by Bryan Davies
Amidst the expletives and tongue-in-cheek comments thrown around by Jets and Patriots this past week (ok, mostly Jets) was an actual game to be played on Sunday. And, like any football game, there are a number of decisions that coaches are given the opportunity to screw up. With the underdog Jets ahead for nearly the entire game, it seemed that a lot of the tougher decisions needed to be made by Belichick and the Patriots. A fake punt on 4th and 4 from their own 38 with time winding down in the first half, a two-point conversion in the third quarter, a 4th and 13 rather than a 52-yard field goal. Well, we know which ones turned out to be good decisions, but were they objectively good decisions without the benefit of hindsight?
Well the truth is, I’m not going to address any of those situations. I’m sure you’ll find enough analysis, both good and bad, that will address them extensively. In the spirit of being an overly pedantic statistically-minded football fan, I thought I’d address Belichick’s incorrect decision to go for an extra point rather than a two-point conversion following the Brady-Branch touchdown with less than 30 seconds to go in the game. In fact, when down 14 points, it’s almost always a better decision to go for two following a touchdownlate in the game.
To be fair, the following analysis is hardly original. It’s been discussed at length at many sites and in many forums, but like most sports analytics, still hasn’t received enough attention. Here’s an excellent (and more detailed) article with the analysis: http://www.thesportjournal.org/article/playing-percentages-when-trailing-two-touchdowns. And here’s a more detailed analysis describing slightly different circumstances: http://www.footballcommentary.com/coltcomeback.pdf. Heck, even Brian mentioned it in the WP graph thread of the NYJ-NE game.
So here’s a typical scenario: You’re down 14 points with 5 minutes left. You score a touchdown. Awesome. Now you’re down 8. Obviously, you should just kick the extra point and hope to get the ball back down 7, right? Let’s see.
(Note: the analysis is conditional on you scoring another touchdown, and your opponent not scoring any points. Regardless of what actually happens, the analysis is still valid.)
We have two choices following the first touchdown: Kick an extra point, or go for two. The second attempt is conditional on the result of the first, but the first attempt should (almost) always be a two-point conversion, as I will demonstrate.
If we use our baseline 98.5% conversion rate for extra points, and 47.9% conversion rate for (normal) two-point conversion attempts (discussed here: http://www.advancednflstats.com/2010/12/almost-always-go-for-2-point.html), we can figure out which combination gives us our best chance of winning.
Scenario 1: Kick the extra point following the first touchdown.
(.985)*(.985) = .970225
About 97% of the time, we’ll force overtime with two successful kicks. But, we can also force overtime with a missed kick and a successful two-point conversion:
(.015)*(.479) = .007185
This leaves us with a total probability of forcing overtime at .97741. Since overtime is a 50/50 proposition, we have a .488705 probability of winning, or just under 49%
Of course, you can always go for two following the successful extra point, but this only leaves you with a 47.9% chance of winning (insert complaint that the Panthers actually have a 10% chance and the Patriots have a 99% chance).
And of course, we can always miss the second extra-point after making the first, resulting in a loss.
Scenario 2: Attempt a two-point conversion following the first touchdown.
Again, the second attempt will be conditional on the first. If we make the two-point conversion, all we need is an extra point to win. If we miss the two point conversion, we need to go for another one just to tie.
Make the two-point conversion, make extra point: (.479)*(.985) = .471815, win in regulation
Make the two-point conversion, miss extra point (.479)*(.015) = .007185, force overtime
Miss two-point, Make two-point: (.521)*(.479) = .249559, force overtime
Miss two-point, Miss two-point: (.521)*(.521) = .271441, lose in regulation
And now it all starts to come into focus. If we split the overtime propositions in half, we get a total win percentage of (.471815 + .0035925 + .1247795) = .600187, or about 60% of the time, we’ll win. The other 40%, we lose.
Conclusion: By simply attempting the two-point conversion when down 8 points late in a game (and only expecting 1 more possession), a team increases their probability of winning by over 11%...as long as you score one more touchdown and your opponent doesn’t score. But even if you don’t score, and your opponent does, or any possible combination you can think of, you’ve still made the right decision (again, as long as it’s late in the game).
So why don’t coaches do this? Well, for obvious reasons. Most probably don’t know. And if they do know, it’s not surprising risk-aversion dominates decision making. After all, by kicking extra points, you’ll only lose outright in regulation a mere 2 percent of the time. If you attempt the two-point conversion first, you lose in regulation a whopping 27.1% of the time. That means that over a quarter of the time, you’ll most likely be fired unless your job is as secure as Belichick’s.
Getting back to Belichick, even he is too risk averse (or ignorant) to follow the strategy. And considering how prolific the 2010 Pats offense has been, I imagine their two-point conversion success rate would be even higher than league average, making it an even better proposition. So after Branch came down with the touchdown to make it an 8 point game, Belichickshould have gone for two. Strange, I know. It turned out to be a moot point though as the Patriots failed to get the ball back, let alone score another touchdown.
A quick note on why this strategy works: Similar to Brian’s article on why underdogs should take more chances (and increase variance and thus increase WP) against the better teams, teams that are current underdogs should also take more chances late in the game. What are you really doing by going for two after the touchdown to go down 8? You’re increasing the chance that you lose by 2 (two missed two-point conversions)…for an increased chance that you can win by 1. Variance is the friend of the underdog. Sacrifice the increased chance for a blowout for the increased chance of squeaking out the win.