1. Determine an "adjusted winning percentage" for each team.
A team's winning percentage is "adjusted" for each game by adding
the winning percentage of the opposing team (in all other games) for each
win and subtracting one minus the opposing team's winning
percentage (in all other games) for each loss.
Example: Michigan (10-1) has beaten Minnesota (7-4). In all other
games besides this ones, Michigan is 9-1 (winning percentage = .900)
and Minnesota is 7-3 (winning percentage = .700). Michigan thus earns
.7 points for this win, while Minnesota loses (1 - .9) = .1 points
for their loss.
Calculate "adjusted" winning percentages for each game in this
way and then divide by the total number of games played to come up with
an average "adjusted winning percentage" for each team. The result of
this calculation is listed under the "Adj. Perc." column in the
rankings below.
2. Determine an "adjusted margin of victory" for each team.
A team's "adjusted margin of victory" is calculated in much the same
way as the "adjusted winning percentage" above. The basic idea is to
adjust the margin of victory in each game in comparison to the opponents'
average margin of victory in all other games.
Example: Michigan has beaten Minnesota by 13 points. Michigan's average
margin of victory in all other games is 25 points. Minnesota's is
7 points. Michigan has thus bettered all of Minnesota's other opponents
by an average of (13 + 7) = 20 points; add 20 points to Michigan's
average margin of victory. Similarly, Minnesota has bettered all of
Michigan's other opponnents by an average of (-13 - (-25)) = 12 points;
add 12 points to Minnesota's average margin of victory.
Calculate "adjusted margins of victory" for all of a team's games in
this way, and then divide the total by the team's number of games played
to come up with an average "adjusted margin of victory" for that team.
In order to even out the effects of "running up the score" on this
margin of victory calculation, I then do a log adjustment on each average
adjusted margin of victory. This basically consists of taking the natural
log of the absolute value of e plus the average adjusted margin of victory
for each team. The result of this calculation is listed in the "Adj.
Points" column in the rankings below.
3. Multiply the results of (1) and (2) together to derive a cumulative
"rating" for each team. The result of this calculation is given under
the "rating" column in the rankings below.
4. Enjoy!