The Gambler's Fallacy and Streak Shooting

One of the problems most people have when they are asked to predict what the flip of a perfectly random coin will yield is that they tend to base their reasoning on what happened the last few times the coin was flipped. If heads came up five times in a row, many people believe tails is more likely to come up next. Yet this conclusion is precisely wrong, not because heads follows heads instead of tails, but because each flip of the coin is an independent event.

Ignoring the independence of each chance event is a problem that is not just associated with casual observers. Even people who gamble for a living, upwards of 20 hours a week, still make the same mistake. And this is where streak shooting comes in.

The beauty of the streak shooting hypothesis is that there is an easily understandable rationale that suggests the shooter's psychological makeup affects whether or not the ball will go in the basket. In fact, a narrative revolving around shooting streaks actually tends to make a game of basketball more dramatic. Most announcers devote significant time to laying out statistics that show what percentage of shots each of the players has been making. Yet nobody pays any attention to the aggregate data.

If a player shoots 49% of his shots accurately over the course of the season, that tells us almost nothing about any particular game. And even within a game, the truth is that having missed the last three shots does not substantially alter the odds of hitting the next shot.

The problem with easily observable, quasi-certifiable rationales extends far beyond the arena of competitive sports. Investors pile into bull markets that have driven stock prices beyond even the most optimistic valuations because of bull market psychology that explains but does not predict. If Jim Cramer could accurately predict the movements of hundreds of stocks each week, even his substantial ego would be more than adequately stroked by the media coverage that would follow him after he becomes the world's first trillionaire if he simply foregoes his television show and sticks his money where his mouth is.