The Mystery of 21 Points

Recently, I’ve been wrestling with a math/sports puzzle and I wanted to share my thoughts with you. The puzzle began when I saw two charts by Seth Kadish of Vizual Statistix. One is a “heat map” and the other a histogram of points scored in every single NFL football game going back to 1920.

The histogram shows pretty much what you’d expect—the more points a team scores, the more likely they are to win the game. But I noticed an exception. There was something odd about teams that scored exactly 21 points.

Since 1940, teams that have scored exactly 20 points have gone 831-753-36 for a winning percentage of 0.524. But for teams that have scored 21 points, that record falls to 557-765-28, which is a winning percentage of 0.423.

Why does one more point translate into worse performance? I couldn’t get this out of my head. Were teams that scored 21 points just unlucky? Couldn’t be…the sample is just too large.

This riddle brought out my best and worst qualities. I love a good puzzle and I’m stubborn as hell. After giving this a lot of thought, I’ve come up with an answer. Let me share that with you.

The reason why 21 is so unlucky is that teams scoring 21 on the nose most likely haven’t kicked any field goals.

Think about it. While field goals aren’t that valuable by themselves, they’re the preferred instrument teams use to win close games. The teams who’ve scored 21 most likely haven’t used one.

As a result, we have a bit of a statistical illusion. Kicking lots of field goals won’t give you lots of wins, but winning games, particularly close ones, means you’ve probably kicked some field goals. (By the way, overtime isn’t a factor. We see the same effect on 21-pointers before 1974 when the NFL didn’t have overtime.) Conversely, this field goal effect also gives a nice bump to the 20-pointers with their numerous 20-17 victories. That’s the most-common football score.

This brings up an important fact about football. The object isn’t to score as many points as possible. Rather, it’s to score more points than the other team. That’s a subtle but important distinction when looking at the data. If a team is trailing by one or two points, or the score is tied, and they have the ball within field goal range, they’ll forgo trying to score a touchdown. They’ll try to burn as much time as they can, and go for the game-winning field goal as time expires.

When we look at the histogram we can see that there are a large number of games settled by three points (17-14, 20-17, 27-24). We can confirm our FG hypothesis by looking at 28 pointers, which is another candidate for few field goals. Teams that have scored 28 points on the nose have gone 622-281-30. Not bad, but it’s still below the 23 pointers at 658-280-8.

So how does this relate to finance (you knew where I was going with this, didn’t you?) The issue I’m raising isn’t about football. Rather, it’s about how we interpret data. Sometimes the numbers can fool us and we have to be clear what we’re looking for.

The similarity between finance and football is that the numbers are aware of themselves. This is very different from an experiment in the physical sciences. Boron doesn’t know it’s boron but the participants in a football know exactly what the score is and that they’re trying to win. As a result, statistics like standard deviation and the normal distribution are hindered.

Likewise, market participants know what the market is doing and the score of that game impacts their decisions. That’s why we see daily changes in the Dow far, far outside what a normal distribution would predict (in other words, fat tails).

One of the constant dangers of finance is the desire to quantify things that are either resistant to it, or simply not needed. The numbers are a picture of reality, not reality itself.

Posted by on January 21st, 2014 at 12:42 am


The information in this blog post represents my own opinions and does not contain a recommendation for any particular security or investment. I or my affiliates may hold positions or other interests in securities mentioned in the Blog, please see my Disclaimer page for my full disclaimer.