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June 29, 2006

Schrodinger's Bat

Variations on a Monetary Theme

by Dan Fox

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"I believe salaries are at their peak, not just in baseball, but all sports. It's quite possible some owners will trade away, or even drop entirely, players who expect $200,000 salaries. There's a superstar born every year... but still there is no way clubs can continue to increase salaries to the level some players are talking about." - Peter O'Malley, 1971

As this article goes to press, your humble author will be enjoying his first Society for American Baseball Research (SABR) convention being held in Seattle. In next week's column I hope to include a full report on some of the more interesting quantitative research presentations, along with a few general takes on the convention itself. I'll also be blogging from the Emerald City, so you'll be able to get a peek at the goings on.

Although not in my normal bailiwick my thoughts have turned to the business of baseball this week since fellow BP'er Maury Brown and I will be presenting a talk at the conference on "The 2006 CBA and the Battles Within It", based largely on the writing Maury has done on SABR's Business of Baseball web site, The Hardball Times, and of course his recent Ledger Domain columns here at Baseball Prospectus along with my lesser contribution.

Probably because my mind was percolating on such subjects, I took particular note of a comment made by Peter Gammons during an ESPN broadcast a week or so ago related to variation in salaries. When discussing a particular team (which escapes me at the moment--why don't I take notes while watching TV?) Gammons made the point that the team in question would likely be dumping some salary in preparation for next year and then supported that course of action by saying that no team since 1985 had won a World Series when as much as 16% of their payroll was tied up in a single player.

The statement raises two questions. First, I wondered whether what Gammons said (and my memory of it) was indeed the case, and second, it got me thinking about measuring salary variation within payroll in general and its relationship, if any, to winning not just a World Series but making the post season and winning games in general.

Payroll Hogs

That may not be the most elegant subtitle for this section, but it does get to the heart of the matter. At the core of Gammon's statement was measuring which players consume the greatest percentage of payroll. Using the Lahman database we can run a simple query that gives us a list of those players with the top salary in terms of percentage of payroll for their teams along with their finish and postseason results.

Quick Note: The salaries in the Lahman database are those reported at the start of the season and therefore do not include in-season trades and signings, nor do they include the entire 40-man roster.

The following table contains the top twenty players since 1990 in terms of hogging their team's payroll; WC, Div, Lg, and WS denote whether the team won the Wild Card, their division, their league, and the World Series respectively, and the monetary figures are presented in millions.

                                              Pct                 Div
Year Team Name                  Sal  Pyrll  Pyrll   W   L    Pct Rank WC Div Lg WS
1996 DET  Cecil Fielder        $9.2  $23.4  39.4%  53 109  0.327    5  N  N  N  N
2004 TOR  Carlos Delgado      $19.7  $50.0  39.4%  67  94  0.416    5  N  N  N  N
1997 DET  Travis Fryman        $6.4  $17.3  37.1%  79  83  0.488    3  N  N  N  N
2003 TOR  Carlos Delgado      $18.7  $51.3  36.5%  86  76  0.531    3  N  N  N  N
1998 FLO  Gary Sheffield      $14.9  $41.3  36.1%  54 108  0.333    5  N  N  N  N
2000 FLO  Alex Fernandez       $7.0  $19.9  35.2%  79  82  0.491    3  N  N  N  N
1999 FLO  Alex Fernandez       $7.0  $21.1  33.2%  64  98  0.395    5  N  N  N  N
1996 OAK  Mark McGwire         $7.0  $21.2  33.2%  78  84  0.481    3  N  N  N  N
2003 TBA  Rey Ordonez          $6.5  $19.6  33.1%  63  99  0.389    5  N  N  N  N
2001 MIN  Brad Radke           $7.8  $24.1  32.1%  85  77  0.525    2  N  N  N  N
2004 MIL  Geoff Jenkins        $8.7  $27.5  31.7%  67  94  0.416    6  N  N  N  N
1991 MON  Dennis Martinez      $3.3  $10.7  31.1%  71  90  0.441    6     N  N  N
2005 KCA  Mike Sweeney        $11.0  $36.9  29.8%  56 106  0.346    5  N  N  N  N
1997 OAK  Mark McGwire         $7.2  $24.0  29.8%  65  97  0.401    4  N  N  N  N
2003 TBA  Ben Grieve           $5.5  $19.6  28.0%  63  99  0.389    5  N  N  N  N
2001 ANA  Mo Vaughn           $13.2  $47.5  27.7%  75  87  0.463    3  N  N  N  N
1995 ML4  Greg Vaughn          $4.9  $17.8  27.4%  65  79  0.451    4  N  N  N  N

Well, when you take a look at this list it would appear that Gammons' statement is basically correct. None of the nineteen teams represented on the list so much as smelled the post season. The two best seasons were those turned in by Brad Radke's (32.1% of payroll) 2001 Twins, who finished 85-77 but still six games behind the division-winning Cleveland Indians, and miles behind the 102-win wildcard team in Oakland, and the Carlos Delgado (36.5%) 2003 Blue Jays, who won 86 games but still finished in third, 15 games behind the Yankees in the AL East. In fact, as a whole the teams on the list were pretty mediocre and played just under .500 ball (.494) while finishing with an average division ranking of fourth.

It's also interesting to note that in addition to Delgado (also in 2004 with Toronto), several other players make the list twice: Alex Fernandez (1999 and 2000) with the Marlins, the oft-injured Mike Sweeney (2003, 2005) with the Royals, Greg Vaughn (1995, 1996) with the Brewers, and Mark McGwire (1996, 1997) with the A's.

But probably more depressing is to contemplate the following:

  • The Marlins spent over 30% on their payroll two years in a row on a pitcher (Fernandez) who threw just 193 1/3 innings and won 11 games
  • The 2003 Devil Rays used 33% of their payroll on Ordonez, a player who would come to the plate just 124 times, and who had a career on base percentage of under .290 at the time he joined the Rays. They also employed Ben Grieve (.230/.371/.345) on whom they spent another 28% of their payroll, adding up to a cool 61% going to players who were basically unproductive
  • The 2001 Angels paid Mo Vaughn 27% of their payroll, and he of course he didn't even play due to injury and was traded to the Mets in December of 2001.
  • Greg Vaughn would hit just .224/.317/.408 for the Brewers in 1995 before turning it on in 1996 in time to get traded to San Diego at the end of July, where he would go on to hit 50 home runs in 1998.

As for teams, as you might imagine it's easier for teams with smaller payrolls to spend a large percentage on one or a few players, since player salaries are basically set by the market, whereas payroll is controlled by individual owners. As a result, you see Florida (1998-2000) and Milwaukee (1995-1996, 2004) making the top 20 three times, and Detroit (1996-1997), Toronto (2003-2004), Oakland (1996-1997), and Kansas City (2003, 2005) appearing twice each.

But what of the claim about 16% and 20 years?

In perusing the top 100 players who consumed scads of the payroll of their respective teams, it turns out the first team to make the playoffs was the 1997 Giants, who ranked 39th on the list when Barry Bonds earned $8.6M (24.4%) of the Giants $35.6M payroll. That Giants team won their division, but they were swept by the Marlins in the division series. Next was the 2005 Houston Astros, who had both Jeff Bagwell and Roger Clemens, 44th and 45th on the list. Each player in 2005 earned $18M which represented 23.4% of the Astros payroll of $76.8M. The complete list of teams that made it to the post season with a player among the top 100 in payroll consumption:

                                                Pct                Div
Year Team   Name                Sal   Pyrll   Pyrll   W   L  Pct  Rank WC  Div Lg  WS
1997  SFN   Barry Bonds        $8.7   $35.6   24.3%  90  72  0.556   1  N   Y   N   N
2005  HOU   Jeff Bagwell      $18.0   $76.8   23.4%  89  73  0.549   2  Y   N   Y   N
2005  HOU   Roger Clemens     $18.0   $76.8   23.4%  89  73  0.549   2  Y   N   Y   N
2003  OAK   Jermaine Dye      $11.7   $50.3   23.2%  96  66  0.593   1  N   Y   N   N
1997  HOU   Jeff Bagwell       $8.0   $34.8   23.1%  84  78  0.519   1  N   Y   N   N
2000  CHA   Frank Thomas       $7.1   $31.1   22.8%  95  67  0.586   1  N   Y   N   N
1991  TOR   Joe Carter         $3.8   $16.9   22.4%  91  71  0.562   1      Y   N   N
2002  MIN   Brad Radke         $8.8   $40.4   21.6%  94  67  0.584   1  N   Y   N   N
2004  HOU   Jeff Bagwell      $16.0   $75.4   21.2%  92  70  0.568   2  Y   N   N   N
2001  OAK   Johnny Damon       $7.1   $33.8   21.0% 102  60  0.630   2  Y   N   N   N
1995  SEA   Ken Griffey        $7.6   $36.5   20.8%  79  66  0.545   1  N   Y   N   N
2003  FLO   Ivan Rodriguez    $10.0   $49.5   20.2%  91  71  0.562   2  Y   N   Y   Y

As you can see, the first team on the list that won the World Series was the 2003 Marlins with Ivan Rodriguez who placed 97th, consuming 20.2% of the $49.5M payroll. So although it would appear that the figures of 16% and none in the last 20 years may be a bit off, this cursory look certainly validates the point being made.

Payroll Distribution

But is there a more comprehensive way to look at salary variation within a team and compare teams across leagues and seasons? It turns out there is.

Rather than looking only at the player with the highest salary, we can instead create a measure for the entire team by calculating the standard deviation of the salary for each team. But we'll need a slightly different approach, since teams obviously have much different average salaries for their players both within the context of a single season (for example the 2005 Yankees average salary was just over $8M, whereas the 2005 Devil Rays was just over $1M) and over time (the highest total payroll in 1990 was--surprise!--the Royals at $23.4M, while in 2005 the Yankees payroll was almost ten times that).

One way to level the playing field is to calculate the coefficient of variation by dividing the standard deviation by the mean or average salary for the team. This produces a dimension-less number we can then use to compare teams both within and across seasons. As an example of this approach, take a look at the following graph which plots this payroll coefficient of variation (CV) against the total payroll for 2005.

What you can see here is that some teams with high payrolls such as the Yankees, Red Sox, and Cubs also have a low Payroll CV, indicating that in spending all that money they're spreading the wealth, so to speak. If we had looked only at standard deviation, the Yankees would rank first since a larger mean is usually accompanied by a larger standard deviation. On the other hand, Colorado, Houston, Kansas City, and Texas all stand out as teams whose payrolls are not very evenly distributed, and of course both Colorado and Kansas City have fairly small payrolls to begin with. This can be contrasted with the Devil Rays, who have the smallest payroll and also one of the lowest Payroll CVs indicating that they're spending their money on a collection of lower-priced players.

We discussed the Astros above, but the Rockies going into 2005 were paying Todd Helton at $12.6M and Preston Wilson at $12.5M when their total payroll was just $47.8M, meaning that together they consumed over 52% of the team's player salaries, and which also ranked them 25th and 26th in the top 100 since 1990. Wilson was subsequently dealt to the Nationals at mid-season, which illustrates the limitations of this approach. And of course Mike Sweeney and the 2005 Royals made the list at number 13.

But is there any relationship between teams with more evenly distributed payrolls and winning?

To look at that question we can calculate the Payroll CV for every team since 1990 and then run a simple linear regression to see how well variation correlates with winning. First, however, we might want to know if variation within payrolls has increased or decreased over time. The following table breaks down the results by showing the average Payroll CV under the three most recent Collective Bargaining Agreements (CBAs).

CBA         Payroll CV
1989-1996   1.25
1996-2001   1.26
2002-2005   1.26

So given that the underlying distribution of salaries within payrolls hasn't really changed, we can now move on and compare the teams across the entire 1990-2005 period. To begin, here's the top and bottom ten teams in terms of Payroll CV.

Top Payroll CV 1990-2005
                               Payroll
Year  Team  Lg     W   L   Pct      CV
1998  FLO   NL    54 108 0.333    2.57
1996  DET   AL    53 109 0.327    2.43
1996  OAK   AL    78  84 0.481    2.27
1997  OAK   AL    65  97 0.401    2.22
1999  FLO   NL    64  98 0.395    2.05
2000  FLO   NL    79  82 0.491    2.05
1996  MIN   AL    78  84 0.481    1.98
1998  CHA   AL    80  82 0.494    1.98
2003  TBA   AL    63  99 0.389    1.97
2004  TOR   AL    67  94 0.416    1.96

Bottom Payroll CV 1990-2005
                               Payroll
Year  Team  Lg     W   L   Pct      CV
1992  CLE   AL    76  86 0.469    0.70
2002  SEA   AL    93  69 0.574    0.74
1991  DET   AL    84  78 0.519    0.74
1991  OAK   AL    84  78 0.519    0.77
1990  PIT   NL    95  67 0.586    0.78
2004  SEA   AL    63  99 0.389    0.81
2001  SEA   AL   116  46 0.716    0.82
1991  NYN   NL    77  84 0.478    0.82
1992  LAN   NL    63  99 0.389    0.86
2003  NYA   AL   101  61 0.623    0.86

One of the immediate things that jumps out is that both of the teams with the most variability in their payrolls lost 108 games or more, and of the top ten, six lost 94 or more and none reached .500. On the contrary, the list with the lowest payroll variability includes four teams with 93 wins or more, two with 100, and just three with sub .500 records.

So is there a relationship here?

Well, it turns out that when you compare Payroll CV, total payroll, average payroll, and maximum individual salary with winning percentage, Payroll CV correlates more strongly than the others as shown in the following table that lists the correlation coefficient (r) which is a measure of the strength of the linear relationship between two sets of data.

Measure          r
Total Payroll   0.297
Average Salary  0.301
Max Salary      0.116
Payroll CV     -0.337

As you can see, the other three measured are positively correlated with winning percentage, while Payroll CV is negatively correlated indicating that as Payroll CV goes up (indicating more money tied up in fewer players), winning percentage goes down. Now, of course, the correlation would be considered weak and in fact can interpreted as meaning that approximately 11.5% (.337 squared) of the differences in winning percentage can be attributed to payroll variation. You can view that relationship graphically where Winning Percentage is plotted against Payroll CV and the strength of the relationship represented by the downward sloping line as shown below.

But what if less variability in a team's payroll has a larger effect in reaching the postseason than in simply winning games during the regular season? For example, one might postulate that while having a few big stars (and hence high salaries) helps during the regular season, it really helps a team get over the hump and into the postseason when those stars do their magic and therefore lead your team to a championship. To gauge whether this might be the case we can create a "postseason index" that assigns weights, albeit somewhat arbitrarily, to the various postseason events as follows:

  • Win a Wild Card berth = 1 point
  • Win a Division Championship = 3 points
  • Win a League Championship = 5 points
  • Win a World Series = 7 points

As an example, the 2005 White Sox earned the maximum 15 points, while Anaheim Angels earned three points by virtue of winning their division but then getting beat in the ALCS.

It turns out that when we assign these weights to all teams since 1990 and correlate again with Payroll CV (excluding 1994 of course), we find that the correlation coefficient is -.173. In other words, making the postseason and succeeding is about half as strongly correlated with Payroll CV as is winning percentage in the regular season. But what if we exclude those teams that didn't make the playoffs on the theory that a few stars may not help you reach the postseason but do help you succeed once you get there? When we do so the correlation coefficient drops a bit, to -.149, providing little support for the theory.

A Team Game

Although the correlations are fairly weak, ceteris paribus, this analysis supports the idea that teams with more balanced payrolls do in fact perform somewhat better on the whole, and of course that makes some intuitive sense. Baseball, unlike basketball as the recent NBA Finals reminded us, is a game where the whole is often greater than the sum of the parts, and a lineup or pitching staff can be adversely impacted by a handful of sub-par performers.

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