The last two days I wrote about Major League Baseball.
First, I took a look at competitive balance
between the American League and the National League and noted that while the
National League (in historical terms) was fairly competitive, the American League
was not.
The following post looked at
MLB team payroll inequality and I showed that since 2011, MLB team payroll
inequality is rather large and increasing.
So are those two facts related?
Specifically, I am looking at team
performance (as measured by each team’s regular season winning percent) and
each team’s relative payroll from 2011 to 2018.
Data is found here.
In order to analyze this, I run a linear regression with team regular
season winning percent (the dependent variable) on team relative payroll (the independent variable), using
robust standard errors.
I find the
following:
first, relative payroll is
positive and statistically significant, meaning that an increase in a team’s
relative payroll leads to an increase in the team’s regular season winning
percent; and statistically significant means that I am at least 95% confident
that this relationship between team performance and relative payroll was not a
random result (assuming that the underlying hypothesis is true).
That is great that we can know the these two
variables are related.
But it would also
be helpful to know the size and by how much they are related.
In terms of the amount, we can use the estimated coefficient
from the regression to answer this question.
In the regression that I ran, I find that the coefficient (marginal
effect) is equal to 0.072997. This
number is interpreted as follows: a one
unit increase in relative payroll on average yields a 0.072997 increase in
regular season winning percent. So how
much is a one unit increase in relative payroll? Relative payroll is average payroll during
each season. Over the 2011 to 2018
seasons, relative payroll equals $128,432,967.
So the regression tells us that if a team increases their team payroll
by $128,432,967 that the average team’s regular season winning percent
increases from 0.500 to 0.507, which over a 162 game regular season means that
teams would win an additional 11.82 games. Another way of looking at it, is
that each win would result in an additional $10,860,711 spent on payroll. Now for an average team that does not seem
like a good deal, but for teams “on the bubble” of making or not making the
post-season, this might be a serious consideration.
Finally, how much does relative payroll explain regular
season winning percentage? In other
words, even if relative payroll is positive and statistically significant, how
much does the variation in relative payroll relate to the variation in regular
season winning percent? To answer that
question, we use the regression’s R2. From the regression results, the R2 is equal
to 0.1302, which I interpret as relative payroll “explains” only 13.02% of
regular season winning percent. Hence,
the explanatory power of relative payroll seems to be not very strong. Think of it this way, if the weather forecast
states there is a 13% chance of rain, will you wear rain boots, a rain coat and
carry an umbrella for just a 13% chance?
I would not. In the same way,
should MLB general managers spend $128 million dollars to increase winning
percent 7%, when the “weather forecast” of rain is 13%?
