1.
Statistical Analysis on MLB’s Decision to Lower the Pitcher’s Mound in 1969:
A Study on League MVP Performance Before and After
Nick Labas
MGMT 6710: Quantitative Methods II
May 6th
, 2015

2. Introduction
From the beginning of MLB’s history, the pitcher’s mound was 15 inches in height, and after the 1968
Season, Major League Baseball changed that rule by lowering the pitcher’s mound to 10 inches in
height. In Baseball, the year 1968 is often referred to as “The Year of the Pitcher”.
In that year, the average runs per game was a combined 6.8 per game. That is two less runs per game
than the historical average. The Major League ERA (Earn Runs Allowed) was 2.98, the best in MLB’s
History. Normally, an ERA of under 3.00, would make you an elite pitcher within the league, but that
year even average pitchers were at 3.00 and under. The National League MVP that year, Bob Gibson,
was a pitcher on the St. Louis Cardinals, and he posted a record that may never be broken with an ERA
of 1.12. That is just over 1 run allowed per game pitched for a whole season.
Topic
Since the lowering of the pitcher’s mound, it has been said to have boosted offense and tilt the playing
field toward the batters. My study will take that a little further and look at what effect the lowering of
the mound had on the best players in the league. I will examine the League MVP’s On Base Percentage
(OBP) before and after the change in height of the mound. I will base this study on the variables of
Games Played, At Bats, Hits, Walks, and Mound Height.
Variables
Dependent Variable (Y) = On Base Percentage (OBP)
Quantitative Variables
Independent Variable (X1) = Games Played
Independent Variable (X2) = At Bats
Independent Variable (X3) = Hits
Independent Variable (X4) = Walks
Qualitative Variable
Dummy Variable (X5) = Mound Height
 (X5) = 0; the 15 inch height from 1911‐1968
 (X5) = 1; the 10 inch height from 1969‐2014
Proposed Model
Y = B0 + B1(X1) + B2(X2) + B3(X3) + B4(X4) + B5(X5) + e

3. Regression Analysis
A normal multiple regression analysis was ran.
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.9935
R Square 0.9870
Adjusted R Square 0.9866
Standard Error 0.0055
Observations 165
ANOVA
df SS MS F P‐value
Regression 5 0.36202 0.07240 2414.1906 0.0000
Residual 159 0.00477 0.00003
Total 164 0.36678
Coefficients
Standard
Error t Stat P‐value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.4187 0.0061 68.7742 0.0000 0.4067 0.4308 0.4067 0.4308
Games Played ‐0.0003 0.0001 ‐2.7885 0.0059 ‐0.0005 ‐0.0001 ‐0.0005 ‐0.0001
At Bats ‐0.0006 0.0000 ‐24.6703 0.0000 ‐0.0006 ‐0.0005 ‐0.0006 ‐0.0005
Hits 0.0015 0.0000 55.2212 0.0000 0.0015 0.0016 0.0015 0.0016
Walks 0.0010 0.0000 44.5687 0.0000 0.0009 0.0010 0.0009 0.0010
Mound 0.0014 0.0009 1.6016 0.1112 ‐0.0003 0.0031 ‐0.0003 0.0031
The results show this regression analysis to be statistically significant with an F‐value of 2414 and P‐
value of 0.0. The analysis also displays that 98.70% of the variation in Y is explained with these given
variables.
For now, the Coefficients of the Variables appear to display the correct information. Games Played and
At Bats will normally give way to a drop in your On Base Percentage based on there is more opportunity
for failure to occur. Hits and Walks obviously are a positive towards your OBP and the results show that
here. It also shows that the lowering of the pitcher’s mound does have a positive affect by slightly
adding to a player’s OBP.

4. Residuals
The residual analysis was done. The plotted points from that analysis does not point to any
heteroskedasticity. There is no noticeable pattern of the residuals fanning out. Further there does not
seem to be any serial correlation with the plots spread out evenly.
Correlation Analysis
The variables seemed to have some sort of correlation with one another based on how they are
compiled. Normally, the more Games Played will lead to more At Bats, which in turn will lead to the
possibility of more Hits and Walks by the player. I ran a Correlation Matrix to confirm, or deny that
notion.
Correlation Matrix
Games
Played At Bats Hits Walks
Games Played 1
At Bats 0.8138 1
Hits 0.5641 0.7819 1
Walks 0.0534 ‐0.4085 ‐0.2586 1
My assumption was correct. Games Played and At Bats are heavily correlated at .8138, and same goes
for At Bats and Hits at .7819. Further analysis will be needed to see if Multicollinearity is present in the
model.

5.
Variance Inflation Factor Analysis
Next I take a harder look at collinearity, aside from the Correlation Matrix. The Variance Inflation Factor
(VIF) will determine this by using the following equation:
VIF = 1 / (1 – Ri
2
)
In order to get the information needed, we will need to run a Regression Analysis for each Quantitative
Variables against the other Quantitative Variables. When I did that, I took the R‐Squared and applied it
to the above equation. Here are the results:
VIF
Games Played 7.5280
At Bats 14.0314
Hits 3.1175
Walks 2.9651
As you can see, At Bats and Games Played exhibit collinearity. Their VIF is greater than 5 which is the
rule of thumb for the existence of collinearity. Because of this, we cannot make any further inferences
on the individual parameters. All the variables will need to be kept in the model, because they are
important to the study and dropping one of them will not add to the analysis.
Final Regression Equation
Y = 0.4187 – 0.0003(X1) – 0.0006(X2) + 0.015(X3) + 0.0010(X4) + 0.0014(X5)
Conclusion
To show how the lowering of the mound impacted performance, I took the averages of the Variables
from 1911‐2014 to plug into the equation.
Games Played (X1) = 149 Games per Year
At Bats (X2) = 560 At Bats per Year
Hits (X3) = 183 Hits per Year
Walks (X4) = 78 Walks per Year
Dummy Variable (X5) = Mound Height
 (X5) = 0; the 15 inch height from 1911‐1968
 (X5) = 1; the 10 inch height from 1969‐2014
The result is a very slight improvement for the greatest players. Using those figures, OBP would be
0.411 for a lowered mound, and 0.410 for when the mound was raised. In conclusion, even if the

6. mound lowering helped improve overall offense for baseball, the impact on the performance of its top
players is still relatively the slim. The top players did not benefit as much as the average player.
References
 "MLB Most Valuable Player MVP Awards & Cy Young Awards Winners | Baseball‐
Reference.com." Baseball‐Reference.com. N.p., n.d. Web. 07 May 2015.
 Kirkjian, Tim. "The 1968 Season Was a Magical Year for Pitchers."ESPN.com. N.p., 8 May 2011.
Web. 07 May 2015.