One of the most controversial claims of sports statistics is the hot hand “fallacy”. Like the gambler’s fallacy, apparent hot or cold streaks are perfectly explainable by random chance and our overactive pattern detection sense. New research seems to show that the scoring of teams in college football, pro football, hockey, and basketball follow a Poisson distribution. Among the fundamental assumptions of this distribution is that there is some expected number of occurances per time periond, but that each occurring is independent of any other. That is, scoring a goal now doesn’t make it any more or less likely in the next 5 minutes.
However, there is a difference depending on the lead. The article says that “While hockey and football teams tend to extend their leads, pro basketball squads play worse when they’re ahead.” So getting an early lead is very important in hockey and football (or drinking games with Janx spirits), since there is an “unstable equilibrium” that exhibits the Matthew effect. Teams that are behind have to take more chances (higher variance strategies) that are more likely to backfire. Specifically, football teams that are trailing need to pass more, and hockey teams send more defensemen into attacking mode. Conversely, hockey teams leading in the third period usually take many fewer shots on goal. Basketball seems to be an interesting exception to this rule and instead has a “restoring force” that makes it more likely for the trailing team to close the gap.