What Is Jose Reyes Worth?

(Bumped from FanPosts. --Eric)

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Recently, I've been reading a lot of AAOP's and they are all excellent. I appreciate everyone's hard work and creative thoughts. One thing that seems to be dividing us as Mets fans is the question of re-signing Jose Reyes. Most of us are huge fans, but some of the numbers have us worried that the Mets might be walking into a trap contract like Vernon Wells' or Ryan Howard's.

I have gone back and forth on this in single conversations. I wrote a comment in one of the AAOP discussions along these lines, but people seem to have either missed my point or I didn't make a good enough one.

So, I decided to take a look at all the research out there and put together some thoughts on what Jose is worth.

*I'm going to avoid any merchandising or ticket-sale arguments and take a quantitative look based on wins and dollars. By no means does this mean that there aren't emotional or other reasons to either re-sign or to let him walk -- I just wanted to review and present other people's research as it relates to the question. You can make your own conclusions.

1. Value

Anyways, given that you're in agreement that wins are the correct way to measure player value, and that WAR measures this to a sufficient degree, then you should simply assign a dollar value to WAR and that is what a player is worth. For example, a replacement player (0 WAR) by definition adds no wins and therefore he must be worth $0 dollars. This is an oversimplification -- a model -- of value and not the real value of a given player. For example, an elite sign-stealing ability is not WAR-measurable, however, it does have value.

This said, I believe that most of a player's value is tied to his individual contributions either offensively or defensively, and that wins are the correct scale, or "currency." The rest of this fanpost will deal with Jose Reyes the individual player as if he were a commodity or a factory that generates wins, as measured by WAR.

If you are not inclined to gauge value in this manner, then I advise you to stop reading because you will probably be very bored.

2. Projections

Anyways, if we were to know Jose Reyes' 10-year future WAR production, then his value would be easy to determine. However, we can't, instead we have projections, otherwise known as "educated guesses."

2.1. The Aging Curve

Many of the projection curves you see for evaluating contracts are based on an aging curve. It's pretty clear that players peak in value in the mid-20's or so, and decline and are out of baseball in their mid to late 30's. The most convincing argument quantifying aging, I believe is Tom Tango's. The methodology is clear and consistent, and the results make sense, although selection bias will always be a problem in aging studies. You can see his results (which use wOBA) here. As Tom writes, "To convert wOBA for a hitter into wins: (wOBA - .338) / 1.15 * 700 / 10.5." This will give you wins above average for offense.

As you see in Figure (1), which I made from the last link, this curve represents the WAR differential in groups of identically aged players who played in back-to-back years (the delta method). This implies that most hitters peak around 25 or 26, with a slow decline until about 32, whereupon the decline starts to accelerate.

Figure 1: Aging Curve for Batters

Using this data, we can roughly project Jose Reyes the average player.

Suffice it to say, it looks like the average player roughly loses half a win through his early 30's. At this rate, Jose Reyes at a $116M/6 year contract is about what he should make based on a 6 WAR peak. Of course, we could argue that it's not quite right to use the same dollar per war figure. If we add in a 5 percent inflation rate, we get $135M/6. It is also possible that 6 WAR is not his true talent level, and that since 6 fWAR is really 5 true WAR, we should only pay $104M/6. I've posted a Jose Reyes value calculator here (apologies for the wait).

Of course all of that was silly, since it looks only at offensive numbers. I'm treating his defense and base-running as staying the same while his batting ability changes over time! Which is clearly not the case. So let's reject this model out of hand.

2.2. Great Players

Tom Tango (who it's clear I like a lot), in this post claims that great players age differently than the average player. He defines great players as "over the preceding 4 seasons had at least 1500 PA, with a WAR/700PA rate of 4+ wins" and "in the preceding season had at least 500 PA, with a WAR/700PA rate of 4+ wins." Jose Reyes qualifies as great coming off his age 28 season with 586 PA this year and 5.28 WAR/700PA over the last four.

Tango's data is customized to Jose Reyes and summarized in Table (2).

I've added a 3% inflation rate, and Tom Tango's numbers for great players. This looks actually a lot similar, and again justifies a roughly $120M/6 year or $130M/7 year contract for Jose Reyes.

2.3 Speedsters

Tango recently as of last year added some results for good speedsters. I'm using his numbers somewhat loosely here, I've added an age 29 season at 5.1 WAR, as I can't seem to find the full results of that study, and assumed the same WAR differential as for great players in that age season. Otherwise, the numbers come from an analysis of Carl Crawford, who is also part of the "good speedster" group, who was a year older going into his next contract.

These numbers look a little better relative to the great hitters as a group. I think a common misconception is that speed-reliant players age poorly. However, if you think about this, this doesn't make that much sense, since speed reliant players cannot use speed alone to create value, they have to get on base. Therefore, it makes sense that a good speedster in baseball is a good hitter primarily, who can run fast. Since hitting (the ability to make contact) doesn't appear to be a purely physical skill, it reasons that speedsters should remain useful players even after their speed diminishes. Compare this to (low average) power hitters remaining useful after the power diminishes -- once the low contact rate is no longer offset by total bases, the power hitter becomes marginal very quickly (right Jason Bay? Hi Adam Dunn!).

2.3 Nearest Neighbor

Finally, I wanted to do a nearest neighbor comparison. Jimmy Rollins is the closest comp, as given by Baseball Reference. I don't think Rollins was ever as good as Jose Reyes, but he's similar in handedness, position and speed. Furcal has more data, but that's a pretty bad comp given that Furcal is physically so much smaller than Jose. Jose is fairly unique at his size and speed. Anyways, Rollins is only through his age 32 season, but I've used the standard .5 win deduction for each year after his last.

If Jose's career closely tracks Rollins', then $102M/6 would be the maximum you'd want to go.

3. Conclusions

Clearly there are justifiable reasons why people toss out the $100M+ over 6 estimates regarding Jose Reyes, and why Carl Crawford got a $142/7 contract from a "saber-metrically" inclined franchise. I don't think it's clear at all that Jose Reyes is worth X amount, but it is interesting to see what kind of contracts result at a given dollar per WAR figure, aging pattern and inflation rate. There are some other aging curves here at Baseball Analysts with which to use the Reyes Calculator, including curves for high-walk vs low-walk players, big vs small, high-strikeout vs low, good defenders vs bad-defenders and more. I wish you had the interest in letting me bore you enough to post more Reyes tables, but if you're interested you can do it yourself.

*Careful with those last aging curves, though -- they might not say what you think they say -- they show the relative increase and decline starting from 0 WAR, so that peak at 1.5WAR does not mean that on average players peak at 1.5WAR. It means that you get a total average increase of about 1.5 WAR between the age of 19 and 26 or so, and then it declines. For example, if you start at 4 WAR as a 20 year old, you'll be at 5.5 WAR on average as a 26 year old.

You'll notice from these last graphs, as Tango noticed, that it appears speedy, good defensive, low-walk guys are inclined to peak early, but age rather gracefully compared to, say the Adam Dunn's of the world.

Given all the above, I can understand a $100M-120M/6 contract range. Playing with the calculator and looking at aging curves makes me feel that $100M+ over 6 years is not awful or crazy -- it is not a Vernon Wells or Ryan Howard deal.

The main assumption is that Jose will not succumb to an injury at some point in his contract that will essentially end his career. If the risk of that is higher for Jose than other players in the studies above, then clearly, that should be modeled. The risk there is difficult to determine and I guess will have to be a topic for another time, however.