “streak” and his “slump” were random events (I’ll leave it to a more dedicated analytics guru to perform a study similar to the one done in basketball in 1985).
Why does this matter? Well, it’s important to be skeptical of the notion that, if a good striker stops scoring after a few games, it’s an indication “his mind’s not right.” First, it does a disservice to the real work and importance in the mental health of athletes. Second, it currently drives a cottage industry of “sports psychologists” ready to give their assessment of Fernando Torres’ confidence problems to a willing media despite not having directly spoken to the player, or having done any research into whether there might be other factors at play. Third, it diverts attention away from other, perhaps less obvious indicators, some of which may not have anything to do with the player himself.
We can’t say with total confidence that the hot hand fallacy definitely applies to soccer, but finding out with clinical accuracy is a far easier task than simply blaming “confidence” when a good player doesn’t score after an arbitrary sample of games.