Clayton Kershaw, Contract Modeling, and Inflation

Clayton Kershaw signed the largest contract for any pitcher in baseball history on Wednesday. In doing so, he became the first player in MLB to agree to a long term deal for an annual average value of more than $30 million, so on a per season basis, he’s also the highest paid player in baseball history. And he got that deal a year before he was eligible to hit free agency, so this price reflects a discount over what the Dodgers believe he would have gotten with competitive bidding. Given these facts, it’s easy to look at this deal as a harbinger of escalating prices and further proof of significant inflation in Major League Baseball.

Interestingly, however, it’s really not that at all. I walked through Kershaw’s expected value about a half hour before the contract was announced on Wednesday, and my guess for the total price came out to $230 million over seven years, a little less than what he actually signed for, but also didn’t include the value to Kershaw of getting to opt-out after year five. Including that offsetting value, I think my guess was pretty decent.

However, in that post, I spitballed Kershaw’s future performance by using a less aggressive aging curve than we traditionally have for other contracts. When evaluating contract prices relative to other deals, we’ve generally used a standard set of assumptions — current price of $6 million per win, a half win per year in decline due to aging, 5% annual inflation in $/WAR — in order to come up with expected values, and standardization keeps things fair for everyone. So, to be fair to the question about what Kershaw’s deal might mean for inflation, I think it’s worth running it through our general model, even if there are reasons to believe that Kershaw is on an earlier part of the aging curve than an average free agent signing.

Anyway, let’s run Kershaw through that model and see what the expected contract price would have been if we had used a standard aging curve that docked him half a win per season going forward.

Season	WAR	$/WAR	Value
2014	6.0	$6.00	$36.0
2015	5.5	$6.30	$34.7
2016	5.0	$6.62	$33.1
2017	4.5	$6.95	$31.3
2018	4.0	$7.29	$29.2
2019	3.5	$7.66	$26.8
2020	3.0	$8.04	$24.1
Total	31.5		$215.1

As a true talent +6 WAR pitcher for 2014, with the standard assumptions that we’ve applied to free agent prices, we’d have expected Kershaw to sign for… seven years, $215 million. Exactly the price he actually signed for. Now, this is a free agent pricing model, and Kershaw isn’t a free agent, so the fact that he was already under contract at a lower price for 2014 would have to be factored in, but then again, so would Kershaw’s youth and the opt-out clause that he was given in exchange for accepting this AAV. Whether those exactly offset or not is probably up to personal perception; I think they probably do, or come close to it, anyway.

Either way, given the remarkable simplicity of the model, the fact that it nailed Kershaw’s price to the dollar is kind of amazing. Or, at least, it would be if it didn’t do this more often. Two years ago, CC Sabathia opted out of his contract and re-signed with the Yankees for $142 million over six years. Using our standard assumptions and a $5 million per win market price at that time, this overly simplistic model projected that Sabathia would be worth… $142 million over six years. WAR is an imperfect model of player value, $/WAR is an imperfect model of market value, and our aging curve and inflation assumptions are generic and applied to different types of players at different spots in their careers, but still, the model serves as a pretty good proxy for what teams and agents end up agreeing to more often than not.

And perhaps most interestingly, that Sabathia example came in a post I wrote a few years ago about the linear nature of the $/WAR market in MLB. This remains a contentious topic with some, as a significant number of our readers continue to believe that +6 WAR is dramatically more valuable consolidated in one player than spread out over two, even if the +6 WAR player costs as much as two +3 WAR players combined. As the argument goes, it is easier to upgrade from +0 WAR to +1 or +2 WAR than it is to upgrade from +3 WAR to +4 or +5 WAR, so your potential overall return is higher with a star and a scrub. After all, replacing the non-scrub with a less scrubby scrub isn’t that difficult of a challenge, so, the price of a +6 WAR player should be significantly higher than it is for two +3 WAR players.

Except it just continues to not work that way, and the Kershaw example is the latest evidence of the linear relationship between dollars and wins in MLB. He’s about as much of a star as you’re going to get on the pitching side of things, and the best bet of all the young arms to maintain his level of production going forward, and yet, the Dodgers — the team that seems least concerned of any in MLB about holding down prices — gave Kershaw a deal that reflects a linear $/WAR relationship. If the escalating value of additional WAR within one player had non-linear value, then Kershaw should have signed for $35 or $40 million per year.

For instance, let’s just say that there is an escalating value to each additional WAR within the same player. Maybe the first +3 WAR are each worth +1 WAR, but then each additional WAR is 25% more valuable than the previous, due to scarcity of high end players. If that was true, and that was how MLB teams paid players, then Kershaw’s +6.0 WAR 2014 season would be worth +7.8 “regular WAR”. Let’s re-do the model using these figures, where the fourth WAR is worth +1.25 WAR, the fifth WAR is worth +1.56 WAR, and the sixth WAR is +1.95 WAR. This is what that model would look like, for Kershaw.

Season	WAR	$/WAR	Value
2014	7.8	$6.00	$46.8
2015	6.8	$6.30	$42.8
2016	5.8	$6.62	$38.4
2017	5.0	$6.95	$34.7
2018	4.3	$7.29	$31.0
2019	3.6	$7.66	$27.6
2020	3.0	$8.04	$24.1
Total	36.3		$245.4

The escalating value model would have expected Kershaw to sign for $245 million, $30 million higher than he actually signed for, and suggests that his market value for 2014 is $47 million. Clayton Kershaw’s awesome and all, but I think we’d have a hard time actually defending those kinds of valuations, considering how different they are from what MLB teams are actually paying out. For star players, the linear model does a better job of predicting MLB contract pricing than a non-linear model.

Again, this isn’t to say that the $/WAR pricing model is perfectly linear at every spot and for every player. We know teams price different skills at different prices, and $/WAR does almost nothing to explain the high free agent prices for Major League relievers, or the low valuations for part-time position player reserves. But for everyday players and starting pitchers, the relationship seems pretty close to linear for most players, and we simply don’t see teams paying premiums to consolidate equivalent WAR totals into one player instead of two.

Kershaw signed the largest contract ever for a pitcher, and is now the highest paid player in baseball, but the reality is that this contract is exactly in line with what we already thought we knew about the market as it stands. This isn’t evidence of runaway inflation, or reason for lesser pitchers like Jon Lester and James Shields to start planning on $200+ million paydays themselves. This isn’t a new direction for the market, or a sign that the Dodgers don’t care about payroll efficiency. And this isn’t a sign that star players are compensated above and beyond their production on the field. This isn’t any of those things.

This is just a reflection of Clayton Kershaw being the best pitcher in baseball. This is what the best pitcher in baseball is worth, even if you boil things down to something as simple as a very basic $/WAR model. This doesn’t set a new price for pitchers; it confirms what we already thought the market price for pitchers was. And it continues to suggest that for all of its simplicity, WAR is actually a pretty decent proxy for how teams value Major League players.