Pythagoras Weighs in on Patriots-Colts

By Daniel Adler

Did you know the Patriots are playing the Colts this week?  Peter King sure does.  As the Monday Morning QB has pointed out, this marks the seventh straight year the teams have played and fifth straight time it has fallen November meeting.  What do those past meetings tell us about these games?  Is this rivalry one where we can throw out the record or do the teams’ results so far give us a hint about what to expect?

We’ll use the Pythagorean Formula (which makes predictions based on points scored and allowed) to try to predict the winner of this year’s game and check to see how reliable of a predictor the formula has proven in the past after the jump…

HSAC has conducted research on the Pythagorean Formula (win % = (points scored/ [points scored+points allowed])^α) for all sports (paper forthcoming) and we have found the exponent (α) to be 2.59 for football.  Granted, the formula is more useful for predicting season outcomes rather than individual games, but a derivation of the formula can come up with a prediction for the winner when two teams square off.

Strength = Points Scored/Points Allowed

Patriots Win/Loss = (StrengthPatriots/StrengthColts) ^2.59

Since this gives us an odds ratio (p(W)/p(L)), we can convert: p(Pats Win)= p(W)/p(L)/([p(W)/p(L)]+1)…Don’t worry too much about the math.

Predicting the Past

The exponent is based on a full season worth of points, but our calculations only consider games played up until Patriots-Colts.  With this very small sample size, we have less predictive power and the exponent should probably be smaller (pushing all projections closer to 50/50).


Week 13 @Indianapolis

Pats: 9-2, 219 points for, 175 points against

Colts: 9-2, 309 points for, 216 points against

Prediction: Colts 59%

Outcome: Patriots 38, Colts 34

AFC Championship @New England

Pats: 15-2, 365 points for, 252 points against

Colts: 14-4, 526 points for, 377 points against

Prediction: Patriots 52%

Outcome: Patriots 24, Colts 14

Season: Patriots Win Super Bowl (17-2), Colts lose in AFC Championship (14-5)


Week 1 @New England

Pats: 0-0, 0 points for, 0 points against

Colts: 0-0, 0 points for, 0 points against

Prediction: Even (duh)

Outcome: Patriots 27, Colts 24

AFC Division @New England

Pats: 14-2, 437 points for, 260 points against

Colts: 13-4, 571 points for, 375 points against

Prediction: Patriots 56%

Outcome: Patriots 20, Colts 3

Season: Patriots Win Super Bowl (17-2), Colts lose in Division Round (13-5)


Week 9 @New England

Pats: 4-3, 159 points for, 180 points against

Colts: 7-0, 189 points for, 77 points against

Prediction: Colts 93%

Outcome: Colts 40, Patriots 20

Season: Patriots lose in Division Round (11-7), Colts lose in Division Round (14-3)


Week 9 @New England

Pats: 6-1, 167 points for, 87 points against

Colts: 7-0, 205 points for, 153 points against

Prediction: Patriots 72%

Outcome: Colts 27, Patriots 20

AFC Championship @Indianapolis

Pats: 14-4, 446 points for, 274 points against

Colts: 14-4, 465 points for, 374 points against

Prediction: Patriots 67%

Outcome: Colts 38, Patriots 34

Season: Patriots lose in AFC Championship (14-5), Colts win Super Bowl (16-4)


Week 9 @Indianapolis

Pats: 8-0, 331 points for, 127 points against

Colts: 7-0, 224 points for, 102 points against

Prediction: Patriots 61%

Outcome: Patriots 24, Colts 20

Season: Patriots lose in Super Bowl (18-1), Colts lose in Division Round (13-4)


Week 9 @Indianapolis

Pats: 5-2, 153 points for, 132 points against

Colts: 3-4, 149 points for, 162 points against

Prediction: Patriots 65%

Outcome: Colts 18, Patriots 15

Season: Patriots miss playoffs (11-5), Colts lose in Wild Card (12-5)

What does it all mean?

Let’s compare our predictions to ESPN’s Tuesday Morning Quarterback Gregg Easterbrook’s favorite picking mechanism: choose the team with the better record and if the records are the same, go with the home team.  For our purposes, we’ll pick the Pythagorean favored team if it’s greater than 60% and the home team if it’s less than 60% (essentially a 10% home field advantage adjustment).

2003, Week 13, Winner: Patriots

Pythagoras: Colts; Easterbrook: Colts

2003, AFC Championship, Winner: Patriots

Pythagoras: Patriots; Easterbrook: Patriots

2004, Week 1, Winner: Patriots

Pythagoras: Patriots; Easterbrook: Patriots

2004, AFC Division Round, Winner: Patriots

Pythagoras: Patriots; Easterbrook: Patriots

2005, Week 9, Winner: Colts

Pythagoras: Colts; Easterbrook: Colts

2006, Week 9, Winner: Colts

Pythagoras: Patriots; Easterbrook: Colts

2006, AFC Championship, Winner: Colts

Pythagoras: Patriots; Easterbrook: Colts

2007, Week 9, Winner: Patriots

Pythagoras: Patriots; Easterbrook: Colts (if using win%, not total wins)

2008, Week 9, Winner: Colts

Pythagoras: Patriots; Easterbrook: Patriots

So in the end, Pythagoras+10% home field goes 5-4 while the Easterbrook system goes 6-3.  It’s a small sample, but it looks like our system does not beat the elegant simplicity of the TMQ system.  Despite Easterbrook’s (odd/personal) vendetta against Harvard, he seems to be on to something.  Regardless of system, this is not an easy series to predict and lately it has gone against both systems more frequently.  If we had the correct home field advantage adjustment (I arbitrarily used 10% in this example, but we could calculate the real thing…something we should do in the future), I imagine this system could be better than the TMQ system.

Actual (Not Too Bold) Prediction


Week 9 @Indianapolis

Pats: 6-2, 225 points for, 115 points against

Colts: 8-0, 217 points for, 108 points against

Prediction: Colts 52%

This projection is probably a little unfair to the Colts since the Patriots points are aided greatly by their 59-0 win against the Titans.  Right now, the Vegas line favors the Colts by 3 points.  They are at home, so that essentially means the line would be 0 at a neutral site.  The numbers suggest that is a good line, but discounting some of the Patriots meaningless points against the Titans (let’s call it a 30-0 win), the Colts become a 60% favorite without home field advantage.  However, I would also put more stock in the latest Football Outsiders’ DVOA rankings, which list the Patriots first.  Especially considering how strong they have been lately (reflected in weighted DVOA), they appear to be the favorite.  The Pythagorean Prediction Formula is much more useful for full season projections and does not appear to be that helpful for single games.

Bottom line?  We’ll stick to stats here at HSAC and avoid making predictions.  We’re not ready to open up a toll-free hotline for our pick of the week.

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1 Comment

  • I’m a Colts fan and an FO reader and I agree with DVOA on this one (i.e. the Pats probably win). The Colts are a little beat up, and the Patriots have righted the ship on both defense and offense. The last two games the Colts have played have been pretty underwhelming. Of course, in a game as close as this, either team can come out on top.

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