Special Problem 4A
Baseball Salaries
Baseball fans everywhere were shocked in December 2000 when Alex Rodriguez signed
a 10-year contract worth $252 million with the Texas Rangers baseball team. This
focused more attention than ever on how much money major league baseball players
make for playing the national pastime. Other average annual values, as of this writing
(9/2006) are third baseman Alex Rodriguez (now with the New York Yankees), $21.7
million, shortstop Derek Jeter (New York Yankees), $20.6 million, and home run record
holder Barry Bonds (San Francisco Giants), $19.3 million. And these figures do not
include endorsements!
Table SP4A gives Major League baseball average salaries since 1967 as compiled by the Major
League Baseball Players Association.
1. Plot the data. The points display neither a linear nor an exponential trend. Nevertheless, extend
the table by recording the ratio of salaries from year to year. Which year(s) produced the salary
that most disrupts the trend?
Stat/Regression/Fitted line plot
2. Transform the data as if the salaries were increasing exponentially. In the plot of log(Salary) vs.
(Year), observe that some of the points seem to line up nicely in a straight-line pattern, while other
points appear “out of line.” Which points are not in the linear pattern?
Calc/Calculator
3. Plot the transformed. Delete the points for which there is a clear reason why they don’t fit the
trend, and reference the extraordinary event(s) in your narrative. Delete the corresponding salaries,
and their logarithms. Then perform least-squares regression on the remaining transformed points.
How well does the LSRL fit these points (Year, log(Salary))? What is the correlation? Find the
exponential equation and overlay this equation on the original data points.
4. Look at your original scatter plot of the data. In 1991, the average salary increased a whopping
54% over the previous year, fueled in part by several relatively large contracts to high-visibility
players. There followed several years of some dissatisfaction among the players, culminating in a
general strike in 1995. That year, the average salary decreased (the only such year in Major League
history). What does your analysis in (3) suggest about the net results after the strike on the growth of
player salaries?
5. Is your model useful for predicting the average salary in the future? If so, then how far into the
future would you be comfortable making a prediction?
6. The average salaries for baseball players for the last decade or so have been significantly higher
than the median salaries. How could you explain this?
7. What other aspects of baseball player compensation would be interesting to explore? Don’t be limited
to the specific questions above.
The Report. Describe your investigation in a report. Follow the conventions as described in the
general guidelines for writing up Special Problems. You will be graded on both the accuracy of your
work and the quality of your written communication.
Deadline: This Special Report will be due by the end of the period.
Appendix
NEW YORK (AP, Wednesday, December 12, 2001) -- Average baseball salary as compiled by the
Major League Baseball Players Association, and the minimum salary. From 1979-2000, salary deferrals
without interest are discounted at 9 percent per year. For 1987-2000, signing bonuses are increased at 9
percent per year, In 2001, salary deferrals, buyouts and bonuses are increased or discounted to the prime
rate in effect on the Nov. 1 following the season plus one percent:
Special Note: Work only with the averages and skip the first two entries.