![]() ![]() The fault seems to rather lie with who made the headline and pubbed it, although their job is probably just to get pageviews in which case I guess they succeeded.Last November, CBS Sports caused a tempest in a teapot with an article with the sensational headline “ Patriots have no need for probability, win coin flip at impossible rate.” From the opening paragraphs:īill Belichick is never unprepared. To be fair, the author of this article did not seem to insinuate that the Patriots were cheating, rather he was just remarking that it was a rare event (although, in reality, it shouldn’t be as unexpected as he makes it out to be). I did this 10,000 times – in 38.71% of these simulations there was at least one sequence with 19 or more heads out of 25.Īnyways, both common sense and statistics will tell you that the Patriots have not been cheating by winning coin flips at an “impossible” rate. We can then check the string for a sequence of 25 games where there was 19 or more heads. ![]() Given that he has coached 247 games with the Patriots, we can randomly generate a string of zeroes and ones corresponding to lost and won con flips respectively. Why not look throughout his career? Did he suddenly discover a talent for predicting the future? Furthermore, given the length of Belichick’s career, we would almost expect him to go through a period where he wins 19 of 25 coin flips by random chance alone. In addition the selection of looking at only the last 25 games is surely a selection made on purpose to make Belichick look bad. ![]() Even if you restricted it to not all 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%. 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. The probability that, with 32 teams, there is not one of them with a result this extreme is 0.9854 32 = 0.6245998. The probability of a team NOT having a result that extreme is 1-0.0146 = 0.9854. The probability of any one team having a result that extreme, as shown before, is 0.0146. The proper way to do this would be via simulation, but assuming independence is much easier and should yield pretty similar results. 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. That is still very low, however given that there 32 teams in the NFL, the probability of any one team doing this is much higher. The probability of winning it at least 19 out of 25 times is 0.0073, which is the number upon which they base their declaration of “impossible”.īut how impossible is it? Really, we are interested in not only the probability of getting 19 or more heads but also a result as extreme in the other direction – i.e. What’s more, they publicized it with the lead: “Have the Patriots found a way to get an edge on coin flips?” Clearly with Deflategate out of the way the media is looking for something to accuse the Patriots of.īesides the fact that accusing anyone of cheating at coin flips is absurd, is the probability of this happening really that low? As said in the article, the Patriots have won 19 of their 25 past coin flips. Late yesterday, CBS Sports put out an article claiming that the Patriots were winning coin flips at “an impossible rate”. ![]()
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