Is Bigger Better? An Examination of the Effects of Size on Performance and
Compensation of NHL Goaltenders
James Pantano
Advisor: Professor Baumann
December 8, 2012
Abstract: Following the 2004-2005 NHL lockout, rule changes limited the size
of goaltending equipment. Despite these rule changes, the average save
percentage and goals against average of NHL goaltenders continued to
improve. The past decade has also seen a rise in the average height of both
drafted and current NHL goaltenders. This paper investigates the effect of size
on salary and on-ice performance of NHL goaltenders in order to test whether
larger goaltenders have been substituted for smaller blocking surfaces. My
estimations suggest that size positively affects on-ice performance in the
post-lockout period, and that larger goaltenders are paid premiums for their
size in the post-lockout period.
1
I. Introduction
In place of the 2004-2005 National Hockey League (NHL) season, a lockout
occurred because of disputes between the NHL and the NHL Players Association.
After the lockout ended and prior to the 2005-2006 season, various rule changes
were implemented to increase the pace and offensive aspects of the game. To create
higher scoring games, the NHL focused on goaltenders, who in the seasons leading
up to the lockout were performing more effectively than ever before in terms of
both average save percentage and goals against. In an attempt to hinder the upward
trend in goaltending performance, the NHL reduced the size and shape of nearly
every piece of goaltending equipment, including gloves, blockers, sticks, chest
protectors, pants, and most notably, leg pads, which were shrunk in width from 12
inches to 11 inches. Although goaltenders are noticeably less bulky since the 20032004 season, the average save percentage and goals against average of goaltenders
continued to improve after the lockout.1
Needless to say, the NHL came up short in its attempts to limit goaltending
performance, even though the post-lockout rule changes took away some of a
goaltender’s ability to stop the puck by reducing the blocking surface of his
equipment. These counterintuitive results raise the question: how have NHL
goaltenders overcome, and conquered, the handicap incurred by the post-lockout
rule changes?
Goaltenders in the NHL have not only experienced an increase in save
percentage, but in height as well. From the 2000-2001 season to the 2011-2012
season, the average height of goaltenders seeing 1,000 minutes or more playing
1
See Figures 1 and 2 in the Appendix.
2
time per season increased from 72.69 inches to 73.73 inches, with standard
deviations of 1.99 inches and 1.42 inches, respectively. These numbers suggest that
goaltenders have not only grown in past seasons, but also that they seem to be
converging around a higher average height. In terms the relationship between
height and save percentage, goaltenders in the bottom 10th percentile in terms of
height (71 inches and below) had an average save percentage of 90.3%, while
goaltenders in the top 10th percentile of height (75 inches and above) had an
average save percentage of 90.9%. Given this height increase from season to season,
and the seemingly higher save percentage of taller goaltenders compared to their
shorter counterparts, does the size of a goaltender affect his on-ice performance
after holding all other factors constant?
I hypothesize the size of a goaltender affects his on ice performance in a
positive way. Because of this reasoning, I also hypothesize that the size of a
goaltender positively affects his annual salary, but it is unclear whether this size
premium will remain after accounting for performance. General managers in the
NHL appear to have noticed the relationship between height and on ice performance
as well, given the increase in the average height of drafted goaltenders from
approximately 72.5 inches in the 2000 entry draft, to 74.5 inches in the 2011 entry
draft. Based on this trend, I identify whether NHL teams are efficient in their move
toward bigger goaltenders by investigating the how the size of a goaltender affects
his on-ice performance and annual salary.
I find some evidence that height has a positive effect on save percentage. I
also find that above and beyond on ice performance, there is some evidence that
3
height has a positive effect on player salary as well. Finally, I also find that height’s
impact on both save percentage and salary is insignificant in the pre-lockout period,
and significant the post lockout period, which suggests that NHL teams have
substituted taller goalies for smaller pads.
II. Literature Review
The existent literature on this topic is in short supply. However, some related
studies offer a few different approaches for my research. Miller (2008) investigates
how the post-lockout rule changes affected productivity for larger players,
measured in points per hour. Miller (2008) uses data from NHL.com for player
statistics from the 2003-2004 and 2005-2006 NHL seasons, and HockeyDB.com for
coaching statistics like games coached and winning percentage. Miller (2008)
excludes players who do not meet the “rookie criterion” by removing players
without a minimum of 25 games played from the data set in order to reduce outliers
in the data. He uses a linear regression for each season, where points per hour is the
dependent variable. The independent variables include height, position (forward or
defenseman), coaching experience, coach’s winning percentage, and team winning
percentage. He finds that height (measured in inches) has a significant effect in both
seasons, with coefficients of .41 and .38 for the 03-04 and 05-06 seasons,
respectively. Despite the small decrease in height’s influence on points per hour,
Miller concludes that taller players are not hindered by the new rules in terms of
their individual productivity, rejecting his hypothesis that height’s influence on
productivity had lessened post-lockout.
4
Berri and Brook (2010) investigates the efficiency of the labor market for
goaltenders in the NHL. In order to investigate the labor market for goaltenders,
Berri and Brook run two regressions, one using the TOBIT model with Vezina votes
(the award given to the best goaltender in the NHL each season based on votes by
each team’s general manager) as the dependent variable, and the other with salary
as the dependent variable. The independent variables for the Vezina regression
include save percentage, goals against average, age, and minutes played. The
independent variables for the salary regression include save percentage, last
season’s save percentage, minutes played, minutes played last season, and age. The
salary regression uses a log linear ordinary least squares model with a sample of
goaltenders that were free agents in the period between the 2002-2003 and 20062007 seasons to avoid long-term contracts. They find age, minutes, and save
percentage to have positive and significant effects on Vezina votes, and save
percentage, last season’s save percentage, minutes played, minutes played last
season, and age to have positive and significant effects on salary. Berri and Brook
(2010) find that NHL general managers correctly identify save percentage, goals
against average, and wins as significant performance measures, but they also find
that there is a large variation in pay with respect to a low variation in performance,
leading them to question general managers who pay more than the minimum salary
for a goaltender. Berri and Brook (2010) provides a solid foundation in the
methodology of researching the goaltending position, particularly in the choice of
dependent, and independent variables.
5
Berri et al. (2005) looks at the competitive balance between both players and
teams in professional sports. They note that “fan attendance in baseball is
maximized when the probability of the home team winning is approximately 0.6”,
and that when the probability of winning exceeds 0.6, attendance begins to decline.2
With the idea of maximizing team revenue in mind, Berri et al. (2005) focus on the
National Basketball Association (NBA), which is found to have the highest level of
competitive imbalance. The authors calculate competitive balance by dividing the
actual standard deviation of team winning percentage by the ideal standard
deviation of team winning percentage, which is derived from the ideal winning
percentage of 60%. They hypothesize that the high level of competitive imbalance in
the NBA comes from the varying height of the players. They argue that within a
sport, there is initially a great difference in skill across the player population, which
declines as time goes on and more players reach their “biomechanical limits”. In
basketball, however, it is more difficult for players to reach their “biomechanical
limits” because unlike in other sports where “training can overcome natural
deficiencies in natural ability, speed, agility, and even weight”3, players cannot train
themselves to be taller. This idea of biomechanical limits could possibly help to
explain the trend of NHL teams acquiring larger goaltenders. If the effect of
goaltender height is the same pre- and post-lockout, the idea of biomechanical
limits, and not simply the reduction in equipment size, could be responsible for the
growth of NHL goaltenders.
III. Data
2
3
Journal of Economic Issues, Vol. XXXIX No. 4, pp 1030.
Journal of Economic Issues, Vol. XXXIX No. 4, pp 1034.
6
Performance measures and other on-ice statistics are extremely important in
testing the role of height in the goaltending position. NHL.com has up to date
performance statistics for all of the players examined in this study, as well as their
physical characteristics like height, weight, nationality, and amateur league. These
data are publically available.
Given that this study revolves around a popular professional sports league,
most salary data are easily accessible, particularly because of the close attention
paid to each teams adherence to the NHL’s salary cap. The salary data for this study
are from USA Today’s website, which has salary data on the major professional
sports leagues in the United States. USA Today has salary data on NHL players from
the 2000-2001 seasons through the current season.
Just as in Berri and Brook (2010), the data set is limited to goaltenders
playing 1,000 minutes or more in each respective season. Goaltenders below 1,000
minutes of playing time are omitted in order to eliminate outliers within the data set
caused by things like luck or “one game wonders”. This control allows for a much
more accurate examination of starting goaltenders or goaltenders who split time but
still play a substantial amount of minutes.
The summary statistics in Table 1 offer a glance at the average NHL
goaltender of the past 11 seasons. The average goaltender in the data is 29.14 years
old, stands 6’1.7” tall, weighs 195.63 pounds, has a save percentage of .908, goals
against average of 2.64, 2,638.07 minutes played per season, wins 21.6 games per
season, and has a salary of $2,368,158. The three Major Junior Canadian leagues
account for over half of the goaltenders in the sample, with the Quebec Major Junior
7
Hockey League (QMJHL), Ontario Hockey League (OHL), and Western Hockey
League (WHL), contributing 23%, 15.7%, and 11.9% respectively. It is also
interesting to note that the two predominant nationalities of goaltenders are
American and Canadian, representing 15.2% and 49.1% of the goaltenders in the
data set respectively.
IV. Methods
In order to evaluate the impact of height on the success of an NHL goaltender,
Berri and Brook (2010) offer a good starting point. Measuring performance can be
difficult with goaltenders given the interconnectedness of statistics like save
percentage, goals against average, and wins. It makes sense that as goaltender’s save
percentage rises, his goals against average falls and wins increases. To avoid this
collinearity, Berri and Brook (2010) run separate regressions, one for each
performance variable. The methods used in Miller (2008) can be applied directly to
the methods used in Berri and Brook (2010) test pre- and post-lockout effects on
NHL goaltenders.
I test the three performance variables used by Berri and Brook (2010) to
isolate the impact of height on save percentage, goals against average, and wins. I
stray away from their use of Vezina votes as a measure of on-ice performance
because only the top goaltenders receive votes for this award. There is also a degree
of randomness in single season success, as a goaltender could have one stellar
season and receive a great deal of Vezina votes in a career of otherwise below
average play. Because only a small percentage of goaltenders receive Vezina votes,
goaltenders like Tim Thomas of the Boston Bruins (who at 5’11” and 3 inches below
8
the average height of his peers has won the Vezina Trophy twice in the past 4 years),
can skew the results of a test based on the Vezina Trophy, thus misrepresenting the
population of NHL goaltenders as a whole. I use each of the performance variables
as the dependent variable in their own respective regressions. I use height, weight,
age, nationality, and amateur league as the independent variables for these
regressions, any of which could have a possible impact on performance. I also use
log-linear regressions for each performance variable, based on higher r-squared
results compared to the linear model. I also use White Standard Errors to correct for
heteroskedasticity.
The first model gives a general idea of how size effects on ice performance
over the entire sample of seasons 2000/2001 to 2011/2012.
ln(Perfi) = ß0 + ß1 heighti + ß2 weighti + ß4 age + ß5 age squared + ß6 nationality + ß7
amatuer leaguei + ei
Next, I identify any change in the effect of size from the pre-lockout period to
the post-lockout period by running the same regression for each of the performance
variables in the pre- and post-lockout periods.
Pre-lockout (seasons 2000/2001 to 2003/2004):
ln(Perfi) = ß0 + ß1 heighti + ß2 weighti + ß4 age + ß5 age squared + ß6 nationality + ß7
amatuer leaguei + ei
9
Post-lockout (seasons 2005/2006 to 2011/2012)
ln(Perfi) = ß0 + ß1 heighti + ß2 weighti + ß4 age + ß5 age squared + ß6 nationality + ß7
amatuer leaguei + ei
I test the impact of size on salary using similar methodology. I begin with a
log-linear salary regression for seasons 2000-2001 through 2011-2012. A salary
regression is run for each of the performance variables (save percentage, goals
against average, and wins), where the respective performance variable is an
independent variable. I use the performance variable from the prior season to
estimate the salary of the current season.
ln(Salaryi) = ß0 + ß1 Lagged Perfi + ß2 heighti + ß3 weighti + ß4 agei + ß5 age squaredi +
ß6 nationalityi + ß7 amatuer leaguei + ei
These regressions estimate the effect of size on salary over the entire sample
of seasons. Similar to the strategy used above, I estimate pre-and post-lockout salary
regressions as well. These estimations identify any changes in the effect of size on
compensation from the pre- to post-lockout periods.
Pre-lockout (seasons 2000/2001 to 2003/2004):
ln(Salaryi) = ß0 + ß1 Lagged Perfi + ß2 heighti + ß3 weighti + ß4 agei + ß5 age squaredi +
ß6 nationalityi + ß7 amatuer leaguei + ei
10
Post-lockout (seasons 2005/2006 to 2011/2012)
ln(Salaryi) = ß0 + ß1 Lagged Perfi + ß2 heighti + ß3 weighti + ß4 agei + ß5 age squaredi +
ß6 nationalityi + ß7 amatuer leaguei + ei
V. Results
Table 2 shows the results of the first regression, in which save percentage,
goals against average, and wins are used as dependent variables across the entire 11
season sample. Height has a positive coefficient for each of the performance
variables. However, it is only statistically significant in the save percentage
regression, where its coefficient is .000821. When applied to the average goaltender
in the sample, this coefficient translates to an increase in save percentage from .908
to about .912 for a five inch increase in height. Despite its statistical insignificance, it
is also important to note that height’s positive coefficient in the goals against
average regression translates to an increase in goals against average for an increase
in height, which is obviously unfavorable.
The contradictory effects of height on on-ice performance are resolved in the
following test, where a regression is run for each performance variable for the
period before and after the lockout as seen in Table 3. Here, the coefficients on
height are positive in the save percentage regressions, and negative in the goals
against regressions. The most important result of these regressions comes in the
comparison of the save percentage regressions pre- and post-lockout. In the prelockout period, height has a positive, insignificant impact on save percentage. In the
post-lockout period, however, the coefficient on height is .001622 and statistically
significant at the 5% level. The magnitude of the post-lockout coefficient is nearly
11
double its counterparts in both the pooled season regression and the pre-lockout
regressions. When interpreted, a five inch increase in height is estimated to increase
the save percentage of the average goaltender from .908 to .915. The results of this
regression provide some evidence that the role of height in goaltending
performance is a post-lockout phenomenon.
Table 4 shows the results of the salary regression for the entire 11 season
sample. All performance variables are significant at the 1% level, reinforcing the
idea that compensation of NHL goaltenders is strongly tied to how well they
perform on the ice. Save percentage has a coefficient of 15.05, meaning that a one
percentage point increase in save percentage is estimated to raise next year’s salary
by 15.05%. In other words, the average goaltender in the sample is predicted to gain
$356,351.89 in salary for every one percentage point increase in save percentage.
Similarly, a reduction in goals against average by .1 goals is predicted to increase
next year’s salary by 3.56%, or $84,188.02 for the average goaltender. For an
increase of one win, next years salary is predicted to increase by 4.02%, or
$95,436.77. Needless to say, small changes in on-ice performance have heavy
impacts on compensation, but what about height?
Table 4 also shows that the model predicts an average increase of about 5%
in salary for each additional inch of height across the three performance
regressions. These coefficients are statistically significant at the 5% level in both the
goals against average and the wins regressions. Using the goals against average
regression as an example, a one inch increase in height is predicted to increase
salary by 6.111%, or $144,718.13. It is important to note that performance controls
12
are included in the salary regressions, which suggests that apart from height’s effect
on on-ice performance, taller goaltenders are predicted to be paid a premium purely
for their height advantage.
The results in Table 5 solidify the importance of the three performance
variables in determining salary, as well as providing further evidence that
goaltender’s pay may change simply based on height. In the pre- and post-lockout
salary regressions, each of the performance variables experiences an increase in the
magnitude of its coefficient in the post-lockout period, suggesting that on-ice
performance has a greater impact on salary after the lockout than compared to
before. Save percentage experiences the biggest increase in its coefficient, growing
from .127 to .164 in the post-lockout period.4 Height also experiences growth in its
coefficient from the pre- to post-lockout periods, suggesting a rise in the impact of
height in determining salary. Height is significant in the post-lockout salary
regression even though the wins performance variable is used. Its coefficient is
.0558 and predicts that a one inch increase in height will increase salary by 5.58%
or $1,32143.22 for the average goaltender in the sample.
It should be said that weight has an inconsistent impact on both performance
and salary regressions and is largely insignificant. Age has an overall positive impact
on both performance and salary, and is significant in most regressions. The results
for both nationality and amateur league dummy variables are inconsistent
throughout the tests, and are furthermore difficult to interpret given the large
number of nationalities and amateur leagues in the data.
Coefficients are divided by 100 because save percentage is measured in decimals
and not percents.
4
13
VI. Conclusion
From the results of both the performance and salary regressions, I find
evidence that the size of a goaltender positively affects both his on-ice performance
and compensation. With that being said, it appears as though height had a greater
impact on both the dependent variables in the post-lockout period. Because the
coefficients on height both increase in magnitude and statistical significance in the
post-lockout period, I find that there is evidence that smaller goaltenders are being
substituted for bigger ones in the NHL, due in part to a bigger goaltender’s ability to
make up for the reduction in equipment size post-lockout.
More specifically, I find evidence that height has a positive and significant
impact on save percentage in the post-lockout period. This finding provides support
for the tendency of NHL general managers to gravitate toward taller goaltenders in
both the entry draft and composing the roster their teams, as they have accurately
identified that taller goaltenders tend to stop more pucks and give their teams a
better chance to win than their shorter counterparts, holding all else constant.
I also find evidence of an inefficiency in the market for NHL goaltenders.
There is weak evidence that beyond a goaltender’s on-ice performance, premiums
are paid to taller goaltenders simply because of their size. This idea is particularly
interesting because it allows for a possible exploitation of the inefficiency. While
NHL general managers correctly expect taller goaltenders to perform better on the
ice, my estimates find that they are overpaying for height. This inefficiency begins in
the entry draft, where future potential, rather than current skill, is heavily
emphasized. NHL general managers should recognize that height’s positive impact
14
on performance, but should not pay the taller goaltender more money for the same
on-ice performance. If NHL general mangers can identify this inefficiency, they could
obtain shorter, high caliber goaltenders for a cheaper price. Identifying this
inefficiency is especially important given salary cap restrictions, where paying one
player more money means paying another player less.
Appendix
Figure 1: average save percentage per season
15
Figure 2: average goals against average per season
Table 1: Summary Statistics
Salary
Mean
2,368,158
Standard Deviation
2,045,068
Minimum
350,000
Maximum
10,000,000
16
Save Percentage
Goals Against Average
Wins
Height
Weight
Age
Minutes Played
Nationality
USA
Canada
Russia
Sweden
Finland
Czech Republic
France
Latvia
Switzerland
Slovakia
South Africa
Kazakhstan
Amateur League
QMJHL
OHL
WHL
USNTDP
USHL
SWEDEN
RUSSIA
SWISS
FINLAND
OPJHL
HIGH-USA
FRANCE
CZECH
MJHL
OJHL
NAHL
CZREP
CIS
.908
2.639
21.595
73.1657
195.632
29.142
2638.071
.012
.400
10.766
1.727
15.685
4.445
1023.563
.860
1.56
2
67
161
19
1003
.94
3.98
48
78
235
43
4697
.152
.491
.038
.058
.094
.061
.012
.012
.031
.017
.013
.019
.359
.500
.192
.233
.292
.240
.107
.107
.172
.130
.115
.137
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
.230
.157
.119
.019
.027
.058
.038
.031
.083
.035
.040
.012
.025
.011
.025
.013
0.23
.050
.421
.365
.324
.137
.162
.233
.192
.172
.275
.182
.197
.107
.156
.107
.156
.115
.421
.312
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Table 2: Performance Regression (all seasons 2000-2011)
17
Height
Weight
Age
Age Squared
R-squared
Ln(svper)
.000821***
(.000468)
.0000193
(.0000448)
.00202
(.00157)
-.0000352
(.0000259)
.1031
Ln(gaa)
.00616
(.00545)
-0.000863
(.000549)
-.0388**
(.0180)
.000659**
(.000299)
.118
Ln(w)
.000409
(.0221)
.00189
(.002055)
.136***
(.0734)
-.002165***
(.00119)
.136
* Statistically significant at the 1% level.
** Statistically significant at the 5% level.
*** Statistically significant at the 10% level.
Table 3: Performance Regressions (Pre- and Post-lockout)
Height
Weight
Age
Age Squared
R-squared
Ln(svper)
Pre-2004
.000742
(.000801)
-.0000079
(.0000652)
.00247
(.003458)
-.000334
(.0000581)
.255
Ln(svper)
Post-2004
.00162**
(.000758)
.00000489
(.0000654)
.00202
(.00210)
-.0000347
(.0000348)
.173
Ln(gaa)
Pre-2004
-.00510
(.00978)
.000327
(.000809)
.120*
(.0387)
.00185*
(.000655)
.335
Ln(gaa)
Post-2004
-.00207
(.00805)
-.00109
(.000753)
-.0344
(.02315)
.000565
(.000387)
.157
Ln(w)
Pre-2004
.0565
(.0416)
-.00482
(.00335)
.598*
(.159)
-.00951*
(.00273)
.328
Ln(w)
Post-2004
-.0497
(.0311)
.00423
(.00298)
-.0138
(.0815)
-.0000545
(.00132)
.138
* Statistically significant at the 1% level.
** Statistically significant at the 5% level.
*** Statistically significant at the 10% level.
Table 4: Salary Regressions (all seasons 2000-2011)
Save Percentage
Ln(salary)
15.0476*
Ln(salary)
Ln(salary)
18
(lagged)
Goals Against Average
(Lagged)
Wins
(Lagged)
Height
Weight
Age
Age Squared
R-squared
(3.299)
-.356*
(.0937)
.0424
(.0259)
.00221
(.00254)
.420*
(.0911)
-.00600*
(.001478)
.396
.0611**
(.0266)
.00136
(.00255)
.399*
(.0912)
-.00565*
(.00148)
.382
.0403*
(.00260)
.0460**
(.0223)
.000579
(.00218)
.354*
(.0771)
-.00509*
(.00127)
.594
* Statistically significant at the 1% level.
** Statistically significant at the 5% level.
*** Statistically significant at the 10% level.
Table 5: Salary Regressions (Pre- and Post-lockout)
Save
Percentage
(Lagged)
Goals Against
Average
(Lagged)
Wins
(Lagged)
Height
Weight
Age
Age Squared
R-squared
Ln(salary)
Pre-2004
12.655**
(5.602)
.0217
(.0371)
-.00102
(.00472)
.283
(.233)
-.00266
(.00385)
.695
Ln(salary)
Post-2004
16.431*
(4.137)
.0341
(.0401)
.00124
(.00340)
.220**
(.10688)
-.00307***
(.00173)
.381
Ln(salary)
Pre-2004
Ln(salary)
Post-2004
-.384**
(.183)
-.416*
(.110)
.0285
(.0396)
-.00106
(.00486)
.136
(.218)
-.000262
(.00356)
.692
.0534
(.0408)
.000192
(.00345)
.208**
(.10575)
-.00293***
(.00171)
.371
Ln(salary)
Pre-2004
.0341*
(.00619)
-.00281
(.0398)
.001825
(.00422)
-.0967
(.1735)
.00322
(.00289)
.768
* Statistically significant at the 1% level.
** Statistically significant at the 5% level.
*** Statistically significant at the 10% level.
Works Cited
Miller, Gregory J. 2008. Does Player Size Affect Productivity in the ‘New NHL’?.
West Chester University, West Chester, PA.
19
Ln(salary)
Post-2004
.0405*
(.00336)
.0558***
(.0313)
-.00187
(.00284)
.239**
(.0920)
-.00338**
(.00150)
.574
Berri, David J., Stacey L. Brook, Bernd Frick, Aju J. Fenn, and Roverto VicenteMayoral. 2005. The Short Supply of Tall People: Competitive Imbalance in
the National Basketball Association. Journal of Economic Issues XXXIX
(December): 1029-41.
Berri, Davd J., and Stacey L. Brook. 2010. On the Evaluation of the ‘Most Important’
Position in Professional Sports. Journal of Sports Economics 11 (April): 157171).
20