Why it’s almost always a bad idea to go for a two-point conversion in the first half

The 2000 Outback Bowl, one of the most entertaining games in the ballyhooed “Big 10 vs. SEC” category, featured (at the time) the “largest comeback” in bowl history. Purdue, on the strength of game MVP Drew Brees’s four touchdown passes, built a 25 – 0 lead in the first twenty minutes. But Purdue lost 28-25 after Georgia tied the game at 25 to send it to overtime and then kicked the game winning field goal in the the extra period. Brees would finish with over 370 yards passing (on 60 attempts!) while Bulldogs quarterback Quincy Carter went 20-of-33 for 243 yards, had no picks and ran for one touchdown while throwing for another. But it was Purdue’s Tiller who was the affair’s de facto protagonist: His first-half gameplan’s featured a brilliant aerial assault which blitzkrieged Georgia coach Jim Donnan’s blitz-happy strategy (in an early example of the folly of trying to outblitz the spread), but some of his in-game decisions lacked, uh, rigor.

The score should stick out to you: 25? Purdue got that odd total by scoring four touchdowns but then following them with a missed PAT and two failed two-point conversion attempts. The missed PAT was not what one hopes for, but the problem was that Tiller then fell into the classic two-point conversion trap: The coach thinks that because his team missed a PAT he “must” go for two so that his team can have the “correct” score (i.e., some multiple of 7). This is wrong. Unless going for two is simply a better strategy in general (more on that later), it is almost always a bad idea to go for two in the first half simply to achieve some desired score because in the first-half there are far too many unpredictable end-game scores for it to make any specific score worth the cost of choosing a suboptimal strategy to engineer that desired number — it’s only at the end of the game that some specific score (seven versus eight versus or two versus three) really makes a difference. Indeed, this effect was even more acute here because Georgia had no points at all, so it’s not as if Tiller could envision what combination of scores Georgia would actually get to match his team. Put another way, given the point differential, why did it matter that his team was up 21 versus 20, or 27 versus 26? Indeed, it turned out the key difference was not between getting the two-point conversion and getting the PAT, it was between getting the PAT and getting nothing at all — having 19 instead of 20, and 25 instead of 26.

This is a  very different question from whether going for two is better in general: it’s generally not, otherwise it would be a dominant strategy (in the game theory sense) and teams should go for two all the time. (Note that for this analysis I’ve assumed you have a good PAT kicker. Not having one can dramatically change the approach in, say, high school. For Purdue this shouldn’t have been an issue, however, as despite the fact that Purdue missed its PAT its kicker was actually an All-American placekicker, so it truly was Tiller just trying to recoup the score.) My criticism of Tiller is that his odds of converting didn’t change when he missed the first PAT (and they possibly went down given some game theoretic alterations in the defense’s response), so the fact that he changed his strategy was not rational and in actual fact ended up hurting his team’s chances of winning.

Those are the universal reasons why I recommend against going for two except as part of an endgame strategy. But another complaint applies to Tiller’s choice to go for two in this particular game when he had such a big lead. Remember, the probability of winning a football game is not only about expected values but also about the variance of those returns. Risky strategies are better for underdogs not necessarily because they increase their expected offensive or defensive prowess, but because the variance is good in and of itself: risky strategies flatten the bell curve; the risky strategies cause a wider disparity in the outcomes, even if the average outcome is the exact same, thus increasing the “tails”, or the underdog’s chance of winning the game. The Citadel is not going to beat Alabama with a strategy of three-yards and a cloud of dust, punts, and “let’s play for field position.” And the phenomenon works the other way too: if you’re expected to win, uncompensated risk (i.e. that doesn’t carry a higher expected return, like Purdue’s excellent passing attack with Drew Brees) is not your friend. And there is no question that going for two is riskier than going for one.

Even if the expected return were higher when going for two than when going for a PAT (PAT = 1 * 99% or so; 2-point = 2 * between 40-60%, so even assuming on the high-end), the chance of getting zero on the conversion multiple times in a row is higher as well. And if Purdue was sitting on a 19 or 25 point lead already they were clearly in the probabilistic driver’s seat and should have been in the business of reducing uncompensated variance, not increasing it.

So coaches should almost never go for two in the first-half, and in the second half of teams should really only go for it when there will not be only one or two more scores and the specific, necessary scores can be reasonably foreseen. And the choice to go for two twice was especially silly for Tiller, as it opened up an increased risk that his team would miss the two-point conversions and make it easier for a desperate opponent to come back.

And that’s how it played out. Georgia caught up by, among other things, getting a two-point conversion and then scoring a touchdown and only needing to kick an extra point with 1:19 to go in the game to tie the game. Had Purdue kicked one additional PAT Georgia would have had to go for two twice (thus reducing its probability of matching at 25), and had Purdue kicked two PATs Georgia likely would have had to score again, something it likely didn’t have time for. In other words, there’s a very good chance that, despite its other second half struggles, Purdue would have won the game had Tiller just kicked a couple of PATs.

Of course, it’s not like the decisionmaking in this area has gotten much better. I’m generally for aggressive decisions, but it’s usually better to just kick the damn extra point.

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