April 22, 2010
Ahead in the Count
When the Marlins traded Miguel Cabrera to the Tigers after the 2007 season along with Dontrelle Willis for a handful of prospects, the familiar voices echoed with the following summary: "Baseball is a business." They talked about how the Marlins "could not afford" to keep those players as their salaries escalated, and would only be able to watch them walk away when they became free agents. That’s what they said, at least. Now, the same "they" are outraged that Forbes reported that the Marlins reported the highest profit of any team last season. Clearly, they infer, the Marlins can afford the talent, but choose not to.
Let's take a step back. If baseball is a business, it should follow some basic rules of economics. The Yankees don’t spend money on their fans because, doggone it, they just like them so much; they spend money on their team because it pays off. The Marlins don’t because it doesn’t pay off. Baseball is a business, and teams invest in labor based on the principle that they think that the revenue added will be greater than the cost added. When players reach free agency, there is an auction for their services. Usually the team that has the highest perceived value for that player wins. The Marlins simply do not have the marginal revenue per win that is high enough to warrant spending like the Yankees.
Now that we know baseball is a business, we need to know the actual value of these services. Cabrera signed a contract with the Tigers promising him $152.3 million for 2008-15. He still had two years of arbitration eligibility in which the $26.3 million he was paid was a good guess about his cost for that span, but were the 2010-15 seasons for $126 million a good deal for the Tigers? That’s a pretty important question. There are $126 million dollars being invested in labor, and it keeps the Tigers from making a lot of other moves, but also provides them with a whole lot of wins, as Cabrera is one of the top offensive players in the game. Big free-agent deals can make or break a franchise this way. Signing Jimmy Rollins for 2006-11 at a cost of $48 million (option included) gave the Phillies a lot more wins than they would have gotten spending that money elsewhere and ultimately helped them win three division titles that they probably would not have won without him. Tying themselves to Vernon Wells at a cost of $126 million for 2008-14 cost the Blue Jays a chance to be competitive.
Pinning down an approximate baseline dollar value that should be paid for free agents is one of the most important things that sabermetrics can do. It’s not the final word, but it really should be the first word. And in fact, evaluating free-agent deals is one of the most common uses of sabermetrics. Between all of the sabermetric websites and team blogs, articles are written about potential and actual free-agent signings throughout the winter. Nate Silver introduced the first version of MORP back in 2005 converting WARP3 into MORP, and Fangraphs has followed with its own version of MORP called "Dollars" which translates WAR into a dollar value.
MORP (Market value Over Replacement Player) estimates to the marginal cost of acquiring a player’s contribution on the free-agent market. In this article, I will introduce my update to MORP and some of the ideas behind it, and in tomorrow’s article I will break down my methodology in full detail. For today, let’s just talk about the basics and how to use MORP. While I am making several adjustments to the process, the most important one regards draft-pick compensation. As I will demonstrate, this is not a small factor. Although evaluating free agents this way is an inexact science, we simply should not ignore the 10-20 percent cut that free agency-eligible players would receive if this type of compensation were removed.
While both Nate Silver’s and Fangraphs’ free-agent valuation methods have strengths and are a solid pair of foundations for me to extend, I am going to change some aspects that are bad. I have already gone into detail on why a non-linear formulation of MORP only made sense when WARP had such a low baseline, but it is now violated by theoretical and empirical evidence at this stage, so I am creating a linear version of MORP.
I also am removing a subtle but crucial bias baked into both Nate’s and Fangraphs’ versions of MORP, in which they only looked at free agents and projections to value players’ contributions. As I showed last week, the set of players whose teams allow them to reach free agency are not a random sample of players. In fact, they routinely underperform their projections, rendering a system that uses projections inaccurate.
Another issue with Fangraphs’ projections is that it only focuses on the first year of contracts. When players in different offseasons have different expected rates of decline, this will bias the sample. For instance, when the big free-agent pitcher acquisition of the 2008-09 offseason is 28-year-old workhorse CC Sabathia, while the big free-agent pitcher acquisition of the 2009-10 winter is oft-injured 31-year-old John Lackey, the former is not being overpaid as much in the first year of the contract, meaning that the dollars per win in the 2010 version of Fangraphs’ dollars will underrate the dollar cost of talent. Lackey’s 2014 compensation may come later, but it’s paying for 2010 production.
A particular strength of both Nate’s and Fangraphs’ versions of MORP is that they only focus on wins. As stated earlier, MORP is the marginal cost of acquiring a player’s contribution on the free-agent market. Note that I have used the word "contribution," because I am referring to wins added. If Mets general manager Omar Minaya wants Jason Bay for his RBI tally or Astros GM Ed Wade wants a reliever for his veteran-osity, this does not give them extra market value according to MORP. MORP measures the cost of talent, not the cost of irrelevant skills that don’t contribute to winning. Is that realistic? Wade and Minaya certainly beg to differ, but pricing in their quirks will only complicate things and will not actually help us figure the cost of baseball talent.
The Basics of my Approach
While I will get into more detail tomorrow, I will briefly summarize my approach in creating the MORP formulas in this section. I gathered all players with at least six years of major-league service time and summed the number of dollars spent on their contracts and the actual number of WARP they produced, regardless of when they were signed. I also went through all of the draft-pick compensation given for those free agents, and all of the draft pick compensation that teams would have received had they not re-signed their players. I adjusted Sky Andrecheck’s draft pick value calculator from Sean Smith’s version of WAR to WARP3 (or WARP/162), and only looking at the amount of WARP that would be produced on average under market value (which is about 70 percent of those players' production during the first six years). This is the formula I arrived at:
WARP3 value of a draft pick = 13.54*(pick number)^-0.49
Then I discounted this at 8 percent for six years, which basically means dividing it by (1.08)^-6. This is because wins in the future are worth less than wins in the present. I am estimating that teams value this year’s wins about 8 percent more than next year’s. This is obviously debatable, but perhaps it is best to think of it in terms of the teams who actually bid on Type-A free agents. They are in win-now mode, when they are on the sweet spot of their marginal revenue curve and typically on the playoff bubble. In six years, they are less likely to be in that situation. With enough frictions in the market than they cannot simply trade away these young players to teams in pennant races, there is bound to be some discounting done by teams bidding on free agents. In addition to subtracting from the win cost of signing these players, I also subtracted the cost of paying for the draft pick which I approximated at:
Signing cost = $(1.8 – 0.02*(pick number)) million
To approximate the cost of wins in future years of contracts, I could have used a simple inflation estimate. However, in the current economic environment, that is tricky because the price of wins has not inflated the last couple years. Instead, I waited until the offseason was over and took all of the dollars that were allocated to players with more than six years of service time in 2010 and weighed that against their expected contribution. Rather than using projections which perpetually overstate the value of free agents, I noticed that the aggregate production of players with at least six years of service time stayed more or less constant over the last three years, and so I was able to estimate the dollar value of a win in 2010 as well.
The resulting formulas are as follows:
To estimate MORP for 2011 and on, you will need to estimate what salary inflation will be. A moderate assumption of five percent might make sense. In the years leading up to the 2008 recession, salaries inflated at about 8-10 percent, so five percent is probably a conservative estimate.
Don't Misinterpret MORP
The first thing that throws people off about dollar values for free agents using these formulas are the ridiculously high numbers that come out. For instance, if salaries inflate five percent in 2011, Joe Mauer will probably be projected to be worth about $34 million that year. The critics of MORP will claim that no one would have paid Joe Mauer $34 million, and that the $23 million he will get paid sounds more reasonable. What is lost here is that while no team would have given Mauer $34 million, he would not have given any team a one-year deal. The eight-year contract he signed last month will probably stretch to a point where Mauer is playing first base or designated hitter, and is worth closer to, say, $12 million a season at the end. The result is that they compromise on a contract that averages $23 million overall, underpaying him in the early portion of the deal while the Twins can use the money elsewhere to build around him, and overpaying him at the back end of the deal to make up for it. It’s not like Mauer was going to spend the extra money right away, but the Twins were.
This starts to make even more sense when we look at the few one-year deals given to great players in recent years. Roger Clemens’ series of one-year contracts were far above the average annual value of deals given to comparable players who were younger and signed multi-year deals. The 2007 contract that Clemens signed with the Yankees was a prorated version of $28 million. Does anybody think that he was as valuable as Alex Rodriguez? Of course not, but Clemens did not require the 10-year commitment that A-Rod did. Now imagine what Rodriguez could have commanded for one year of his services in 2007 if he was projected to be worth about five wins. Does $36 million sound that unreasonable in contrast with Clemens’ $28 million?
Let's analyze a couple of recent contracts based on this formula.
This past winter, the Phillies signed Placido Polanco to a three-year contract worth $18 million, which increases to $22.5 million if the Phillies pick up his 2013 club option. Ignoring the option for a moment, we can see that Polanco is projected to be worth 2.7 wins in 2010 by PECOTA, followed by 2.2 in 2011 and 1.7 in 2012. Fortunately for the Phillies, signing Polanco did not cost them a draft pick like signing Chone Figgins would have. Now, we do have estimates for 2011 and 2012 MORP, and with an approximate five percent inflation rate, the 2011 MORP $5.25*WARP and 2012 MORP $5.5*WARP (in millions). Thus, he would be worth: (5.0)*(2.7) + (5.25)*(2.2) + (5.5)*(1.7) = $34.4 million more than a replacement player who costs $400,000 for three years each, so he is worth $35.6 million. Figure that the option’s surplus value is worth maybe $200,000 assuming the Phillies will exercise only if makes sense (and it probably won't) and that makes the contract worth about $35.8 million. Thus, the Phillies got quite a deal by only paying $18 million.
Of course, keep in mind that when a team re-signs its own player, he typically does better, and when a player signs with a different team, he typically does worse. Perhaps PECOTA is overvaluing Polanco in this case for that reason, but the methodology is the important point here. All I am saying is that Polanco really only needs to produce about 3.5 wins over the next three years to earn his contract, while PECOTA sees him racking up 6.6 wins. Chances are that Polanco earns his contract and then some, but the same could not be said as easily if signing him required draft-pick compensation.
Which brings us to this next example, where the Tigers surrendered the 19th pick in the 2010 draft to sign Jose Valverde to a two-year deal worth $14 million, which would be worth $22 million if the Tigers exercise a 2012 club option. Valverde is projected for 1.8 WARP this year and 1.6 WARP next year. Ignoring the draft-pick compensation, Valverde’s contract would look pretty good: he would provide (5.0)*(1.8) + (5.25)*(1.6) = $17.4 million more than a replacement-level player, so he would be worth $18.2 million if you ignore the draft picks.
However, the 19th pick would cost about $1.4 million to sign, so that is saved, adding value to the deal, but the 19th pick would also provide 3.3 wins over the first six years, which is about 2.1 wins when discounted to today. Since 2010 wins are priced at $5 million, this is $10.5 million in foregone wins, with only about $1.4 million of signing bonus saved. Therefore, the net cost of the 19th pick is $9.1 million. Thus, the value of the contract is (5.0)*(1.8) + (5.25)*(1.6) + 2*(0.4) – 9.1 = $9.1 million. Add an extra $900,000 in value for a reasonable option, and it’s still only $10 million in value for $14 million. Thus, Valverde’s deal appears to be a poor value according to MORP.
Rather than plugging into the formula all the time, a good ballpark estimation of draft pick costs is that if you surrender a late first-round pick, you add $13 million to the cost of the deal, if you surrender an early second-round pick, you add $9 million, and if you sign your own Type-A player and forego a pick and compensation, you cost yourself $23 million extra. It’s also prudent to subtract a fraction of that money off the deal if the player is likely to be a Type A free agent after the contract is complete.
This should provide you with a solid framework to refer to for the value of free-agent contracts. The key addition of adjustment for draft-pick compensation makes a particularly non-trivial difference in compensation and that is what I believe is the primary addition is here. In tomorrow’s article, I will get into the gory details more precisely and some of the methodological arguments for doing things the way that I have.