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Wednesday, January 26, 2005

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).

2 comments:

gaius marius said...

thank you, mr agonistes, for your work. i'm trying to broadcast your important conclusions vis-a-vis the cubs at this moment.

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