I posted an article on November 14 about the scoring tendencies of NFL teams.   This article is a continuation of that research, and you should go back and read that article now if you have not. ..or else stop reading this one and go pet your kitty; anyway, this article won’t make a lot of sense if you haven’t read that one.

            In that article we assumed that the number of points scored in a football game is a product of the Scoring and Allowing (S&A) tendencies of the two competing teams.   If Denver plays Arizona we would expect 50 points to be scored in the game, since Denver has an S&A tendency of 7.08, Arizona an S&A tendency of 7.05, and 7.08 * 7.05 is just a hair short of 50.

            It occurred to me, however, that one could approach the issue not by multiplying the S&A tendencies of the teams, but by adding them together.   In other words. . .in their first games of the season Carolina beat San Diego 26-24.   If we make the initial assumption that each team has an S&A tendency of 22.257—the league average—then, from Carolina’s point of view, we estimate based on this game that their S&A tendency is 27.743, since 22.257 of the points in the game are “explained” by San Diego’s S&A tendency.   The remaining points—50 minus 22.257—must be explained by Carolina’s.

            It’s the same system we were using before, it’s just arithmetic, rather than geometric.   In the other system I assumed that the points resulted from the interaction of San Diego and Carolina; now we are assuming that each has an individual S&A tendency, and that the points scored will be the sum of the tendencies of the two teams.

            I put this assumption into the method, to see whether we could derive arithmetic S&A tendencies, but what happened was the same thing that happened when I first tried to derive geometric tendencies.   In the first round of calculations, Carolina had an output average of 18.056.   I then used 18.056 as their initial assumption for the second round of calculations—but the results for every team simply returned to the norm, 22.257.  

            To prevent that from happening, then, I did the same thing I had done with the geometric calculations.   I added the league average—22.257—to each team’s first-round output, and divided by two.  For Carolina, this makes (18.056 + 22.257) / 2 = 20.156. And again, that worked perfectly; teams zeroed in on their individual S&A tendencies in relatively direct fashion, although for some reason it takes more cycles to work with arithmetic tendencies than with geometric ones.

            Anyway, this produced Scoring and Allowing Tendencies for each NFL team as follows:

            The 32 teams rank in the exact same order here as they did in the other system. 

            At this point it was my intention to plug these two systems into the actual NFL results for this season, to see which was the more accurate at “predicting” (retroactively) the number of points that would be scored in the game.   However, I didn’t do that because it doesn’t make any practical difference.   The two systems produce results which are so nearly the same that it would be impossible to determine which was more accurate without studying some very large number of games—probably more games than have been played in NFL history, I’m guessing.   The largest discrepancy in predicted points between this system and the other would be about .06.  

            It makes more sense to me, intuitively, that the S&A tendencies would be interactive, rather than independent, so I will stick with the other method.