By Neil deMause

With the Yankees' signing of Jacoby Ellsbury, it's officially the season to goggle at the premium price tags being placed on this year's free agent crop. Already this year we've had crazy money thrown around on some store-brand names: "Jhonny Peralta is worth $13 million a year?!?" and "Ricky Nolasco is getting more than any free agent in Twins history!?!" are both in the early running for the prized Most Pundit-Outraging Winter Signing crown, claimed last year by the Tigers' re-signing of Anibal Sanchez, which, um, actually worked out pretty well. And now that Ellsbury is set to be paid more than $20 million a year to chase flyballs across the street from where DiMaggio and Mantle roamed, we can expect to see the winter's first round of "I know he's good, but that good?"

This being the age of advanced baseball statistics, there have been multiple attempts to come up with ways of proving, once and for all with hard numbers that must be right because math, which free agent salaries are truly ridiculous and which only seem so when compared with what you're making not to hit a ball with a stick. Baseball Prospectus took its metric of total player value VORP (Value Over Replacement Player) and concocted MORP (Market value Over Replacement Player), which got updated a few years later before quietly disappearing from the site. FanGraphs has the store-brand-named Dollars, which helpfully tells us that Ellsbury was worth a whopping $28.9 million last year, while Peralta has been worth an average of $17.1 million each of the last three years - significantly more than Ellsbury's new Yankee teammate Brian McCann, if you believe their numbers.

As fun as these stats are to play with, though -- it's always nice to put complex decisions about how much a player will actually contribute to a team into simple my-guy-contributes-more-points-than-your-guy fantasy baseball terms -- they have two big drawbacks. First off, the average cost of a win can't be calculated until the signing season is over: We can't know whether, say, Jhonny Peralta (roughly a three-win player according to FanGraphs, BP, or Baseball-Reference, compared to the average scrap-heap player he'll replace) is being overpaid until we know what Robinson Cano (eight wins in 2013) and Shin-Soo Choo (five wins) end up being paid as well.

Even then, though, all this will tell us is whether Peralta is going for about what above-average major-league starters are going for. That's certainly interesting -- it would mean that Cards GM John Mozeliak can expect to make it through next week's winter meetings without other GMs laughing and pointing -- but it doesn't tell us anything about whether players overall are being paid what they're worth. In other words, $13 million a year might be the going price for a three-win player, but are wins really worth $4 million apiece?

"Worth" in pay is a dodgy concept. Cano -- or Robert Downey Jr., or for that matter Tony Stark -- would argue that they can do something not everyone can do, so they deserve top dollar. Other folks -- let's say, for example, Walmart workers, or hot dog vendors, or Pete Kozma -- can point out in their defense that while they may be replaceable, they're helping make possible a massively profitable enterprise and should share at least partly in the boodle.

For movie stars, the assumption is that they earn their pay at the box office: Downey may come at a premium, but better that than risk moviegoers refusing to see Iron Man 4 starring Patrick Warburton. For athletes, it's the same principle: By putting fannies in seats and eyeballs onto TV screens, they're presumably generating enough revenue to justify salaries ten times what they were in Chico Escuela's day. But do they?

For that, Dollars and MORP and other measures based on average free agent pay are useless, because they just tell us how players are paid compared to their peers. To tell whether GMs are actually spending money as a wise investment or just because they have it to burn, we need to answer another question: Will the extra wins that a player generates bring in enough new revenue to pay off the team's investment?

I dipped my own toe into this topic a few years ago, thanks to the work of two baseball numbers minds far greater than mine. The pioneering baseball economics researcher Doug Pappas -- who tragically died young in 2004 while on a hiking trip -- had come up with a stat called Marginal Payroll per Marginal Win (MP/MW), which was simply an attempt to suss out which teams were spending money the most wisely. (Teams that spent and spent and went nowhere in the standings came out poorly here; the late-Ripken-and-Anderson-era Orioles were inevitably at the bottom of the MP/MW standings.) Pappas didn't do any fancy math - he just divided the numbers of wins a team had above what a team of minimum-wage scrubs could do (the 2013 Astros not having been invented yet, he used a hypothetical 113-loss team as his baseline), but it was good enough for a rough estimate.

A few years after that, a not-yet-uber-famous Nate Silver, writing for the Baseball Prospectus book Baseball Between the Numbers, dissected revenue figures attached to ticket sales, club seats, TV revenue, and anything else he could plug into Excel, in an attempt to concoct a more accurate measurement of precisely how much money a team could expect to rake in from each additional win. (The result was actually a curve, with victories around the 90-win mark worth the most, since they're the most likely to make the difference between reaching the postseason and spending October sending out "Thanks for putting up with us this year!" emails to fans.) Also writing for BP at the time, I had the bright idea of putting the two sets of numbers together - and realized that not only could I get a more accurate sense of who was spending money best and worst (the Orioles, now saddled with an $8-million-a-year Kris Benson, were still doing terribly), but I could use the same numbers to figure out who was spending more on players than those players were earning them in new revenue.

The result: pretty much everyone. Other than the Moneyball A's, the Twins, and the Marlins, every team in baseball appeared to be spending more on players than they earned from the additional wins those players brought. Either team owners genuinely cared more about winning ballgames than making money -- or baseball teams as a whole were being amazingly stupid about how much cash they were shelling out.

Would these numbers look any different today? Silver isn't immediately available to update his chart, having since ascended to a higher plane of existence, but given that average MLB salaries have risen more than 20% since then, while overall inflation has only been 16%, it's not looking promising. (And before anyone mentions it: Yes, MLB revenues are rising far faster than inflation, but that's not the same as a rise in marginal revenues from a win; if every team owner is guaranteed a hefty check just by showing up and putting his games on cable, that actually makes it less worthwhile to sink those dollars into a Cano or Ellsbury in hopes of a few extra wins.)

The best attempt at updating Silver's numbers that I've been able to find actually comes from a Brown University undergraduate thesis from last year, in which honors economics student Graham Tyler conducted an insanely thorough analysis to determine how much each additional win was worth to each and every team in baseball. His conclusion: Wins are worth more once you get above a .500 record, but even then the average team gets only about an extra $1.5 million in revenue from each win - meaning even if Jhonny Peralta is "worth" his new contract based on what the market rate is for shortstops, he's only likely to bring the Cardinals an extra $4.5 million next year, while being paid nearly three times that.

This is an absolutely crazy notion, and requires an explanation. Some of the leading options, none entirely convincing:

  1. Incomplete information: GMs are signing players based not only on what they hope they'll do on the field, but on where they hope they'll be in the standings. Or to put it more simply: Dayton Moore is convincing himself that Carlos Beltran is going to be the Carlos Beltran of old, and that his Royals will be close enough to the pennant race that this will make a difference, either of which could happen, but neither of which is anything close to a sure bet.
  2. Butt-covering: The GMs who are making spending decisions are primarily concerned with saving their jobs, not maximizing revenue - and nobody ever got blamed for spending too much en route to winning the World Series.
  3. Eyes glazing over: If you threw up your hands at some of the math above - even before clicking on that Brown paper with its regression coefficients- think of how you'd handle it if you were sitting on the other end of a phone line from Scott Boras. ("I know your guy had a great year last year, Scott, but you're failing to understand the principle of multicollinearity.") It's far easier to just ask your boss for a budget and then spend whatever you're given - which makes no sense from any kind of rational economic perspective, since every team owner has to know that you have to spend money to make money.
  4. All the other kids are doing it: As the growing field of behavioral economics has found, consumers are likely to make spending decisions less on the basis of some rational economic incentive, and more because it's what they've seen other people do, and grown accustomed to doing themselves. We're back to Mozeliak knowing no one's going to laugh at him in Orlando next week, even if a $13 million Peralta makes as much economic sense as a $5 latte.

For baseball fans, it doesn't matter all that much which explanations are correct -- after all, it's not like team owners are going to give us lower ticket prices if they're not spending as much on players. (On that question, the evidence is clear.) Still, it's a bit of an eye-opener to conclude that there's no rhyme or reason behind baseball salaries beyond "if we don't give this guy $13 million a year, someone else will."

Or maybe not. After I found Tyler's paper, I did a quick Google search to see where he might be found these days. And lo and behold, the fresh college graduate has a new job.

So maybe not every team is ignoring economic reality come free agent time. And maybe if the Rays take a pass on any big signings this winter, we can credit Stuart Sternberg with being more than just a cheapskate.

* * *

Neil deMause is a Brooklyn-based journalist who has covered sports economics for Slate, the Village VoiceBaseball Prospectus and a bunch of other places you wouldn't remember. He runs the stadium news website Field of Schemes, and co-authored the book of the same name.