Show Me the Money

One of the interesting aspects of the Lahman database is that it contains salary data that goes back to 1985. While I can’t vouch for it’s accuracy (I believe the data originally came from the late Doug Pappas’ database but I’m not certain) I thought it might be interesting to run some numbers related to team payroll.

Baseline
For the analysis that follows I only used the data from 1992 forward (376 team seasons) since it appears the data is fairly spotty before that time. For example, there are several teams in 1987 that have salaries for only a handful of players. In any case, given the years since 1992 it appears there is pretty good data and the following shows the average, maximum, minimum, and standard deviations for payrolls during that time.

Year	Avg	Max	Min	Std

1992	$31.0	$44.8	$9.4	$9.0

1993	$32.2	$47.3	$10.4	$9.1

1994	$33.1	$49.4	$14.9	$8.4

1995	$34.0	$50.6	$12.4	$9.3

1996	$34.2	$54.5	$16.3	$10.5

1997	$40.3	$62.2	$10.8	$12.8

1998	$42.6	$72.4	$10.6	$15.1

1999	$49.8	$86.7	$17.9	$20.2

2000	$55.5	$92.3	$16.5	$21.1

2001	$65.4	$112.3	$24.1	$24.3

2002	$67.5	$125.9	$34.4	$24.3

2003	$70.9	$152.7	$19.6	$27.5

2004	$69.0	$184.2	$27.5	$32.3

What you can immediately see from this is that while the average team payroll doubled from the years 1996 to 2004, the maximum payroll more than tripled while the minimum payroll didn’t quite double. This trend is illustrated by the fact that the standard deviation tripled as well and regularly surpassed the minimum payroll with the exception of 2002. In graph form the data looks as follows:

In the rest of this article I’ll examine a few issues that came to my mind as I looked at this data.

Dollars and Wins
One of the obvious questions that might be answered with this data is to measure the correlation of wins and losses to payroll. Much as I did in my post on A Mathematician at the Ballpark, I used Excel’s CORREL() function to calculate the correlation coefficient (r value) for payroll compared to record. However, to make the calculation more precise and remove the inherent salary inflation I calculated what I call the Normalized Payroll, defined as the payroll divided by the average payroll for the year and then calculated its correlation with winning percentage. Doing so produced a correlation of .432, a value that indicates that while the correlation is positive, it is weak (an r value > .70 would be considered strong). You can see below the scatter plot of Normalized Payrolls versus winning percentage and the linear regression line that shows the positive correlation. The graph also shows the coefficient of determination (r^2) and the regression equation. This analysis indicates that payroll plays a part in fielding a winning team, but is far from the determining factor explaining less than 19% of the variation in winning percentage.


Team Efficiency
A second way to look at the data is to determine which teams were the most efficient with their payrolls. In other words, who got the most bang for their buck in terms of dollars per win? Using Normalized Payroll it’s simple to calculate a value I call Payroll Efficiency by dividing winning percentage by Normalized Payroll. By this measure, higher numbers are better. The top teams of the last 20 years were:

Year Team      Wins Payroll  PE

1997 Pittsburg  79  $10.8  1.82

1998 Montreal   65  $10.6  1.61

1992 Cleveland  76   $9.4  1.55

2000 Minnesota  69  $16.5  1.43

2001 Minnesota  85  $24.1  1.42

It’s not too surprising that all but one of these teams are below .500 since any major league team will win 30% of their games just by showing up regardless of how low their payroll is. The first team with a winning record is the 2001 Twins who ranked 5th when they won 85 games with a PE of 1.42. The top really good team on the list is the 2001 A’s who ranked 10th and won 102 games with a payroll of just $33.8M in a year when the average payroll was $65.4M for a PE of 1.22. The A’s repeated the trick in 2002, ranking 19st with a PE of 1.07.

I was surprised, however, that teams from the last few years such as the Twins, A’s, or Expos didn’t crack the top five. In fact, the top team of more recent vintage was the 2003 Devil Rays who won just 63 games and did it with a PE of 1.41. The 2004 Brewers, 2004 Devil Rays, and 2004 Indians all cracked the top 30 as well.

On the bottom of the scale the least efficient teams of the last 20 years are:

Year Team    Wins Payroll    PE

2004 Yankees  101  $184.2  0.23

2003 Mets      66  $116.9  0.25

1995 Blue Jays 56  $50.6   0.26

1992 Dodgers   63  $44.8   0.27

2002 Ranges    72  $105.2  0.28

Although the bottom of the spectrum is also dominated by bad teams, the Yankees recent orgy of spending has made them the notable exception. Even winning 101 games last year didn’t save them from being the least economically efficient team of the last 20 years. Their 2003 season when they also won 101 games ranks 7th worst as well.

Dollars and the Post Season
Finally, another way to look at the data is to see how well payroll correlates with post season appearances.

Criteria           Teams  Normalized Payroll

Post Season          122   1.19

Wild Card             20   1.21

Division Winners      75   1.24

League Winners        22   1.36

World Series Winners  11   1.36

This can also be broken down into periods

1992-1997

Criteria          Teams Normalized Payroll

Post Season          52   1.19

Wild Card             6   1.30

Division Winners     32   1.18

League Winners       10   1.31

World Series Winners  5   1.42

1998-2004

Criteria          Teams Normalized Payroll

Post Season          62   1.26

Wild Card            14   1.17

Division Winners     43   1.29

League Winners       12   1.42

World Series Winners  6   1.31

Clearly this data shows a relationship between high payrolls and getting to the postseason. At the very least it appears a team needs to spend in the range of 20% more than the league average in order to be competitive and 30% more to compete for a league championship or World Series victory. The standard deviation of Normalized Payroll is around .35 and so World Series champions are more than one standard deviation above the mean.

There is also a predictable relationship between payroll and how well a team finishes within their division. Since 1992 the numbers are:

Rank  NPayroll Teams

1	1.24	75

2	1.05	73

3	0.97	75

4	0.90	73

5	0.83	59

6	0.79	15

7	1.01	6

While these values don’t appear too alarming it looks a bit different when you break it into periods:

1992-1997

Rank  NPayroll Teams

1	1.18	32

2	1.05	32

3	0.96	33

4	0.91	31

5	0.91	24

6	0.83	8

7	1.01	6

1998-2004

Rank  NPayroll Teams

1	1.29	43

2	1.06	41

3	0.98	42

4	0.89	42

5	0.77	35

6	0.76	7

Now you can see that over the last few years, if a team is being outspent, they’re going to find themselves in the second division.

Cubs and Royals
Since I follow the Cubs and Royals I thought I’d end by showing how these two teams have done in Normalized Payroll and Payroll Efficiency.

First, the Cubs…

            	    Payroll 	WPct	Npayroll   PE

1992	 $    29,829,686.00 	0.481	0.963	0.500

1993	 $    39,386,666.00 	0.519	1.223	0.424

1994	 $    36,287,333.00 	0.434	1.095	0.396

1995	 $    29,505,834.00 	0.507	0.868	0.584

1996	 $    33,081,000.00 	0.469	0.967	0.485

1997	 $    42,155,333.00 	0.420	1.047	0.401

1998	 $    50,838,000.00 	0.552	1.193	0.463

1999	 $    62,343,000.00 	0.414	1.252	0.330

2000	 $    60,539,333.00 	0.401	1.090	0.368

2001	 $    64,715,833.00 	0.543	0.990	0.549

2002	 $    75,690,833.00 	0.414	1.122	0.369

2003	 $    79,868,333.00 	0.543	1.126	0.482

2004	 $    90,560,000.00 	0.549	1.312	0.419

As you can see last year the Cubs finally broke the “magical” 130% of average payroll but have historically not gotten much for their money.

The Royals…

            	    Payroll 	WPct	Npayroll   PE

1992	 $    33,893,834.00 	0.444	1.094	0.406

1993	 $    41,346,167.00 	0.519	1.284	0.404

1994	 $    40,541,334.00 	0.557	1.223	0.455

1995	 $    29,532,834.00 	0.486	0.869	0.559

1996	 $    20,281,250.00 	0.466	0.593	0.786

1997	 $    34,655,000.00 	0.416	0.861	0.483

1998	 $    36,862,500.00 	0.447	0.865	0.517

1999	 $    26,225,000.00 	0.398	0.527	0.755

2000	 $    23,433,000.00 	0.475	0.422	1.127

2001	 $    35,422,500.00 	0.401	0.542	0.740

2002	 $    47,257,000.00 	0.383	0.700	0.546

2003	 $    40,518,000.00 	0.512	0.571	0.897

2004	 $    47,609,000.00 	0.358	0.690	0.519

This tells a different story as the Royals payroll has plummeted since the early 90s to where it is now a paltry 70% of the average. Rest assured, given that level of spending and past history it is unlikely that the Royals can be competitive. The only bright spot is that they occasionally have been fairly efficient with their money (a PE of .567 is average).