## Wednesday, November 16, 2016

### Football, Probability, and Two-Point Conversions

Sunday night, I did something I haven't done for a long time: I watched a football game. Specifically, the Cowboys-Steelers game. I didn't do this on purpose, and I should caveat that I didn't watch the whole game. My husband and I went out to dinner. The restaurant was crowded but there was plenty of room in the bar, so we ate there. On the bar TV, they were showing the Cowboys-Steelers game. I started paying attention to the game when I saw one of the teams going for a 2-point conversion, which I commented that I didn't see very often. But there's good reason for NFL teams to do more of that, according to some statistical analysis from FiveThirtyEight:
According to ESPN Stats & Information Group, there have been 1,045 two-point conversion attempts since 2001, with teams converting 501 of those tries. That’s a 47.9 percent conversion rate; given that a successful attempt yields 2 points, that means the expected value from an average 2-point try is 0.96 points.

Interestingly, that’s almost exactly what the expected value is from an extra point these days. Since the NFL moved extra-point kicks back to the 15-yard line last season, teams have a 94.4 percent success rate, which means that an extra point has an expected value of between 0.94 and 0.95 points.

This means that, all else being equal, the average team should be indifferent between going for two or kicking an extra point. Unless the game situation (i.e., late in the second half) or team composition (e.g., a bad kicker, or an offense or an opposing defense that is very good or very bad) changes the odds considerably, the decision to go for two or kick an extra point shouldn’t be controversial. In the long run, things will even out, because the expected value to the offense is essentially the same in both cases.
As an aside, I should mention statisticians love sports. There are mounds and mounds of data online, ripe for complex modeling, and sports are one of the few topics where, after we run our models and make our predictions, we can get accurate data to see how well the model held up. Sports isn't the only situation where that is true, obviously (election polls are another example). But for many of the topics I study, where I'm trying to understand attitudes, information processing, behavior, and so on, a lot of the predictions we make based on our models is of things that aren't easily measured. We rarely get to confirm our results in the same way we can with sports. And to have all that data readily available - meaning I don't have to collect it myself - makes sports research even more fun.

Now, in the case of the Cowboys-Steelers games, the two-point conversion attempts were unsuccessful. In fact, there were six attempts, none of which yielded points. FiveThirtyEight points out: "Before Sunday’s game, according to Pro-Football-Reference.com, the NFL record for combined failed 2-point tries by both teams in a game was four, set four times." So this game set a new record, not in a good way.

But what was good about this game? Relive those moments here. My personal favorite was this gorgeous touchdown, scored by Ezekiel Elliott in the final seconds of the game, which won the game for the Cowboys. Seriously, look at how we just glides right through: