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Division I-A College Basketball Schedule StrengthWhat is strength of schedule?The primary difficulty in ranking college football teams is that each team's performance must be evaluated relative to a different schedule. Strength of schedule becomes a key component in doing so: other things (usually wins and losses) being equal, we'd rank a team with a more difficult schedule higher than one with an easier one. But what makes a schedule difficult? Most strength of schedule measures rely on the average quality of a team's opponents. For example the Ratings Percentage Index (RPI) is a weighted average of a team's winning percentage, their opponents' collective winning percentage and their opponents' opponents' collective winning percentage. Though no longer used, the Bowl Championship Series (BCS) contained a strength of schedule component which was a weighted average of opponents' winning percentage and opponents' opponents' winning percentage. The problem with averagesThere are two serious problems with using an average measure like opponents' winning percentage (or variants thereof):
We'll illustrate these issues with a pair of examples. Example #1: First, consider Auburn's 2004 season. Originally slated to face Bowling Green (at the time a Top-25 team from the respected Mid-American Conference), Auburn scrambled to schedule I-AA the Citadel to fill the slot after Bowling Green backed out to play Oklahoma instead. This game hurt the Tigers' strength of schedule and made it easier to dismiss them in the national championship conversation (which almost entirely revolved around Southern Cal and, ironically, Oklahoma). While Auburn was unlikely to lose to the Citadel, they were even less likely to lose to a bye week, however by considering opponents' average strength Auburn's strength of schedule was lower than had they simply not played at all. Example #2: The other problem with averages is they don't contain any information about the variation in schedule composition. For instance, suppose there are three types of teams: good, average, and bad. If two teams have the same classification, each team has a 50% chance of winning a head-to-head game. Further, let's assume: (1) good teams beat average teams 75% of the time, (2) good teams beat bad teams 95% of the time and (3) average teams beat bad teams 80% of the time. Now consider these two schedules: S1 = {Good, Good, Good, Bad, Bad, Bad} Both schedules have the same average difficulty, but depending on how good your team is, you might prefer one to another. If you were a good team, you would prefer the second schedule because you could expect to win 4.5 games and lose 1.5 vs. winning 4.35 games and losing 1.65 against the first one. However, if you were a bad team, you'd prefer schedule number 1, since you would win 1.65 games on average vs. 1.6 games for schedule 2.
Expected Losses and Voting SchemesThe preceding examples might suggest using the expected number of losses as a measure of schedule difficulty, however as example #2 illustrates, the expected number of losses depends on the team playing the schedule. What's worse, in the example, the teams couldn't agree on which schedule was more difficult! However, if there was a third schedule consisting entirely of good teams, S3 = {Good, Good, Good, Good, Good, Good}, any pair of teams would agree that this is the most difficult. Our method first determines the teams' individual offensive and defensive strengths and the influence of venue. Then, using the SportsQuant ratings, compute expected game outcomes which determine strength of schedule. For every possible pair of teams, we consider the relative difficulty of their two schedules. The SportsQuant football ratings allow us to predict the probability that any team would win a game against any other (at home, on the road or at a neutral site). These are aggregated to arrive at the expected number of losses for any team against any other team's schedule. If both teams prefer one to the other, then that schedule is easier. If the two can not agree, then the schedules are equivalent. By considering all pair-wise equivalences and inequivalences1 we can estimate the relative difficulty of schedules. The mechanics of our approach are a little more involved2, but that's the gist of it. ALL other strength of schedule methods try (unsuccessfully) to determine a strength of schedule and then use it as an input when ranking teams. 1. Believe it or not, this is actually a word.2. If you want to know the details, send us a note.Back to Top |
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