Want to amaze your friends at that Super Bowl party you're going to? All you have to do is hit 'em with some Super Bowl math fun facts. Keep on reading to learn what they are!
Does the Coin Toss Matter in Football?
Our second question for today has to do with a part of the game that takes place before the game even kicks off: the coin toss.
Namely, does it matter if a team wins or loses the coin toss? Does it increase the odds that a particular team will win if they win the toss?
So as not to keep you in too much suspense, I'll let you know right off the bat that the answer is that winning or losing the coin toss has no statistically significant impact on the outcome of the game (so there's no need to hold off on placing your bets until after the toss). How do I know this? Thankfully, a physicist named Matt Springer (who was a Ph.D. student at Texas A&M University when he wrote about this topic in 2010) looked at the actual impact of the coin tosses in the first 43 Super Bowls. He found that the winner of the coin toss went on to win 20 and lose 23 of those games.
Does it matter if a team wins or loses the coin toss?
Aha! you say. So it appears that winning the toss puts a team at a slight disadvantage. No, not really. Just as you don't expect to always get heads exactly 50 times whenever you toss 100 coins—sometimes you might get 47, sometimes 57, and so on—you also shouldn't expect that the winner of the toss in a football game will go on to win the game exactly half the time.
In fact, statistics predicts that if the coin toss in a football game truly has no impact on the outcome of the game, then the winner of the toss will win between 18 and 25 of those 43 Super Bowl games with about a 70% probability. There's about a 95% chance that they'll win between 15 and 28 of those 43 games. In truth, this analysis is a bit of an oversimplification of things, but it's fine for our purpose and it's good enough to tell us that the results through the first 43 Super Bowls are perfectly consistent with a perfectly unimportant coin toss.
What Scores Are Possible in Football?
Today's third and final Super Bowl math fun fact is actually more of a puzzle. The question is: What are all of the scores that are possible in a football game? Or, turning this around, are there any scores that are impossible?
To answer this, you need to know the different numbers of points that can be awarded:
- 2 points for the relatively rare safety
- 3 points for a field goal
- 6 points for a touchdown
- 7 points for a touchdown and a successful extra-point kick
- 8 points for a touchdown and a successful two-point conversion
Given these, is it possible for a team to score 11 points? How about 37? Can you figure out some way to prove which scores are possible…or impossible? Give it some thought (which should be fun!) and we'll talk about the answer next time.
Okay, that's all the Super Bowl math we have time for today.
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Football field image from Shutterstock.