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.

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Dave is a co-founder of and contributes to the Wall Street Journal.

63 Responses to “Clayton Kershaw, Contract Modeling, and Inflation”

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  1. tz says:

    Waiting for the first troll to pounce on your use of two data points to make an assertion….

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    • ankle explosion hr celebration says:

      why would that person be a troll? Personally, I’d like to see a more general comparison of this model, expanded to consider all the major free agent contracts. I don’t think that makes me a troll.

      It’s very easy, even subconsciously, to pick suitable data points which support one’s model while ignoring all of the points which don’t support the model. It’s reasonable to be skeptical that such a simplistic model works so well in all cases.

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      • murphym45 says:

        Agreed, it would be nice to see a table with a large number of signees from this year (or the past few years) and see how their projected contract using this model stacked up against how much money they were actually given.

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        • Doozie Felton says:

          Furthermore, the desired conclusion seems to be drawn in this particular article. You can subtact $10M from each data set due to the expected $20M salary he would have gotten in 2014 (this is even mentioned early in the article then ignored when evaluating the data sets) and subtract more for the opt-out clause. I would argue that Kershaw was valued closer to the 2nd data set.
          LAD could be paying to keep him from free agency, but that could be offset with injury risk and coming off a superb season.
          On top of all of that, I feel Kershaw wants to be there and this is all a little team friendly. But that is based on incremental value increase I believe an ace pitcher has in the playoffs (in conjunction with LAD’s strength in relation to their division) and that may not be a point LAD and Casey Close touch upon.

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      • tz says:

        Not saying that questioning the analysis makes someone a troll. But there are far too many posters here who get a bit hyper about the analysis being flawed in some way (without bothering to read the caveats in the actual article) and then getting way too snarky about it.

        Fortunately most posters (like yourself, ankle) make reasonable and informed comments about these articles. As I commented on one of Jeff Sullivan’s posts, the audience on Fangraphs actually allows the writers to “crowdsource” some of the choice of follow up steps, and these guys are very good at responding to these. That’s what makes this website work as well as it does.

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        • #6org says:

          There’s truth to what you say–the audience is reasonably adroit at spotting a wooden nickel when presented one and is rarely hesitant to point it out.

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  2. RMD says:

    Escalating value to each additional WAR should really only apply to position players. Pitchers are just too much of an injury risk. Teams know that when they’re negotiating. As much as an ace provides unique value… you’re still investing in a guy who’s paid to abuse his arm several days a month.

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    • Beau says:

      When a commodity is rare there is always a buyer regardless of risk.

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    • Goat Fondler says:

      Kershaw has never had a legitimate injury, arm-related or not. He has a clean, repeatable delivery and is only 25. He’s one of the least risky pitchers you could sign and in my opinion is not much more of a risk than your average position player.

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      • Kevin says:

        When you consider it being realistically just a 5 year deal, this wasn’t a fiscally dumb deal by LA. It actually was one of their more responsible ones.

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        • RC says:

          It’s not a 5 year deal.

          It’s a 5 year deal with a $65M payment to Kershaw at the end if hes hurt or not very good.

          The option is not good for LA, in any sense.

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  3. Dan says:

    Honestly, it makes perfect sense that the increase is linear. If you have a 6 WAR player and a 0 WAR player versus a 3 WAR player and a 3 WAR player, yes, the star/scrub team has an advantage of, as you put it, being able to replace a scrub with a less scrubby scrub if there is a star player. However, that also means that an injury to your star player leaves you with nothing, while spreading the production over multiple players reduces that risk.

    Business is all about risk/reward, and it looks like it balances out here.

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    • Ian R. says:

      This. As much as GMs are thinking about roster flexibility for future upgrades, they’re also thinking about putting all their eggs in one basket.

      A related factor: there just aren’t many teams willing to pay $25 or $30 million for one player. Guys at the extreme high end of the value scale (like Kershaw) see their prices artificially deflated because only a few teams are bidding for them.

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      • RMD says:

        Yeah, but the few teams that can afford the $30 million player are Desperate for that player because they have so much invested in the team. They’re pot committed.

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        • Ian R. says:

          Not necessarily. Teams that have that much money to spend also have plenty of ways to spend it. They can buy three $10 million players, or two $15 million players, or whatever else they want. The large-market Red Sox just won the World Series without a single player making even $20 million – though, granted, that’s partly because they dumped their big contracts on the Dodgers.

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    • bob dole says:

      this would only balance out if the likelihood of injury risk is equal to the likelihood of finding a less scrubby scrub.

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      • Dan says:

        Not exactly. You should look at the WAR differential.

        If you replace a scrub with a less scrubby scrub, you’re looking at a difference of maybe 1 WAR.

        If you lose a star, (in this hypothetical) you’re talking about 6 WAR/162 games. So even a star missing 30 games or so offsets the less scrubby scrub’s season long performance.

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    • AK7007 says:

      There’s also a payroll component to it. MLB teams are limited by their own self-imposed budgets. If they start valuing wins non-linearly, and pay that 6 win player in a non-linear manner, they won’t have the money to make that hypothetical upgrade over a scrub player.

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    • TKDC says:

      I think one thing that gets past some people is the projected decline. One 6 WAR player is better than two 3 WAR players after the year in question (assuming both are in decline). The 6 WAR player is worth 25 WAR over 5 seasons (6 + 5.5 + 5 + 4.5 + 4). The two 3 WAR players both declining at the same rate would be worth 20 WAR (6 + 5 + 4 + 3 + 2).

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      • Doozie Felton says:

        I would think that players age-decline at a parabolic rate. If a tool is negatively effected the same for a 3 WAR player and a 6 WAR player, the 6 WAR player should lose slightly more value.

        I believe your point still holds true but not at the rate you describe.

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      • philosofool says:

        3 WAR players don’t usually get 5 year contracts.

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    • Joshua_C says:

      The problem with the risk argument against valuing a 6 WAR player more highly is that unless I’m one of the very few teams (maybe Red Sox, Dodgers, Cards) who project to 90+ wins, I have a strong incentive to pursue high-variance strategies given that with such limited playoffs, almost everyone is effectively an ‘underdog.’

      To put it another way, if my mean expected number of wins is less than the number we might think we let me reach the playoffs, and I think the ‘6 WAR and non-scrub’ model can squeeze another win or two out of my roster (but introduce a new risk), then I think it’s the right decision to embrace the risk given that utility returns to wins aren’t linear.

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  4. Dustin says:

    If the model is linear, Adeiny Hechavarria owes the Marlins something like $11.8 million.

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  5. Compton says:

    I’m not part of the readership that champions the non-linearity of $/WAR, but I still take issue with your descriptive reasoning. Just because some MLB teams seem to evaluate $/WAR as linear doesn’t mean they are correct in doing so, right?

    I thought a large part of baseball analysis was discovering inefficiencies in what MLB teams are currently doing and not assuming that their current decisions are necessarily the correct ones.

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    • AK7007 says:

      The conversation right above your post talks about why it is probably a wash. Too much risk tied up in one great player means that they end up being valued linearly, even if intuition would imply otherwise.

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    • tz says:

      You’re correct about the role of baseball analysis, but I like to look at this issue in terms of the financial markets:

      – Market inefficiencies occur when individuals systematically over- or under-value an individual commodity. For widely-traded assets with a huge market, these should reduce over time once the poorer evaluators recognize their flaws and adjust their methods. For less liquid assets (like baseball players), these differences can persist and are more exploitable

      – The linearity of player value, however, is more consistent with the principle of arbitrage. If the combination of a player worth $20 million/yr on the market plus a player worth $1 million/yr was as valuable as two $12M/yr players, eventually the market would recognize this and the first player would be worth $23 million on the market.

      Note that the arbitrage argument just depends upon the market values AND the market participants having a similar enough valuation system. It doesn’t necessarily require WAR to be the commonly used proxy for value.

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      • RC says:

        “eventually the market would recognize this and the first player would be worth $23 million on the market.”

        The flaw here is people assuming that Eventually=now.

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  6. Lenard says:


    This is totally off topic, but something I thought of reading all the contract signings today.

    It applies most specifically to the Yankees, but other teams near the luxury tax cap too. Do option years count against a contracts AAV? Theoretically, could the Yankees have offered their arbitration eligible players a below market 1 year deal with a player option attached that is for above market value in order to lower their payroll for this year?

    For example, instead of the contract he signed today, Gardner signs a 1 year deal for $1 million dollars with a $18 million player option for next year. Something he would obviously not decline, but it would make up for the salary difference. Obviously the commissioners office would void that deal, but these numbers are just an example. If the numbers were a little closer could it be done?

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    • astropcr says:

      Player options could against AAV for luxury tax purposes. Team options don’t. I believe mutual options don’t either.

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  7. Lazy says:


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  8. Pedro says:

    Kershaw is entering his age-26 season, so I’m not sure we should expect him to decline by 0.5 per season, like most free agents

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    • DD says:

      Agreed. I think it’s unfair to expect such a decline when he is in the midst of his prime.

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      • chuckb says:

        There’s some evidence to suggest pitchers peak earlier than position players so I wouldn’t necessarily assume that Kershaw hasn’t already reached his peak.

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    • Eric R says:

      …and Dave forgot to adjust down 2014 since it was an arbitration year or factor in a value for the opt-out.

      Granted, if you figured him for ~$20M in arbitration and call the opt-out worth ~$15M, then the two roughly cancel out… so, perhaps fair to ignore those two factors.

      Going with 6WAR in 2014 and -0.5 for age 30 onward:
      Season WAR $/WAR Value
      2014 6.0 $6.00 $36.0
      2015 6.0 $6.30 $37.8
      2016 6.0 $6.62 $39.7
      2017 6.0 $6.95 $41.7
      2018 5.5 $7.29 $40.1
      2019 5.0 $7.66 $38.3
      2020 4.5 $8.04 $36.2
      Total 39.0 $269.8

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      • Owen says:

        Dave’s previous post had a more forgiving aging curve, based no doubt on the idea that 25 year olds should decline as fast as 29-31 yros. He had something between this one, and the one posted by Eric R. above (which I think is a bit bullish). His was 5.5/5.5/5/5/5/4.5/4.5, for 35 WAR and $242.5 mil. We also don’t know how much of a pitcher’s decline is age-related and how much is “mileage” on the arm. (Or are there studies on that?)

        If you split the difference between Dave’s “kind” aging curve and the one above, you get $230 million, which is the contract Dave suggested once he factored in the Dodger’s $20m option for 2014. So the Dodgers may have gotten a little bit of a discount, but we’re talking about an underpay of about 7% at most, which isn’t huge.

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  9. Roger says:

    “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.”

    Not necessarily. I’m pretty sure the Dodgers would be happy paying what they believe to be market value in order to prevent him from reaching free agency.

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  10. cody.stumpo says:

    Looking at the data of 2014 free agents.
    First make a line reflecting the total pool (82 signings so far) AAV/E[WAR].2014
    Relief pitchers almost all get above this line.
    For everybody but relief pitchers, players forecast to give 0-3 WAR almost all got below this line.
    For everybody but relief pitchers, players forecast to give 3-6 WAR almost all got above this line.

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  11. Hank says:

    A couple of days ago, using a different aging curve, this same author determined he was worth ~242mil

    The model may be simple, but the inputs are not. And when an author changes the methodology (and it’s not just Kershaw), it is hard to view this as anything but getting the model to spit out the # desired. Don’t like the # – change the aging curve (either the magnitude or when it starts), change the inflation rate, maybe change the starting $/WAR figure or you could also play with how you determine the starting player skill level (sometimes you can do a 3 year average, sometimes use a forecast, maybe use a weighted 3 year average, maybe use an average of forecasts)

    This article concludes that Dave Cameron values wins linearly if he tweaks the #’s properly, I don’t see how one can conclude this is how baseball values it without seeing their inputs or without a consistent methodology applied across a lot of different contracts to validate the approach.

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  12. I miss you already Kinsler says:

    Does anyone actually think Kershaw is going to be worth just 3 wins above replacement during his age 32 season? That’s not necessarily even past his prime. We are talking about a historically great pitcher thus far. You need to give him a little more credit on his aging curve especially considering how hard of a worker he is.

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    • ankle explosion hr celebration says:

      yeah… Dave and his linear “-.5WAR/year” decline assumption. It makes no sense, but he sure sticks with it.

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    • philosofool says:

      If he stays healthy, few people would say that he won’t be a 4+ WAR pitcher then, but Pedro was basically done at 34, and was at least as historically great as any pitcher had ever been at 33.

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    • RC says:

      So was Tim Lincecum. He’s not even a starter anymore.

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  13. pft says:

    Generally teams like to discount long term deals as a hedge against injury. The fact there is no apparent discount is a win for Kershaw.

    Also, league wide the value of 1000 WAR in dollars is about 6.6 million wich reflects the leagues 6.6 billion revenue. We know teams prefer to limit payroll to 50% of revenue, as any good capitalist knows you need to save some for overhead and profits.

    The idea teams would pay a player 100% of any expected revenue gains from a players performance seems not logical, so I have to believe the incremental cost of a win for large market teams is significantly higher than it is for small market teams.

    In other words, the Dodgers may see his value as being more in line with something like 9 million a win or more and have discounted the long term deal enough so that it only looks like Kershaw is being paid a market rates for a 1 yr deal.

    If you did the same analysis for Cano I am pretty sure you would find Cano was underpaid relative to the market, but that’s because Seattle would not value a win much more than the league average and have a hefty long term discount.

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    • TanGeng says:

      That’s why cost controlled WAR is so important and having good young players is more important than free agency acquisitions. $6million/WAR is the estimated free agency pricing.

      Discounting of long term deals is a tug of war between factors.
      How much teams don’t like guaranteeing money verse preventing other teams from joining in the bidding.
      How much players want to be getting the most money verse securing long term stability in both life and finances.

      Both of these factors push long term prices down, but not by that much.

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  14. B N says:

    I’ve posted this before, but apparently it just doesn’t seem to stick: there is value to having WAR consolidated in a single player. However, because building a team has at least two constraints (salary and roster spots), only one constraint will typically be active at a time.

    I don’t quite understand why Dave keeps touting “But look how linear it is!” without bothering to consider the fairly basic optimization model that would tell us a lot more about the actual relationships for a normative analysis. The truth is, I wouldn’t particularly expect to see big non-linearity for top free agents. Guys worth 6+ WAR are rare, but so are teams who can afford them. Guys worth 3+ WAR are actually also fairly rare. Finding a 4+ WAR guy to replace your 3 WAR guy might be almost as hard as finding a 6 WAR guy. I’d expect the 6 WAR guy to receive no more than two 3 WAR guys, because 3 WAR guys are actually still quite hard to find. Heck, 2 WAR guys don’t grow on trees.

    On the other hand, would you expect six 1-WAR guys to pull down the same salary as Kershaw ($30m AAV for 7, or $36m total in 2014)? Unless we’re talking about relievers (for which WAR obviously does not match up well with salaries), $6m for a 1 WAR player seems on the high side. Here are the guys Steamer projects for exactly 1 WAR: Corey Dickerson, Michael Saunders, J.P. Arencibia, Eric Sogard, Rafael Furcal, Nick Hundley, and Lance Berkman. Obviously, nobody would pay $30m over 7 for this bundle. But how many would hit $6m on the open market for even one year?

    Getting down into the weeds of non-relievers projected for 0.5 WAR, I’m sure they’d be quite happy to be offered $3m for one year. However, I don’t think that is going to happen, nor do I think any sane person would trade a year of Kershaw for 24 known commodities projected for 0.25 WAR at even money (also known as a “Star for Scrubs” team). While these are obviously contrived, they do demonstrate there is a non-linear win value. Since no one will be able to pay a whole team of 3 WAR players (75 WAR team, anyone?), it seems like a strawman to look for it at the top.

    I mean, looking at this for instance ( About 6% of players have 4+ WAR. About 19% have 1-4 WAR (so say… about 6% +/- 2% for 2, 3, and 4 WAR players- the curve is fairly linear). Next, 50% of players gain only 0-1 WAR and another 25% go negative. Looking at this, you’d expect a pretty even exchange rate for 6 WAR and 2*3 WAR guys. You’ll always be short on 3 WAR guys, since only about 250 players meet that criteria (i.e., salary constraints beat out roster constraints).

    With 720 roster spots, you’d expect the non-linearity to occur lower on the curve. There are ton of guys in the 0.25-1.25 WAR range (~1000), and the error bars are high enough that it’s unlikely teams will want to pay at a rate of $6m/WAR. Would you pay a $2.5m premium over league minimum if you expected a player would be worth only 0.5 WAR more than a replacement? At the bottom, you’d expect roster constraints to be more of a factor. Obviously, teams have money to sign a ton of guys around the 1 WAR level. However, a team of 25 1-WAR guys for $150m seems a bit steep, doesn’t it?

    It doesn’t mesh with what I’m seeing descriptively on the FA market, nor what I’d expect from a normative model. While they may not be flashy big signings, the aggregate money at baseball’s “bottom of the pyramid” is significant in aggregate. If the league, in total, bought ~1 WAR guys for even $0.5m cheaper and there are about 300 of them, you’re talking about $150m (or $5m/team). Anyhow, on a totally unrelated note, anyone notice how the A’s, a team notorious for trying to take advantage of inefficiencies, tend concentrate their value across a lot of players ( Probably totally unrelated.

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    • B N says:

      TL;DR Version:
      – Linear dollars per win is probably accurate for almost anything over 2 WAR.
      – At zero WAR, it is clearly non-linear as you have to pay league minimum, regardless of how little they will contribute.
      – Below 2 WAR, and certainly below 1 WAR, is where you would expect potential non-linearities to occur, as salary becomes less of a constraint.
      – Someone who has the salary data on-hand should actually look at an optimization model for this.
      – I would not trade Kershaw for 24 guys each worth 0.25 WAR, with salaries of $1.5m each (in case you were trying to broker a trade between the Dodgers and Astros).

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    • ALEastbound says:

      Take a shot everytime you read WAR

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    • Joshua_C says:

      Very, very well-stated. I have not seen a convincing case made against non-linearity, and I think you’re correct in your argument that the 6 WAR/3 WAR argument is perhaps the wrong way to model it because 3 WAR players are comparatively rare themselves.

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  15. Brad Johnson says:

    “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.”

    I wonder if there are positive interactions between two 3 WAR players that we’re not picking up with WAR. A single 6 WAR player should be worth more than two 3 WAR players – that’s just how scarcity works. But if two 3 WAR players actually provide enough hidden value above six wins, they could offset

    Let’s assume the existence of a hidden effect. And let’s say we have players A, B, and C – all worth 3 WAR. If player A is an OBP machine and player B is a power hitter, there is an interactive effect. Let’s say player A is a stout defender at 3B and player C is a soft-tossing starter. There’s another effect. These are fairly obvious examples that can be measured. In most cases, I suspect that the interaction is less obvious.

    Adding or removing any above average player will set off a chain reaction of moves. If the Red Sox re-sign Drew, Bogaerts goes to 3B (where his defense will probably be elite), Middlebrooks slides to the bench, and some less utile bench player gets bumped off the roster. In the case of injury to either starter, Middlebrooks steps in as an above average backup. Without injury, the defensive efficiency of the left side of the infield is probably +10 runs over a season. The lineup could see some effects too (not necessarily positive given that Middlebrooks could be a better hitter than Drew). And that’s ignoring so-called intangibles.

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    • B N says:

      I think part of the issue is that 3 WAR players are still VERY scarce. As in, 3+ WAR players are the top 125 players scarce, but there are 720 spots to fill. You’ll never get a full team of them, so they’ll always hold their value. If you think about it as an optimization problem for assignments, it makes sense: for guys who will always be a big upgrade to a couple teams’ open roster spots, value should hold up. I’d guess even 2-WAR guys can usually manage that.

      However, for the guys closer to the bottom, it’s musical chairs. Somebody has to fill those last 50-100 roster spots with about zero leverage. At least 2/3 of roster spots are going to guys in the sub-2 WAR range, competing head-to-head for prospects for jobs. Worse, their expected value may be low enough that a team would rather use the slot to simply audition lesser prospects during uncompetitive seasons (which, like panning for gold, can lead to discovering value).

      So I’m fairly sure that at least the high-performing players’ salaries don’t even need interaction effects (which are typically small, with the exception of stacking the right pitching/defense/park combination).

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  16. Sandy Kazmir says:

    Those contract valuations are based on a one-year deal, yes? It’s perfectly conceivable that a nearly 8-WAR pitcher would get something approaching $50M on a one year Free Agent deal. The fact that you have not accounted for player give-back in lieu of more guaranteed years casts serious doubt upon your analysis here. Good luck showing those punks wrong next time, though.

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  17. TanGeng says:

    Feels a lot of confirmation bias is here.

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  18. snydeq says:

    The opt-out clause is definitely interesting in terms of the two data sets Dave proposes here.

    Three scenarios: (1) If Kershaw is better than an expected 3.5 WAR pitcher in 2019, at $7.66M/WAR, you would expect that he would opt out of the contract to land a longer-term deal pegged to that higher initial value. (2) If he is worse than an expected 3.5 WAR pitcher in 2019 (or injured), he probably sticks with the contract in hopes of rebuilding that value. (3) If he hovers around the expected 3.5 WAR, things get a little more interesting.

    In instance (1) the Dodgers likely receive at minimum $165 million in value, according to the linear model, for $150 million over five years, and for the nonlinear model, $193 million. (Granted he could have been hurt for early or middle years of the contract and then come back blazing and walk out without the Dodgers getting that kind of value.)

    In instance (2) the Dodgers would be on the hook for $65 million for 2019 and 2020 for a player that, given today’s reclaimation contracts, would probably be valued at about $15 million for those two years. According to the linear model, with adjustments to 1 WAR in 2019 and 2020, the Dodgers would receive $180 million in value over 7 years; for the non-linear model, $209 million.

    In instance (3) Kershaw probably tests the market. With an expected value of $51 million in 2019-2020 and $65 million left on his contract, Kershaw could leverage being a 3.5 WAR solid middle-rotation guy with high upside at 30 years old to get a more desirable longer-term contract, even at a lower AAV. If he sticks with the Dodgers, depending on any trade clauses, they either hold on to him for an expected $215 million value over 7 years in the linear model, or a $245 million value in the non-linear model. Or, they have a pretty solid trade chip in 2019-2020, which could factor into any extension negotiations between Kershaw and the Dodgers, not to mention Kershaw’s decision to stick through the initial contract vs. test the free agent waters and have a better chance of determining where exactly he wants to play vs. being traded.

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  19. Big Daddy V says:

    The second table does not really make sense. In such an environment, the amount of total WAR in the league would be higher, with salary remaining the same, and so the $/WAR would have to be something less than 6. But you have completely ignored this.

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  20. Moo cow, moo! says:

    Ignoring the rest of the article completely, is no one else concerned that just randomly inflating every WAR past 3 doesn’t somehow affect the value of a win?

    You’ve just increased the total number of “wins” that players are worth, so you need to deflate the value of each. Just imagine if he’d started inflating wins by 50% for every WAR after 2!

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  21. George Stovey says:

    We need to stop pointing to the price that a single team pays to a single player as evidence of what “the market” thinks at this instant. All the teams’ markets are different, at different times, and the high bidder at any moment doesn’t really speak for the rest. How much the Trolley Dodgers are willing to pay per expected WAR has no meaning for how much the Brewers or Royals or Jays ought to pay.

    It’s interesting to note how often we pat teams on the back for paying “fair market value” for a guy, and shortly thereafter the team demonstrates strong regret over that deal. A-Rod’s deal is a ridiculous example, of course, but we also have the Red Sox peddling Crawford, Beckett, and A-Gonz to the Dodgers — who now would be delighted to offload at least 2 and maybe all 3 of those deals. Then there’s Pujols and Hamilton in LAA. The list is long.

    Yes, we can build simple models that track with such disappointing deals — but that doesn’t mean the teams placing those bets are behaving wisely.

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