Comments on: On $-per-Win Estimates of Baseball Players’ Worth http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/ Economic Thinking about Baseball Sun, 09 Jan 2011 17:16:18 +0000 hourly 1 https://wordpress.org/?v=4.6 By: Questions and Answers with J.C. Bradbury | The Wages of Wins Journal http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110746 Wed, 24 Nov 2010 15:48:32 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110746 […] success. Sabermetricians have used some financial models to connect player performance and worth, but these simple approaches are too limited to proxy the impact of performance on revenue. What’s missing from sabermetric value assessments is economics.  I approach the problem using […]

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By: Friday Links (19 Nov 10) – Ducksnorts http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110716 Fri, 19 Nov 2010 14:36:06 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110716 […] On $-per-Win Estimates of Baseball Players’ Worth (Sabernomics). J.C. Bradbury discusses methodology. I haven’t sunk my teeth into this one yet, but it looks interesting. Tango responds. [h/t Hardball Times] […]

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By: Ernie King http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110661 Mon, 15 Nov 2010 20:10:05 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110661 I’m econ drop-out but this one seems pretty easy. You’re comparing apples to oranges here. FG is looking at the marginal COST of a win and JC is looking at the marginal REVENUE of a win. Mind you, in a perfectly competitive market, marginal cost = marginal revenue = price, BUT I don’t think MLB is anywhere close to satisfying that condition. Thus, we should expect a difference between MC and MR, with that difference being the level of inefficiency in the MLB market and I would guess the level to which wins are overpaid/underpaid for (I would assume overpaid for in the aggregate.) So wouldn’t we want to use both approaches and compare? As an owner, or a player, I would want to know how much additional revenue an additional win will produce and use that to evaluate how much to offer, or how much to ask for (as a player). Or am I missing something, or a few things, here?

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By: JC http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110660 Mon, 15 Nov 2010 19:04:09 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110660 Joe,

There is not a set value for a win. It depends on how many wins a player adds, and how many wins the team has. That’s why the non-linearity is important.

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By: Colin Wyers http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110659 Mon, 15 Nov 2010 19:00:17 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110659 I took a quick look at this – not so much to pretend I did a study of the issues at hand, but to see if I could visualize it for myself. So I took this:

http://www.baseball-reference.com/leagues/MLB/2010-value-batting.shtml

And focused on just players listed as “free agent” or “waiver.” (I understand this is no way duplicates the Fangraphs study – again, I’m just trying to work through this with some data in front of me, to help me visualize this.) If I take the sum of salary divided by the sum of WAR, I get roughly $4.9 million per win. If I run a regression, I get a constant of 3320576.267 and a coefficient on WAR of 1339016.354. (This reflects as much as anything a failure of looking at observed WAR rather than projected WAR – I suspect a large number of those 0 WAR or thereabouts players were ones who were given contracts in anticipation of far greater amounts of playing time.) If I fix the intercept of the regression at 0 (I know, I know – again, just trying to work through some of the ideas here) the coefficient on WAR rises to 2260335.473, still far less than $/WAR.

If I take and draw a scatterplot of actual salary to wins, and then draw a similar scatterplot of WAR*(sum of dollars/sum of WAR), it looks pretty much like the textbook illustration Bradbury presents.

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By: Joe http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110658 Mon, 15 Nov 2010 18:51:44 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110658 So according to you, JC, how much is a “win?”

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By: Sky http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110656 Mon, 15 Nov 2010 17:31:04 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110656 Ok, let’s remove the “free agent rate” part from Fangraphs’ model. I agree it has some problems (but also some uses). One could use their same process, but instead use the money paid to ALL players, not just free agents. Instead of about $4.5M per win, it’s maybe $2.25M per win. With those numbers, it all adds up to total salaries paid out, instead of a much larger number (since not all players are paid at the free agent rate).

Anyway, I guess I could see an issue using the y=0 constraint here, because it ignores revenue issues and only uses the amount of money teams are currently spending on payroll. It’s the difference between “how much of MLB’s marginal revenue is a player’s production worth” and “what how much of MLB’s payroll expenditure does a player’s production deserve”.

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By: JC http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110654 Mon, 15 Nov 2010 17:00:14 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110654 Sky,

You are using the term “marginal” different from they way I’m using it. The $-per-win approach takes the aggregate number of dollars for players who are considered to be adding “marginal wins,” then divides by the aggregate number of wins produced. When this calculation is made, the intercept is then assumed to be zero. Marginal, in the economics sense, is the value added following a change in wins. As the first diagram above show, the change is not linear. The second diagram, which is theoretical and not directly applicable to the numbers here, shows the marginal impact to be linear, and with a less-steep slope with a positive y-intercept.

If you want to estimate worth from market salaries, you should use a multiple-regression approach like Krautmann, which does not constrain the intercept to zero. If it is zero, then it will be estimated to be so.

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By: Sky http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110653 Mon, 15 Nov 2010 16:46:25 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110653 But Fangraphs is using marginal dollars and marginal wins… That’s NOT forcing the y-intercept to be zero on the absolute axes. It’s translating the origin to a point that makes logical sense in a marginal sense. Now, one could challenge where that point is placed, but once you place it, it IS the zero point. Moving the frame of reference back to the absolute graph, the regression line is NOT constrained to a y=0 intercept.

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By: JC http://www.sabernomics.com/sabernomics/index.php/2010/11/on-per-win-estimates-of-baseball-players-worth/comment-page-1/#comment-110652 Mon, 15 Nov 2010 16:42:34 +0000 http://www.sabernomics.com/sabernomics/?p=3475#comment-110652 Past estimates by Krautmann are linear. I believe this aspect of the model is mistaken. When I refer to the Krautmann approach, I am referring to using market salaries to estimate player worth, not the specific estimates.

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