### NFL teams win more often with 13 points than with 14 points

NFL teams who score exactly 13 points in a game win more often than teams who score exactly 14 points.

That bit of information comes from a ~~Doug Drinen~~ Chase Stuart post at pro-football-reference.com here.

Overall, teams who scored 13 points were .285 in those games. Teams who scored 14 were only .199.

The same unexpected result holds for 20 and 21 points: 20-point teams were .566, but 21-point teams were .461. (There are other such pairs, too: see the study for details.)

It turns out the reason for the anomaly is that the lower-scoring teams held down opposition offenses much better than the higher-scoring teams. For instance, the 20-point teams held their opponents to 19 or less 56% of the time, but the 21-point teams did that only 41% of the time.

So it's not that the extra point hurts you, it's that it somehow makes the opposition score more. Why might that be? Stuart suggests it might be time of possession. A 20-point team (most likely) scored on four possessions, while a 21-point team scored on three. The three-possession game gave the other team more time to score and beat them.

I'm not sure that's right: teams get roughly an equal number of possessions, regardless of time – so a team with low time of possession contributed to that with bad offense and/or bad defense. That is, it seems to me that how much you score causes time of possession, not the other way around.

Another theory by Doug Drinen is that a team that's behind by four or more late in the game won't go for a field goal. Instead, they'll gamble on fourth down. Therefore, teams with more field goals are more likely to be leading (and eventually winning) than with than those with fewer field goals. Put another way, losing teams score more touchdowns and fewer field goals than you would expect, which makes touchdown teams slightly less likely to win than field-goal teams with identical points.

I think Doug's right, and that's most of the answer. Also related is the fact that teams are more likely to kick game-winning field goals with no time left than score game winning touchdowns.

There's also a follow-up post from Doug, in which he finds something even more interesting – teams who score 13 points are not just more likely to win that particular game, but are also more likely to win games in the future! He writes,

Home teams that scored 13 points won 46.8% of the rest of their games (N=389).

Home teams that scored 14 points won 44.8% of the rest of their games (N=422).

However, the effect in this study wasn't as strong as in the single-game study (as you might expect), and, in fact, it didn't hold for 20 and 21 points at all (with future winning percentages .481 and .494, respectively).

And, even in the 13/14 case, winning was much more important than points. Teams that lost with 13 or 14 points had a much lower future winning percentage than teams who won with 13 or 14 points. That strongly suggests that it's the likelihood of winning that "causes" the team to score only 13, and the likelihood of losing that "causes" the 14.

Again, I think Doug's don't-go-for-3-when-behind theory is the right one.

(Thanks to curling afficionado Bob Timmermann for an e-mail linking to the study.)

## 5 Comments:

I tried the "win% by winning score" thing for NBA ball from 73-74 to 05-06. Here's the plot. A pretty linear relationship, nothing nearly as interesting as NFL.

As I noted in the comments of the follow post, teams scoring their 13th point are then usually leading or tied. Teams scoring their 14th point are usually still trailing. To me, that looks like strong evidence for the reverse causality effect.

Just to set the record straight, that wasn't my post. It was on my blog, but it was Chase Stuart's post.

Oops! Sorry, Doug and Chase, will fix that. Doug, the second post was yours, correct?

Not to brag, but it was my comment that spurred this discussion on the PFR blog!

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