Our Question
We were curious: Do teams with one
player occupying a large percentage of
payroll win more games than other
teams without such a player? We felt
that this was an interesting question that
could be analyzed using a t-test.
Summary of Research
We decided to study this
question in two leagues: the
NBA, and the MLB. We
collected team payroll and
player salary data for the 5
most recent full seasons in
each. Using this data, we
determined the percentage of
team payroll occupied by the
highest paid player.
Summary of Research (continued)
Looking at the results, we set a
threshold of 25% in the NBA,
and 20% in the MLB. We then
found the number of wins for
all teams for each season, and
separated them depending on
whether or not they exceeded
the threshold.
Raw
Data
•
Data Collection
Problems
• Inconsistent Data
o
•
Different sources gave slightly
different salary and payroll
figures.
Limited Data Available
o
For the NBA, payroll data was
only available going back to
2007 on the website used.
NBA - Teams with Player Salary ≥ 25% of Team Payroll
= 45.8 wins
s
= 13.36 wins
WINS
In our NBA data set, 40 out of the
the 150 teams met our criteria.
NBA - Teams without Player Salary ≥ 25% of Team
Payroll
= 39.25 wins
s
= 12.85 wins
WINS
These are the remaining 110 teams
from our NBA sample.
Seems significant!
Better run
a t-test!
Parameter: We are interested in determining
whether or not there is a difference in number
of wins between teams with one player
occupying 25% or more of payroll compared
to teams without such a player.
y= team with a player occupying 25% or more of team payroll
n= team without such a player
We will be using a 2 sample t-test.
Conditions
SRS - We took a census, using every team for a period of 5
years.
Independent - The values are not independent because
one team winning means another loses. This condition
fails.
Normal - Each sample size is greater than 30 so the
distribution is approximately normal.
These failures and the fact we are extrapolating means
that our conclusions should be used with caution.
(45.8-39.25) - 0
=2.6822
.
sq((13.362/40)+(12.852/110)
-Value = .0092
Interpretation
Because the P-value is
significant at the a=.01
level, we reject the null
hypothesis. There is
strong evidence that
there is a difference in
the number of wins
between teams with one
player occupying 25% or
more of payroll
compared to teams
without such a player in
And now... The MLB
Raw
Data
MLB - Teams with Player Salary ≥ 20% of Team
Payroll
= 74.93
s
= 10.54
WINS
In our MLB data set, 27 out of the
the 150 teams met our criteria.
MLB - Teams without Player Salary ≥ 20% of Team
Payroll
= 82.45
s
= 10.96
WINS
The remaining 123 teams
Parameter: We are interested in determining
whether or not there is a difference in number
of wins between teams with one player
occupying 20% or more of payroll compared
to teams without such a player.
We will again be using a 2 sample t-test.
Conditions
SRS - We took a census, using every team for a period of 5
years.
Independent - The values are not independent because
one team winning means another loses. This condition
fails.
Normal - Based on our data and the histogram, it is safe to
assume it is approximately normal.
These failures and the fact we are extrapolating means
that our conclusions should be used with caution.
(74.93-82.45) - 0
.
sq((10.542/27)+(10.962/123)
P-Value = .0018
=-3.3328
Interpretation
Because the P-value is
significant at the a=.05
level, we reject the null
hypothesis. There is
strong evidence that
there is a difference in
the number of wins
between teams with one
player occupying 20% or
more of payroll
compared to teams
without such a player in
Conclusion
Over the time period sampled, there was a
difference in wins for teams with a player
taking up a high percentage of payroll in both
the MLB, and the NBA. In the NBA, teams
with a player making 25% or more of team
payroll were more successful, and in the MLB
teams with a player making 20% or more of
team payroll were less successful.
•
Limitations and Improvements
Small Sample Size
o Use data from greater
number of years
•
•
Arbitrary Threshold
o Pick, say, top 20% of teams
rather than teams with
more than x percent
•
Lack of independence
o Values are not independent
because teams play each
other.
Need to Extrapolate
o Increase the sample size
to make better informed
conclusions