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Can Pythagoras Predict NFL Games?

A couple months ago, Cassieper asked me to look at the Pythagorean formula, and see if it is good predictor of games.  Since I was also interested in this, I thought I'd look since 2001 to see how well it did.  For those not familiar with the Pythagorean formula for wins, here it is:

Points Scored ^ 2.37 / (Points Scored ^ 2.37 + Points Allowed ^ 2.37)

This originated from a baseball formula Bill James invented back in the early 80's, and was modified for the NFL.  It has been shown to be a more accurate predictor of the following year's record than just wins and losses, but (to my knowledge) hasn't been closely looked at on a game-by-game basis.  So here's what I did:

  • For each game, I calculated what the expected wins were up until that point in the season.  Then looked to see which team had the higher expected win total, and if it matched who won, it was a correctly predicted game.
  • Since in Week 1 there is no season numbers, I used the entire previous year.  Obviously this isn't a perfect way of doing it, but it is better than not predicting Week 1 games.
  • Any ties in Expected Wins (there were one or two), I just didn't count.  

So how did it turn out?  I had to put the table after the jump (too wide), so hit the link to see the analysis.

Star-divide

Week 2001 2002 2003 2004 2005 2006 2007 2008 Total
Win Loss Win Loss Win Loss Win Loss Win Loss Win Loss Win Loss Win Loss Win Loss Pct
1 8 7 8 7 9 7 10 6 6 10 9 7 6 10 8 8 64 62 0.508
2 7 7 12 4 7 8 5 11 8 8 11 5 12 4 9 6 70 53 0.569
3 7 7 14 0 10 4 9 5 10 4 10 4 9 6 9 7 78 37 0.678
4 8 7 5 9 9 5 10 4 8 6 7 7 8 6 5 8 60 52 0.536
5 9 5 8 6 7 7 9 5 8 6 10 4 11 3 8 6 70 42 0.625
6 7 6 10 4 12 2 10 4 10 4 5 8 8 5 6 8 68 41 0.624
7 7 7 5 9 7 7 7 7 9 5 6 7 8 6 7 7 56 55 0.505
8 9 5 10 4 7 7 8 6 9 5 9 5 11 2 9 5 72 39 0.649
9 11 4 6 8 5 9 7 7 11 3 8 6 9 5 10 4 67 46 0.593
10 9 6 8 5 7 7 11 3 10 4 9 7 6 8 11 3 71 43 0.623
11 11 4 13 3 11 5 12 4 9 7 10 6 12 4 11 4 89 37 0.706
12 10 5 9 7 12 4 11 5 12 4 10 6 13 3 8 8 85 42 0.669
13 10 5 10 6 10 6 10 6 14 2 11 5 11 5 10 6 86 41 0.677
14 10 5 11 5 10 6 14 2 11 5 12 4 14 2 10 6 92 35 0.724
15 11 4 9 7 13 3 10 6 10 6 9 7 10 6 8 8 80 47 0.630
16 8 7 10 6 11 5 11 5 8 8 9 7 12 4 11 5 80 47 0.630
17 9 6 10 6 9 7 7 9 8 8 9 7 8 8 9 7 69 58 0.543
Total 151 97 158 96 156 99 161 95 161 95 154 102 168 87 149 106 1258 777 0.618

 

  • As you can see, the overall average is 61.8%, which isn't too bad.  My predictor from last season got 62.1% right, so they are very close together.  As difficult as it is to predict NFL games, this is pretty good, and better than expected.
  • The best year was 2007 with 65.9% correct, pretty much 2/3 of the games.  The worst year was 2008, where it only got 58.4% right.  Still not bad, but you would have done poorly against myself and shake in predicting games.
  • Strangely enough, the best week of the season for predictions is Week 14 at 72.4%, including a 14-2 week in 2004.  Some care to try to explain this one, because I'm stumped.  I also expected Week 1 to be a low percentage, since it using data from the previous year.  However, Week 7 was worse!  Week 17 was also low, which is also expected, since some teams don't play their starters for more than 1 series.
  • The only perfect week was Week 3, 2002, at 14-0.  Impressive.
  • I'll eventually get to the Against the Spread numbers (although I only have that data back to 2003) to see if they are any better/worse.  I'm guessing worse, but it's just a hunch.

I'll be adding this into the Prediction Contest for the upcoming season, to see how it does in real time.  I have to say, I'm surprised it's this good at predicting games.  I was thinking it would be closer to 50/50, but I guess that's why you run the numbers.

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Impressive

That old Greek dude was on to something.

I have a few thoughts on why some weeks are better than others. Logically, you’d think that it would improve as the season went along, except for wk 17 as noted. It seems to have roughly done this, which tells me it’s generally a keeper. But why would there be any anomalies aside from Week 17?

The same reason Indy won the SB in 2006 and not other years: matchups. It’s a 53 on 53 game and even a team that averages plus 7 pts a game can lose to a team that is roughly even because of matchups.
1) Was that +7 average beefed up by drubbing somebody 30-0? (the implication is that early season with fewer games could be skewed by a single outlier more than late season).
2) Was the breakeven team playing all SB contenders, and therefore doing quite well breaking even?
3) Did the +7 team face creampuffs for the past few weeks?
4) How do these particular teams match up? Any key injuries? Home/away correlation? If HFA is worth 3 theoretical points, that could also be calculated in, no?

The reason the Steelers beat the Colts in the 2005 playoffs, why the Colts won the 2006 SB (no Chargers), and why the Giants came close to beating in week 17 and did beat the Pats in the SB the next year, all come down to matchups. The Giants had the right D package to get to Brady and nobody else really did all season. They matched up well. If the Colts had WRS who were 6-3/220 in 2003 and 2004, how would those playoff losses changed because NE’s “bump and mug” D technique no longer matched up as well?

So it really comes down to team- and individual matchups. While Pythagoras is a good rough rule of thumb, it’s no substitute for actual knowledge of the game. Or, like Diane Chambers on Cheers used to do when she won the betting pool every week in one episode (Yes, I am dating myself here—I was in HS at the time): “Sam, the Lion’s over the Dolphins. Come on, how is a dolphin going to defend itself against a lion? Eagles eat cardinals, don’t they?” Clearly she had no knowledge of the actual game coming up next Sunday. Neither does Pythagoras—he only has past knowledge, which, like they say in investment prospectii, is no guarantee of future results.

I hate Joe Namath. That's how long I've been a Colts fan.

by Bobman on Jun 11, 2009 1:22 AM EDT reply actions  

Thoughts

The number clearly improves as the season progresses until you get to weeks 15-17 where I think you might start seeing the affect of both the best teams starting to ease up and coast as the playoffs approach and their seeding is starting to lock in, and players on generally bad teams start playing for their jobs (or to get new jobs with other teams for the following year).

I wonder if some of the weakness/variability in the model in weeks 3,4,5,6,7 might come from the affect of bye weeks. Good teams without rest playing a previously poor performing teams coming off a bye week might have an edge and create a forcing in the numbers. I think you almost have to throw out weeks 1 and 2 as statistically irrelevant to the mission. If you throw the first and last 2 weeks out of the average you improve to 63.3%. If you threw out the weeks affected by bye weeks you improve to almost 66%. You might be able to make money at that rate.

by Rob-Westside on Jun 11, 2009 10:55 AM EDT reply actions  

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