From 2002 to 2021, NFL teams converted 38.9% of all third down attempts. Third down performance is really meaningful when it comes to winning games, but it can also be pretty random from sample to sample. So as a result, third down performance has an outsized performance on who wins and loses that game, but is probably not all that predictable as to who will win the next game.

I thought it would be interesting to look at this in the context of the pre-game point spread. Let’s start with a few basic numbers, looking at this 20-year period.

• Teams that were favored by 1 to 5.5 points won 58.7% of their games.
• Teams that were favored by 6 to 8 points won 73.6% of their games.
• Teams that were favored by more than 8 points won 83.4% of their games.

But let’s say you know that the favorite would lose the third down battle. How does that change things?

• Teams that were favored by 1 to 5.5 points but were worse on third downs won only 43.4% of their games.
• Teams that were favored by 6 to 8 points but were worse on third downs won only 54.2% of their games.
• Teams that were favored by more than 8 points but were worse on third downs won 68.2% of their games.

Now, saying an underdog just needs to win the third down battle is not very helpful, and only a little more precise (and about as useless) as saying they just need to score more points. But it does help to provide some guardrails about the magnitude of third down performance. It can flip a big favorite into a coin flip, and a huge favorite suddenly has a real chance of losing.

Can we quantify exactly how important third down success is? I’m glad you asked. As we know, each team has a 38.9% chance of converting an average third down. Suppose each team has 15 third down attempts in the game. Let’s say one team coverts 10 of 15, while the other only converts five opportunities. The expected number of third down conversions for both teams is 5.8 (0.389 multiplied by 15), so one team converted 4.2 more first downs than expected, while the other converted 0.8 fewer than expected. The net difference, of course, is five conversions — let’s call that the net third downs added.

How meaningful is that? We would project the team that converted 10 of those third downs to win by 15 points! How did I get that result? I ran a regression using net third downs added as the input and points differential as the output; the R^2 was 0.25, indicating a slightly positive correlation, and the weight on each additional third down added was 3.01 points. Does that number feel very large to you? I went and checked, and as it turns out, there were 226 games from 2002 to 2021 where a team had between 4.5 and 5.5 net third downs added; those teams won by an average of 15.6 points (winning 89% of those games).

Remember that teams convert 38.9% of all third downs. Since we know that a net third down added is worth 3 points, and that each successful third down is worth 0.611 third downs added, then each successful third down — knowing nothing else at all, including distance — is worth 1.84 points added. ^[1]That’s just the product of 0.611 and 3.01.

Does that number sound right? Over the last twenty years, 1st and 10 at your own 25 is worth, roughly, +1.0 expected points. So if your opponent has 1st and 10 at their 25, that’s worth -1.0 points to you. Therefore, trading 50 yards of field position but losing possession is worth -2.0 points. Given that the average punt will gain a bit less than 50 yards, that seems like a reasonable back of the envelope check that converting a third down, on average, is worth 1.84 points. I am sure EPA models would differ and come up with a more precise answer, but 1.84 is probably in the ballpark of being correct.

What if we instead run a regression using the point spread *and* the net third down added number as our inputs, and the points differential as our output? In that case, the R^2 jumps to 0.36. The coefficient on the points spread variable is -0.79 (favorites have a negative point spread) and the coefficient on the net third down added number falls to 2.49 once we have more information. ^[2]And both variables are statistically significant, of course, as you would expect given the enormous sample size.

How do we interpret these results? Using this formula, a team that is a 5-point favorite would be given about 4 points (-5 multiplied by -0.79). So to overcome that four point delta, the underdog would need to win the net third down battle by 1.6 net third downs added. If, for example, the underdog went 7 for 14 on third downs (+1.55) and the favorite went 4 for 11 (-0.28), we would now expect the 5-point underdog to win the game by 0.6 points. In other words, that sizable third down advantage (+1.83 net third downs added) is more meaningful than the 5-point spread. You would now pick the favorite to lose the game if those were the only two things you knew about the game. Thought of another way, once we incorporate the point spread (which gives us more information about the quality of the teams), each additional third down converted is worth 1.52 points (as opposed to 1.84 points).

What do we do with this information? I’m not really sure. But I’ve written enough for now. What do you think?