Margin of Victory

Background

The best known rankings systems for college basketball are the AP and the ESPN/USA Today Coaches polls. While these are well-known, oft-quoted, and useful if you only care about the relative rankings of the top schools, these two polls suffer from three shortcomings:

  1. They only cover the top 25 teams (with enough information to figure out the rankings of the next few)
  2. They don't tell you how much stronger one team is than another. In mathematical terms, they are an ordinal measure, not a cardinal measure. (Although some information can be gleaned by looking at the number of votes)
  3. The relative rank of each team, measured by the number of votes, cannot be translated easily into expected performance on the court, except in a very limited way, i.e, a higher rated team is expected to beat a lower rated team on a neutral court.

The RPI index improves upon the polls in two ways:

According to the RPI measure, the gap between TN and CT is far larger than between CT and OK. While fans may differ with these assessments, if these were mid-year numbers, it would be far easier for OK to pull ahead of CT than for CT to pull ahead of TN, assuming they were playing comparable competition. However, while this measure gives some indication of the relative gaps between teams, it doesn't translate easily into a measure that is easy to explain. In addition, some people question the simple mechanical formula used to calculate the RPI, and don't believe it captures many aspects of relative team strength that can be informally included in poll results.

Mike Greenfield's Power Rankings improves on the polls and on the RPI formula. It is mathematically driven, so it may not capture all the factors that can be considered in a poll (notably, it doesn't consider injuries). On the positive side, the rankings do rank every team, and more importantly for our purposes, they provide a measure to estimate how teams will stack up on the court.

Simply stated, if two teams are playing on a neutral court, one can look up the team ranking for each team, subtract one from the other, and the result is the "expected" margin of victory. ("Expected" is in quotes, because the actual formula used to determine how teams will do head-to-head is somewhat more complicated, but this simple approach is within a point or two of the more complex formula.

Of course, teams usually play at one home court or another, but the site also gives the home court advantage for each team. So it is possible to estimate the "expected" margin of victory by subtracting the team rankings, and then adjusting for the home court advantage.

Results

I did this calculation for each of the 39 games in the season. To keep the graphs reasonalbly sized, I put the first 15 regular season games in the first graph, the other 15 regular season games in the second graph, and the nine post-season games (three Big East Tournament, six NCAA Tournament) in the third graph.  The results are striking. In many cases, UConn managed to win by a margin very close to that indicated by the rating measure. A series of seven games, starting with the Ball State game (first graph below), were almost all exactly as predicted. The one major exception in the first 15 games is the Pittsburgh game—expected to be a fairly easy win, but ended up being a blowout.

(Click on image to enlarge.)

ctmargin1

The Providence game (third to last regular season game, was also a blowout even beyond expectations. The notable exception in the other direction was the Virginia Tech game, which we all remember as closer than it should have been. Interesting, the graph indicates that the Virginia Tech game was part of a four-game "funk", each of which were wins by well under the expected margin. One factor not considered in the Power Rankings is injuries. I don't recall any key injuries during that period, but maybe someone can refresh my memory.

(Click on image to enlarge.)

ctmargin2

The tournament games largely continue the same picture. The final two games in the Big East Tournament were wins by a healthy margin over the expected, but the others are fairly close. How good is this measure? According to Power Rankings, UConn should beat Oklahoma on a neutral court by 12.6 points. UConn won the National Championship with a victory margin of 12.

(Click on image to enlarge.)

ctmargin3

Analysis

So what else can we conclude?

Can we tell how the team improved over the year? The answer is a qualified yes, as improvement can only be measured in a relative sense. One expects the daily practices and the games to improve the skills of the players. They certainly are better players at the end of the season than at the beginning. But, of course, their opponents aren't sitting still. So looking at how the margin of victory changed over the course of the season tells you whether the team has improved faster or slower than your opponents.

I didn't reproduce the graph here, but it is simple enough to look at the difference between the actual margin of victory, and the computer expected margin of victory, and determine whether it is trending up, or down, or remaining flat.

Before giving the answer, one can get a general impression simply by looking at these three graphs. A team improving faster than the competition would win early games by smaller than expected margins (or lose!), and win the later games by more than expected. That doesn't seem to be the case.

It turns out there is a modest positive trend. About 9 hundredths of a point each game. While this sounds tiny, it adds up to a team that is roughly three points better at the end of the season than at the beginning. It is worth repeating—this doesn't mean that the year-ending UConn team is three points better than the beginning of the year team, it means they have improves by three points more than their opposition. While that is still a fairly modest amount, I'll argue it is moderately surprising. I wouldn't have been surprised at a slight downward trend.

Before I get lynched by loyal Huskie fans, I'd better explain myself. The 2001-2002 UConn team started the year as one of the most experienced teams in their history. More to the point, it was very experienced relative to its opposition. Four of the starting five were seniors, with only one sophomore in the starting lineup. In addition, the roster size was relatively small compared to some other teams. Consequently, the team at the beginning of the year was extremely experienced, with National Championship experience for most starters. Contrast this to a team like Kansas State, who started five freshman. One would expect that team to start a little rocky, and gel over the course of the season. In that context, it wouldn't have been surprising if the team had started out strong, and continued to get better, but at a slightly slower rate than some less experienced teams.

It will be interesting to watch the 2002-2003 team, which is almost the mirror image, starting possibly three freshman, and certainly no seniors. We may see a trend steeper than last year, but we don't yet know at what level it will start.



This page last updated on 9 Nov 02.