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The Predictive Power Of The Super Bowl Coin Toss

This article is more than 8 years old.

Does it matter who wins the coin toss before the Super Bowl? Should you care if your team loses the toss?

Full disclosure: I don't really pay much attention to professional football (I'm more of a baseball guy and opening day can't come soon enough). I grew up in North Carolina, so naturally my social media feeds are full of my friends' excitement about the impending Super Bowl 50 matchup between the Carolina Panthers and the Denver Broncos. However, I was born in Wisconsin, so I'm contractually obligated to be at least a nominal Green Bay Packers fan and therefore indifferent to this Sunday's big game.

But I got to thinking about it and wondered how often the winner of the coin toss goes on to win the game. Luckily this information is readily available, and I even discovered that some people bet on the coin toss. More on that tidbit below.

In Super Bowl I, back in 1967, the Green Bay Packers won the coin toss and went on to defeat the Kansas City Chiefs 35-10. The next year, the Packers lost the toss but won the game 33-14 over the Oakland Raiders anyway. In total, across the 49 Super Bowls to date, the team that has won the coin toss has gone on to win the game 24 times. So the winner of the coin toss goes on to win slightly less than half the time (48.9% to be precise). Given that the coin toss is presumably a 50-50 event, it seems that it doesn't really matter if your team wins the toss or not. The real predictor is the odds made by Las Vegas: the favored team has won the game 33 times and lost 15 (last year's matchup between New England and Seattle was a toss-up).

What really fascinates me, though, is that people actually bet on the coin toss. Sequences of coin flips generate more false intuition than just about any other chance event. Of course, casino operators depend on the all too human instinct to look for patterns, the result of which often leads us to make fallacious assumptions. For example, if I flip a coin ten times and it comes up heads every time, what is the probability that the eleventh flip is heads? The answer is 1/2, of course, since the eleventh flip is independent of the first ten. But many people will reason that since it is so unlikely for a coin to land heads 11 times in a row it must be more likely that the next flip will land tails. It's true that the probability of 11 consecutive heads is small (1/2048 = 0.048%), but that doesn't affect the probability of the eleventh toss being heads.

This can be calculated explicitly using conditional probability. Given two events, A and B, we denote by P(A|B) the probability of event A happening given that event B has happened. There is a formula for this: P(A|B) = P(AB)/P(B); that is the conditional probability is the probability that both A and B happen divided by the probability that B happens. In the case of consecutive coin tosses, let A be the event that the first eleven tosses are heads and let B be the event that the first ten tosses are heads. Then the probability of both of these happening is simply probability of A happening (if the first eleven tosses are heads then the first ten were) and so P(A|B) = (1/2048)/(1/1024) = 1/2; that is, the probability of the eleventh toss being heads, given that the first ten were heads, is still just 1/2.

What could possibly lead someone to bet on the Super Bowl toss, given that it is an even chance event? I think it's because they want to believe there's a pattern. Here are the results of the first 49 tosses:

HTHHT  HHHTH  THHHT  TTHTT  THTHH  HHTHT  HTTTT  HTTTT  HTHHH  HHTT

(I've separated them into chunks of five for legibility.) See a pattern? I hope not. Heads has come up 24 times; tails 25 times. There is a string of five consecutive heads (Super Bowls XLIII-XLVII), but there are also two strings of four consecutive tails (and one string of four consecutive heads). So, how should you bet on this year's coin toss? Well, you shouldn't of course, unless you just like to randomly give away money, but the flawed instinct would be to give a slight preference to heads, given that the last two flips came up tails. After all, the probability of three consecutive tails is only 1/8, right? But wait, heads has come up only 24 of the 49 times, so it's more likely to come up this time to even it out, right?

Protip: don't bet on the coin toss. If you must place a bet, the oddsmakers tend to know what they're doing and can guide you much better than a random coin flip can.

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