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Predicting Head-to-Head Matchups

Copyright Iain Fyffe, 2003

Let's get right into this one. Say you have a team (Team A) with a .600 winning percentage. They're playing a team (Team B), that has a .400 winning percentage. What is A's chance of winning? Since Team A is playing a below-average team, their chance of winning should be greater than .600. But how much greater? 100 points? 150 points?

Rather than develop something myself, I took the easy way out and adapted some of Bill James' work to answer this question. Using his "log5 method" for predicting batter-pitcher matchups, I extrapolated the following formula to determine the chance that Team A will win:

(A x (1-B)) / ((A x (1-B)) + ((1-A) x B))

Where A is team A's winning percentage and B is team B's winning percentage. After doing this, I found that James also used the formula for team head-to-head matchups, preferring to present it like this:

(A - (A x B)) / ((A + B) - 2(A x B))

Which is the same as the formula above, with some terms rearranged.

This is all well and good, but how do we know it works? Well, Bill James knows what he's doing, but perhaps hockey is different. So let's test the formula to see how well it works.

I took all NHL teams from 1998/99 and 1999/2000 and calculated their winning percentages, for a total of 55 team-seasons. I then divided these teams into five groups, based on winning percentage (I used a 7/12/17/12/7 distribution):

Very Good (VG): 98/99 Dallas, New Jersey, Ottawa; 99/00 Philadelphia, Washington, St. Louis, Detroit.

Good (GD): 98/99 Colorado, Toronto, Philadelphia, Detroit, Boston, Buffalo; 99/00 New Jersey, Ottawa, Toronto, Florida, Dallas, Colorado.

Average (AV): 98/99 Pittsburgh, Carolina, St. Louis, Phoenix, Anaheim, San Jose, Florida, Edmonton; 99/00 Pittsburgh, Carolina, Los Angeles, Phoenix, Buffalo, Montreal, San Jose, Anaheim, Edmonton.

Bad (BD): 98/99 Montreal, NY Rangers, Washington, Chicago, Los Angeles, Calgary; 99/00 Nashville, Boston, NY Rangers, Vancouver, Chicago, Calgary.

Very Bad (VB): 98/99 NY Islanders, Tampa Bay, Nashville, Vancouver; 99/00 NY Islanders, Tampa Bay, Atlanta.

I then calculated the simple average winning percentage for each group, as follows:

VG: .647

GD: .576

AV: .507

BD: .434

VB: .318

Using these figures I calculated each group's expected winning percentage against each other group. I then compiled the actual results for these two seasons for each group against each other group. The results are summarized in the following table. Note that each matchup is only included once (i.e., BD versus GD is not listed because GD versus BD already is).

Pred is the predicted results, Actual is the actual results, and Diff is the absolute value of the difference between Pred and Actual.

Overall the method works extremely well. The average error is about 2.5% of the mean.

In conclusion, to answer the question I began with, .692.