1. Hitters vs. Pitchers: The Anomaly of the DH Rule
Max Miller
max@uoguelph.ca
0629437
Abstract:
This study aims to determine how rules in the MLB (Major League Baseball) influence the framework of
the game – and in turn determine the optimal player pricing actions for GM’s. This paper will focus
specifically on the DH rule, and the inherent differences that it creates between the American League
(AL) and National League (NL). Just as Billy Beane, GM of the Oakland Athletics, understood the
framework of a league without a salary cap, and changed the dynamics of the game – this paper will try
to bring a better understanding to the framework created by the DH rule. By doing so, this analysis will
prove that GM’s need not only to find undervalued talent in the market (à laMoneyball), but also need
to focus on proper allocation of the available talent.

2. Introduction –
Baseball, like all sports, has a fundamental characteristic of uncertainty, which dominate the possible
outcomes of the game. Although this uncertainty has been found to lead to an increase in gate-receipts
(El-Hodiri and Quirk, 1971), in order to be successful – a team’s general manager (GM) should focus on
decreasing uncertainty in outcome – in order to build a roster that maximizes total wins, even when at
the expense of forgone revenue. This relates to the fact that a GM’s compensation, and legacy for that
matter, is based on how well their team performed, and not how much money the team earned during
their tenure. By focusing on decreasing uncertainty and maximizing winning percentage, all involved
parties should be better off, and owners should still earn a fair return.
The rules of the game, which govern how the players act, lead to the creation of a general framework
that influences how outcomes are determined. Therefore by gaining an in-depth understanding of the
framework these rules create, a GM can produce strategies that effectively decrease uncertainty of
outcome and in turn increase their team’s chances of winning.
Similar to a mutual fund manager, GM’s are constantly managing a portfolio of players (equity), in a
market full of uncertainty, looking to maximize total return (wins). Therefore, a vital question constantly
on the mind of professional sports GM’s should be – What is the most efficient way to allocate salary in
order to maximize total return? To answer this important question – GM’s must take an objective, rules-
based approach – allowing them to properly allocate salary in a way that reduces uncertainty of team
outcomes, stacking the odds in their favor.
I hypothesize that due to the DH rule, a framework is created, in which teams in the AL should
consistently spend a higher proportion of their salary on offense (non-pitchers), when compared to NL
teams, and that teams that don’t distribute salary in accordance to this framework, will be improperly
constructed, and thus will lead to a lower winning percentage. I also hypothesize that the proportion of
salary spent on offense (non-pitchers) will have a larger effect on the winning percentage in the AL
compared to the NL.
Literature Review –
An interesting review of how rules in the MLB can impact the pricing decisions of GM’s can be found in
the 2003 bestseller, “Moneyball: The Art of Winning an Unfair Game”, by Michael Lewis. This book
chronicled the perennial success of the Oakland Athletics and their GM Billy Beane – despite having one
of the lowest payrolls, in a league that lacks a salary cap.
The salary cap, which puts a ceiling on the amount each team is allowed to spend on its players, is a rule
that is generally used to level the competitive playing field for small market teams in professional sports.
Instead of a salary cap, the MLB utilizes a form of luxury tax, in which teams whose total salary exceeds
a certain figure are taxed on the excess amount. In the past, this luxury tax system has been ineffective
at stopping large market team’s form spending high amounts of salary. For example, the New York
Yankees who have paid approximately 92% of all luxury tax collected by MLB have also participated in 40
of the past 109 World Series (MLB, 2012).

3. Although the luxury tax has been ineffective at maintaining equality in MLB team payrolls, as the world
learned with the release of “Moneyball” – spending doesn’t always equate to a higher winning
percentage.
For many years, Billy Beane had dealt with the issues of competing with large market teams that could
afford to maintain high salaries. In doing so, he was able to gain a total understanding of the framework
created by the lack of salary cap, coming to the realization that he couldn’t compete in the market for
conventional talent. Therefore Billy and his assistant Paul Depodesta created a new strategy, which
valued empirical gauges of player performance over the traditional, subjective wisdom of baseball
scouts (Lewis, 2003). This strategy allowed the Oakland Athletics to solve a serious issue which had
plagued the MLB: competing by obtaining first rate talent without a large payroll.
The success of this Billy Beane’s strategy is clearly evident in the data. Since Beane took over as GM of
the Oakland Athletics in 1998, the team has won approximately 55% of their games – good for the 5th
highest winning percentage of all 30 MLB teams, behind only the New York Yankees, the Atlanta Braves,
the Boston Red Sox and the St. Louis Cardinals (Regan, 2012).
However, like all great strategies, once the secrets have been exposed, the potential opportunity to
exploit for gains greatly decreases. As the Moneyball method became more widely used, and more
popular throughout the MLB, it inherently became harder to take advantage of undervalued assets in
both the free agent and trade market. According to Hakes and Sauer (2006), a year after the publication
of Moneyball, the strategy had been completely diffused throughout the MLB. This became an even
larger issue when large market teams, such as the Boston Red Sox, started adopting these Moneyball
techniques on top of their vast payrolls.
In order to re-gain a competitive advantage over the big spenders, small market GM’s must gain a
deeper understanding of the rules in the game. This study will focus specifically on the DH rule and its
effects on the optimal salary distribution in the MLB.
While a large amount of literature has been published on the effects of salary dispersion in the MLB, a
majority of these studies focus on dispersion inequality, rather than determining an optimal distribution
based on the available constraints. Jewell and Molina (2004) and DeBrock et al. (2004) found a negative
relationship between the intra-team salary dispersion and team performance in MLB. The findings from
these studies are due to the large nature of MLB rosters – by concentrating a high proportion of salary in
a small number of players, GM’s are unable to build well-balanced teams.
The next section of this paper will try to understand how the DH rule influences the framework of the
game – and in turn determine the optimal player pricing actions for GMs.
Research Question:
How does the DH rule effect the optimal player pricing actions of GMs in the MLB?

4. Hypotheses:
1) The DH rule creates a framework, in which, AL teams should spend a higher proportion of salary
on offense (non-pitchers), and small-market teams (teams with a salary below the league
average) that don’t spend according to this framework, will have improperly constructed teams,
and therefore will lead to a lower winning percentage.
2) The proportion of salary spent on offense (non-pitchers) will have a larger impact on the
winning percentage in the AL, compared to the NL.
Data
The data for this section consists of MLB team salary figures for the past six years (2007-2012). This data
was taken from USATODAY (http://content.usatoday.com/sportsdata/baseball/mlb/salaries/team),
which lists a collection of professional sports salary data. The baseball salary database contains year-by-
year listings of salaries for MLB opening day rosters, including players on the disabled lists. This data is
based on documents obtained from the MLB Players Association (MLBPA), club officials and Major
League Baseball’s central office.
Hitters vs. Pitchers: The Anomaly of the DH Rule
The DH Rule – which only applies to the AL – allows a designated hitter (DH) to replace the pitcher in the
batting lineup. This means that the batting lineup in the AL consists of nine full-time batters, whereas an
NL batting lineup consists of eight full-time batters and one pitcher. In theory, due to the added hitter in
the lineup, thisrule creates league-wide dynamic that causes the structure of AL teams to be more
offensively oriented. According to this framework, AL teams should consistently spend a higher portion
of salary on hitters (non-pitchers), than their counterparts in the NL. This analysis will try to first
establish the fact that AL teams spend a higher proportion of salary on offense, followed by measuring
the performance of teams that didn’t follow the DH rule framework.
Hypothesis 1:
2012 AL NL Change in % 2009 AL NL Change in %
% Non-Pitcher 57.62% 50.64% 6.98% % Non-Pitcher 58.43% 53.86% 4.57%
% Pitcher 42.38% 49.36% % Pitcher 41.57% 46.14%
2011 AL NL 2008 AL NL
% Non-Pitcher 60.76% 53.79% 6.97% % Non-Pitcher 58.86% 53.05% 5.81%
% Pitcher 39.24% 46.21% % Pitcher 41.14% 46.95%
2010 AL NL 2007 AL NL
% Non-Pitcher 57.78% 50.55% 7.23% % Non-Pitcher 57.96% 53.07% 4.89%
% Pitcher 42.22% 49.45% % Pitcher 42.04% 46.93%
58.57%
52.49%
6.08%Total Change in % Non-Pitcher:
Average % Non-Pitcher NL
Average % Non-Pitcher AL

5. As hypothesized, the above figure proves that over the past six years, AL teams spent approximately
6.08% more on hitters (non-pitchers), when compared to NL teams. This figure accounts for the fact that
designated hitters in the AL are generally well-paid, middle of the lineup power bats – whereas when NL
teams play under AL rules they have to resort to using a backup player to fill the DH role.
Chart 1 (Appendix 1) represents a scatter plot diagram of all the small-market AL teams over the past six
years and their proportion of salary spent on offense (non-hitters). This chart focuses specifically on
small market teams (teams with salary below the league average) due to the fact that large market
teams, who can afford to have high salaries, can spend a smaller proportion of their salary on offense,
but still be spending an higher actual dollar value. For example, although the Boston Red Sox spent
below the average non-pitcher percentage in 2011, they still spent just under 85 million on hitters alone,
which is almost as high as the average MLB team salary.
When considering the discussed framework created by the DH rule, teams in quadrant 1 should have
more optimal allocation of salary when compared to teams in quadrant 2 – and therefore should lead to
a higher winning percentage.
When comparing the winning percentage of the data points from the above chart (Appendix 2),
hypothesis 1 is confirmed. Only 20% of the teams in quadrant 2 finished with a record above .500,
whereas 40% of the teams in quadrant 1 finished above .500. Also the average winning percentage in
quadrant 2 (46.75%), is less than the average winning percentage in quadrant 1 (48.84%). This results in
a 2.09% winning percentage differential, which is approximately a 3.40 difference in total wins (# of wins
= winning % * 162).
Hypothesis 2:
This section will try to measure the effect of increasing the proportion of salary invested in hitters on AL
teams versus NL teams. To do so, I ran the simple regression model below for both the AL and NL:
Average NL Non-
Pitcher %: 0.525
Average AL Salary:
$97,107,964
0.38
0.43
0.48
0.53
0.58
0.63
0.68
0.73
0.78
20000000 40000000 60000000 80000000
Non-Pitcher%
Total Salary
I
II

6. Win % = β0 + β1*Salary +β2*Non-Pitcher %
In the above regression, the dependent variable (Y variable), is the winning percentage – whereas the
independent variables (X variables) are total salary and non-pitcher percentage. Therefore, the results
from these regressions should be able to distinguish whether the proportion of salary invested in
offense (non-pitchers) has a greater effect on winning in the AL over the NL. These results would
confirm that the DH rule does in fact create a framework, in which AL teams are more offensively
oriented and therefore should devote a higher proportion of their salary to offense (non-pitchers).
When looking at theresults from this study (Appendix 3 and 4), as expected, we see that salary (β1) has a
definite positive effect on winning % in both leagues. More importantly, when looking at these results,
we see that non-pitcher % (β2) has a slightly positive effect on winning percentage in the AL (coefficient
= .02858), whereas, the same coefficient has a negative effect in the NL (coefficient = -.1191). This
verifies the second hypothesize that the proportion of non-pitchers has a larger effect on the winning
percentage in the AL.
It’s easy to dismiss the above models due to a low R2, only explaining around 15%(11% = salary, 4% =
non-pitching %) of the variation in winning percentage. However, if one considers all variables in
baseball that affect winning percentage – total salary and non-pitcher expense cannot be
consideredperfect predictors. Baseball games are intensely competitive in nature and outcomes are
based upon many competing variables, including opponent, starting pitcher, umpires, injuries,
attendance and even weather.
Conclusion
The main conclusion derived from the analysis of this study is that due to the DH rule, a framework is
created in the MLB, which affects the optimal salary distribution– increasing the importance of offense
in the AL. This conclusion was a result of evidence demonstrating lower winning percentages amongAL
teams that deviated from this framework. This conclusion was also strengthened by the use of
regression analysis, which proved that the proportion of salary allocated to non-pitchers has hada
positive impact on the winning percentage in the AL, and a slightly negative effect on the winning
percentage in the NL.
Overall, this analysis proves that due to the DH rule, a reliable relationship exists between salary
allocation and winning percentage in the MLB. This relationship should be properly understood by GM’s
– allowing them to allocate salary in a way that decreases uncertainty of outcome, and maximizestheir
team’s potentialwinning percentage.
Coefficients R Square
Intercept 0.426737591
Total Salary 6.39008E-10
Non-Pitching % 0.028577299
0.159356798
AL LEAGUE SUMMARY OUTPUT
Coefficients R Square
Intercept 0.498486503
Total Salary 6.98652E-10
Non-Pitching % -0.119099243
NL LEAUGE SUMMARY OUTPUT
0.141025583

7. Work Cited List
Debrock, Larry. "Pay and Performance: The Impact of Salary Distribution on Firm--Level Outcomes in
Baseball." Journal of Sports Economics 5 (2004): 243-61. Sage Journals.Web. 27 Feb. 2013.
El-Hodiri, Mohamed, and Quirk, James."An Economic Model of a Professional Sports League." Journal of
Political Economiy 79.6 (1971): 1302-319. JSTOR.Web. 22 Feb. 2013.
Hakes, Jahn K., and Raymond D. Sauer."An Economic Evaluation of the Moneyball Hypothesis." Journal
of Economic Perspectives 20.3 (2006): 173-85. JSTOR.Web. 25 Feb. 2013.
Jewell, Todd, and David Molina."Testing the Determinants of Income Distribution in Major League
Baseball." Economic Inquiry 42.3 (2004): 469-82. Scholars Portal.Web. 27 Feb. 2013.
Lewis, Michael. Moneyball: The Art of Winning an Unfair Game. New York: W.W. Norton, 2003. Print.
MLB."Standings | MLB.com " Major League Baseball. 12 Mar. 2012. Web. 25 Feb.
2013.http://mlb.mlb.com/mlb/standings/
MLB. "World Series Overview | MLB.com: History." Major League Baseball. 12 Mar. 2013. Web. 25 Feb.
http://mlb.mlb.com/mlb/standings/http://mlb.mlb.com/mlb/history/postseason/mlb_ws.jsp?feature=a
l_clubs
Regan, Colin. "The Price of Efficiency: Examining the Effects of Payroll Efficiency on Major League
Baseball Attendance." Applied Economics Letters 19 (2012): 1007-015.Scholars Portal. Web. 25 Feb.
2013.

8. Quadrant 1 Quandrant 2
Team Year Non-Pitcher % Win % Team Year Non-Pitcher % Win %
CLE 2007 0.395757647 0.593 MIN 2007 0.555078073 0.488
TEX 2007 0.440179746 0.463 BAL 2007 0.591630929 0.426
KC 2007 0.440300582 0.426 TB 2007 0.633573072 0.407
TOR 2007 0.449876136 0.512 DET 2007 0.67567725 0.543
CLE 2008 0.456740571 0.5 OAK 2007 0.705497705 0.469
TEX 2008 0.469825207 0.488 OAK 2008 0.541099752 0.466
KC 2008 0.48013406 0.463 TB 2008 0.575541333 0.599
TEX 2009 0.483303504 0.537 BAL 2008 0.620003594 0.422
CLE 2009 0.485735171 0.401 MIN 2008 0.667326896 0.54
CHI 2009 0.490311687 0.488 OAK 2009 0.795056973 0.463
CLE 2010 0.507870643 0.426 TOR 2009 0.53906899 0.463
KC 2010 0.508788 0.414 KC 2009 0.545840855 0.401
KC 2011 0.509743932 0.438 TB 2009 0.575541333 0.519
KC 2012 0.518358646 0.444 BAL 2009 0.628821943 0.395
CLE 2012 0.520357796 0.42 MIN 2009 0.669184643 0.534
0.467533 TEX 2010 0.555881839 0.556
BAL 2010 0.595313218 0.407
OAK 2010 0.609525911 0.5
TB 2010 0.63237076 0.593
SEA 2010 0.662333834 0.377
TOR 2010 0.707383424 0.525
TOR 2011 0.585182794 0.5
TB 2011 0.616833064 0.562
OAK 2011 0.6474266 0.457
TEX 2011 0.674752444 0.593
SEA 2011 0.686030331 0.414
CLE 2011 0.696447892 0.494
BAL 2011 0.704275429 0.426
OAK 2012 0.530678586 0.58
TB 2012 0.55863869 0.556
SEA 2012 0.560271585 0.463
CHI 2012 0.57231001 0.525
TOR 2012 0.592409245 0.451
MIN 2012 0.617686135 0.407
BAL 2012 0.639182596 0.574
0.488429
Appendix
1. American League Scatter Plot
2. American League Small Market Teak Winning % (Highlighted = Win % >.500)
Average NL Non-
Pitcher %: 0.525
Average AL Salary:
$97,107,964
0.38
0.43
0.48
0.53
0.58
0.63
0.68
0.73
0.78
$20,000,000 $70,000,000 $120,000,000 $170,000,000
Non-Pitcher%
Total Salary

9. 3. American League Regression Output
4. National League Regression Output
Regression Statistics
Multiple R 0.399195188
R Square 0.159356798
Adjusted R Square 0.138600176
Standard Error 0.06329462
Observations 84
ANOVA
df SS MS F Significance F
Regression 2 0.061514501 0.03075725 7.677395497 0.000884655
Residual 81 0.324502924 0.004006209
Total 83 0.386017425
Coefficients t Stat P-value Lower 95% Upper 95%
Intercept 0.426737591 0.054357126 7.850628259 1.47823E-11 0.31858396 0.534891221
Total Salary 6.39008E-10 1.68275E-10 3.797414223 0.00028134 3.04195E-10 9.73822E-10
Non-Pitching % 0.028577299 0.092586936 0.308653689 0.758377418 -0.15564166 0.212796259
AL LEAGUE SUMMARY OUTPUT
Regression Statistics
Multiple R 0.37553373
R Square 0.141025583
Adjusted R Square 0.122553015
Standard Error 0.062130905
Observations 96
ANOVA
df SS MS F Significance F
Regression 2 0.058940795 0.029470397 7.634324684 0.000851296
Residual 93 0.359003195 0.003860249
Total 95 0.41794399
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.498486503 0.04099418 12.1599336 6.33462E-21 0.417080186 0.579892819
Total Salary 6.98652E-10 2.10367E-10 3.321106244 0.001282299 2.80904E-10 1.1164E-09
Non-Pitching % -0.119099243 0.066623156 -1.787655376 0.077088886 -0.251399627 0.013201141
NL LEAUGE SUMMARY OUTPUT
NL LEAUGE SUMMARY OUTPUT