BennettRank is our predictive, data-driven power ranking system for every team in all three divisions of NCAA volleyball (among other sports). Early in the D1 Women's volleyball season, BennettRanks are anchored on past team and conference performance. Teams move a bit week to week, but not a whole lot. We just don't have enough data on the current version of each team to rank them comprehensively. This is not ideal. But this week, we are excited to announce, we have enough data from this season's games to migrate to our full-featured BennettRank system, and enter the realm of sophisticated mathematics.
Before we get into how BennettRank is calculated, it might help to compare it to something most fans are already somewhat familiar with: the Rating Percentage Index. The RPI is used by NCAA Tournament selection committees from several sports as part of their selection criteria. It uses computer algorithms to rank every team within a division based on the combined results of every game they have played to date. BennettRank is different (and we think better) in three significant ways:
The first difference is the biggest. Instead of just wins and losses, which are the RPI's focus-statistic, BennettRank uses an adjusted margin of victory/defeat statistic. We believe the margin tells a more complete story than just a W or L. A 3-0 win tells us something different than than a 3-2 win.
The next difference between the RPI and BennettRank is that the RPI considers all games equal, no matter when they are played, while BennettRank gives each game more weight as the season progresses toward playoffs. After Week 3, each week's games are worth 4% more than games from the week prior. Thus, the last few games of the season are worth 50-60% more than the first few games of the year.
The final difference between BennettRank and the RPI is that BennettRank accounts for a slight home-court advantage. Mechanically, this means we adjust margin of victory by 0.25 sets per game — the average margin by which home teams improve on their home court .
How is BennettRank Calculated?
The number underlying a team's BennettRank is a combination of two things: their average adjusted margin of victory, and the average BennettRank of every team they have faced.
In the volleyball domain, the margin of victory is a bit stunted. Unlike football or basketball, where scores are reported in points, and margins can be in excess of 30 per game, volleyball scores are reported in terms of sets. They're capped at three. Thus, if a team plays many poorly-ranked teams in the beginning of the season, they don't get much credit for it. As they play tougher teams, their rank will increase because of the second part of the equation: the average BennettRank of every team they have faced.
That second part of the equation is really what complicates things though. Since each team's BennettRank is dependent upon the BennettRanks of their opponents and visa versa, we have to run the calculation repeatedly to get to the final product each week. This process is known as an iterated function. We run the equation as many times as we need to until each team's raw BennettRank score changes by less than 1/1000th with each subsequent iteration — sometimes it takes up to 100 repetitions.
These raw scores are then sorted into ordinal ranks, which are BennettRank. Because there's so little data early in the season, rankings sometimes jump erratically in the first few weeks. You might notice some of that this week. Ranking changes get smaller from here on out.
This year we added a new feature we call "PowerScore." To calculate each team's PowerScore (PWR), we take the raw BennettRank data for a whole division and scale it to fit between 1.000 and 0.000 (with the top team at 1.000, the bottom team at 0.000, and every other team at some point between). PowerScore is an attempt to show how far apart teams actually are, at a glance.
Empirically, how well does BennettRank do? We really don't like to compare ourselves to anything, but we do look over our shoulders just to make sure something is not amiss in our complicated formulas. In last years NCAA tournament, the BennettRank top 25 (before the draw), won 51 games, the Top 25 Coaches Poll won 49, and the RPI (which establishes the brackets) also had 49. The computer based system was as good a predictor as coaches eyeballs and the rankings system which helped establish the matchups/seeds in the tournament. It certainly can't be said that BennettRank is "worse". Parenthetically, we see this same result across all sports and all divisions that we rank.
Early in the season, the rank variations from week to week can swing wide. As more games are played the variations narrow.