Wednesday, November 4, 2009

"Hot hand" and "gambler's fallacy" revisited

In cricket, batsmen and bowlers are often credited with enjoying a rich vein of form (or a "hot hand" or "streak") during which period they either score more runs or take more wickets than their career average would appear to suggest. This form is translated into expectations of similar performance in the next match in the minds of their viewers. Their opponents though try to rationalize and form expectations of an imminent failure based on the "law of averages".

Behavioural psychologists describe the "hot hand" belief as an example of "representative bias" and the belief that a long streak increases the chances of a different result in the next go as "gambler's fallacy". They consider both beliefs as examples of cognitive biases that distorts the perceptions of human beings and rejects the opinions formed thereof.

In a famous experiment that examined the shooting records of Philadeplphia 76ers, Amos Tversky, Tom Gilovich and Robert Vallone had found "no evidence for a positive co-relation between the outcomes of successive shots". They attributed the belief in "streak shooting" or "hot hand" and predictions based on previous outcomes to "a general misconception of chance according to which even short random sequences are thought to be highly representative of their generating process".

In another equally famous experiment Isreali flight instructors found that criticism (after a very bad landing) improves performance of student pilots in their next flight while praise (for an exceptionally good landing) does the exact opposite with the next landing. Daniel Kahneman attributed this observation to "regression to the mean" - if an unusual result (either a positive or negative deviation from the mean performance) happens today, it is more likley to be followed by a result closer to the statistical average - and not to the impact of reward and punishment.

However, the aforementioned line of analysis may not convey the full story, atleast in certain contexts. There may be a strong basis in the "hot hand" belief.

The behavioural psychologists make the fundamental mistake of assuming that these events (shootings or runs in successive innings) are random and therefore independent of each other. For example, despite the equal statistical probability of a batsman losing his wicket or surviving a delivery, the performance of a cricket batsman can hardly be described as random. It cannot be denied that his performance (apart from his talent and hardwork) is a function (and at the highest levels, these factors differentiate between an exceptional performance and an average one) of intangible factors like self-confidence and opposition's assessment of his prowess, both of which positively feed into his performance. A batsman enjoying a rich vein of form, being at the peak of his confidence and having intimidated his opponents, is more likely to score heavily than fail in his next innings. It is therefore natural (and even rational) to anticipate the hot hand.

Interestingly, in contact games like football or basketball, another, albeit unexpected, outcome is possible. A "hot hand" in scoring goals or shooting baskets will immediately invite the attention of opponents who deploy tactics that would seek to immobilize the player. Faced with such extra attention, the player is less likely to match his earlier performance. However, on the positive side, the extra attention on the "hot" player is likely to adversely affect the overall strategy of the opponent and therefore increase the propsects for his compatriots to score goals or shoot baskets.

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