Paul M. Sommers

Peter R. Smith

Russell K. Banker

English

Research Papers in Economics

 
 
HERE’S THE SCOOP: GROUND BALLS 
WIN LACROSSE GAMES 
 
by 
 
Paul M. Sommers 
Peter R. Smith 
And 
Russell K. Banker 
 
 
 
 
March  2010 
 
 
 
 
 
MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO. 10-10 
 
 
 
 
 
 
 
 
DEPARTMENT OF ECONOMICS 
MIDDLEBURY COLLEGE 
MIDDLEBURY, VERMONT 05753 
 
http://www.middlebury.edu/~econ 
 
 
 
 
 
                                                                                                                                             2 
 
 
 
 
 
 
HERE’S THE SCOOP: GROUND BALLS 
WIN LACROSSE GAMES 
 
 
 
by 
 
 
 
 
Peter R. Smith 
Russell K. Banker 
Paul M. Sommers 
 
 
 
 
 
 
 
 
Department of Economics 
Middlebury College 
Middlebury, Vermont 05753 
psommers@middlebury.edu                                                                                                                                             3 
 
 
 
HERE’S THE SCOOP: GROUND BALLS 
WIN LACROSSE GAMES 
 
 
 
  Lacrosse, a game popular with Native Americans long before Europeans first settled in 
North America,
1 has received scant attention from statisticians relative to other “stick-and-ball” 
games, like baseball and golf.  Easily quantifiable measures of performance abound in baseball 
(for examples, slugging average, on-base percentage, and earned run averages) and golf (for 
examples, distance of a player’s tee shot, greens in regulation – or the percentage of time that a 
player gets his ball onto the putting green within two shots of par, and the average number of 
putts per hole).  But, what about lacrosse?  In this brief note, we focus on one key statistic: 
ground balls.  In lacrosse, a “ground ball” is when the ball is scooped up off the ground.  When 
the ball is on the ground, however, neither team has possession.  And, since records are kept of 
the number of times in a game each team successfully scoops up a ground ball, we will determine 
whether or not “ground balls” are critical to team winning. 
  All colleges in the New England Small College Athletic Conference (hereafter NESCAC) 
play Division III lacrosse.  We examined the box scores of every men’s lacrosse game for all but 
one of the ten NESCAC schools from 2005 through 2009.
2  Over the five-year period, Wesleyan 
and Williams won one NESCAC title each (in 2009 and 2008, respectively).  Middlebury College 
won seven consecutive NESCAC championship games since the inception of the NESCAC 
Men’s Lacrosse Tournament in 2001.  Of the ten NESCAC schools examined here, Middlebury 
College had the best overall record since 2005 (69 wins and 19 losses for a .784 winning 
percentage) and Colby had the worst (26 – 44, .371). 
  To test the null hypothesis that ground balls won is not related to games won, we use a 
chi-square test.  All lacrosse games are either won or lost; there are no ties, with as many 
“sudden-death” overtime periods as are necessary to break ties at the end of regulation.  We                                                                                                                                             4 
 
excluded games where the number of ground balls for and against each team was the same.
3  All 
games for each NESCAC school are divided into four groups as shown, for example, by one 
NESCAC school, Middlebury College, in Table 1.  In 54 [9] games, Middlebury College 
recorded more [fewer] ground balls than her opponent (that is, “ground balls for” exceeded [was 
less than] “ground balls against”) and Middlebury College won [lost] the game.  The calculated 
chi-square (
2 χ ) statistic is 5.476.  The probability that the chi-square test statistic will be as large 
as this (or larger) is only .019.  The diagonal elements in the contingency table in Table 1 were 
much larger than would be expected if the null hypothesis were true.  That is, when Middlebury 
College scooped up more (fewer) ground balls than her opponent, more often than not 
Middlebury won (lost) the game.  The results for all of the other NESCAC schools are reported in 
Table 2.  And, in every case, the diagonal elements of the contingency table are 
disproportionately large.  Still, in other words, ground balls (for) are indeed key to success. 
  Table 3 shows the results of regressing (for each game at each NESCAC school over the 
five-year period, 2005-09) the margin of victory (that is, “goals for” minus “goals against”) 
against the percentage of ground balls won.  How well the regression line fits the scatter of points 
(as measured by the R
2 or the coefficient of determination) is best for Amherst and is shown in 
Figure 1.  In every case (that is, for all ten NESCAC schools), there is evidence of a strong direct 
relationship between the team’s margin of victory and the percentage of ground balls won.  One 
can use the regression results in Table 3 to find the percentage of ground balls won above which 
the winning margin is greater than or equal to “1” goal (as reported in the last column of Table 3). 
Three of the four schools with the best winning records over the five-year period 
[Middlebury, .784 winning percentage; Wesleyan, .766; and Tufts, .679] had minimum threshold 
percentages of ground balls won less than 50 percent of the time.  For these schools, while 
“ground balls for” is important, other facets of the game (collectively) might be even more 
important (for examples, goalie save percentage, extra-man opportunities, and man-down                                                                                                                                             5 
 
defense).  Curiously, the school with the worst winning record over the five-year period 
[Colby, .371] needed to win, on average, at least 58.4 percent of ground balls to win a game. 
 
Concluding Remarks 
 
  The evidence presented here for Division III schools in the NESCAC conference suggests 
that ground balls win games in men’s lacrosse.  Lacrosse involves numerous body and stick 
checks (as long as contact is from the front or side and above the knees but not above the 
shoulders and one’s opponent has possession of the ball or is within five yards of a loose ball).  
As a consequence, the ball is knocked loose from the pocket of a player’s stick and frequently 
ends up on the ground.  An errant pass or shot suffers a similar fate.  What we have found is that 
the team that wins the battle for ground balls more often than not wins the game.  After all, more 
ground balls scooped up leads to more possessions.  More possessions in turn lead to more 
scoring opportunities.  And, more possessions by one team decreases the opposing team’s time of 
possession and scoring chances.                                                                                                                                               6 
 
 
 
 
Table 1.  Contingency Table Relating 
Ground Balls Won and Games Won, 
Middlebury College, 2005-2009 
 
 
 
 ____________________________________________________ 
 
                                              Ground Balls Won? 
                                                                  ________________________________ 
 
                                                                              Yes                           No 
 ____________________________________________________ 
 
           Won Game? 
 
   Yes  54  14 
 
   No  10  9 
 
 ____________________________________________________ 
  
 
                                                   
 
 
 
 
                                                                                                                                             7 
 
 
 
 
Table 2.  Summary of Chi-Square Tests, 
Men’s Lacrosse in NESCAC, 
2005-2009 
 
 
 
        Won Game,  Won Game,  Lost Game,  Lost Game, 
      School  Won GBs  Lost GBs  Won GBs  Lost GBs 
2
Calc χ   p-value  
 
 
 
  Amherst 24 5 9 25  19.880  <.001 
 
 Bates  17  9  8  25  10.081  .001 
 
  Bowdoin  33 10 13 16 7.647  .006 
 
 Colby  21  2  17  24  15.174  <.001 
 
  Middlebury  54 14 10  9  5.476  .019 
 
 Trinity  30  3  13  23  22.017  <.001 
 
 Tufts  40  13  8  16  12.494  <.001 
 
 Wesleyan  51  21  1  21  29.957  <.001 
 
 Williams  21  9  5  23  15.921  <.001 
 
                                                                                                                                                  8 
 
 
 
Table 3.  Summary of Regression Results, 
Men’s Lacrosse in NESCAC, 
2005-2009 
 
 
 
       Dependent variable:      Winning margin (Goals for – Goals against) 
 
 
        Percentage of                                     Percentage of 
 School  Constant  ground  balls  won  R
2   ground  balls  won, 
         winning  margin  ≥ 1
              
 
 
 Amherst  -24.702  .482  .482  53.3 
   (<.001)
* (<.001)   
 
 Bates  -15.454  .313  .328  52.6 
   (<.001)  (<.001)   
 
 Bowdoin  -13.152  .262  .257  54.0 
   (<.001)  (<.001) 
 
 Colby  -22.770  .407  .358  58.4 
   (<.001)  (<.001) 
 
 Middlebury  -14.443  .326  .209  47.4 
   (<.001)  (<.001) 
 
 Trinity  -21.016  .404  .401  54.5 
   (<.001)  (<.001) 
 
 Tufts  -15.947  .341  .376  49.7 
   (<.001)  (<.001) 
 
 Wesleyan  -14.798  .352  .315  44.9 
   (<.001)  (<.001) 
 
 Williams  -11.644  .260  .282  48.6 
   (<.001)  (<.001) 
 
*Numbers in parentheses are p-values.                                                                                                                                             9 
 
 
 
   
Figure 1.  Margin of Victory v. Percentage of Ground Balls Won, 
Amherst College, 2005-2009 
 
 
Percent of Ground Balls Won_Amherst
M
a
r
g
i
n
 
o
f
 
V
i
c
t
o
r
y
_
A
m
h
e
r
s
t
70 65 60 55 50 45 40
15
10
5
0
-5
-10
S 4.03145
R-Sq 48.2%
R-Sq(adj) 47.3%
Fitted Line Plot
Margin_Amh =  - 24.70 + 0.4821 PercGBWon_Amh
 
                                                                                                                                             10 
 
 
References 
 
 
1. D.M.  Fisher,  Lacrosse: A History of the Game, Johns Hopkins University Press,  
  Baltimore, MD, 2002. 
 
2.  D.G. Pietramala and N.A. Grauer, Lacrosse: Technique and Tradition,  
  Johns Hopkins University Press, Baltimore, MD, 2006.                                                                                                                                             11 
 
 
Footnotes 
 
 
1.  For a brief history of the game of lacrosse, see, for examples, Fisher [1] and Pietramala 
  and Grauer [2]. 
 
2.  NESCAC schools include: Amherst, Bates, Bowdoin, Colby, Connecticut College,  
  Hamilton, Middlebury, Trinity (in Connecticut), Tufts, Wesleyan, and Williams. 
  The archive (at each school’s Web site) for all schools but Connecticut College reported 
  box scores for individual games from 2005 through 2009.  Hamilton College competes 
  in the Liberty League in men’s lacrosse. 
 
3.  Over the five-year period, we excluded: three ties each for Amherst and Tufts; two ties 
each for Bates, Trinity, and Williams; and one tie for Middlebury College.  In some  
  instances, the number of ground balls would be reported for the home team, but not  
  for its opponent.  And, in such cases, we checked the box score (for the same game) on 
  the opponent school’s athletics Web page.         
 

Here’s the Scoop: Ground Balls Win Lacrosse Games

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