I don’t know what you guys are getting out of all this NFL stuff, but I’m enjoying it.   For at least twenty years people have asked me regularly whether I ever did anything with the other sports.   I always gave the same answer:  I have never yet had any insight into football or basketball that I didn’t later discover that someone else had already had.

            I never got anything done in the other sports, in part, because I never had any place to go with it.   Ideas are like baby kittens:  they die if nobody takes care of them.   Occasionally I’d have an idea about one of the other sports, but I had no way to take care of it.   I’m not suggesting that this stuff I have done on the NFL has any great intrinsic merit, but I have the feeling that I am beginning to work out the rudimentary framework of the mathematics of the NFL.  

            We’ve had some little successes.  When Buffalo was 4-0, we realized that they really weren’t good; they had just played a nothing schedule.   We realized early on that the Patriots of 2008 were not the Patriots of the last five years; OK, our early mathematical model dramatically overstated the dropoff, but at least we saw it.   We were probably wrong, the first half of the season, on the Giants, too skeptical.  

            One of the things I’ve done wrong here is to dribble out comments, rather than consolidating them into a once-a-week NFL commentary.    From now on I’ll try to focus.   OK, I’ve got six things to get through this week:

1)  Reviewing predictions from last week

2)  Predictions for this week

3)  Updated Rankings

4)  Rankings Experiment

5)  A change to my Scoring and Allowing Tendency metric

6)  NFL Team temperatures

1)  Predictions from last week

            We were 11-4-1 on Week Eleven, making us 73-40-1 on the season.    For the first four weeks we made predictions we were under 60%.   For the last four weeks we’ve been over 70%--suggesting that perhaps we just jumped the gun, making predictions on too limited data.

2)  Predictions for this week

3)  Updated Rankings

4)  Rankings Experiment

            Ignoring for the moment the home field advantage. …The way our ranking system works is, we add together the values for the two teams, divide by two, and then add on half the margin of victory.   Suppose that Oakland played Detroit on a neutral field, and Oakland won by 7 points.    That would be Oakland (89.4) plus St. Louis (88.4), total 177.8, divided by two is 88.9, plus 3.5 for Oakland is 92.4, minus 3.5 for Detroit is 85.4; we’d score the game as Oakland 92.4, Detroit 85.4, seven-point edge for Oakland.

            Suppose, however, that Pittsburgh played Detroit on a neutral field, and Pittsburgh won by 7.   We’d score that Pittsburgh (108.2) plus Detroit (88.4), total 196.6, divided by two is 98.3, plus 3.5 for Pittsburgh is 101.8, minus 3.5 for Detroit is 94.8; we’d make it Pittsburgh 101.8, Detroit 94.8.

            There is a logic to this.   We’re assuming that Detroit, to come that close to beating Pittsburgh, must have played better that week than they normally do, whereas against Oakland, to lose by seven to another team as bad as they are, they must have had an off week.  

It’s not illogical, perhaps, but it has always bothered me that, if Oakland beats Detroit by 7, we score Oakland at 92.4, whereas if Pittsburgh does exactly the same thing, we score Pittsburgh at 101.8.   If Pittsburgh beating Detroit by 7 is 101.8, shouldn’t Oakland beating Detroit by 7 also be 101.8?

I decided to try it that way.    I decided to replace the formula that I usually use with one that simply says that if you beat Detroit by 7 points, we figure you’re 7 points better than Detroit is--actually 5.5 better than Detroit if you do it at home, 8.5 if you do it in Detroit, but you get the idea.

In a sense this is also illogical.   If Pittsburgh beats Detroit by only 7 points, this creates an output score for Pittsburgh of 95.4—seven points better than the Lions—and an output score for Detroit of 101.2—seven points worse than the Steelers.  We are concluding, based on the fact that Pittsburgh beat Detroit by 7 points, that Detroit is six points better than Pittsburgh.   It doesn’t quite make sense, but I wanted to try it.

It makes no difference.   Well, very little difference.   I re-ran the rankings with that assumption.   What happens is that you get wildly different outcomes for individual games, but almost exactly the same rankings for the teams at the end of the day.   Tennessee winds up at 111.3 rather than 111.1, Pittsburgh winds up at 107.9 rather than 108.2, the Jets wind up at 102.5 rather than 102.4.   Basically, you get the same end product no matter which method you use, although, for some reason, this (experimental) method cuts toward those rankings in a much more direct path, reaching finality with many fewer iterations of the process.  

5)  Team Scoring and Allowing Tendencies

            Last week I introduced a method to predict the number of points scored in an NFL game.    It is essentially this:  that if Pittsburgh is playing San Francisco and Pittsburgh has a Scoring and Allowing Tendency (S&A) of “6” and San Francisco has a Scoring and Allowing Tendency of “7”, then there should be 42 points scored in the game.  

            To derive these numbers I used a “stabilizing” number of 6.67, the purpose of which was to keep the numbers from constantly jumping back to their starting point.   A couple of readers suggested helpfully that perhaps the stabilizing number was artificially reducing the dispersion of the S&A numbers, for which I snarled at them, but they do have a point; in fact, I reluctantly acknowledge that they may have had a very good point.   The highest S&A tendency in the league, by this method, would be Houston at 7.09, but the average Houston game this year has seen 52.3 points.  That’s more than 7.09 squared—thus, more than could be predicted by my method.

            I revamped my method in this way:  That, instead of taking the average of the S&A tendencies as measured by games, adding 6.67 and dividing by two, I took the average, added .0667 and divided by 1.01.   This changed the output scores, but not very much.   These would be the S&A tendencies for this week:

             That creates a slightly wider dispersion of S&A scores, but it still has a problem.   An average NFL team this season has now scored 22.15 points per game, which creates 44.30 points per game for the two teams.   An average NFL S&A score is thus 6.656—the square root of 44.30.

            An average Pittsburgh game, however, has featured only 35.90 points.   35.90 divided 6.656 is 5.39—but Pittsburgh’s S&A score calculates by this method as 5.99.

            5.99, by an interesting coincidence, is the square root of 35.90.  It seems pretty clear that the number should be more like 5.40 than 5.99.

            I snapped at my reader for suggesting that the “stabilizing element” was cutting the dispersion in half.   On a very narrow point I may have been right:  I don’t think it is actually the stabilizing element that is doing this.   I think it is happening because the derivation system just doesn’t work, with or without a stabilizing element.  In any case, what we can clearly conclude is that this method still needs work.

6)  NFL Team Temperatures

            I had a lot of fun last summer tracking baseball’s hottest hitters, hottest pitchers, hottest teams, etc., so I decided to create a method to track the “temperature” of NFL teams.   These are the current temperatures of the 32 NFL teams:

             How does this differ from the rankings?   Three ways:

            1)  It is centered at 72º, rather than at 100.0,

            2)  The formula is set up to react much more actively to recent games,

            3)  The rankings formula is set up to weight all games on the season evenly.   This system is set up to weight 50% of the temperature on the team’s last two games.

            Buffalo is a kind of NFL-average type team, but they’re cold; their temperature is 58º.   The Bears are a good team, but they’re cold. 

            The way the formula works is this:  At the start of the year, every team is at 72º.   After each game, we

            a) multiply that by .70,

            b) add 21.6,

            c) add the “output score” for the last game, and

            d) subtract 100.

            Three games ago the Bears had a temperature of 88º.   When they struggled to beat Detroit (27-23), that created an output score for that game of 96.1, so their temperature dropped to 79º:

            88

            Times .70 =  61.6

            Plus 21.6 =   83.2

            Plus 96.1 = 179.3

            Minus 100 =  79

When they lost to Tennessee, they stayed at 79º.   But when they got massacred by Green Bay, they dropped to 67º.