Some Fallacies of Probability
The point of examining these heuristics and noting the errors that they pro- duce is not to suggest that we should cease relying on them. First, there is a good chance that this would be psychologically impossible, because the use of such heuristics seems to be built into our psychological makeup. Second, over a wide range of standard cases, these heuristics give quick and largely accurate estimates. Difficulties typically arise in using these heuristics when the situation is nonstandard—that is, when the situation is complex or out of the ordinary.
To avoid such mistakes when making important judgments about proba- bilities, we need to ask, “Is the situation sufficiently standard to allow the use of heuristics?” Because this is a mouthful, we might simply ask, “Is this the sort of thing that people can figure out in their heads?” When the answer to that question is “No,” as it often is, then we need to turn to more formal procedures for determining probabilities.
In a remarkable study,3 Thomas Gilovich, Robert Vallone, and Amos Tversky found a striking instance of people’s tendency to treat things as statistically significant when they are not. In professional basketball, certain players have the reputation of being streak shooters. Streak shooters seem to score points in batches, then go cold and are not able to buy a basket. Stated more precisely, in streak shooting, “the performance of a player during a particular period is significantly better than expected on the basis of the player’s overall record.” To test whether streak shooting really exists, the authors made detailed study of a year’s shooting record for the players on the Philadelphia 76ers.
