Authors: Christiana E. Hilmer1

1Department of Economics, San Diego State University, San Diego, CA

Corresponding Author:

Christiana Hilmer, PhD
5500 Campanile Drive
San Diego, CA 92182-4485
[email protected]
619-301-9388

Christiana E. Hilmer, PhD, is a Professor of Economics at San Diego State University in San Diego, CA. Her research interests include the economics of sports, applied econometrics, labor economics, and resource and environmental economics.

An analysis of the factors impacting win percentage and change in win percentage in women’s Division 1 college lacrosse

ABSTRACT

What factors in women’s NCAA Division 1 college lacrosse led to an increase in win percentage in a single season and a change in win percentage across two consecutive seasons? Do these factors differ between teams at the top and the bottom ends of the win distributions? Using data from the 2023 and 2022 lacrosse seasons, we find that goals, assists, unassisted goals, and participation in the NCAA Championship tournament have a positive impact on win percentage, while opponent’s goals and if the team was new in 2023 have a negative impact on win percentage. The most crucial factor that explains the change in win percentage between the 2022 and 2023 lacrosse seasons is an improvement in the change in total shots ratio, while changes in attacking efficiency and defending efficiency are also important, all together explaining 58% of the variation. Teams at the bottom of the distributions have similar characteristics for both win percentage and change in win percentage as those teams in the middle and the top of the distributions, although there are some slight differences in the magnitudes of the statistically significant variables. These results suggest that lacrosse players and coaches should focus on obtaining additional goals and assists while concurrently minimizing the opponent’s goals to increase win percentage and changes in win percentage.

Keywords: distributional impacts, quantile regression, women’s college lacrosse

INTRODUCTION

Since the advent of sabermetrics pioneered by Bill James and the popularity of Lewis’s (5) Moneyball, the use of statistics to analyze sports has exploded in popularity. Reep and Benjamin (7) applied statistical analysis to team-wide factors in soccer where they investigated how the passing skill and position of a player on the field impacts goals. When analyzing a team’s performance, it is essential to determine which factors lead to a team’s success. Most research in this field has focused on professional sports. Busca et al. (1) examine eleven high-stakes international soccer tournaments to determine where a penalty kick is most likely to be struck. Pelechrinis and Winston (6) develop a framework that is comprised of publicly available data to determine the expected contribution of an individual professional soccer player to the probability of his team winning the game. Alberti et. al. (1) examine goal-scoring patterns in four different professional soccer leagues and find that the majority of goals are scored in the second half of the game with the most goals being scored in the last fifteen minutes of play. Castellano et. al. (3) analyze professional soccer match statistics to determine which factors impact winning, drawing, and losing a game and find that shots, shots on goal, and ball possession are important on the offensive end of the field, while total shots received and shots on target received are important on the defensive end of the field. A notable departure from research that focuses on professional soccer is Joslyn et al. (4), who examines the factors that improve the change in win percentage in men’s Division 1 (D1) college soccer. They find that improving shots, attacking, and defending positively impact the change in win percentage between two consecutive seasons.

This research utilizes the tools found in the team-focused literature from soccer and extends it to lacrosse. Soccer and lacrosse have many similarities, especially regarding possession, assists, goals, and defense. There are also marked differences between the two sports in addition to the obvious one: in soccer the ball is kicked while in lacrosse the ball is played with a net attached to a stick. Lacrosse is a higher-scoring game due to the presence of a 90-second shot clock and defending a women’s lacrosse player is more difficult in lacrosse than it is in soccer. One reason for this is that in lacrosse it is a foul to “move into the path of an opponent without giving the opponent a chance to stop or change direction, and causing contact” (page 51, 2022 and 2023 NCAA Women’s Lacrosse Rules Book (6)), while there is no such rule in soccer. Another reason is due to a rule in women’s lacrosse called shooting space (page 54, NCAA 2022 and 2023 Women’s Lacrosse Rules Book (6)), which states that “with any part of one’s body, guarding the goal outside or inside the goal circle so as to obstruct the free space to goal, between the ball and the goal circle, which denies the attack the opportunity to shoot safely and encourages shooting at a player” while soccer does not have a comparable rule. According to NCAA Statistics (7), the average number of goals per game scored in D1 women’s college lacrosse in 2023 was 12, while the average number of goals per game scored in D1 women’s college soccer in 2023 was 1.39. Another notable difference between lacrosse and soccer is that the offside rules are very different. The offsides rule in lacrosse states that there must be at least five defenders behind their defensive restraining line and at least four offensive players behind their offensive restraining line (page 61, NCAA 2022 and 2023 Women’s Lacrosse Rules Book (6)). The offsides rule in soccer is much less stringent and it states that when in the opponent’s half of the field “the player is not closer to the opponent’s end line than at least two opponents” (page 52, NCAA 2022 and 2023 Soccer Rules Book (7)). These disparities between lacrosse and soccer may result in differences in which factors impact win percentages and changes in win percentages.

This research examines which factors lead to an increase in win percentage and change in win percentage for women’s Division 1 college lacrosse teams. We also seek to determine if these factors differ among teams in the 25th, 50th, and 75th percentiles for win percentage and the change in win percentage. Using data from the 2023 women’s D1 college lacrosse season, we explain 86% of the variation in win percentage. Goals, unassisted goals, and participation in the NCAA Championship tournament have a statistically significant positive impact on win percentage, while opponent’s goals and if the team was new in 2023 have a statistically significant negative impact on win percentage. The most crucial factor explaining the change in win percentage between the 2022 and 2023 lacrosse seasons is an improvement in the change in total shots ratio, while changes in attacking efficiency and defending efficiency are also statistically significant, all together explaining 58% of the variation. The variables that explain both win percentage in a single season and the change in win percentage between seasons are similar between the 25th, 50th, and 75th percentiles. This suggests that teams at the bottom of the distributions should focus on the same factors as those at the top when they seek to improve during a season and between seasons.

METHODS

Data Source
Win percentage was collected from the National Collegiate Athletic Association (NCAA) archives for the 2023 and 2022 seasons. A win was awarded one point while a loss was awarded zero points. Offensive and defensive statistics for the 2023 and 2022 seasons were collected from each University’s women’s lacrosse website housed in the season’s cumulative statistics. It is important to note that these data are provided by individual institutions and therefore the statistical findings of this research is dependent on the accuracy of the information provided by each school. In addition to winning percentage, data was collected on goals, assists, shots, opponent’s goals, opponent’s shots, unassisted goals, ground balls, turnovers, caused turnovers, draw controls, whether the team was new to NCAA D1 lacrosse in the 2023 season, and if the team made the NCAA Championship tournament in 2023. Of the 126 D1 women’s lacrosse teams, 123 had information on every variable listed above.

Variables and Distributions

This analysis aims to determine what factors impact a single season winning percentage and which factors impact the change in win percentage across two consecutive seasons. Figure 1 is a histogram of win percentage for the 2023 women’s lacrosse season. The average win percentage was close to 50% at 48.27%; the minimum win percentage was 0 for the two teams that lost every game during the season, while the maximum win percentage was from a team that won 95.65% of their games. The team with the second-highest win percentage won the 2023 NCAA National Championship tournament.


Summary statistics for the 2023 D1 women’s lacrosse 2023 season are found in table 1. The average number of goals and opponent’s goals nearly offset each other at 211 and 210, respectively. There was an average of 495 shots with a large standard deviation of 105. Below half the goals were aided by an average of 92 assists, while over half of the goals resulted from an average of 119 unassisted goals. There were nearly twice as many turnovers as there were caused turnovers, 7% or a total of 8 teams were new D1 lacrosse teams in 2023, and 24% of the D1 lacrosse teams made the NCAA end-of-season tournament.


Figure 2 contains a histogram of win percentage change, which is constructed by taking the win percentage in the 2023 lacrosse season and subtracting the win percentage in the 2022 lacrosse season. There are fewer observations in the change in win percentage because the seven teams who were new in the 2023 season did not have any statistics for the 2022 season. On average, most teams had a similar win percentage in 2023 as they did in 2022, with an average change in the win percentage of .16. The team with the lowest change in win percentage between the two seasons of -51.47 had a win percentage of 75% in 2022, dropping to 24% in 2023. At the other end of the spectrum, the team with the highest change in win percentage won 12% of their games in 2022 and improved to winning 50% of their games in 2023.

Following Joyce et al. (4), we construct three measures of team success to explain the change in winning percentage: total shots ratio, attaching scoring efficiency, and defending scoring efficiency. The first measure, total shots ratio, is constructed as

The total shots ratio in both 2022 and 2023 is .5, which means, on average, teams are matching their opponent’s shots with their own shots with a range in values from .23 to .7 in 2023 and .3 to .63 in 2022.  This finding for lacrosse compares favorably to what Joyce et al. (4) found for D1 college soccer, where the total shots ratio ranged from .24 to .69 in D1 men’s soccer.

            The second measure of team success is attacking scoring efficiently or goals to shots ratio.

The average attaching scoring efficiency for 2023 and 2022 was .42. This measure had a relatively smaller variability than the total shots ratio, with a minimum of around .3 for both years and a maximum of .5 in 2023 to .58 in 2023. This maximum means that the teams with the highest attacking scoring efficiency earn an average of one goal for every two shots. Being able to convert shots into goals is an essential aspect of winning games. Lacrosse teams are much more likely to convert shots into goals, as Joyce et al. (4) found an average attacking scoring efficiency of .1 or 1 goal for every ten shots in D1 men’s soccer.

The third measure of team success is the defending scoring efficiency, which is contracted as

This final measure determines if teams can prevent opponents from turning shots into goals. The average values for defending scoring efficiency are slightly higher than attaching scoring efficiency, with an average of .43 in 2023 and .44 in 2022. The variability is higher for defending scoring efficiency than attacking scoring efficiency, with a minimum of .31 in 2023 and .34 in 2022 and a maximum of .66 in 2023 and .77 in 2022. Teams that are better at preventing shots from being converted into goals typically have a higher win percentage.

Regression Model
The first step in our regression analysis is to empirically estimate the degree to which offensive and defensive statistics impact the win percentage for the 2023 lacrosse season. The win percentage regression model takes the form:

where  is the error term and i is the individual women’s lacrosse team.  This model is estimated using ordinary least squares to obtain the average marginal impact of each of the 11 variables, as well as using quantile regression at the 50th, 25th, and the 75th percentiles of the win percentage.  Quantile regression is a statistical method that estimates the association between the explanatory variables for a conditional quantile of the dependent variable, see Walmann (8) for a more detailed explanation.  In this application, we use quantile regression to determine if teams at the lower end of the win percentage distributions display different characteristics than those at the median and the top end of the distributions.

            The second part of the analysis follows Joyce et. al. (4) to determine what factors impact the change in win percentage between the 2023 and 2022 lacrosse seasons.  The regression model is as follows

where ε_i is the error term and i is the individual women’s lacrosse team. As with the individual season analysis, this model is estimated using ordinary linear regression and quantile regression at the 50th, 25th, and 75th percentiles.

RESULTS

Table 3 contains the results for the estimation of equation (4) from the 2023 lacrosse season with robust standard errors in parentheses. Looking first at the results from the ordinary least squares model, 86% of the variation in win percentage is explained by the 11 independent variables. Turning to the variables that are statistically significant, each additional goal results in an increase of .18 in win percentage, while each opponent’s goal results in a decrease of .2 in win percentage, with goals and opponent’s goals nearly offsetting each other. On average, one additional unassisted goal results in an increase of .13 in win percentage. Being a new D1 women’s lacrosse team in 2023 results in a 9 point marginally statistically significant decrease in win percentage relative to teams that have been in the league in previous years. This result suggests that new D1 teams have a difficult time navigating their first year likely due to players and coaches lacking experience and chemistry, making obtaining wins more difficult. Women’s lacrosse teams who participated in the 2023 NCAA Championship Tournament have a statistically significant almost 5 point higher win percentage than those who did not participate in the tournament. This finding is not surprising given that the two ways to get a team into the tournament are to either receive an automatic bid by winning their conference tournament or earn an at-large bid by having a compelling enough record during the regular season and conference playoffs.


The last three columns of table 3 contain quantile regression results at the 50th, 25th, and 75th percentiles of the win percentage distribution. Opponent’s goals are the only statistically significant factor to explain wins across all three percentiles. The magnitude of opponent’s goals is largest at the 25th percentile at -.24 and is -.20 for both the 50th and 75th percentile. Teams at the 25th and 50th percentiles of the win percentage distribution that participates in the NCAA end-of-season tournament has a statistically significant 7 point and 6 point higher win percentage, respectively, relative to those who did not participate, while this variable is not statistically significant at the 75th percentile. This may be because most, 73%, of the tournament participants come from the teams at the top 25% of the win percentage distribution, while most teams at the middle and bottom of the distribution did not participate in the tournament. Aside from this difference, the results are similar between the models at the three points in the win percentage distribution.

Table 4 contains the second part of the regression analysis which estimates equation (5) that attempts to determine what factors impact the change in win percentage between the 2023 and 2022 seasons. The variables contained in this analysis mimic those in Joyce et. al. (4) for men’s D1 college soccer. Looking at the OLS results, teams that had a one unit increase in the change in total shots ratio between the two seasons had a 2.4 increase in the change in win percentage. Teams with a 1 unit increase in the change in attacking efficiency had a 1 unit increase in the change in win percentage, and teams with a one unit increase in the change in defending efficiency decreased the change in win percentage by 1.2 points. The statistical significance between these lacrosse results and those found for soccer by Joslyn et al. (4) are identical, suggesting that even though there are many differences between the two sports, the same factors are important in explaining the change in win percentage between consecutive years. Comparing magnitudes between the two applications is not possible because the estimation methods differed. The statistical significance of the variables included in the quantile regression evaluated at the 50th, 25th, and 75th percentiles were the same as in the OLS regression. The quantile regression performed at the 25th percentile of the change in win percentage had the highest impact for the change in total shots ratio and the change in attacking efficiency, while the change in defending efficiency had the smallest impact. The change in total shots ratio and the change in attacking efficiency had the smallest impact for those teams at the 75th percentile, while the change in defending efficiency had the largest impact for those teams at the 50th percentile. These results suggest that the factors that impact the change in win percentage are similar across teams at the bottom and the top of the change in win percentage distribution, although the marginal impacts differed slightly between the percentiles.

Discussion

It is not surprising that additional goals led to an increase in win percentage and an increase in opponent’s goals led to a decrease in win percentage. However, it was unanticipated that many of the other offensive and defensive statistics included in the regression were not statistically significant. It is likely that these other factors either lead to the team’s ability to score goals, such as shots, ground balls, and caused turnovers, or lead to the opponent’s goals, such as turnovers. One drawback of this research is that it does not investigate how these other factors impact goals and opponent’s goals. One adage in lacrosse is “win the draw, win the game.” Even though draw controls are not statistically significant in explaining win percentage, there was no information contained in the box scores on how many goals were obtained when the team won the draw control or how many goals were conceded when the team lost the draw control. More detailed information would be needed to investigate this relationship further. Other factors that likely explain win percentage and changes in win percentage such as team chemistry, the presence of a star player, the experience of the players and the coaches, and how different game management strategies, such as the usage of substitutes and quickness of play, are not included because they are difficult to measure, not included in the box scores, or both.

For a lacrosse coach or lacrosse player who is looking to improve win percentage between seasons, it is comforting to note that focusing on improving the changes in total shots ratio, attacking scoring efficiency, and becoming better at defending by decreasing the opponent’s goal-to-shot ratio will lead to an increase in the change in win percentage. One major drawback of this research is that it does not point to the factors that cause improvements in these variables and how they feed into additional goals or fewer conceded goals.

CONCLUSIONS

This study is the first to analyze which factors impact win percentage and changes in win percentage for NCAA D1 women’s lacrosse. The regression results suggest that goals, unassisted goals, and those who competed in the NCAA tournament had a positive impact on win percentage, while opponent’s goals and teams that were new in 2023 had a negative impact on win percentage. These factors were similar across the distribution of win percentage at the 25th, 50th, and 75th percentiles. Changes in win percentage between the 2023 and 2022 seasons are positively impacted by the change in the total shots ratio and attacking scoring efficiency and negatively impacted by the change in defending scoring efficiency. Even though there are many differences between lacrosse and soccer, the findings of this research and those of Joyce et. al. (4) that focus on college soccer suggest that the factors that explain changes in win percentage are similar between the two sports. These results also suggest that the statistics that explain win percentage and change in win percentage are similar between teams at the bottom, at the middle, and at the top of the distributions.

Applications In Sport

Women’s lacrosse programs at the collegiate level as well as at the national level can use these results to determine which factors to focus on when attempting to improve their win percentage within a specific year or over the course of several years. This research suggests that teams should emphasize their efforts in practice and in games on factors that increase goals as well as those factors that prevent goals. The lack of empirical analysis at the collegiate level, especially for women’s sports, can be rectified using available data. Additional publicly available information would make individual game analysis more informative such as how winning a draw control impacts goals as well as how focusing on specific factors such as caused turnovers or increasing assists increases goals and therefore positively impacts a team’s chances of winning.

REFERENCES

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