1. Team Payrolls... Yay, or nay?

2. 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.

3. So what did we do?

4. Well I'll tell ya!!

5. 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.

6. 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.

7. GIVE ME THE DATA!

8. Raw Data

9. 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.

10. NBA - Teams with Player Salary ≥ 25% of Team Payroll In our NBA data set, 40 out of the the 150 teams met our criteria. = 45.8 wins s = 13.36 wins WINS # OF TEAMS

11. NBA - Teams without Player Salary ≥ 25% of Team Payroll These are the remaining 110 teams from our NBA sample. = 39.25 wins s = 12.85 wins WINS # OF TEAMS

12. Seems significant!

13. Better run a t-test!

14. 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

15. 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. We will be using a 2 sample t-test. These failures and the fact we are extrapolating means that our conclusions should be used with caution.

16. (45.8-39.25) - 0. sq((13.36 2 /40)+(12.85 2 /110) =2.6822 -Value =.0092

17. 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 the NBA.

18. And now... The MLB

19. Raw Data

20. MLB - Teams with Player Salary ≥ 20% of Team Payroll In our MLB data set, 27 out of the the 150 teams met our criteria. = 74.93 s = 10.54 WINS # OF TEAMS

21. MLB - Teams without Player Salary ≥ 20% of Team Payroll The remaining 123 teams = 82.45 s = 10.96 WINS # OF TEAMS

22. 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.

23. 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. We will again be using a 2 sample t-test. These failures and the fact we are extrapolating means that our conclusions should be used with caution.

24. (74.93-82.45) - 0. sq((10.54 2 /27)+(10.96 2 /123) =-3.3328 P-Value =.0018

25. 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 the MLB.

26. 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.

27. 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