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April 10, 2014

Explaining Spending

How the Market Sets the Price of a Win

by Lewie Pollis

This article started with the realization that I had been wrong. Believe it or not, it’s happened before; unlikely as it seems, it may happen again. I think I’ve got it right this time, but in the spirit of intellectual honesty and taking responsibility for my past arguments, I wanted to note that I’ve been down this road before.

If you’ve seen…well, just about anything I’ve published about baseball over the last several months, you may know that I am particularly interested in how markets in baseball work (and I don’t just mean for players). At some point in the months-long process of writing my senior thesis, I had what I thought was an epiphany: If MLB teams are anything close to rational, the cost of a win on the free agent market must be approximately equal to how much a marginal win is worth across the league. It seemed logical, and it was eloquent in its simplicity.

I now have a different idea about where the cost of a win comes from—it’s more convoluted, but it also makes more sense. And in order to properly explain why I think I’m right this time, I have to start with why I was wrong before.

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Related Content:  Spending,  Cost Of A Win

18 comments have been left for this article. (Click to hide comments)

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I think you are missing one important point in your construct. Given the "25 roster spot" constraint, I think there is also a different marginal value per win for the highest WAR players (since their supply is especially limited, and their value to the richest teams is uniquely higher). I end up with the Canos, Ellsburys and Tanakas valued at $8 or $9 million per win because their wins are more efficiently packaged vs. roster spots, but a 0.5 WAR player only commands $4-5 million per win (since there are far more of them, and a finite supply of roster spots to employ them). You get test this hypothesis by seeing if the residuals are positively skewed vs. your "average" valuation for the most expensive players.

Apr 10, 2014 04:27 AM
rating: 2

Excellent point. When the picture of Hanley that accompanies the article was captioned "If Hanley hits free agency, he'll hope the cost of a win continues to climb." I was hoping that this was the reason why. He's precisely the kind of guy who could get the elite player bump.

Apr 10, 2014 04:57 AM
rating: 0
Lewie Pollis

That's a good point, but as I said the idea of the roster constraints actually limiting how many wins you can be is a truly extreme case.

If the Dodgers were trying to put together literally the best team money could buy then yes, they'd be willing to pay a premium for being able to condense it into one roster spot. But that would really be an exceptional scenario.

To use the Cano example, are the Mariners really a good enough team that having Cano and his X wins is more valuable to them than having two players who would each be worth X/2 wins? I strongly doubt it that their replacement level is that high. That doesn't mean that they're not willing to pay a premium for a star, but it does mean that doing so isn't rational.

Matt Swartz has done some good work on this in the past that showed that, in general, the cost of a win is linear—i.e., a player worth X wins really does make about double what a player worth X/2 wins makes. I believe Dave Cameron found evidence of a premium for star players this past offseason, but his methodology is less similar to mine than Matt's is and he noted that this winter was the exception to the norm.

Apr 10, 2014 07:11 AM
rating: 1

PECOTA thinks Cano is worth 5.2 WARP. In CF, they start Abraham Almonte (0.5), But at every other position, the Mariners field a player worth 1.5-2.5 WARP.

Absent Cano, they'd presumably play Nick Franklin (2.5 WARP in 2013) at 2B. Franklin's value is glove-heavy, so they can't slide him to DH, and thus lose him to AAA. So adding Cano is still +2.7 WARP, despite a worst-case situation where the backup choice looks unusually good, but yet can't move laterally to replace a different starter.

Yet adding two half-Canos looks worse unless one can play CF, since they'd be replacing MLB starters who average around 2.0 WARP each, and the Mariners would only total +1.2 WARP for the two Half-Canos (+2.6 each).

Keep in mind that high-end free agents displace starters, not the 25th man, and starters aren't usually worth 0.0 WARP. Now, the starter they displace often does displace the 25th man, but with reduced playing time, the value of that is minimal unless an injury happens.

A more thorough study (for example, constructing a 'what-if' tree for each team's WARP change upon losing each starter) could find the optimal strategy. Matt Swartz answers what teams _are_ doing (a start), but not necessarily what they _should be_ doing. As your thesis shows, those don't always intersect.

Apr 10, 2014 07:51 AM
rating: 3

But there is another problem -- it is not entirely clear at least intuitively that each players financial contribution to the team can be measured by wins, especially in the short term. For example, how much was Mariano Rivera worth to the Yankees in attendance, souvenirs, TV audience, refreshments, etc. last year? His financial impact to the team may well have been significantly greater than his proportionate "win" value. And that is not only a Yankees phenomena -- Mets attendance when Matt Harvey pitched versus all other games; keeping Giancarlo Stanton in FLA; the Phils not blowing up the team; Miggy's contract extension all may make a lot more financial sense than they do if you just took total WAR of free agents/ total spending to come to an average. Many people pay to see the stars, even if two regulars add up to the same number of wins. My point is that the outlier players are likely to get disproportionate payment, even apart from the roster limitation/opportunity cost issue.

Apr 10, 2014 10:02 AM
rating: 0
Lewie Pollis

You're right about that, and that's something I'll be exploring in my next article. The problem with that way of thinking is that those kinds of marquee players are very much the exceptions, not the rules. Of the dozens of free agents who hit the market every year, how many of them really carry that kind of celebrity value? I'd guess at most only 10-20% of them bring any significant amount of extra revenue besides their on-field performance. Sure, it matters for a few players, but I'm not convinced that it would have a substantial impact on the market price of a win.

Apr 11, 2014 08:51 AM
rating: 0

In the example, is the next win valued at 1 million because of budgetary constraints? If that's the case, after they sign player 1 to a 7 million dollar deal, they should now be and to offer player 2 four million, which means player 2 will still get 5 million from the second team pushing the value of the win above five million.

Apr 10, 2014 07:56 AM
rating: 0
Lewie Pollis

Not necessarily.

Imagine a team that's 90% sure it will make the playoffs. Adding one more win could maybe bump its odds up to 99%, so that could be worth a lot. But any additional wins beyond the next one don't matter very much. That's more what I had in mind.

Apr 11, 2014 08:53 AM
rating: 0

And you wanna be my latex salesman? :) I'm no Art Vandelay but he told me you guys are awfully good at math. What I glean from this discussion is that dbiester is on to something.
I thought it would come out in the piece but the Yankees must win consistently or the edifice topples. Their winning is worth so much more money than anywhere else. This has been written about elsewhere.

Apr 10, 2014 10:19 AM
rating: 0

Yes, but the article acknowledges that different teams have different priorities on the demand side, so a win to the Yanks may be worth more than one to the cubs, and then you get into marginal win values and play off scenarios, but there is also a value above the win contribution for certain players -- call it the "celebrity value" if you will, which makes the "average" value of a win interesting but incomplete.

Apr 10, 2014 10:27 AM
rating: 0

Another perspective on this: I'm sure you're not advocating that teams in any way get together to reach "collective rationality", as that would have extremely serious implications for baseball's antitrust exemption. Thus, another factor in this calculus is that teams are essentially required to operate in the dark, at least at the micro level.

Apr 10, 2014 10:53 AM
rating: 0

The market will never be flat because, first the teams have widely variable budgets (so $3M to Miami means more to them that $3M does to the Dodgers), and due to relative wins.

By this I mean that, as another poster said, the Free Agent will be displacing another starter with some value. As different teams have different valued starters, the relative wins the Free Agent adds depends on who is being displaced.

For example, if a team has no incumbent at Shortstop, then the value of the Free Agent would be its highest, or equal to their wins. However that same player going to another team with a serviceable incumbent, would have less value because there is a difference in wins. And another team might actually have a better incumbent than the Free Agent, but want to bring them on board as insurance. So its not as simple as buying wins.

Also, because new players are always graduating to the major leagues, and are all relatively free, there is always certain downward pressure on free agent costs on those teams with good player development. So 2 teams with similar payrolls in similar markets will value the same player differently if one's farm system is better than another. They aren't as desperate to fill the hole and possibly block a free player in the future.

Apr 10, 2014 12:20 PM
rating: 0

One thing that a lot of people taking this approach don't take into account is something I like to call "Someone's Gotta Play The Games."

Assuming relative rationality on the part of teams, the management is reasonably aware of a team's chances of competing in a given year. But even if a team isn't going to compete, they are still responsible for putting a reasonable entertainment product on the field. Now the traditional response from the sabermetric community has been, "This is no problem, freely available talent, replacement-level players!"

The problem is that running out a squad of 4-A guys concedes to everyone--both the industry and, probably more importantly, local fans--that the towel is out before the first game is played. Beyond that, the 4-A guys may end up being a lot worse than advertised or may end up being embarrassments at the Major League level in conduct, bonehead mistakes, etc.

As a result, while it drives sabermetric types crazy, I'd argue it actually is rational to pay some amount of money above the Major League minimum salary to veterans who project to play at or below replacement level simply to purchase a kind of respectability--even if that purchase nets the team no wins.

Apr 10, 2014 14:13 PM
rating: -1

Is that you, Dayton Moore?

Apr 10, 2014 14:30 PM
rating: 2
Lewie Pollis

I buy that for sure and I think it fits very well with my theory.

If you'll notice, I haven't made any claims about what any individual team's demand curve for wins actually looks like nor what it should look like. What you're basically saying (I think?) is that the 50th win is generally worth more to a team than the 80th win. That actually explains why even bad teams enter the market every year.

Apr 11, 2014 09:05 AM
rating: 0
Nathan Aderhold

I was following along pretty well until you introduced the "equilibrium quantity Q" stuff. Would you mind elaborating on that concept for the uninitiated?

Apr 10, 2014 15:58 PM
rating: 0
Lewie Pollis

In any given market, there is a quantity Q and a price P of goods/services produced/provided. If you have graph with supply and demand curves (both are expressed as Q as functions of P), the equilibrium point—i.e., where the market will produce—will come where the two lines cross. At that point, the price will lead consumers to purchase exactly as much as producers are willing to supply.

In this case, we take the equilibrium quantity Q as given because the supply of free agent wins is basically static regardless of price. The question, then, is: at what price P will the 30 teams combine to want to buy exactly Q wins?

Apr 11, 2014 09:09 AM
rating: 1
Nathan Aderhold

Thanks, Lewie! That clears things up for me considerably.

Apr 15, 2014 11:08 AM
rating: 0
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