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).
2003
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)
2004
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)
2005
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)
2006
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)
2007
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)
2008
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
2009
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.
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.