For the 2015 NFL season the NFL adopted a new provisional rule for that season about extra points. The new rule states that an extra point field goal attempts will be done at the 15 yard line instead of the 2 yard line and additionally if a defense blocks the field goal they can run it back for 2 points. Likewise for a 2 point conversion if a defense intercepts or recovers a fumble they can run it back for 2 points. These rules were provisional for the 2015 season and then made permanent for the 2016 season.

So I started to wonder when should a team should go for a 2 points instead of the regular field goal after a touchdown. Now, I’m considering the general case and not a specific scenario of, “We just scored a touchdown and we are down by 2 points with 30 seconds left, should we go for two or one?” The answer is pretty clear in that example.

A way to find out which option to choose is to take the average of each option, otherwise known as the expectation or the expected value. So we can take the possible point values for each option and assign them probabilities to get the expected value of each option. So for a field goal attempt we have point values of 1, 0, and -2 and likewise for a 2 point attempt we have 2, 0, and -2.

So we want to find,
$$\mathrm{E}[2 \text{pt}] = 2p_{g} +0p_{n} + -2p_{l}$$
$$\mathrm{E}[1 \text{pt}] = 1p_{g} +0p_{n} + -2p_{l}$$

Where $$p_{g}, p_{n}, p_{l}$$ represents the probability the attempt gains points, no points, and loses points, respectively.

Now the more difficult part is finding the probabilities. In this case I just went with the last two years since the rule was instituted. I did not include earlier years because with the new rule allowing the defense to score it will change the behavior of the defense. So below you’ll find the data for 2015 and 2016.

2 Point Conversion
Total961021
YearAttempt is Successful (2pts)Attempt is Unsuccessful (0pts)Defense Scores (-2pts)
201545490
201651531
Extra Point Field Goal
Total22651461
Attempt is Successful (1pt)Attempt is Unsuccessful (0pts)Defense Scores (-2pts)
20151146701
20161119760

Of course, there are some limitations to this data. For instance, it only covers two years and the 2 point conversion data is very small with only 199 attempts total. But for now it’s good enough.

From the table we can find $$p_{g}, p_{n}, p_{l}$$. So after doing the computations and rounding we end up with $$\mathrm{E}[2 \text{pt}] = .955$$ and $$\mathrm{E}[1 \text{pt}] = .938$$. This leads to a difference of .017, or .02.

So what does this mean? If you’re an NFL coach, not much. A difference of .02 is hardly something to revolutionize your game plan over. If the kicker on the team is good, go for the kick. If he’s bad, then go for the two point. If the NFL really wanted to increase the number of two point attempts they should move the extra point kick back even more. I’ll update this post after the 2017 NFL season with the 2017 season data, but I suspect the numbers won’t change much.