|Analysis of Division I Men’s Lacrosse Statistics|
|By Michael Mauboussin|
Michael Lewis’s bestselling book Moneyball raised the awareness of how statistics could lend insight into player performance and strategy in professional baseball. Despite this, many sports operate without taking full advantage of the information that statistical analysis offers. This paper provides a high-level look at Division I men’s lacrosse using statistics. The game is broken down into its core elements, possessions and possession efficiency, and the main contributory factors are evaluated. This type of analysis provides insight into how games are won, allows for the quantification of the value of certain contributions, and provides a path for quantifying individual player contributions to wins.
In recent years, there has been a flurry of analysis showing that many decisions in professional sports are suboptimal when viewed using statistics. For example, Major League Baseball teams frequently overpay aging players, coaches in the National Basketball Association play their high draft picks for more minutes than they deserve, and National Football League teams don’t go for it frequently enough on fourth down. These are leagues where the stakes are high and data are readily available.1
The main reason that professional sports teams are mismanaged is that they are run by managers and coaches who operate with certain biases. For example, when you play a sport, you develop a set of views about how the game works and what is important. Unfortunately, these perceptions are often misplaced, misguided, or idiosyncratic. Michael Lewis makes this point in his bestselling book Moneyball when he notes that baseball scouts often evaluate players based on how they look rather than how they perform. Progressive managers in all sports have reduced their reliance on perception and have integrated statistical analysis into their decision making.
Statistical analysis in lacrosse is in its early phase. The stakes at the college level may not yet be high enough to induce major changes in behavior. While a few coaches appear to have developed an effective approach (Bill Tierney, the coach at the University of Denver, is a great example), there remain opportunities to use statistical analysis to improve recruiting, to better evaluate player contributions, and to sharpen training techniques.
This paper provides a high level analysis of Division I men’s lacrosse. While a number of useful insights emerge, the analysis needs to be taken to the next level. This entails much better data gathering, including time of possession, detailed shot analysis (place on field as well as spot on goal), and more specifics on individual player actions.
At its core, lacrosse is a game very similar to basketball. The key to winning boils down to the number of possessions and possession efficiency, or this simple expression:
You win if: Your number of possessions * % of possessions that lead to goals > the number of possessions (opponent) * % of possessions that lead to goals (opponent)
Lacrosse is different than basketball in a few meaningful ways. First, the number of possessions in lacrosse is lower. For instance, the average number of possessions in a college lacrosse game is estimated to be about half that of a college basketball game (35-40 versus about 70). Second, whereas in basketball the team that was scored on automatically gets possession, in lacrosse each possession following a goal is contested through a face-off. This means that one team can dominate the number of possessions.
Finally, lacrosse rules stipulate that when a ball goes out of bounds following a shot, the team of the player closest to the ball when it goes out of bounds gets possession. So shots that are wide of the goal but are “backed up” by the offensive team do not end a possession. Possessions and possession efficiency lead to goals for your team, and same metrics for your opponent leads to goals against your team. This allows us to express a simple equation that predicts the number of wins:
(Wins are bounded by zero on the downside and by games played on the upside.)
In plain words, this equation says that goal differential (goals for minus goals against per game) for a season times a constant (α – .08 gives a best fit) added to .500 and then multiplied by the number of games played predicts actual wins (with error term ε).
For example, North Carolina’s goals per game were 10.5 and its goals against per game were 8.8 in its 16 games in 2011. Plugging these numbers into the equation yields 10 wins, which closely matches the team’s actual record. [Wins = (.500 + .08(10.5 – 8.8)) * 16 games = 10.2 wins]
Exhibit 1 shows the correlation between predicted wins and actual wins for all teams in Division I for the 2011 season. This simple equation has an r-squared of over .90. The challenge, as we will see later, is using these inputs to predict performance.
[Squaring the correlation, which can range from -1.0 to +1.0, and then multiplying by 100 yields R2% or what is often called “variance accounted for.” In other words, for the graph below, about 90% of the variation among teams in actual wins can be accounted for or explained by knowledge of predicted wins. Correlation doesn't by itself imply causation, but that doesn’t diminish its predictive utility.]
This analysis, while still at a very high level, shines a light on what is important. Player actions that contribute to scoring goals or preventing the other team from scoring goals are valuable. Scoring goals boils down to possessions and possession efficiency. Primary sources of possessions include face-offs won, ground balls, turnovers by the opponent, saves, and opponent violations. Possession efficiency can be evaluated through shots per possession, shooting percentage (the percentage of shots that are goals), turnovers, and shot analysis (analysis of the shots that don’t go in).
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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