The author makes the following pithy conclusion: 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. 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.
The article goes on to note the obvious cherry-picking used in selecting the data… in other words, picking the 25 consecutive games that would make the Patriots look like they were somehow cheating on the coin flip. 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 article begins by noting that while the Patriots may have been lucky the last 25 games, it’s not surprising that some team in the NFL was lucky (and the lucky team just happened to be the Patriots).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. Unfortunately, this is far too simplistic an analysis to accuse someone of “winning the coin flip at an impossible rate.” Rather than re-do the calculations myself, I’ll just quote from the following article from the Harvard Sports Analysis Collective. That’s less than three-quarters of one percent.Īs far as the math goes, the calculation is correct. The Pats have won the coin toss 19 of the last 25 times, according to the Boston Globe‘s Jim McBride.įor some perspective: Assuming the coin toss is a 50/50 proposition, the probability of winning it at least 19 times in 25 tries is 0.0073.
#PATRIOTS COIN FLIP HOW TO#
When other coaches struggle with when to use timeouts or how to manage the clock, the Patriots coach, almost effortlessly, always seems to make the right decision.īelichick has also been extremely lucky. 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.
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