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Dorktown: NFL teams that score 16 points win more often than teams that score 21. Why?

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Dorktown: NFL teams that score 16 points win more often than teams that score 21. Why?

It’s not just that. Teams who score 13 have a better winning percentage than teams who score 14. 20> 21. 23> 24. 27> 28. What is going on here? While researching the historically bad NFC East for a recent Dorktown column, I accidentally found something really, really weird.
In the post-merger era (1970 through Week 11 of the 2020 season), there have been 11,653 regular-season games. Within these games, teams have finished with nearly every possible score between 0 and 62 points. Here’s their winning percentage by points scored.

Looks weird, right? Why do teams who score 16 points have a better winning percentage than teams that score 20 points? Why does 23 win more often than 25? Why does 26 win more often than 32? If we were to chart baseball or NBA scores in this way, I’m sure it would look like a staircase, with each score performing better than the last without exception.
The explanation for this might seem fairly cut-and-dry at first. For one, NFL seasons last no more than 16 games, which gives us a far smaller sample than other sports. For another, as those familiar with the concept of Scorigami can attest, there are many scores that almost never happen. Teams have only scored 32 points 97 times, so about twice per season. We can’t expect the data to completely smooth itself out with samples this small.
So let’s remove all those oddball scores. Here’s the same chart, but only with scores that offer a sample of at least 500 games. In other words, the most common scores:

HUH? We removed all the small samples! Each of these scores feature samples in the hundreds! This was supposed to be smoothed out! Are those TEETH?
If even one of these scores resulted in a worse winning percentage than a lower score, it would be a pretty interesting curiosity. But here it’s the rule, not the exception. The winning percentages of the scores 3, 7, 10 and 13 behave as you’d think they would, but past that it snakes up, down, up, down, up down, like clockwork. And remember, this is not an easy maneuver. The gods, or fates, or whoever did this, had to drag samples sizes of hundreds of games back and forth to orchestrate this.
Look at this! Typing it out is such a gruesome feeling:

Teams who score exactly 16 points: 826 games, .452 win percentage
Teams who score exactly 21 points: 1,019 games, .422 win percentage

That’s only the most egregious … I was about to call this an outlier and then I caught myself, because this lunacy is apparently the norm here. Teams who score 13 points win more than teams who score 14 points. 16> 17. 20> 21. 23> 24. 27> 28. These are all by fairly dramatic margins, too.
Let’s try to find an explanation for this beyond “God is bored.” Something like this could really only happen in football, a sport in which we score in big, awkwardly-sized, incongruent chunks. Often, you can look at a score and make a good guess as to how exactly its team got there. Specifically, how many field goals they had to kick:

It’s profoundly evident that kicking more field goals correlates with winning more often. Every zero-FG or single-FG score has a multiple-FG score right below it that’s more successful despite the minor detail of, you know, having fewer points. Are field goals the gut flora of the scoreboard? Seemingly icky things that are nonetheless signifiers of good health?
We tried to find an explanation for this. We really, really tried. I can at least walk you through our three best guesses.
My best stab at an explanation was : if you’re kicking multiple field goals, you’re signaling that you aren’t hard up for points — or, at least, you’re not as hard-up for points as a touchdown-or-bust team.
But the more I thought about it, the more I doubted that this applies to very many cases. Unless it’s pretty late in the game, teams typically take whatever kind of score they can get. Suppose it’s somewhere around the middle of the game and a team is down by 14 points. They’ve got 4th and 3 at their opponents’ 20. Do they go for it? Maybe, but I doubt their calculus has much to do with that 14-point deficit. They simply make what they think is the smartest play, independent of whatever the scoreboard says.
Alex initially wondered whether more field goals correlates with more winning because game-winning scores are more likely to be field goals. After running the numbers, we were surprised to find that this isn’t even true in the first place. Using these parameters:

final three minutes of the fourth quarter
point differential between -2 and 0 for field goals, and -6 and 0 for touchdowns

in the post-merger era, we found 1,204 such touchdowns and just 459 such field goals. I wouldn’t have guessed touchdowns to be so much more common, but here we are.
And finally, I asked our old buddy Spencer.

It’s a very interesting theory that seems to rely on too many variables to serve as a singular explanation.
And I think he was EXACTLY RIGHT.

The turnover differentials produced by teams that finish with these scores follow a pattern that is eerily similar to that of their winning percentages. Remember our 16-point heroes, who present a superior winning percentage to the 21-pointers? Here they are again. 16-point teams offer a barely-positive turnover differential of +0.01, far better than the 21-pointers’ -0.43. That’s a difference of nearly half a turnover per game. Considering the size of these samples, that’s a fairly huge and meaningful margin.
But this is what’s really freaking me out:

Connect the dots according to how many field goals are typically necessary to complete these scores, and it turns out that the trend between points scored and turnover differential are close to linear in ALL FOUR CASES. The zero-FG and three-FG groups come damn close to falling along a straight line. And the one-FG and two-FG groups? Hold up a sheet of paper to those lines if you want to. They’re almost perfectly linear.
Of course, none of this is instructive in any meaningful way. It teaches us that winning the turnover battle is good, which is something everybody already knew. It’s more of a fascinating puzzle than anything.
I’m left amazed by two things. The first is, of course, that a final score in and of itself doesn’t perfectly correlate with winning percentage, and that 16-point teams really do win more often than 21-point teams.
The second is that after Alex and I had spent days throwing ideas against the wall, and were fully prepared to just throw in the towel and tell all of you we didn’t know what was happening here, Spencer took a wild guess and was exactly right. Not just right, but scarily right. No one has any business being that correct.

Previously on Dorktown:

Nori Aoki went a whole MLB season without seeing the bases loaded. Here’s how unlikely that was.
The Memphis Grizzlies’ improbable run of free-throw defense
Peter Warrick was the least-efficient wide receiver of all time
Video: The History of the Seattle Mariners

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