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January 18, 2010

Ahead in the Count

Revising Player Contract Valuation, Part 1

by Matt Swartz

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The first of a three-part series.

Rumors pertaining to Johnny Damon's eventual contract, not just as far as potential suitors go, but also what they might offer are increasing in frequency. If one were to buy into the hype, Damon could get anywhere from a one-year deal worth $4 million to one paying $33 million over three years. To come up with reasonable price estimates of his services, analysts are looking at recent deals doled out to comparables like Bobby Abreu and Mike Cameron, and it certainly seems like whoever brings Damon aboard will pay a similar price, a tad shy of the $10 million mark. Of course, when Matt Holliday was still on the free-agent market, there were no other comparable players getting deals. Holliday provided a WARP3 of 20.7 over the last three years compared to Damon's 11.4. Considering age and basic regression factors, it stands to reason that Holliday is about twice as good as Damon, but does that mean he should be getting twice as much in salary? Is he worth more than twice as much? Evaluating the monetary value of free agents presents a tricky proposition, but an important one worthy of discussion nevertheless.

One of my upcoming projects at Baseball Prospectus is the development of a new version of MORP, or Market Value Over Replacement Player. Nate Silver developed MORP here for Baseball Prospectus in 2005 as a means of gauging the monetary value added by players and based the metric on the formula for WARP, which has since changed. Nate also developed the stat in a different market, when very few teams had sabermetricians in their front offices and Billy Beane could roam free. Times change, and with the changing market, MORP needs a makeover.

MORP's purpose is not to estimate what the average team would get in value from a given player. It also does not attempt to answer what would happen if everybody in the league were a free agent at once. The latter situation would represent an entirely different labor market and it would be futile to speculate about what players would be paid in this case. MORP should only attempt to estimate what the market value would be for a given amount of production, holding everything else constant.

It is also important to acknowledge that players have different values to different teams. Matt Holliday made a lot more sense for the Cardinals than the Orioles. As teams bid on free agents in an auction format, the market value of a player becomes his value to the highest bidder, or really, the second-highest bidder. However, the difference between Holliday's value to the Cardinals, Yankees or Red Sox might be very small compared to the difference between his value to the Cardinals and Pirates. Nate showed us that the marginal value of a win is much higher to teams who are on the cusp of making the playoffs because of the extra revenue the postseason generates. Therefore, a player's monetary value to a team will be based on how much he would add to a squad in a situation of being projected to win, for example, 87 games but miss the playoffs, because those teams will get the most bang for their buck from the signed players.

To estimate the monetary value of players, we are limited by the fact that we do not have each team's financial records and also cannot truly evaluate how many extra tickets fans would buy if a free agent is signed. Thus, we can only judge the value of players by what teams pay and simply determine what a given level of production is worth.

There are two basic ways that this is estimated, the first of which is the older version of MORP as developed by Silver, still available on PECOTA cards. This version fits a curve around salaries and WARP3 values in an attempt to approximate the market value of production.

FanGraphs also evaluates the dollar value of talent by multiplying a player's WAR, their wins above replacement statistic, by a constant dollar amount per win. As it stands, there are a number of problems with FanGraphs' valuation, including the fact that using projections to predict WAR is particularly difficult when projection systems overestimate production, his dollars per win constant is developed only by looking at the first year of free-agent contracts. This proves problematic, because multi-year deals require teams to approximate how much they value future wins and future dollars at the same time that they approximate current wins and current dollars.

The dollar values of players in the eyes of both metrics often seem outrageous for a couple of reasons. First, people tend to respond by noting that if you added up the MORP for every player on a team, the average payroll would hover around $200 million, which would obviously outstrip revenues in many cases. Of course, as I showed in previous weeks, about two-thirds of WARP3 totals come from players who are not free agent-eligible. Tim Lincecum's MORP will answer the question of how much he might be paid if he were suddenly a free agent, but everyone else kept their contract status. It would not define his value if everyone were a free agent at once. Therefore, it is not a logical step to add up everyone's MORPs as we would not be looking at a situation where every player was pushing the team over the playoff hump.

Current free-agent contracts are usually given out to players who are likely to help a team cross that final playoff hurdle because of cheap talent the team already has in place. I recently explained how much non-market production teams get and this process revealed how rare it is for teams to make the playoffs without starting with an abundance of non-market production in place then using a few free-agent wins to put them over the top.

The other reason that these values often seem outrageous is that great players get multi-year deals with similar amounts each year, but the reality is that they are being paid lower than their worth now to be paid more later. Thus, when I said that Roy Halladay would have gotten over $30 million per year if he had auctioned off his services on a three-year deal rather than sign the deal he did with the Phillies, people argued that he would more likely have gotten paid somewhere closer to $25 million. Of course, if Halladay had gone on the free-agent market, he probably would have gotten a six-year deal that would have paid about $25 million annually, but would have been worth over $30 million for the earlier years and under $20 million for the later, uncertain years in his late 30s, because of expected inflation rates.

One of the big differences between FanGraphs' method and MORP's method of developing monetary valuations of players is that the former represents the dollars-per-win tradeoff linearly while MORP uses a curve where a four-win player is worth more than twice as much in monetary terms as a two-win player. This is plausible, but not necessarily accurate, requiring a deeper understanding of how to value players in the context of the baseball labor market. In my next two articles, I will first look at when this type of framework is appropriate by looking at the tradeoffs that teams face when they go out to buy talent on the free-agent market then examine whether that best reflects the value of free agents in today's game.

Matt Swartz is an author of Baseball Prospectus. 
Click here to see Matt's other articles. You can contact Matt by clicking here

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