Accounting for injuries

Many of the most vexing cases for the selection committee involve teams that played games without key players because of injuries. While the committee can't assume a different outcome in these games, they must take this into account when making selection and seeding decisions.

Ken Pomeroy, the hardest working man in college basketball sabermetrics, has compiled efficiency stats for each team for each game during the 2008-2009 season. These efficiency stats can help us look at how a team performed in games without a key player compared to their other games beyond the win or loss result. If you're not familiar with efficiency stats, take a look at Pomeroy's overview of tempo-free statistics before reading on.

Pomeroy uses his offensive and defensive efficiency stats, after adjusting for the competition, to generate predictions for future games. The adjusted efficiencies of the two teams in each game are combined (factoring in home court advantage) to generate raw offensive efficiencies for each team, and those are combined with the predicted tempo to create a projected score.

The predicted raw efficiencies give us a good way to estimate in a tempo-free manner how two teams would perform against each other. If we use replace one of the teams with an "average" team (that is, a team with average offensive and defensive efficiency), we can get a baseline for comparing performance in actual games.

This is a perfect spot for an example.

Consider Thursday's Big East tournament game between Marquette and Villanova. Before that game, their adjusted efficiencies looked like this:

This game was played on a neutral court, so there is no need to adjust for home court advantage. (As Ken says in his ratings explanation, the standard home-court adjustment is 1.4%.) The predicted offensive efficiencies are 106.9 (all efficiencies here are points per 100 possessions) for Villanova and 106.1 for Marquette, making this game nearly a tossup with Villanova being a slight favorite (which, perhaps not coincidentally it happened to be).

We can also estimate how an "average" team would perform against Villanova. The average efficiency listed on kenpom.com as of Thursday is 101.2, so against Villanova an "average" team would score at an efficiency of 91.2 and give up a rate of 114.8, or a margin of -23.6.

After a team plays Villanova, we can compare the actual efficiency margin in the game to the "average" team's predicted margin to measure that team's performance against a common baseline. In other words, we eliminate the strength of the opponent from the comparison and therefore can compare performance across many games using a common, tempo-free baseline. I will call this difference between the actual efficiency margin of a game and the "average" predicted margin the net efficiency margin (NEM). The higher a team's NEM in a game, the better they performed compared to the hypothetical average team's expected margin.

For example, let's look at Marquette's back-to-back games at South Florida and Villanova in February. An average team at South Florida would expect to have an efficiency margin of -7.9 while an average team at Villanova would expect to have an efficiency margin of -29.4. Villanova is a much better team than South Florida, so this makes sense. Marquette's actual efficiency margin against South Florida was -1.7 in a 57-56 loss, so their NEM was -1.7 - (-7.9) = 6.2. Against Villanova, their actual margin was -23.5 in a 102-84 loss, so their NEM was an almost identical -23.5 - (-29.4) = 5.9.

This means that Marquette's performance in the two games (as measured by tempo-free statistics) was essentially the same, despite the difference in scores. Since Villanova is much better than South Florida, most teams will perform worse against Villanova. This is what happened to Marquette in these two games, and the DEM statistic captures this.If we do this for a team over a full season, we can compare how teams performed with and without an injured player and estimate how much of a difference the player made, at least from an efficiency standpoint.

Admittedly we're dealing with a small sample size in an already small number of games in the season, so we have to be careful about the conclusions we draw. Even the most consistent teams have game-to-game variations in their performance. That said, it's a better way to gauge the effect of a missing player than looking only at wins and losses.

St. Mary's

The two broken metacarpal bones on the right hand of sophomore Patty Mills are probably the most discussed injury of this bracket season. While certainly not the Gaels' only talented player, Mills is certainly their driving force. St. Mary's lost Mills after halftime of their January 29 game at Gonzaga and went on to lose that game and three of their next four. Mills returned in the WCC tournament, but could not stop the Gaels from losing in the WCC final to Gonzaga.

The committee must determine (1) whether Mills is back to the same level he was before his injury and (2) whether St. Mary's with a healthy Mills is worthy of an at-large selection. We can use the efficiency-based method described above to measure with the Gaels' performance with and without Mills to help answer both questions.

With only three games under their belt (including a post-WCC game against Eastern Washington), it is very difficult to determine statistically or with the "eye test" whether Mills is 100% and St. Mary's is back to their previous level. Including the game in which he was injured, St. Mary's had a 19.3 NEM with Mills before the injury.

The overall efficiency is not quite back to their previous level yet, but their offensive NEM in yesterday's game against Eastern Washington was 19.9. With another week of recovery for Mills, the Gaels could be much closer to the team they were in January. They certainly hope the committee sees it that way; the extra game against Eastern Washington could be just what the doctor ordered.

Marquette

Dominic James left the February 25 game against Connecticut with a season-ending broken foot. Despite losing five of six, has Marquette actually performed better without James?

Well, yes and no. If we eliminate often-inconsistent early season games and only look at conference games, Marquette had a NEM of 26.5 before losing James, so their performance has dropped slightly without him. Also, the sans James NEM is somewhat skewed by their demolition (+57.9 NEM) of St. John's in the Big East tournament. Their NEM in the five post-James losses is a respectable but nonetheless worse 16.3. Closing the regular season with a UConn/@Louisville/@Pitt/Syracuse stretch, followed by Villanova at MSG will give most teams fits.

Oklahoma

Blake Griffin's two-game absence from a concussion (which, as is often the case, didn't look nearly as bad as it was) was probably the second-most discussed injury this season.

The Sooners certainly did not perform as well without Griffin in the lineup these two games. However, the committee cannot assume they would have won either game with him. Playing Texas in Austin, an average team should have an efficiency margin of -24.8, and against Kansas in Norman, an average team should have a margin of -19.6. The Sooners had an average NEM of 18.8 in their final three games, so based on recent performance both games would have been toss-ups even with Griffin.

Connecticut

The Huskies lost Jerome Dyson to a knee injury five minutes into their February 11 victory over Syracuse. Most thought Dyson's absence would affect Connecticut more on the offensive end, given that he led the team in possessions used at the time of his injury. The results seem to confirm that:

While the defense has stepped up, the Connecticut offense is playing only 6 points per 100 possessions better than the average team without Dyson. Connecticut's overall efficiency is down 5, though still very good at 26 points per 100 possessions better than the average team. This is the team the Huskies will have for the Big Dance, so we'll have to see whether it is good enough to carry them to Detroit.

What have we learned?

Not all injuries are the same. While they often disrupt a team's rhythm, some can have unexpected positive consequences (can you say Wally Pipp?) by allowing an underutilized player to fill the missing minutes. The committee has to tread carefully when dealing with injuries and only in the most obvious cases should they significantly override a team's full body of work with speculation.

The trick for improving our model's handling of injuries is to identify the obvious cases and how much to adjust. I plan to research this more before next season and include some basic accounting for injuries in next year's version.