Eat The Rich (Part 1)

Sports - September 20, 2007

I try not to be surprised when people tend to their own self-interests in the name of the greater good, so it did not exactly surprise me that someone worth over $1.5 billion thinks that the economic distress of people who are not in fact billionaires means that monopoly power should be used in order to keep his costs of labor down.

(I never said I wouldn’t be disgusted, just not surprised.)

But the Mark Teixeira signing has a lot of people that aren’t Drayton McLane pining after a salary cap, or at least some sort of brake on the enormous salaries we’re seeing this offseason. Leave a little money for the little guy, huh? Love of the game and James Earl Jones voiceovers for everyone!

The reality is that MLB is a business like any other, and if they end up with price controls on their main source of labor, it doesn’t seem likely that they’ll turn around and lower ticket prices out of the kindness of their hearts. It’s a nifty little trick ownership has pulled, however; in a battle between millionaires and billionaires it seems everyone is ready to side with the billionaires.

So let’s go ahead and ask a question: How much is a baseball player worth to his team, in cold, hard coin of the realm? Logically, it would proceed that a player’s value to his team—economically, at least—is tied up into how much additional revenue he brings in.

There are three different sorts of revenue a team earns:

  1. League revenues, or money that is shared between all clubs: national TV contracts, merchandising, MLB.tv and Extra Innings, etc. There is little to nothing a team can do to increase (or decrease) these figures.
  2. Long-term club revenues: things like local TV contracts, sponsorships, euchring a new stadium out of your local municipal government, etc. Because these involve contracts spread out over several years, they aren’t immediately responsive to on-field performance, although you’re obviously better off having a good team than a bad team when it comes time to renew those deals.
  3. Gate receipts: This is any money that a team can lay its hands on as you enter and exit the ballpark. Gate receipts are the aspect of revenue that is most pliable to a team’s one-year performance.

Our best source of publicly-available revenue data is currently the Forbes team financial estimates. I would be remiss if I didn’t mention that there is some controversy surrounding the Forbes estimates, with MLB teams referring to them as utter fabrications. (It also should be noted that this was essentially the reaction from the US Congress to MLB’s own published revenue figures.) In this instance, I’m chosing to stick with the Forbes numbers, mostly because it’s all I have. (I also believe that Forbes is at least trying to be wholly truthful with their figures, which I’m not convinced is true regarding MLB’s periodic disclosures.)

For the years between 2002 and 2007, Forbes only breaks revenue down into two categories: gate receipts and other revenue, lumping our first two categories together. This is unfortunate, but again, we’re at the mercy of the data we have.

Taken alone, the Forbes data tells us little about how teams happen upon those revenues, so we want to add some data to the mix. For the time being, I’ve taken team performance data from the Baseball Databank, and mixed in population data from the U.S. Census. (Unfortunately, that means excluding Canadian teams.)

Let’s keep it simple to start with, and let’s see how well population, win percentage, runs scored, and runs scored correlate with team revenue:

Gate
Other
Total
Population
0.484
0.425
0.576
Win%
0.457
0.086
0.395
R
0.423
0.214
0.429
RA
-0.248
0.029
-0.179

Population is, at least among those four figures, the single-biggest factor in determining how much revenue a team will make. This conclusion will probably be regarded as somewhat obvious, and so I won’t belabor the point.

Just looking at the figures real quick, though, and something pops out at you—and it may be regarded as obvious as well, but I’ll go ahead and belabor this point as it seems to fly in the face of sabermetric orthodoxy: scoring runs seems to get you more money than preventing them, perhaps more than winning. I’m sure we’ve all heard the cliche “chicks dig the long ball,” but it’s another thing to see it carried out to three significant digits.

Running a quick little linear regression, and it really drives the point home: from 2002-2007, a marginal run scored on offense was worth $231,480, and a marginal run saved on defense was worth $86,490. It’s long been a point of contention that teams overvalue a player’s offensive contributions relative to his defensive contributions. It’s plausible, however, that teams aren’t so much ignorant as responding to market conditions.

So now let’s extrapolate out from our regression to a year-by-year basis, using yearly revenue:

Off.
Def.
2002
$188,952
$70,600
2003
$199,870
$74,679
2004
$220,624
$82,434
2005
$239,891
$89,633
2006
$258,521
$96,594
2007
$278,090
$103,905
2008
$300,338
$112,218
2009
$324,365
$121,195

2008 and 2009 are estimated based upon an 8 percent inflation rate year-to-year.

So if Tex is 50 batting runs above replacement level, then his salary value based upon his offense is roughly $16 million in 2009. Accounting for defense and position and you get to shave roughly $700,000 off that value.

Why are the Yankees paying him $20 million for 2009, then? There are several things that are being missed in our simple model:

  • The Yankees could very easily have a higher estimation of Teixiera’s skills (either on offense or defense) than the CHONE projections. Or they might think that his overall impact on their offense is understated by linear weights (top offensive players have a small but meaningful impact on the run environment of their team’s lineup which linear weights doesn’t capture.)
  • Making the playoffs is a great source of bonus revenue for a club, and that’s something that’s not explicitly accounted for in the regression.
  • A player’s impact on single-year revenues is only part of their value, especially in the case of a long-term contract.
  • Teixera’s value to a typical MLB team is not necessarily reflective of his value to a team like the Yankees—we know that market size is a major driving force of revenues, and the Yankees are perhaps the poster child of that. The question is whether or not the relationship between market size and revenue per run/win is linear or not.
  • Forbes could simply be wrong about the amount of revenue MLB teams are pulling in; that would in turn be undercounting the value of each player. For what it’s worth, MLB teams are notorious for hiding revenue using related-party transactions, like giving team-owned regional sports networks sweetheart deals for broadcasting rights, or hiding money in other assets like stadiums. (The Red Sox are astoundingly good at this.)

We’ll examine those issues in Part II.

References & Resources
Thanks to Rodney Fort for his collection of the Forbes data.

Population data comes from 2007 estimates from the US Census.

Team data courtesy of the Baseball Databank.

John Beamer looks at some of the problems with the Forbes numbers and provides some suggestions on how to better estimate a baseball team’s finances.

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