In what ways are hot and cold streaks in sports real, as opposed to statistical illusions?

Last night, Dallas kicker Brett Maher missed his first four extra point attempts in the team’s playoff game. Along with his one (missed) PAT in the team’s final regular season game, that gave him a streak of five consecutive misses.

Prior to this streak, Maher’s career NFL stats for PAT attempts included 128 successful kicks in 133 attempts (96%). His stats for this season were 50 for 52 (also 96%). Now if his performance in this regard is genuinely random, like flipping a coin five times that comes up heads 96% of the time, the odds of a particular five-attempt iteration resulting in five misses or five tails are less than a million to one, if my figuring is correct.

So the idea that this was a genuinely random outcome is incredibly implausible, statistically speaking. Instead, Maher seemed to be suffering from what golfers call, in regard to putting, “the yips,” — that is some stress-induced reaction to pressure that caused a massive decline in his normal level of performance.

This also makes perfect sense from a purely subjective perspective: it’s a rare athlete who will deny that it’s harder to perform in a high pressure than a low pressure situation. This was a playoff game, so by definition a relatively high pressure situation. On the other hand, for an NFL kicker, who in most cases is just a few bad weeks from losing his job — high level kicking talent is far more plentiful than the 32 jobs available at any time, and note that Maher himself wasn’t able to secure an NFL job until the advanced age of 29 (he’s now 33) — all games are pretty much by definition high pressure situations, since as a practical matter these guys are always performing with their jobs on the line.

So who knows why the pressure got to Maher last night, but it surely must have — otherwise we would be talking about an almost inexplicably freakish event.

Relatedly, players, coaches, management, and fans all believe in the reality of hot and cold streaks. But there’s also a lot of evidence that what appear to be such streaks or often (usually?) just statistical illusions. Consider this analysis, which broke down the performance of every major league hitter throughout the entire 2019 season, and found that there was essentially no statistical correlation whatsoever between how well a hitter had done in his previous five games and how he would do in his next five games. That a hitter went 13-22 over five games, or conversely went 1-22, told you nothing at all about how he would do in the next five, relative to his expected output, given his normal baseline performance. (Similar results have been found when looking at shooting streaks in NBA games).

So how do we reconcile these things? It’s clear that sometimes players do worse (or better) than their normal baseline performance, in part, because of a kind of cascade effect, of the sort that may well have drowned Brett Maher’s NFL career last night. But it’s extremely difficult to document this happening in the kind of large data samples put together in regard to MLB hitters and NBA shooters.

Thoughts?