# What Math Can Tell You about Who Will Win Sunday's Football Game

Written By: Dave Martin
• Math Software
• 2/1/2018

In Part 1 of this article, we started looking at how we can use PTC Mathcad to analyze the coin toss that starts the Big Game. Surprisingly, we found that regardless of the results of the coin toss, the visiting team has won 30 out of 51 times. Let’s continue crunching the numbers to see what else we can find.

More Results

Next question: How do the conferences stack up in terms of winning the coin toss?

Wow! The NFC has won more than twice as many times as the AFC. But how does this translate to performance?

Even though the NFC has an overwhelming advantage when it comes to winning the coin toss, they are just about even with the AFC in terms of victories.

Let’s take a look at how winning the coin toss correlates with winning the game. Again we’ll use a similar program to compare the two vectors:

Whoa! The winner of the coin toss has lost the championship game more than half the time! Again, it’s almost an even split, but winning the coin toss is supposed to provide an advantage (at least psychologically). This suggests that winning the coin toss at best provides no advantage, and at worst, is a detriment. Perhaps the winner might want to choose the side of the field to defend, and let the “loser” choose whether to kick, receive, or defer.

2008 Rule Change

Until 2007, the winner of the coin toss usually chose to receive the ball first. Starting in 2008, the winner of the coin toss was granted an additional choice: to defer choosing whether to kick or receive until the start of the second half. Since then, the choice to defer has increased from 7.8% in 2008, to 82.5% in 2016 during the regular season, and 88.9% in the championship game.

Since then, only one team in the Big Game has chosen to receive and not defer until the second half: the 2009 New Orleans Saints. (At the start of the second half, they surprised virtually everyone with an onside kick, which they recovered. They went on to defeat the Colts 31-17, but with a sample size of n=1, our confidence in any conclusions is low.)

How has the winner of the coin toss fared since the rule change?

A minor tweak to our for-loop reveals that since 2008, the winner of the coin toss has won only 4 out of the 9 match-ups (44.4%). Even with the rule change, the winning the coin toss does not appear to provide any measurable advantage.

Anomalies

If you take a look at the coin toss history, you can see some interesting streaks. For example, the NFC has won the last four coin tosses. We can use PTC Mathcad’s Binomial Distribution function to determine that the probability of this happening is 6.2%:

If we look back even further, the NFC has won 18 of the last 20 coin tosses. The chance of this happening is 0.0181%:

In that run, the NFC won an astonishing 14 times in a row! How rare is that? Let’s check PTC Mathcad:

Weird, huh?

Conclusions

Sometimes a coin toss is just a coin toss. Don’t fall for the Gambler’s Fallacy. Coins don’t remember or care about history. For example, what happens when we analyze a strategy of calling the opposite of last year’s flip?

It ends up being just about the same as calling the same as last year’s flip. Besides, it’s not even the same coin, the same city, or the same person flipping it. You know what does matter? The years spent training and mastering the craft of football. The hours the coaches spend developing players, analyzing game film, and devising plays and strategy. Who’s completely healthy, who’s recovering from an injury or illness, and who handles stress and pressure better.

So what have we learned? With PTC Mathcad, you can read in data, slice it, and dice it to reveal all kinds of interesting results, correlations, and coincidences. What data are you sitting on that begs to be analyzed? Send me your ideas, and you may see it in an upcoming blog post.

Tags:
• Math Software