|Analysis of Division I Menís Lacrosse Statistics|
|By Michael Mauboussin|
Breaking down the statistics to evaluate past performance is a useful exercise. But the real goal is to use statistics to predict performance on a player and team level. Such prediction can be useful in recruiting and in allocating playing time.
A useful statistic meets two criteria: it is persistent (i.e., this periodís result is highly correlated with last periodís result) and predictive (i.e., doing well or poorly as measured by the statistic correlates with expected wins). For offense, the statistics that meet these criteria are goals scored per game and the factors that drive them, shots per game and shooting percentage.
For defense, we can analyze goals allowed per game, which is derived from shots allowed per game and shooting percentage yielded. To do this analysis, we compare team totals from the 2010 season to the 2011 season.
Shots per Game. Exhibit 10 shows the results for shots per game. There is a general trend, as indicated by the upward sloping best-fit line, but it is clear that there is a fair bit of variation from year to year.
Shooting Percentage. Next we examine shooting percentage in Exhibit 11. Here, we see a better correlation from year to year. It turns out the shooting percentage of most players tends to be quite similar from year to year. So this correlation can be explained by a combination of the personnel and offensive scheme.
Goals per Game. The product of shots per game and shooting percentage is goals per game, one of the key drivers of the wins expression. Exhibit 12 shows the correlation between goals per game in 2010 and 2011. At almost 50, the r-squared percent is decent. Still, you can see that some teams make marked improvements or declines from the prior yearís result.
Shots Yielded per Game. Now we turn to defense. Exhibit 13 shows shots yielded per game for 2010 vs. 2011. The correlation is good, and for these two years itís much better than for shots taken. Good defenses seem to stay good, and bad defenses stay bad.
Shooting Percentage Against. Shooting percentage that teams yielded, interestingly, seems to have relatively little year-to-year persistence, as Exhibit 14 shows. The r-squared is just 16 percent. This is a statistic weíll have to watch over time to determine if the low correlation in 2010/2011 data is just a fluke.
Goals Against per Game. Exhibit 15 wraps up the analysis of the components of the win expression by looking at the correlation between goals against per game in 2010 and 2011. The fit here is quite good, with an r-squared of 48 percent. So most of the components that make up the win equation have some predictability from season to season, despite the fact that roughly one-quarter of the players on the roster change each year.
Scoring Differential. Finally, we finish by looking at the simplest of prediction models by simply assuming that the subsequent yearís goals per game minus goals allowed per game differential will be the same as that in the prior year. Exhibit 16 shows that this naÔve method yields pretty solid results. Generally speaking, the good programs stay good from season to season, and the poor programs stay bad.
Endnotes can be found at the bottom of Part 5. Appendix A appears in Part 6, and Appendices B and C are presented in Part 7.
Michael Mauboussin works an as investment strategist. He is a lacrosse fan, youth coach, and retired player. For more, see www.michaelmauboussin.com.
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