13 is worth more than 14

In the NFL it is, anyway. Maybe.

I read a fair bit about sports, and in particular I have an interest in the statistics that people use to try to analyze them. One thing I've heard a few times as an example of a counter-intuitive stat is this: NFL teams scoring 13 points in a game win more often than teams scoring 14 points. I've recently come into possession of a database of game data, so I thought I'd have a look at this for myself.

My data contains all the regular-season and playoff games back to the 1978 season, so it's a pretty good sample size of about 7500 games. The first item to look at is the 13 vs. 14 thing, and sure enough:

13: 225-562-2 28.6%

14: 144-670-2 17.8%

There you have it - teams scoring 13 win significantly more often than teams scoring 14. Of course, the real question is what (if anything) this means. The most likely cause for this effect is the unusual way points are scored in football. Almost all scoring is through 3-point field goals and 7-point touchdowns. This means that 13 can really be thought of as 2 field goals and 1 touchdown, and 14 as 2 touchdowns. Maybe field-goal-heavy scores outperform touchdown-heavy scores in general. Let's see:

6: 18-307-0 5.5%

7: 16-621-2 2.7%

16: 249-256-0 49.3%

19: 160-129-0 55.4%

20: 543-432-2 55.7%

21: 308-405-0 43.2%

27: 568-176-0 76.3%

28: 328-152-2 68.3%

That certainly seems to support the FG vs. TD explanation, and in fact it's quite striking how poorly the multiples of 7 perform. 7 points wins 3% of games; it performs worse than 5, 6, 8, and 9 points. 14 wins 18%; it performs worse than 11, 12, and 13. 21 points is the highest score that loses more than half its games, and it performs worse than 16 (!). 28 does worse than 23, and so on.

The FG vs. TD explanation makes sense for a few reasons. First, the time one team is scoring is time that the other team isn't. 3 successful possessions, for a TD and 2 FGs, will generally take more time than 2 successful TD possessions, leaving the opponent with less time to score their own points. Second, teams that are trailing by a large amount won't try for field goals. That is, a team losing 20-7 will have to go for a touchdown, while a team losing 10-7 is more likely to take a field goal. Finally, there may be game conditions making certain games conducive to more field goals. For instance, a game with heavy snow or fog might reduce offense, causing both teams to score few TDs.

I must admit, though, that this effect doesn't last forever. Teams scoring 49 or 56 points have won 100% of their games since 1978. I guess the lesson is that if you're going to score touchdowns, you should try to score 7 or 8 of them, not just 2 :).