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April 24, 2014

Explaining Spending

Deriving Teams' Optimal Spending Strategies

by Lewie Pollis

A couple weeks ago, I made the argument that the cost of a win on the free agent market for a given season does not represent a generally homogeneous league-wide conception of what a win is worth. Rather, the more logical explanation is that it reflects the largest amount any team would be willing to pay for the Nth win available after the first N – 1 wins were hypothetically distributed in accordance with who valued each of them most highly. (Economic theory can sound weird when you apply it to real life.)

As an economics student and baseball fan I find this idea to be fascinating, but I admit that the origin of the price of a win doesn’t have many practical uses in concrete baseball analysis. However, if I am correct, this theory does have two important implications for understanding how MLB teams (should) operate: that the price of a win and the value of a win are two different things, and that this uncoupling means a marginal win can be worth significantly different amounts to different teams.

With these assumptions in our minds, it is possible to construct a reasonably simple model for a team’s optimal player-signing and front office employee-hiring strategy in the league labor market.

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Related Content:  Spending

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

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You might consider applying the theory to fantasy baseball auctions. The PFM and Mike Gianella provide some guidance, but a bit more economic theory could be useful.

Apr 24, 2014 10:29 AM
rating: 0

You might want to include two additional terms for "covets", and "fetishes". They could go a long way to explaining some of the inefficient market practices.

Apr 24, 2014 13:58 PM
rating: -1

I enjoyed this article and would love to see more like it.

This whole topic is really complex, since establishing those expected values for wins and price-per-win is not a trivial process. Even if you figure out how many wins each available player/employee is worth to each team, and how much total money each team is willing to spend, you still have to make guesses about how they are going to split their money when they can't have all their optimal players (will they pay full price for the one that gives the most marginal utility? Will they go after a bunch of smaller utility guys that have lower costs? etc), and that's really tough to do, even in the more straightforward setting of, say, a fantasy auction draft.

Even if you try to aggregate the numbers, you can easily make a really bad estimate. Let's say that there are 3 teams, and 5 players. Team A has $20 mill to spend, and will get 5, 4, 3, 2, and 1 win, respectively, from the players. Team B has $15 mill and will get 3, 3, 4, 3, and 0 wins, and Team C has $10 mill and will get 6, 3, 3, 4, and -1 wins.

5 4 3 2 1
3 3 4 3 0
6 3 3 4 -1

If you got price per win by summing the maximum win value for each player, and summing the total cash available, then dividing, you'd get 19 wins, and thus ~$2.37 million / win. If you took the average win value of each player, you'd get 14.33 wins, and thus ~$3.14 million / win. But with neither of those estimates can team C afford player 1, so not only is there a big discrepancy between the estimates, there's also going to be an effect from budget concerns. Which is why certain players not signing can cause the whole market to pause. Until player 1 is off the table, team C might want to wait and see if players 2 and 3 go for high enough prices to give them a shot at player 1.

Apr 24, 2014 15:44 PM
rating: 2

J-sub-T might also be significant in cases where a team needs to make a 'statement' to its fans, e.g., Granderson & the Mets might represent such a case

Apr 24, 2014 15:56 PM
rating: 0

Building on schlicht's comment, Vin Scully's J-sub-T is higher than most non-player employees.

Apr 25, 2014 10:19 AM
rating: 1

You're absolutely right. I thought of Vin Scully instantly when reading that part of the article.

Certainly there's a large number of baseball fans who are not Dodgers' fans, but watch Dodgers' games solely to listen to Vinnie call the game and regale them with stories about baseball.

Apr 27, 2014 00:49 AM
rating: 0
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