Analysis of Division I Menís Lacrosse Statistics
By Michael Mauboussin

Goals For/Against per Game

The win equation also shows that teams win through a combination of offense and defense. A great offense with an average defense will do the job, as will a great defense with an average offense. But the teams that win championships tend to be better than average on both sides of the field.

Exhibit 2a shows the correlation between goals per game and win-loss record and Exhibit 2b goals against per game and win-loss. The correlations are not as strong as the win prediction model, which takes offense and defense into consideration, but are very solid nonetheless.

Offensive Possession and Possession Efficiency

Face-offs. Letís start with the primary source of possessions, face-offs. The results from the face-off analysis tend to be the most surprising to lacrosse players and fans. From year to year, face-off winning percentage tends to have among the lowest correlations with win percentage of the statistics we will examine. Yet most people in the lacrosse community believe face-offs to be crucial to success. Both views, their lack of explanatory power over a season but perceived significance, can be explained.

First, Exhibit 3 shows the correlation between face-off wins and win-loss record. The r-squared percent, at 35, is not too bad. But this is the highest value for face-offs in years. The correlation is generally in the .10-.20 range. For example, the r-squared percent was 14 in 2010, 18 in 2009, and 13 in 2008. In terms of explaining wins, face-offs are well down the list of factors.

Hereís one way to think about it. Over 80 percent of teams win between 40 and 60 percent of their face-offs. There are, on average, 22 face-offs per game. So the differential between the really good teams (.6 * 22 = 13.2) and really bad teams (.4 * 22 = 8.8) is about 4.4 possessions. This translates into about one goal per game. So the teams with the really good face-off units contribute about one win per year, with the very best contributing about two wins, and those with the poor units detract about one win per year, with the worst detracting two or three wins. But again, face-offs donít add or subtract many wins for the vast majority of the teams over a season.

Still, most observers believe that face-offs are crucial to the game. The way to reconcile the perceived importance of face-offs with their actual importance is to look at the pattern of face-off wins and losses. You may remember from a statistics class that there are many more streaks in random series of coin tosses than most people expect. For example, if you flip a coin 300 times Ė a sum lower than the average number of face-offs a team takes during a season Ė there is almost a 100 percent probability that youíll get a run of at least six heads or tails in a row. There is also streakiness in lacrosse face-offs. Even a team that wins 50 percent of its face-offs over a season will have wins and losses come in bunches. These streaks are momentum changers in the short-run and hence are perceived as very significant.

Of course, lacrosse face-offs are not the equivalent of random coin tosses. Some face-off men are better than others, although there is a lot of transitivity (i.e., player A beat B, player B beats C, player C beats A).2 But it is reasonable to think about face-offs as coin tosses that are biased by the quality of the face-off men. Even if one player has an edge, face-off wins will show a pattern of streaks. Over a season, these streaks tend to even out, which is why the aggregate effect is not large. But for a given game, the effect can be enormous. This is one facet of the game that reflects a large dose of randomness.

Ground Balls.The next source of possession is ground balls. Exhibit 4 shows that the correlation between ground ball differential and win-loss record is just below 50 percent. Ground balls are undisputedly important.

On average, a team gathers about 30 ground balls per game. A substantial percentage of these ground balls are associated with face-offs. In fact, thereís over a 70 percent correlation between ground ball per game differential and face-off win percentage.

Teams with a ground ball differential of 5 per game or more win almost 60 percent of their games.3 Teams with a ground ball differential of -5 per game or worse win only about one-quarter of their games. Notwithstanding the fairly clear definition of what constitutes a ground ball, this is likely a statistic that is gathered in an inconsistent manner.4 Still, ground balls are a vital source of possessions.

One way to quantify the value of ground balls is to look at the ratio of goals to ground balls. On average, this ratio is 0.32. Said differently, a ground ball is equivalent to about one-third of a goal. This figure can be further modified. For instance, a ground ball in the defensive half of the field that requires a clear is worth about 0.26 goals, because the rate of successful clears is about 80 percent (0.32 * 0.82 = 0.26). Further, winning a contested ground ball creates a roughly 0.6 swing in expected goals, because the winner gets 0.32 and the loser drops 0.32.

Division I lacrosse teams average about 17 turnovers a game, roughly half of which are caused. Having a favorable turnover ratio is clearly desirable but the correlation between turnover differential and win-loss record is relatively low, less than .20.

Shots per Game. Now we turn to the first measure of possession efficiency, which is shots per game. Ideally, weíd like to analyze shots per possession, but there are no consistent and reliable possession data. The average shot-to-possession ratio looks like itís in the 80-100 percent range. Following the lead of basketball, we consider a backed up shot a continuation of the same possession. So, while some possessions yield no shots, other possessions generate multiple shots.

On average, teams take about 34 shots per game. Almost every team has an average of between 30-40 shots per game. Logically, the objective is to have more shots than the opposing team. Exhibit 5 shows the strong correlation between shots per game and average goals scored per game.

Shooting Percentage. Of course, it is not shots per se that matter but how many of those shots end up as goals. This directs our attention to shooting percentage. It turns out that the correlation between shots per game and shooting percentage is very low. Some teams take lots of shots and maintain a high shooting percentage, while others take a meager number of shots that score at a low rate.

Shooting percentage, of course, is vital on its own. On average, about 28 percent of shots in Division I lacrosse end up as goals, and the standard deviation of this average is about 3.5 percentage points. In other words, about two-thirds of teams are expected to have a shooting percentage between 24.5 and 31.5. In 2011, 9 of 61 teams averaged over 31.5 percent for the season (including both national championship finalists, Maryland and Virginia) and 10 teams were below 24.5 percent.

Exhibit 6 shows the correlation between shooting percentage and goals per game. This is another strong relationship. Not surprisingly, both the quantity and quality of shots matter, and lots of either variable can lead to good offensive production as long as the other variable isnít too bad.

Combining shots per game and shooting percentage, we can see that on average each team scores 9.6 goals per game (33.9 * 28.2% = 9.6).

When a player shoots, there are three possible outcomes: he scores, the goalie saves the shot, or the shot misses (which includes hitting the post, blocked shots, and goal stops of shots that are not on goal). For all of Division I lacrosse, roughly 41 percent of the shots miss, 31 percent are saved, and 28 percent are goals.

Naturally, coaches want players who shoot at a high percentage, and the objective of an offensive scheme is to generate high-percentage shots. But what is often overlooked is that there is a big difference between a wide shot and a saved shot. A wide shot, properly backed up, extends the possession most of the time. A saved shot, by contrast, is a change of possession a high percentage of the time.

So player evaluation should not stop with shots per game or shooting percentage but should also consider the percentage of shots that the goalie saves. A team should strive to have less than 30 percent of its shots saved (about one-third of Division teams achieved that mark in 2011), and coaches should include saves in turnover statistics for individual players.

No discussion of shooting percentage is complete without discussion of the impact of Canadian players. In 2011, Canadians represented less than 5 percent of Division I players yet scored in excess of 10 percent of the goals.5 Further, they did so with extraordinary efficiency. The attackmen scored on 39.8 percent of their shots (over three standard deviations above average), and the midfielders scored at a 31.4 percent rate (almost one standard deviation above average) for a combined rate of 37.1 percent. See Appendix A for more details.

The proficiency of the Canadians strongly suggests that American youth coaches should look to adopt some of the Canadian training methods by practicing in tighter spaces and practicing shooting on much smaller targets. Less focus on velocity and more focus on efficiency would likely serve youth players well.

About 55 percent of goals are assisted in Division I. There is little correlation between the percentage of goals that are assisted and overall shooting percentage. It may be the case that shots following passes score at a higher rate, but the aggregate data donít allow for a determination of that one way or another.

In sum, offensive play should be evaluated using shots per game and shooting percentage. Coaches and players should understand clearly how their shots per game stack up versus the averages and how well they shoot. Shooting should be further broken down into goals/misses/saves, and shots should be charted based on where they were initiated on the field as well as the location on goal. The best offenses are able to take a large number of high quality shots.

  Part 1    Part 2    Part 3    Part 4    Part 5    Part 6    Part 7  

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

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