Payroll Leverage: Asessing Bang-for-your-Buck

[GOOCH]

As I've mentioned in previous threads, I'm interested in examining the relationship between payroll and wins obtained by a team. Naturally, the purpose of increasing payroll is to field a more competitive product, and hence it is natural to look at payroll and wins as one would the performance of any business. The more you pay, the better you expect your outcome to be.

Of course, it doesn't always work out that way. Sometimes you don't get what you paid for. In baseball, perhaps you overpaid for an outlier season, and are getting much less production than the contract you gave to the player (i.e. Tino Martinez). Lesser production yields fewer wins on the field. Or, perhaps you've been unlucky---> a previously productive player whom you've allocated a substantial portion of your payroll to is injured and thus unavilable to your team and thus you're mising his production entirely (i.e. Chris Carpenter). Or the player may have been injured and, while on the field, is providing much less production (i.e. Scott Rolen).

But that's just one side of the coin. Given the institutional structure of baseball, there are bargains to be had as well. Young players can be highly productive and yet, because of the rules of MLB, cannot demand salaries commiserate with their on-field production (i.e. Albert Pujols, 2001). Or perhaps you've signed an oft-injured and rarely productive veteran who suddenly 'rediscovers' his ability and puts up numbers closer to his prime than he has in years. Here we see the flipside of the payroll issue: you can considerably outperform the payroll you've allocated to your team.

So how to assess this phenomenon? How do we tell if a team is getting what they paid for? Or much less or much more than they paid for? One way is to take a season and look at the relative performance of all the teams in baseball in regards to their payroll and the wins. I've provided a scatterplot here that does exactly that:

http://www.donaldgooch.com/scat.gif

Note we can see that in 1985 St. Louis does pretty well for itself...it's located towards the upper-middle of the pack, but posts the best record in baseball. Contrast that with Atlanta. The Braves have one of the higher payrolls in 1985 but post one of the worst records that season. They aren't getting much bang for their buck.

Now, while a scatterplot showing payroll as a function of wins (or vice versa) is helpful, it doesn't provide for precise comparisons. For that we need to represent this relationship numerically. Now, the problem here is that team performance and payroll use different scales (payroll is in dollars and TP/wins are in...well, wins...). We can resolve that by putting one in terms of the other (dollars per win or wins per some fixed dollar amount). For example, St. Louis paid $117,000.82 for each win in 1985.

While that method will work for each year, another problem is apparent if we wish to compare bang-for-the-buck over time. Much like the problem of inflation when comparing prices two decades apart, major league payrolls have exploded over the last few decades. Wins are comming much more expensive in 2007 than they did in 1987. So, the trick is to be able to compare a bargain or bust payroll/win in 1985 with a bargain or bust payroll/win in 1995.

This is where a bit of math comes in. In order to compare teams corss-sectionally as well as in a time-series, one solution is to standardize all of the variables according to one scale. This is done with a "standardized score" (often called a z-socre), where I represent observations in terms of standard deviations rather than their actual figures. In the context of this problem, it means representing payroll and team wins according to deviations from the mean values for those two variables for each year:

P* = [(P - Pm) / Psd]

In the case of payroll, where P is the payroll of the team for a year (say, 1985), M is the mean (or average) payroll for 1985 in all of baseball, and SD is the standard deviation (or standard variance) of payrolls in all of baseball for 1985.

W* = [(W - Wm) / Wsd]

In the case of team performance, where W is the wins of the team for a year (say, 1985), WM is the mean (or average) wins for 1985 in all of baseball, and WSD is the standard deviation (or standard variance) of wins in all of baseball for 1985.

For example, in 1985, the St. Louis standardized payroll is:

[(11817083 - 10075565.23) / 2470845.43)] = 0.70483

And the standardized wins for St. Louis in 1985 is:

[(101 - 80.8076923 ) / 12.5730481] = 1.60600

This means that the St. Louis payroll was 0.70 standard deviations above the mean payroll in 1985, while its wintotal was 1.61 standard deviations above the mean wintotal in 1985.

So now we have standardized scores for both payroll and wins. OK, you've probably guess where this is going. Now that we've got payroll and wins on the same scale, we can represent them directly as one score and compare them across time. Hence the formula for payroll leverage is:

L = (W* - P*)

The key to understanding this figure is understanding that it is centered around zero: a perfect translation of payroll to wins for a given year will yield L = 0. So a positive L means that you're getting more bang for your buck in terms of spending on payroll and team performance, while a negative L means that you're getting less bang for your buck in terms of spending on payroll.

Again, returning to the St. Louis example:

(1.60600 -0.70483) = 0.90117

This means that St. Louis got alot of 'bang for the buck' in 1985. Their payroll leverage score was nearly a full standard deviaiton above the mean leverage in 85. What's neat about this figure is that it relates payroll and wins directly. That means that even if a team does well, if they spent alot of money for that win total, they can have a negative leverage. And a team that does poorly may have a positive leverage score if they aren't paying much for that win total. Below I provide a graph of the Cardinal's Payroll Leverage from 1985 to 2007. Remember, anything above zero means the Cards are getting more bang for their buck, and anything below means less.

http://www.donaldgooch.com/lev.gif

As you can see in the graph, the Cards' payroll leverage tanked in the early 90's...with a bloated payroll relative to the rest of the league and not much to show for it. The mid 90's saw the cards recover (mostly through a reduction in payroll relative to the rest of the league) to post positive leverage scores. The mid 90's saw a bump in payroll that didn't immediately yield results, hence the negative leverage scores. But eventually performance caught up with the Cardinals investment, and through most of the oughts the franchise posted positive leverage scores. Of course, the Cardinal bubble burst in 2006 (all those injured players not contributing during the regular season) and the situation has worsened in 2007 (and that's bye-bye to Walt).

I think this fairly represents the 'bang-for-your-buck' concept. Asessing the extent to which teams are able to leverage their payrolls to produce sucess on the field is important in understanding and comparing franchises both within a season and across time. I invite thoughts, suggestions, and criticisms. D.GOOCH

[GOOCH]

For those curious, here are the Cubs.

http://www.donaldgooch.com/image002

[GOOCH]

http://www.donaldgooch.com/levthree

This graph illustrates a point I want to emphasize: a good payroll leverage does not mean you're fielding a competitive team. It just means that you're getting more wins than your payroll would indicate. For extremely low payrolls, you don't need alot of wins to end up on the 'positive' side of things. The fact that should be apparent here is that getting what you pay for isn't all that great when you're paying for crap.

[Grey's Anatomy # 1 Fan]

How's does the Cardinals winning a World Series and those other teams not figure into the equation or does it?

[GOOCH]

Doesn't. I'm looking at regular season only.

And to finish off the Central, here is Houston:

http://www.donaldgooch.com/levv

[GOOCH]

Here are the Yankees:

http://www.donaldgooch.com/yanks

Unsurprisingly, the Yankees don't seem to be particularly focused on getting the best 'bang-for-the-buck' out of their payroll / win decisions. They only time over this period that they creeped into positive territory was during their championship run and before Steinbrenner ratched up the payroll stakes in 2001. Since then, as is apparent from the graph, the Yankees are paying *alot* for their wins. D.GOOCH

[MissouriBird]

Wow! Great work, Gooch. Interesting that the Cards' payroll was actually larger than the Mets in '85. (Did I read that correctly?)

In your Reds-Pirates-Brewers graph, which color is which team?

Oh! Sorry 'bout that - my screen wasn't big enough to pick up your legend on the right side of the picture.

Never mind.

[CardsFanInCanada]

Originally Posted by Grey's Anatomy # 1 Fan

How's does the Cardinals winning a World Series and those other teams not figure into the equation or does it?

The Reds won the WS in 1990, sweepng the Larussa led Oakland A's.

[Lewis]

It does remind one of the Red Sox win in 2004.

[GOOCH]

Thanks to Larry over at Viva El Birdos for the link:

http://www.vivaelbirdos.com/story/2007/10/12/84121/237

Note to posters: I have leverage for all the teams in MLB over the period, so if there's a team or teams you'd like to see, let me know. D.GOOCH

[Migratory Redbird]

Originally Posted by GOOCH

I think this fairly represents the 'bang-for-your-buck' concept. Asessing the extent to which teams are able to leverage their payrolls to produce sucess on the field is important in understanding and comparing franchises both within a season and across time. I invite thoughts, suggestions, and criticisms. D.GOOCH

It's certainly interesting. I'm not sure that it goes much beyond that. Just because numbers are fun to play with doesn't mean that what you built with them while you were playing has any significance whatsoever.

As you pointed out, getting high "bang-for-your-buck" ain't that great if you're buying caca, whereas a team that spends all their money on the equivalent of cavier can lead the MLB in wins while having the worst ''bang-for-your-buck" in the game.

I observed with some interest that the best Cardinals seasons shake out like this:

RANK  SEASON  FINISH         MANAGER     GENERAL MANAGER
  1    1993     3rd           Torre         Maxville
  2    2004   Pennant       La Russa        Jocketty
  3    2005     1st         La Russa        Jocketty
  4    2000     1st         La Russa        Jocketty
  5    1987   Pennant        Herzog         Maxvill
  6    1985   Pennant        Herzog         Maxvill
  7    2002     1st         La Russa        Jocketty
  8    1991     2nd           Torre         Maxvill
  9    1992     3rd           Torre         Maxvill
 10    1986     3rd          Herzog         Maxvill
 11    2001  wild Card      La Russa        Jocketty
 12    1996     1st         La Russa        Jocketty 
 13    1994     3rd           Torre         Maxvill
 14    2003     3rd         La Russa        Jocketty
 15    1989     3rd          Herzog         Maxvill
 16    2006 World Champs    La Russa        Jocketty  
 17    1999     4th         La Russa        Jocketty
 18    2007     3rd         La Russa        Jocketty
 19    1998     3rd         La Russa        Jocketty
 20    1988     5th          Herzog         Maxvill
 21    1997     4th         La Russa        Jocketty  
 22    1995     4th     Torre/Jorgenson     Jocketty  
 23    1990     6th      Whitey/Red/Joe     Maxvill

If I rank the managers and general managers according to average "bang-for-your-buck", it breaks out like ths.

Manager/GM    Avg. Rank
Torre                  10.6
Maxville               11.0
La Russa              11.2
Jocketty              12.8
Herzog                 14.3

Not that I think it means anything one way or the other.

What would be a lot more interesting would be calculating marginal dollars per marginal win and comparing that for each manager/GM combination. However, it would still be subject to the same chance factors that bedevil any GM assembling a team -- who gets injured and whose performance either drops off the table or shoots through the roof.

A better measure is to look at marginal dollars per marginal win. Using MLB's accounting, the cheapest possible team would cost its owner about $13,000,000: $5,000,000 for 25 players making the major league minimum of $200,000; another $800,000 for four minimum-salaried players on the DL; $1.2 million for the remaining 11 men on the 40-man roster; and $6 million for benefits. I estimate that such a team would win 30% of its games, roughly a 49-113 record, 13 games worse than the 2001 Devil Rays and five games behind the 1998 "fire sale" Marlins. (The exact number used doesn't matter when comparing teams from the same season.)

A team's marginal spending per marginal win thus equals its payroll, minus postseason revenues and minus the $13 million minimum, divided by its winning percentage minus .300, times 162 games. Using the Yankees for an example: ($118,000,000 payroll - $16,000,000 postseason money - $13 million minimum) / ((.594 - .300) * 162), or $89 million/47.6 wins, or about $1.87 million per marginal win. That's the same as the Cincinnati Reds spent to finish 66-96.

The above was written in 2002. The formula would have to take into account how baseball minimum salaries changed from year to year, but that wouldn't take too long to enter into a spreadsheet. Entering each team's record from year to year would take a little longer but, if you've already got that information entered into a spreadsheet, adding the formula and minimum salaries wouldn't take long.

[GOOCH]

I looked at marginal wins, it doesn't change the payroll leverage number because all it does is change the scale, and leverage is based on the relative distiance between wins & payroll...not the absolute difference.

The only way to assess payroll & wins against an absolute standard would be to weight wins in terms of importance. I've been pointed to a recent effort to weight wins according to the likelihood that each win will get a team into the playoffs...now that would change the results as it would change the relative distance between win totals. I haven't had a chance yet, though, to look at it. D.GOOCH