Pairwise Resume Comparison

© Copyright 2008, Paul Kislanko

One way to seed a putative playoff (or to rank teams based upon their resume) is to identify candidate teams and compare each of them to every other one of them based upon a pre-defined set of criteria. Division 1 Hockey uses such an approach with a hockey-specific set of criteria.

For FBS football, we begin by defining "teams under consideration" as all FBS teams with non-losing records. The "pairwise score" is formed by comparing every team in the field to every other team in the field according to the following criteria:

Head-to-Head Each team gets 1 point for each win over the other Record vs common opponents For theams that have not played each other: A team with a better winning percentage against common opponents gets 1 point; if the winning percentage vs common opponents is the same, each team gets ½ point. For teams that have a head-to-head record, better record versus common opponents is worth ½ point, and if the records versus common opponents are the same a quarter point. If there are no common opponents, no points are awarded. Record vs teams under consideration Compare winning percentages using #wins over non-losing teams ÷ (#wins over non-losing teams + all losses). The team with the better record gets 1/4 point. # Wins vs teams under consideration The team with more total wins against this field gets 1/2 point. In addition, if one team has played more games against teams in the field, that team gets 1/4 point. Record in last 4 games A team with a better record over the last 4 games than the other gets an eighth of a point. (This serves mainly as a tiebreaker.) Best overall win Defeated opponents' that are not common opponents ranks are converted into sextiles (1:20→0, 21:40→1, ... 101:120→5, FCS→6) and if one team's best is lower than the other's that team gets 1/4 point. Worst overall Loss Opponents that are not common opponents who defeated the team's ranks are converted into sextiles as above and if one team's worst is lower than the other's that team gets 1/4 point.

*- Any ranking can be used. By default I use the majority consensus of those published by Kenneth Massey.

For each of the N FBS teams with non-losing records, count a "pairwise win" over one of the N-1 other teams if its score compared to the other team is higher than the other team's score compared to it. For equal scores, count a "pairwise tie" and otherwise a "pairwise loss."

If we let WW = #pairwise wins, LL = #pairwise losses, and TT = #pairwise ties, then we can define a "pairwise winning percentage" in the usual way:

PW% = (WW+TT/2) ÷ (WW+LL+TT)

Pairwise winning percentage is not likely to distinguish all teams in the "field." As a tiebreaker we can use the difference in total pairwise points (P) between each team t_i and every other team t_j. If we call the pairwise score of team x vs team y P(t_x,t_y), we can sum scores over all pairs by:

Delta(ti) =  N ∑ { P(ti,tj) − P(tj,ti) }  j = 1*

*j ≠ i

Of course, this is only one of many possible resutls analyses, but it is an especially useful one since it makes visible the comparisons that lead to the ranking.