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The Trials and Tribulations of Player MRP

posted by Shawn, on November 30th, 2007 at 08:27 am, in category Uncategorized

Next time you read that X player’s contribution in Y year was worth $Z million, ignore it.

There’s been a great deal of research into valuing players based on performance, from academics, bloggers, academic bloggers, and a whole host of others. The goal is to determine a player’s marginal revenue product (MRP) to his team; in essence, how much money is he really worth?

But this doesn’t work. Or at least, it hasn’t worked yet, in the public domain of baseball research. Yes, it is certainly possible, but it is much more complex than most would have you think.

In sports economics classes around the country, teachers generally present MRP as a simple function of marginal revenue per team win, and wins added by the player. Many popular systems around the blogosphere do the same. And as an extremely simplistic indicator, the resulting numbers more or less pass the laugh test.

But a team considering a free agent signing cannot rely on simple indicators. A multi-million dollar investment is a multi-million dollar investment, no matter the industry. Sabermetricians have always berated teams for spending huge sums without the proper information, so why aren’t we berating ourselves when we advocate simplistic information that is also clearly imprecise?

Consider just the primary issues involved in current MRP valuation systems. Before even getting into the fine details, we can see that the two primary factors are both inherently flawed. Marginal revenue per win is different for every team, and not just because of the win curve, or the team’s market size. The Blue Jays, Orioles, and Devil Rays will usually have to win more games in order to compete than, say, the Cubs. And Pirates tickets will always be more elastic than Cardinals tickets.

Even wins added, for as much progress as we’ve made, is still far from perfect. Yes, we can pinpoint offensive contributions pretty well, but fielding is still very inexact. The current systems can generally differentiate between good and bad, but can only give rudimentary consensus estimates on the run values of those performances. Without these numbers, no wins added metric can represent more than an educated guess.

And then there’s the 1,000 pound gorilla in the room: replacement level. While we have a general idea of what a freely available player might produce, this doesn’t take into account a very important point: every team has a different replacement level for every single position. Andruw Jones would have much more value to a team like the Phillies than he would to the Indians, who already have a very good centerfielder for the long term.

And what about a player’s impact on the rest of his team’s roster? While the size of A-Rod’s first contract had disastrous consequences for the Rangers, it fit in relatively nicely within the Yankees’ cost structure.

There is a solution to all this, and I suspect several teams are doing it internally: better evaluation systems, with the results fed into an evolutionary algorithm.

Evolutionary algorithms take an unlimited number of factors, and perform thousands, or even millions, of trials until it has perfected itself. The results are still estimates, but these estimates are far more accurate than any simple model could possibly generate. This tool will drive many businesses in the coming years, and I would be pretty stunned if certain teams weren’t already using them. It is important to note, though, that evolutionary algorithms require a pretty hefty amount of computing power, which most individual researchers can not yet afford.

These researchers also lack another pretty key piece of data: real financial figures. Without this information, it is nearly impossible to break down a player’s true value. And meanwhile, trying to forecast the sport’s overall economic health may need an evolutionary algorithm for itself.

With all this said, it is no wonder that MRP systems are still mostly lacking. This is why it may better to go the logical-if-unscientific route for the time being.

Feedback? Write a comment, or e-mail the author at shawn(AT)squawkingbaseball.com


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  1. on December 1st at 01:19 am
    melissa said:

    Do these calculations also try to factor in the players marketability? For instance the number of jerseys sold and peripheral merchandise that fans desire because of a given player. Do they try to calculate what kind of an attendance draw the player is? There are certain individual players that do draw attendance at home and on the road especially if they happen to be in pursuit of some kind of record. It would be interesting to see if there would be a way to take into account these factors. It seems like it would be hard to correlate an individual’s direct effect on attendance over the long term.

  2. on December 2nd at 03:04 pm
    Jim said:

    I agree with your broad point that each team needs to make a unique model for a player’s impact on MRP. The market wage would then-theoretically- be the highest of those bids. However, I don’t think the “1000 pound gorilla in the room” is as big a concern as you say. The current models don’t predict an individual team’s bid for a player; they predict the salary he would get on the free agent market. Each player is unique, so shouldn’t the market price simply reflect the reservation price of the highest bidders? The Indians might not even participate in the market for Andruw Jones due to transaction costs and the threat of a bad reputation for making unreasonably low offers.

  3. on December 4th at 12:28 pm
    JC said:

    Which system are you criticizing? I use an MRP system, and your critique doesn’t describe much of what I do with my system; yet, as far as I know, I’m the only one out there publishing updated estimates using the term MRP. So, I guess this is targeted at me. Let me provide a few answers.

    1) I abhor “replacement level”, and don’t use it. (Maybe you’re not talking about my estimates).

    2) How much wins differ across teams is an interesting question. I’m of the opinion that though there are differences they are not too big to throw out one number. Furthermore, a player’s MRP IS one number: the opportunity cost of the next highest offer. What that next offer is, is difficult to tell. I base my system off the average team. As long as we acknowledge that this, I see no problem. And if you want to look at some other estimates that account for cities. Vince Gennaro does weight his estimates heavily by individual team characteristics.

    3) I use Forbes estimates, not real financial figures. Gerald Scully (inventor of the two-step MRP method) used ticket sales. Where am I supposed to get these actual estimates? MLB hasn’t been so accommodating, nor should it be. Thus, we are left to chose some non-official estimate or give up.

    4) Until we see the estimates of these evolutionary algorithms, I’m not sure we can judge them to be superior. I’m not sure what anyone calculating MRP ought to give it up because of a hypothetically superior system.