Two-Point Conversions

From time to time, I like to take the opportunity to challenge my own perceptions about football. One strategy that’s often debated is whether teams should attempt a two-point conversion after a touchdown.

Decades ago, legendary coach Dick Vermeil, then a coordinator at UCLA, created a chart that’s still in popular use today. It’s not a chart I used when developing Front Office Football, but it’s not that different. Some of it is obvious; for instance if you trail by two after scoring a touchdown, you should try and tie the game. But even then, when in the game should you start consulting the chart?

Some of it is complex, or even controversial. You’re supposed to go for two when you lead by four after scoring. The idea is that if you make it, a subsequent field goal will give you a two-score lead. But if you miss, a subsequent field goal will leave your opponent the opportunity to tie on a touchdown without going for two.

Since the two-point conversion rate in the NFL is about 45% and the extra-point rate with the new distance rule is about 97%, I’d hesitate to start using any chart until well after halftime. Just take the point.

A few months ago, when working on a percentage win calculator that I’ve yet to put into any product, I analyzed a few seasons’ worth of play-by-play data and compiled a chart that could be useful for making these decisions. As an aside, I do this kind of thing a lot. Most of what I discover on these odysseys never amounts to meaningful work within my products. This might well fall into that category. But it could also be useful in compiling a more fine-tuned chart – one that even incorporates time remaining.

Today, I watched a good part of the Lions’ opener against Arizona. With 3:07 left in the third quarter, the Lions scored to cut the Cardinal lead to two. Some might say it was too early to start using a chart, but no one would question the wisdom of the decision in the closing moments. The Lions tried the conversion and failed. How did that change their win chances?

I have my play-by-play data broken into 100-second increments. To take a broader brush to include as much as is reasonable, I used the categories from the end of the third quarter to 6:40 remaining in the third quarter. There have been 2,797 plays undertaken with the score tied and a team with the ball, 1,031 plays with a one-point lead and 397 with a two-point lead. Not an overwhelming amount of data, especially since you can’t assume a reasonably uniform distribution of field position within that small a data set with the two-point lead. But in 1,629 of the tied scenarios (58%), the team with the ball won (possession matters – Arizona would have possession after the ensuing kick). In 574 of the one-point lead scenarios (56%), the team with the ball won and in 280 of the cases with a two-point lead (71%), the team with the ball won.

This is a great example of where sample size lets you down. The reason I’m writing about this is to give you some insight into my process when examining a particular question. When do you make a conclusion and when do you accept that you just don’t have enough information? This is several seasons’ worth of complete play-by-play data (350,000+ plays broken down by lead and time to go blocks), and the raw data set still isn’t good enough to make solid conclusions.

What the above numbers suggest is that the value of the extra point is immaterial, but there’s a 10-15% game-win cost in going for two and failing. That just doesn’t feel like a reasonable conclusion. When I was doing the initial work with this particular data set, I ran a whole series of rolling averages to come up with a win-percentage chart that supported the data with less precision, but a consistent set of percentages that required the least amount of intervention on my part (making “decisions” about interpretation and then using those decisions to influence how the rolling averages were applied). I feel more confident in presenting that chart as reasonable, at least in the sense that it could be used to help with this kind of decision. If this work results in use in any product, I would use that more processed chart.

Going back to the analysis of the first Lions decision: I come up with a 55.8% Arizona win percentage when tied during that time block, 61.1% with a one-point lead, 64.3% with a two-point lead. So, -3.2% for Detroit with a failure, +5.3% with success. Assuming 45% success on two-point tries and 97% success on extra points, the decision to go for it, in itself, raises Detroit’s win percentage by about a half a percentage point. I think it’s reasonable to conclude that it was a good decision. In general, my data supports this case up to about midway through the third quarter. Earlier than that, I would advise against ever going for a two point conversion except when desperate and in need of multiple positive results (let’s say you score and trail by 18).

The second Lions decision came with 9:27 remaining in the game. This time, they led by four. Vermeil’s chart says “go for it.” I don’t know if Jim Caldwell uses this particular chart, but he went for it. The Lions failed. The value of success and penalty for failure is explained at the start of this article. Now to break down it down using the data…

If the Cardinals gain possession with a six-point deficit (Detroit makes the conversion), they have a 29.2% chance of winning. With a five-point deficit, that’s 36.0% and a four-point deficit, that’s 41.0% percent. Factoring in analysis of success and failure, that amounts to, again, about a half-percentage-point increase in the Lions’ win chances. This surprised me a little, but, as it turns out, a six-point lead is quite a bit better than a five-point lead, even relatively early in the game.

Vermeil’s chart may be old, but it holds up even in the modern game.