The New England Patriots have long been accused of going beyond the rules to gain an advantage over opponents -- spying, deflating footballs, what have you. There is no way to definitively say what impact their alleged transgressions have had. Big or small, the overall picture is pretty clear: Somehow, someway, the Patriots find a way to win, even when it comes to silly things like coin flips.
Seriously, coin flips.
According to the Boston Globe, the Patriots have won 19 of their last 25 coin flips, which is a freak occurrence if taken in a vacuum. The odds of winning a coin toss 19 times in 25 tries is 0.0073, as CBS Sports points out, or less than three quarters of 1 percent. Unless head coach Bill Belichick is also the mastermind of a complex pregame coin-switching scheme, it appears that the Patriots may really just have all the luck, in which case we can't rule out any form of dark arts for their success. Witchcraft, voodoo, Satanism, necromancy -- it's all on the table.
Sure, it could just be a fluke. The Harvard Sports Analysis Collective noted that, across a 32-team league, that sort of streak should be expected to occur at some point.
To do an easy calculation we can assume that all tosses are independent, which isn't entirely true as when one team wins the coin flip the other team loses. The proper way to do this would be via simulation, but assuming independence is much easier and should yield pretty similar results. The probability of any one team having a result that extreme, as shown before, is 0.0146. The probability of a team NOT having a result that extreme is 1-0.0146 = 0.9854. The probability that with 32 teams there is not one of them with a result this extreme is 0.985432 = 0.6245998. Therefore, with 32 teams, we would expect at least one team to have a result as extreme as the Patriots have had over the past 25 games 1- 0.6245998 = 0.3754002, or 37.5% of the time. That is hardly significant. Even if you restricted it to results as extreme in either direction but just results of 19 or greater, the probability of one or more teams achieving that is still nearly 20%.
But the fact that the fluke came out in favor of the Pats, in particular, is maddening to anyone who has watched the team get the benefit of the fates more often than not. Fumbles are supposed to be random occurrences too, relatively speaking, and the Patriots do it much less often than anyone else.
Even the biggest skeptics must agree that Belichick has at least looked into devil magic at this point. The next NFL investigation should be spearheaded by a third-party shaman.