6 ideas
Players, coaches and fans believe a shooter who has just made several baskets is more likely to make the next one. Shot records from the Philadelphia 76ers, free-throw data from the Boston Celtics and controlled shooting experiments showed that the chance of a hit after a streak of hits was no higher than after a streak of misses. The streaks people see as 'hot' are the ones chance alone would produce.
People expect random sequences to alternate more than they actually do. This makes the ordinary runs and clusters that chance produces look too regular to be accidental. The false expectation that small samples should look like the process that made them leads people to find patterns and invent causes, such as the V-1 bomb hits on London, where none exist.
People judge relationships mostly from confirming cases, where the action was taken and the outcome followed. They neglect the cells of the 2x2 table that are needed to test the link: the action taken with no outcome, and the outcome without the action. Many cases are also invisible. Admissions officers, for example, never see how the applicants they rejected would have done, so their judgments seem validated whether or not they are.
Extreme performances tend to be followed by more average ones through regression to the mean alone. People fail to expect this and instead credit whatever intervention came after the extreme: treatments given at a symptom's worst, punishment after a bad performance. This makes useless remedies look effective, and it teaches that criticism works better than praise.
For conclusions we want, we ask 'Can I believe this?' and accept one supporting piece of evidence. For conclusions we dislike, we ask 'Must I believe this?' and demand overwhelming proof. Motivation seldom makes people believe anything outright. It works through this uneven scrutiny, which keeps the feeling of objectivity intact while reliably pushing conclusions toward what we prefer.
Stories passed along by others are routinely simplified, exaggerated and made more entertaining or more meaningful than the events behind them. Most of what we 'know' about ESP, health scares and remarkable cures arrives through this channel. The right question about a vivid story is how it was selected and shaped before it reached us.