# Math Meets Football: Is the New Extra Point a Game-Changer?

This piece is going to be quick. *Very* quick. Why? Because I don’t think there’s particularly much to be said. In case you missed it, extra points are being moved to the 15-yard line. What does this mean?

Little to nothing!

But, won’t extra points be significantly harder now that they’re so much farther back? Won’t this incentivize coaches to go for two?

No, and no.

Good data on field goal success rate is somewhat hard to come by, unless you’re looking at ranges of field goals. Lucky for me, a few guys from MIT already did the heavy-lifting for me.

In their paper “Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression”, Torin K. Clark, Aaron W. Johnson and Alexander J. Stimpson do just as advertised and come up with a model for field goal success based off of a number of conditions, including distance, field type, precipitation, altitude, temperature and wind condition.

However, for our purposes, let’s assume it is a typical day (temperature above 50 F, no rain or snow, winds lower than 10 MPH and altitude less than 4,000 ft). To compensate for the ideal conditions we have placed here, we will also assume that we are on a grass field surface, which has a lower field goal success rate in the model.

Under these prescribed conditions, the model looks as follows:

P(field goal success) = 1 / 1+ e^- (5.953-.106xdistance)

*Where the distance is the distance of the kick, in yards.*

Based off this model, field goals at the two-yard line have a success rate of 98.1 percent. However, at the 15-yard line, the success rate is only 92.8 percent.

For context, let’s compare this to the likelihood of two-point conversion success. Between the years 1994 and 2012, 1,469 two-point conversions were attempted, with 658 successful. This results in a success rate of 44.8 percent. This is a significantly long time period to use as an estimate, and this does not account for and remove aborted kick attempts. So, let us look to Brian Burke of*Football Outsiders*, who did just that.According to Mr. Burke, after removing aborted kick attempts, the success rate for two-point conversions between 2000-2009 was 47.9 percent.

It doesn’t take a probability theorist to know that the expected points (the sum of each possible point outcome times the likelihood of each occurring) of the two-point conversion is now higher than that of an extra point kick:

E(two-point conversion) = 2x.479 + 0x(1-.479) = .958 points

E(extra point) = 1x.928 + 0x(1-.928) = .928 points

It’s simple math, right? The expected points for two-point conversions is greater, so of course all 32 NFL teams are going to do away with extra points and go for two every time, right?

Not so fast.

Just because the expected points of one endeavor is greater than the other, doesn’t mean it is what coaches are going to do.

Why? Because, as you might have surmised at some point, NFL coaches are risk averse. Coaches like low variation, and a difference of .03 expected points per extra point is not nearly enough to deter them from the safer choice of going with a slightly longer kick (which has variance of .07) as opposed to the much riskier two-point conversion (which has variance .25).

There may be some who embrace the new system and take advantage of this opportunity, but my guess is most won’t.

Also, if you’d like to peruse an article measuring the risk-averse nature of NFL coaches based off onside kicks, check out this paper written by a John Urschel much older and wiser than me.

I guess it runs in the family.