The Cost of a Win in the 2014 Off-Season

While there are still a few lingering holdouts — or, perhaps more simply, a few players who still aren’t yet convinced that they’re not worth what they’re asking for — the off-season is pretty much over at this point. In fact, we’re only a couple of weeks away from a pair of actual baseball games that count in the standings. The 2014 season is almost here, so we can begin to make some declarations about what we can learn from the recently completed off-season. And one of the things I like learning the most about is the economics of baseball’s closest proximation to a free market.

For every team, their off-season goal can essentially be drilled down to the attempt to purchase future wins. Whether they’re signing a free agent, making a trade, claiming a player on waivers, or even building academies in foreign countries, most decisions made by a baseball operations staff are in the pursuit of buying wins for their team on the field. They aren’t always wins that manifest in the short term, and the exchange of dollars for wins is not always so straight forward, but this is the transaction that front offices are hired to make. Buy wins, as many as you can afford.

The most obvious market for this exchange is free agency; players market themselves and the wins they can bring to an organization, and the team that bids the most usually lands the player. While players come in all shapes and sizes, they are all essentially selling the same product, just in different types of packaging. If a team finds one player’s asking price too high, they’ll simply buy their wins in a different form. Free agency is the great equalizer, allowing players of all varieties to sell themselves next to players who they are rarely compared against, and for the observing public to find out exactly what teams think different packages are worth.

The resulting bids can essentially be translated into dollars per wins, or $/WAR, as we often refer to it around here. And now that we’ve got most of the free agents signed, let’s look at what wins were going for over the winter.

Back in November, I looked at the first dozen contracts signed and extrapolated that the price of a win, early in the free agent period, looked to be around $6 million or so. It was certainly a bit of a back-of-the-envelope calculation, as it took forecasts from just the Steamer projection system, used the same generic aging curve for every player, and didn’t make any adjustments for the present versus future value of a dollar. The basic calculation works fine as an overview, but for a full recap, we can make some better assumptions to tweak things a bit.

For this exercise, I’m using both the Steamer projections as well as the ZIPS forecasts, combining the WAR projections both systems have listed on our leaderboards as 50% of the calculation. Using a combination of the two systems helps ensure that we’re not basing our evaluations simply on the difference between what MLB teams see and what one particular forecasting tool sees. ZIPS and Steamer are both terrific projection models, and I like having the combination of the two for analysis.

Additionally, I’ve tweaked the aging curve assumption so as to hopefully represent player contribution a little more fairly, rather than just knocking half a win per season off everyone’s forecast in perpetuity. This is particularly important for role players, where half a win may represent 50% of their projected value, and they’re likely to be used in such a way that it cutting their value in half from one year to the next is simply an unrealistic assessment of their future production. The aging curve that has been applied in this calculation gives players 90% of their prior year forecast for seasons up through age-30, then 85% of prior year for ages 31-35, and 80% of prior year for ages 36 and up. These results line up quite well with our general understanding of how players age, and produce results that are similar to what systems like ZIPS produce when creating long term forecasts.

Finally, I’m also providing two Net Present Value calculations in addition to the simple division of total dollars divided by total forecast WAR over the life of the contract. While on one hand it is correct to say that a team that pays $240 million for 26 forecast WAR is paying a little over $9 million for each win they’re buying, it is also true that $24 million in 2014 and $24 million in 2023 are not equivalent, and adding them together can skew the picture a bit on multi-year deals.

In reality, the high priced free agent contracts often are structured in ways that are simply deferment allowances; teams often don’t expect any real return at the end of these seven, eight, or nine year contracts, but by they’re using the length of the deal to delay payment far into the future. In many cases, a 10 year deal could simply be seen as a five year contract with five years of deferred payments, as the expected value in the back half of the deal comes primarily from allowing the team to afford the player for the first five years. In some senses, these long term deals are essentially just a team making itself an interest free loan so that they can buy something today and pay for it later. The depreciating value of the money being guaranteed is factored into the team’s decision to make the offer, and we should include that benefit in our calculation.

One final point before this overly long explanation comes to an end. The $/WAR calculations below were applied to all the free agents that were signed to Major League contracts as reported by the MLBTradeRumors Free Agent Tracker, with two groups being excluded: relief pitchers and players who defected from Cuba. We’ll do another post on reliever valuation, but the nature of relief pitcher usage means that WAR is often too blunt of a tool for that market, and adding them in simply skews the numbers for everyone else when they are really a market unto themselves. Additionally, Cuban defectors were excluded because of both the wide range of forecasts that could be applied to their production, as well as the fact that they are the rare free agent types who are often signed for their long term value, not short term production, making it difficult to value their performance in the same way as traditional free agents.

Okay, now that we’re over 1,000 words in and I haven’t actually given you any data yet, let’s get to it. Below is a table of 83 free agents signed this off-season, with the years and amounts of their contracts as reported by MLBTR. The only adjustment I made was for Masahiro Tanaka, whose acquisition cost included both the $20 million posting fee and an opt-out after the fourth season; for these reasons, I list his contract as $108 million over four years, which is what the Yankees will have paid if he performs well and exercises his right to opt out. He’ll only opt-in to the final three years if something goes wrong, meaning that the 4/$108M number is the Yankees best case scenario, and there is only really downside risk from there.

Okay, for real, have some data.

Player Age Years Amount AAV 2014 WAR Contract WAR $/WAR NPV5% NPV10%
Robinson Cano 30 10 $240.0 $24.0 4.9 25.5 $9.4 $7.3 $5.8
Jacoby Ellsbury 29 7 $153.0 $21.9 4.0 18.9 $8.1 $6.7 $5.6
Shin-Soo Choo 30 7 $130.0 $18.6 3.3 14.9 $8.7 $7.2 $6.1
Masahiro Tanaka 25 4 $108.0 $27.0 4.3 14.8 $7.3 $6.5 $5.8
Hunter Pence 31 5 $90.0 $18.0 2.4 8.9 $10.1 $8.8 $7.7
Brian McCann 29 5 $85.0 $17.0 3.5 13.5 $6.3 $5.4 $4.8
Curtis Granderson 32 4 $60.0 $15.0 1.8 5.7 $10.5 $9.3 $8.3
Jhonny Peralta 31 4 $53.0 $13.3 2.2 6.9 $7.7 $6.9 $6.1
Matt Garza 29 4 $50.0 $12.5 2.3 7.6 $6.6 $5.8 $5.2
Ubaldo Jimenez 29 4 $50.0 $12.5 2.8 9.1 $5.5 $4.9 $4.3
Ricky Nolasco 30 4 $49.0 $12.3 2.6 8.3 $5.9 $5.2 $4.7
Carlos Beltran 36 3 $45.0 $15.0 2.3 5.5 $8.2 $7.4 $6.8
Tim Lincecum 29 2 $35.0 $17.5 2.0 3.7 $9.4 $8.8 $8.2
Mike Napoli 31 2 $32.0 $16.0 2.1 3.9 $8.2 $7.7 $7.1
Jason Vargas 30 4 $32.0 $8.0 1.5 4.6 $6.9 $6.1 $5.5
Omar Infante 31 4 $30.3 $7.6 2.0 6.2 $4.9 $4.3 $3.9
Scott Feldman 30 3 $30.0 $10.0 1.6 4.1 $7.3 $6.6 $6.0
Carlos Ruiz 34 3 $26.0 $8.7 2.6 6.8 $3.9 $3.5 $3.2
Phil Hughes 27 3 $24.0 $8.0 1.7 4.5 $5.4 $4.9 $4.4
Bronson Arroyo 36 2 $23.5 $11.8 1.5 2.6 $9.0 $8.4 $7.8
Tim Hudson 37 2 $23.0 $11.5 1.9 3.4 $6.7 $6.3 $5.8
Scott Kazmir 29 2 $22.0 $11.0 2.0 3.7 $5.9 $5.5 $5.2
James Loney 29 3 $21.0 $7.0 1.2 3.2 $6.6 $6.0 $5.4
Jarrod Saltalamacchia 28 3 $21.0 $7.0 1.6 4.3 $4.8 $4.4 $4.0
Bartolo Colon 40 2 $20.0 $10.0 2.1 3.7 $5.4 $5.0 $4.7
A.J. Burnett 36 1 $16.0 $16.0 2.4 2.4 $6.7 $6.3 $6.1
Marlon Byrd 35 2 $16.0 $8.0 1.4 2.6 $6.2 $5.7 $5.4
Hiroki Kuroda 38 1 $16.0 $16.0 3.0 3.0 $5.4 $5.2 $4.9
Juan Uribe 34 2 $15.0 $7.5 2.2 4.1 $3.7 $3.4 $3.2
Justin Morneau 32 2 $12.5 $6.3 1.2 2.1 $5.9 $5.5 $5.1
David Murphy 31 2 $12.0 $6.0 1.7 3.1 $3.9 $3.7 $3.4
Mike Pelfrey 29 2 $11.0 $5.5 1.4 2.7 $4.1 $3.8 $3.6
Nate McLouth 31 2 $10.8 $5.4 0.6 1.1 $9.7 $9.0 $8.4
David DeJesus 33 2 $10.5 $5.3 1.0 1.9 $5.7 $5.3 $4.9
Rajai Davis 32 2 $10.0 $5.0 0.4 0.6 $15.4 $14.4 $13.4
Dan Haren 32 1 $10.0 $10.0 2.1 2.1 $4.8 $4.5 $4.3
A.J. Pierzynski 36 1 $8.3 $8.3 1.7 1.7 $5.0 $4.8 $4.5
Josh Johnson 29 1 $8.0 $8.0 1.1 1.1 $7.6 $7.3 $6.9
Nelson Cruz 32 1 $8.0 $8.0 1.3 1.3 $6.2 $5.9 $5.6
Dioner Navarro 29 2 $8.0 $4.0 1.5 2.9 $2.8 $2.6 $2.4
Garrett Jones 33 2 $7.8 $3.9 0.2 0.4 $20.9 $19.5 $18.2
Chris Young 29 1 $7.3 $7.3 1.2 1.2 $6.0 $5.8 $5.5
Michael Morse 31 1 $6.0 $6.0 0.2 0.2 $30.0 $28.6 $27.3
Jason Hammel 30 1 $6.0 $6.0 1.1 1.1 $5.7 $5.4 $5.2
Corey Hart 31 1 $6.0 $6.0 1.1 1.1 $5.5 $5.2 $5.0
Willie Bloomquist 35 2 $5.8 $2.9 - - - - -
Mark Ellis 36 1 $5.3 $5.3 1.1 1.1 $4.8 $4.5 $4.3
Ryan Vogelsong 35 1 $5.0 $5.0 0.6 0.6 $9.1 $8.7 $8.3
Edinson Volquez 29 1 $5.0 $5.0 0.6 0.6 $9.1 $8.7 $8.3
Brendan Ryan 31 2 $5.0 $2.5 0.7 1.2 $4.2 $3.9 $3.9
Skip Schumaker 33 2 $5.0 $2.5 - - - - -
Roberto Hernandez 32 1 $4.5 $4.5 0.5 0.5 $10.0 $9.5 $9.1
Jose Molina 38 2 $4.5 $2.3 0.6 1.0 $4.5 $4.2 $4.2
Gavin Floyd 30 1 $4.0 $4.0 0.9 0.9 $4.4 $4.2 $4.0
Jeff Baker 32 2 $3.7 $1.9 0.1 0.1 $40.0 $37.2 $37.2
Eric Chavez 35 1 $3.5 $3.5 0.3 0.3 $11.7 $11.1 $10.6
Ryan Sweeney 29 2 $3.5 $1.8 0.7 1.2 $2.8 $2.6 $2.6
Geovany Soto 30 1 $3.1 $3.1 1.2 1.2 $2.5 $2.4 $2.3
Nick Punto 35 1 $3.0 $3.0 0.3 0.3 $12.0 $11.4 $10.9
Rafael Furcal 34 1 $3.0 $3.0 1.2 1.2 $2.6 $2.5 $2.4
Kelly Johnson 31 1 $3.0 $3.0 1.3 1.3 $2.4 $2.3 $2.2
Kurt Suzuki 29 1 $2.8 $2.8 1.4 1.4 $2.0 $1.9 $1.9
Raul Ibanez 41 1 $2.8 $2.8 0.2 0.2 $18.3 $17.5 $17.5
Paul Konerko 37 1 $2.5 $2.5 0.3 0.3 $10.0 $9.5 $9.5
Brayan Pena 31 2 $2.3 $1.1 0.4 0.6 $3.5 $3.3 $3.3
Chris Capuano 34 1 $2.3 $2.3 0.7 0.7 $3.5 $3.3 $3.3
Jerome Williams 32 1 $2.1 $2.1 0.7 0.7 $3.2 $3.1 $3.1
Tommy Hanson 27 1 $2.0 $2.0 0.9 0.9 $2.2 $2.1 $2.1
Clint Barmes 34 1 $2.0 $2.0 0.7 0.7 $3.1 $2.9 $2.9
Brian Roberts 35 1 $2.0 $2.0 0.3 0.3 $6.7 $6.3 $6.3
J.P. Arencibia 28 1 $1.8 $1.8 1.0 1.0 $1.8 $1.7 $1.7
Felipe Paulino 29 1 $1.8 $1.8 0.5 0.5 $3.9 $3.7 $3.7
Paul Maholm 31 1 $1.5 $1.5 0.6 0.6 $2.5 $2.4 $2.4
Wil Nieves 35 1 $1.1 $1.1 - - - - -
Casey McGehee 31 1 $1.1 $1.1 0.7 0.7 $1.6 $1.5 $1.5
John Buck 32 1 $1.0 $1.0 0.7 0.7 $1.5 $1.5 $1.5
Franklin Gutierrez 30 1 $1.0 $1.0 0.2 0.2 $5.0 $4.8 $4.8
Luis Cruz 30 1 $0.8 $0.8 0.4 0.4 $1.9 $1.8 $1.8
Grady Sizemore 29 1 $0.8 $0.8 0.1 0.1 $7.5 $7.1 $7.1
David Adams 27 1 $0.6 $0.6 0.5 0.5 $1.3 $1.2 $1.2
Francisco Peguero 26 1 $0.6 $0.6 - - - - -
Francisco Pena 24 1 $0.5 $0.5 0.3 0.3 $2.0 $1.9 $1.9

Let’s start off by talking about the three $/WAR calculations on the right hand side. Furthest in, we have the most basic division model, which just takes total contract forecast WAR divided by total dollars paid. To the right of that, we substitute in Net Present Value with a 5% discount rate for the total dollars, which brings the costs down by depreciating future dollars by 5% per year. And in the final column, we have the same NPV calculation, only with a 10% depreciation instead of 5%.

You can see for yourself just how big a difference using an NPV calculation can make, as the cost of Robinson Cano’s deal goes from over $9 million per win to under $6 million per win if you apply a 10% discount rate to future dollars. From my perspective, it’s hard to believe that MLB can continue to sustain the kind of growth they’ve achieved recently — and I probably lean towards the 5% model, personally — but there’s no question that MLB has tapped into massive revenue streams, and given that many owners may not even be writing the checks in 10 years, they may very well put an exceptionally high discount rate on future commitments.

Keep in mind, though, that if you decide you like the 10% discount rate model, you can’t use it to argue that the Cano deal was under the market rate of $6 million per win, because that estimate came from applying no discount to future spending. Each model has their own “market rate”, and so here are the baselines for each of the three calculations.

Baselines $/WAR NPV5% NPV10%
Average $7.0 $6.1 $5.8
Median $5.9 $5.3 $4.9

You’ll notice that the average is significantly higher than the median in each case; this is essentially because of a few very high $/WAR calculations that are the result of some near replacement level projections for players who got some modest short term contracts this winter. Michael Morse, for instance, checks in at a whopping $30 million per win because both ZIPS and Steamer think he’s basically a scrub who the Giants wasted $6 million to sign. The projections like Jeff Baker even less, so they grade him at out a hilarious $40 million per WAR. These huge outlier numbers come from having very small numbers in the denominator, but all it really takes is for these systems to be off by half a WAR or so for these contracts to look totally normal relative to the market, and that’s why the median price may be a better reflector of the actual market price over the off-season.

Regardless of which model you pick, the range is somewhere between $5 and $7 million per win, which nicely supports the earlier $6 million estimate. Dan Szymborski has been using $5.5 million per win as his assumed price in transaction analysis pieces for ESPN, and that lines up nicely with the median of the 5% NPV model. Lewie Pollis and Matt Swartz have both used different methods of calculations to determine price paid per actual win of past contracts, and have both ranged a little higher, with Lewie recently presenting his calculations at $7 million per win.

One of the reasons I’m presenting the three different calculations is that reasonable people can disagree about many of the assumptions that go into making these calculations, and the reality is that there is no simple and clearly correct way to calculate $/WAR. Like WAR itself, this model requires some trade-offs to be made, and decimal point precision isn’t really the goal. What we’re generally interested in is being able to establish some kind of norm for how the market values wins at a given point.

And right now, I think we can say that the market has decided to pay roughly $6 million per win. Maybe it’s a little more, maybe a little less, but it’s in the $6 million range. Later this afternoon, we’ll break things down a little bit more, and look at where some of the differences in valuations occur.




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

87 Responses to “The Cost of a Win in the 2014 Off-Season”

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  1. PWR says:

    great article. Is it okay to use Steamer projections now? I thought somebody mentioned that there some sort of inflated run environment going on there?

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  2. Vlad the Impaler says:

    Would it be interesting to look backwards one year to see how the FA class of 2012-13 actually fared in the 2013 season?

    You could compare those $/WAR numbers to the projections and see what kind of variance you got, too.

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  3. Mike Green says:

    It does look like the $/WAR figure does increase on average with AAV. At least this year.

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    • RC says:

      It does every year.

      I don’t know why Dave keeps insisting otherwise.

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      • Eric R says:

        There are 79 players listed with $/WAR figures, breaking them into four groups:

        Top 25% $16M AAV $7.7M/win
        Next 25% $8M AAV $7.0M/win
        Next 25% $4M AAV $8.1M/win
        Bottom 25% $2M AAV $5.4M/win

        Something is up with those small but not too small deals to just say that teams pay more per win for higher win players

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        • Mike Green says:

          The median $/WAR figure for the $16M AAV+ group is $8.1 million. The median figure for the $8M-$15.9MM is $6.2 million. And it decreases from there.

          The figures are more accentuated if you take into account contract length. It sure looks like teams this year played much more for stars.

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        • placidity says:

          But the median length is 4.5 years, or longer than any other contract given out this offseason. Which is why we use discounting.

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  4. derekcarstairs says:

    Do teams pay much attention to $/WAR data in FA offers and contract negotiations? Put another way, to what extent does $/WAR shape the market for players?

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    • RonnyRocket says:

      None at all. I enjoy fangraphs, but far too many articles over the past several months have been reliant on WAR. A decade from now, Mr. Cameron will be writing an article from deep inside his moonbase about how silly it was for the analytical community to become so fixated on a single stat.

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      • RC says:

        Fangraphs-WAR isn’t the stat used, but teams most certainly are using advanced stats to come up with a WAR type stat and using that (combined with aging models) to find total value for a contract.

        Do you really think its a coincidence that so many of the guys who pioneered advanced stats now work for MLB teams?

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        • derekcarstairs says:

          Do you think, just maybe, that a team may start out with good intentions by making an offer that is based on WAR-projections, but that WAR value is often abandoned once teams start bidding for the same player and the marketplace takes over?

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        • Catoblepas says:

          how do you think they decide to stop bidding? once someone else bids, execs aren’t just like “ZOMGZ MUST WIN, BID HIGHER!”, they ask if the price has risen above the value they think they’ll get. There’s no point where they just throw out metrics.

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        • derekcarstairs says:

          I am off by one player, but the breakdown of $/WAR projections is -
          5 players – $1-1.9 million
          9 players – $2-2.9 million
          8 players – $3-3.9 million
          8 players – $4-4.9 million
          12 players – $5-5.9 million
          10 players – $6-6.9 million
          5 players – $7-7.9 million
          4 players – $8-8.9 million
          6 players – $9-9.9 million
          4 players – $10-10.9 million
          2 players – $11.7-12 million
          5 players – $15.4-40 million
          4 players – unsigned

          Does this distribution suggest that teams are guided by WAR projections or the natural workings of the marketplace?

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      • Jason B says:

        I think, pretty obviously, that WAR is a useful framework from which to analyze these deals, both individually and collectively. I would dare say that every one of the FG writers recognize that it’s just that – a framework, and not immutable gospel.

        And if you have a more useful, user-friendly framework from which to compare all contracts for all players, I think we’re all very open to that; feel free to share.

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        • tz says:

          I like your use of “framework” to describe WAR. There are disagreements on what the ingredients are, or how they ought to be calculated, but the framework always comes back to:

          An estimate of how many more wins a team would have with Player X on their roster than if they filled that roster spot with an easily-exchangeable “replacement” player.

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        • Eric R says:

          By framework it is more that WAR isn’t a giant black box stat, but several components added together. on Fangraphs, that is batting, base running, fielding, positional adjustment, league adjustment and replacement.

          Add them up and you have runs above replacement; roughly divide by 10 and you have wins above replacement.

          If you think the fielding component is bad, it is easy to swap out theirs for whatever you prefer.

          If you have additional components– like maybe you’ve devised a statistical value to represent player leadership value. So long as it is runs relative to average, you can insert that right in the middle and add it in before the runs-to-wins conversion.

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      • Simon says:

        What other stat should they use that is a better way of fully quantifying the value of a player?

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      • jim says:

        It’s a real shame that guy stood with a gun to your head and forced you to read all that free content.

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    • I think a fair amount of teams look at analytical stats. See Atlanta Braves, Andrelton Simmons and contract extensions.

      And, speaking of that position, especially allowing for positional scarcity, Peralta is shown as being paid just about right.

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  5. vivalajeter says:

    Very interesting information. It’s a shame we can’t get front office insight into how much they value the cost of a win, since their projections won’t necessarily align with Zips/Steamer. For instance, I really doubt the Mets’ front office expects 1.8 WAR out of Granderson this year and 5.7 WAR over the duration of the contract. They probably think he’s more likely to put up 5.7 WAR by the end of 2015 (and the Fans agree, although they might be too optimistic). So while they may have paid $10MM/WAR based on the projections you used, it might be closer to $6MM/WAR based on their own projections.

    Same thing for Cano. 4.9 WAR is well below his established performance over the last four years. If Seattle expects him to be at or above 5.5 WAR this year, then they won’t think they’re paying over $9MM/WAR.

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    • Hurtlockertwo says:

      Do you actually think teams are using WAR to make these signing assessments?? (not being snarky, just asking a question)

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      • vivalajeter says:

        I don’t think they use the actual WAR that we’re looking at, but I assume that their thought process is similar to what Dave laid out, with different inputs. They’d lay out their projections, make adjustments for their specific teams needs (on and off the field), and come up with what they think someone’s worth. But much like an auction, I’m sure several GMs have gotten into situations where they bid more than they thought, because they don’t want to lose out.

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      • RC says:

        Their way of calculating it is probably different (and probably more accurate), but yeah. I’d guess that the analytical teams have adjustments for opponents faced, park, etc.

        But I’d guarantee at the end theyr’e getting to some sort of “total player value” projection stat and some sort of comparison of how much each unit of value is worth on the market.

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      • Kyle H says:

        I remember hearing the Colorado Rockies GM saying basically thats exactly what they used

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      • Joebrady says:

        I doubt it. FG has come up with some huge valuations for players, particularly longer term players, that have never come to fruition.

        I think most GMs look around to see what comparative players are signing for. I assume the contract looks something like WAR/$, but my guess is that Dombrowski looked at Pujol’s contract before giving Fielder his final number.

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        • RC says:

          If a team’s valuation says that a player is worth 6/$100, and nobody else is offering more than 5/$50, would you really expect the player to get full value?

          The best place to gain value is to find places where you think the market is undervaluing something. You don’t gain value if you keep bidding something up to what its worth.

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      • Ryan S says:

        If you didn’t want to be snarky, you wouldn’t have used the word actually

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      • Bradsbeard says:

        Why, yes they do. Here is an article from today in which Frank Wren discusses locking up his young players in part because of their WAR.

        http://m.washingtonpost.com/sports/nationals/atlanta-braves-have-strong-young-core-under-contract-for-years-to-come/2014/03/03/611d9aa2-a2f8-11e3-8466-d34c451760b9_story.html

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      • Some Guy says:

        While I admit I have no evidence for the following, I would imagine that one input that would carry equal weight with WAR would be a fairly in-depth calculation of a player’s downside and upside risks. I think this would go beyond a basic calculation of statistical uncertainty and would include an effort to model a player’s potential outcomes based on the probability of that player making certain adjustments or advancements. I think that the kind of information that would go into such a model might be more likely to come from scouts.

        The whole exercise might be as simple as a scout saying “I like this guy because I think we could teach him how to do x, coach y in our minor league system is good at that,” and then coach y would say, “yeah I can see how I would teach him that; get me that guy.” Then a stats geek can try to translate the adjustments that coach y proposes to make into projections. Other organizations might not have a coach that possesses the same eye for a particular shortcoming as coach y, so that doesn’t enter into the player’s evaluation (I’m thinking of Don Cooper and his supposedly legendary ability to develop pitchers here…I imagine this might have been a factor in the White Sox bringing on Paulino this year). While this applies more to developmental players than established free agents, I still think it’s a big part of the evaluation process.

        Plus, as we learned from executive interviews with Blake Bortles at the NFL combine, the hotness of the player’s wife/girlfriend, how often she’ll be around, and how she would dress if she were to drop by is probably ~20% of the equation.

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      • Trotter76 says:

        One factor that I haven’t heard anyone mention that actual GM’s need to consider that is not in WAR is marketability. “Robinson Cano, former Yankee All-Star and Home Run Derby Champ, is coming to Seattle! Step right up and get your ticket!”

        Remember, to a team owner, wins are not an end. Wins are a means to get to the true end, money. So maybe they have a stat that works out to Revenue Above Replacement. Nick Franklin sells zero tickets. Cano sells thousands of tickets. Cano is worth the money. Done.

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        • Jason B says:

          But in most markets, I would think that attendance pretty closely tracks winnings (perhaps less so in the prime markets or those that always do well, or moribund Tampa), and the best way to get at more wins, generally speaking, is with better players.

          In other words, I think fans are more apt to attend “Seattle, 87-70, right in the thick of the wild card chase!” than “Seattle, come see a past Yankee All-Star on a 70-87 team!”

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      • arc says:

        We don’t have to guess. Multiple execs have stated publicly that they do.

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    • Vlad the Impaler says:

      Here’s an article from 2012 where Cleveland Pres Mark Shapiro put the value of $/WAR at 9 million per win. So teams have a much different valuation method internally.

      http://www.lonestarball.com/2012/10/24/3549442/indians-president-mark-shapiro-talks-stats-war-and-much-more

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      • Darren says:

        They must have been using a much lower replacement level than Fangraphs. Otherwise I am sure it is based on the same ‘replacement level’ framework.

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      • Catoblepas says:

        and really, that doesn’t matter a lot. maybe 1 cleveland win = 2/3 fWAR, which makes the numbers look different, sure, but as long as it’s consistent across the league, the relative values don’t change, and that’s what matters. So just saying that they have some sort of (almost-)all-encompassing value stat is what’s interesting.

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      • RC says:

        He could also be saying that a WAR produces 9M in revenue, despite the fact that the FA market hasn’t caught up to that value yet.

        Also, don’t discount the fact that most of our $/WAR data comes from multi-year deals, which are naturally discounted for risk.

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  6. For the averages, did you take the average of the columns or did you weight it by years e.g. Cano’s avg was used 10 times as opposed to one?

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    • Steven says:

      I assume (and calculations agree) that it is simply Contrast $ Total/ Contract WAR total. So it is weighted.

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  7. RC says:

    You still going to insist that teams pay the same $/WAR at different talent levels, or are you going to give that up?

    [IMG]http://i60.tinypic.com/25z76lt.jpg[/IMG]

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    • Simon says:

      It’s much less clear cut when you take into account inflation and the impact it has on longer contracts. Using the MPV5% ot NPV10% column is much more appropriate than the $/WAR.

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  8. williams .482 says:

    Youkilis is on the list with a 1 year, $4M contract, but he is going to be playing in Japan this coming season.

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  9. Marcus Tullius Cicero says:

    Is it just me, or is Mujica not on there?

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  10. Steve M-P says:

    It would be interesting to compare this with the cost of buying out young players arb and early FA years as the Braves have done with Freeman, Teheran and Kimbrel.

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  11. nsacpi says:

    Is there a discount also applied to wins as they go out in the future? Should clubs consider a win in 2014 to be the same as a win in 2020?

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    • Jeffrey Loria says:

      The Marlins are considering banking some unused wins in 2014 so they are worth more next season.

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    • Matthew Murphy says:

      It’s much easier to project wins in 2014 than 2020, and teams spending big are probably at a higher leverage point in the win curve in the next few years and therefore place a higher value on a win. While I think the numbers show that this pretty clearly factors into teams decisions, it’s quite difficult to even attempt to adjust for this in the model.

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  12. MBellamy says:

    I find it interesting that you used a 0.9 value over the previous year´s WAR for players under 30. I would have gone with an increase, and then start decreasing, probably at the same rate you did, after turning 30. I may be wrong, but I think it would make WAR values a little more accurate.

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    • Darren says:

      Most free agents are over 27 and thus are already in their decline. Other than Tanaka, I dont think there are any players that would be in their ‘growth’ stage.

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  13. derekcarstairs says:

    Dave – One suggestion: re-calculate the NPV’s based on up-to-date interest rates, like 1% and 2%, instead of 5% and 10%. It has been several years since 5% and 10% were in the ballpark, so to speak. The current Fed Funds Rate is only .25%. 10-year Treasury yields are on the order of 2%.

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    • Cliff says:

      The Fed Funds rate is irrelevant to this analysis. What matters is the growth rate of baseball revenues

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      • derekcarstairs says:

        The subject matter is not baseball. It is the present value of money.

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        • vivalajeter says:

          No it’s not. He’s not discounting based on a risk-free rate of return. He’s discounting based on future inflation of baseball salaries.

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        • pinch says:

          achievement unlocked — freshman econ!
          congratulations! you now know just enough to sound like a total idiot on the internet!

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        • pft says:

          Yeah, the value of money to purchase 1 WAR from a player. That WAR is worth much more in the future, about 5% more per year

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        • Jason B says:

          Pinch – my thoughts, almost exactly! Attending the first week (and first week only) of Finance 301 may be a dangerous thing. :)

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        • derekcarstairs says:

          I approach the question of cost of a multi-year contract as someone in the business world would, specifically someone responsible for the cash-management function. If you ask the cash manager what is the present value of a contract with a stream of future payments, he will look at the applicable actual interest rates to reach his answer.

          Now, if you want to do analyses based on estimated industry revenue growth or inflation projections, those can be interesting, too, but then you are answering a different set of questions.

          What is the topic again?

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        • Jason B says:

          Uh-oh! Someone got butt-hurt…

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    • pft says:

      Players salaries have been increasing at 5% per year for over a decade, along with MLB revenues.

      The general inflation rates are much higher than the governments CPI which manipulates the numbers downwards to keep COLOA’s in check. For example if steak prices rise, they say you can eat hamburger, and if hamburger prices go up too much they say you can eat dog food, etc. LOL. Price increases for TV’s, automobiles, etc are eliminated as so called “improvements” which are made each year to these products. Pretty much any other item which increases in price is handled the same way where the increase is largely wiped out by the calculated value of the improvement made to the product or service.

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      • vivalajeter says:

        Where are you buying your TV’s? If you’ve been seeing price increases, then you’re getting ripped off. They’re dirt cheap compared to 10 years ago.

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        • I Agree with that gentleman says:

          True story. My first plasma purchased in like 2006 cost about 2-3x more than any (same size or larger) flat screen I’ve purchased since.

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        • vivalajeter says:

          My 55″ DLP, purchased at costco in August 2005, was easily the most expensive TV I ever bought. I bought a 60″ and 70″ a few months ago, and both wound up costing the same (combined) as the 55″.

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  14. Joebrady says:

    Two other things.

    1-Players with performance bonuses are probably too complicated to be included. As a RS fan, Sizemore caught my eye. You have him as 0.1 and $7.5M. He almost can’t have both. He’ll earn $2M if he makes the roster, but in order to earn his $7.5M, he has to log a lot of PAs. And he won’t do that unless he is healthy, productive, and playing every day.

    2-I’m not sure why you are discounting players with one year contracts. If you are trying to calculate 2014 WAR value, you would not discount a 2014 contract.

    3-Glad you finally dropped the ridiculous WAR calculation for RPs. You can only compare RPs with other RPs, not SPs. You’d probably be better off calculating WAR/IP.

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    • vivalajeter says:

      Maybe he changed it since you commented, but when I look at Sizemore it says that he’s making $0.8MM for 0.1 WAR, which is $7.5MM/WAR. It’s not saying he’ll make $7.5MM in 2014 for providing 0.1 WAR.

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  15. Matt Bertelli says:

    Look at how much the Marlins are paying per win at 1st base this year with there platoon of Jeff Baker and Garrett Jones. Just throwing around that money.

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  16. Kyle says:

    Carlos Ruiz is listed with a 1.4 WAR for 2014, but Steamer and ZiPS have him at 2.6 and 2.7, respectively.

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  17. Dexter Bobo says:

    Shouldn’t some assigned $ value of the draft pick lost in signing players offered a qualifying contract be subtracted from their contract total for these purposes? Clearly 4/50 for Garza and 4/50 for Jimenez are not quite equal in terms of how much their new clubs valued them.

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  18. Matthew Murphy says:

    I’m most interested in the modification of the aging curve. It certainly makes intuitive sense, but do the numbers back it up or favor the more traditional model?

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  19. Nathaniel Dawson says:

    I wouldn’t exactly call it an interest free loan. Teams are almost certainly paying more in guaranteed money if they are paying less up front than what the player is worth, and shifting money to the back end of the deal.

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    • pft says:

      The money is worth less at the back end of the deal. That same dollar today buys less 10 years later, and is worth less

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  20. Jason Powers says:

    Here’s a visual of what Mr. Cameron just calculated. The contracts line up well, with a 90%+ R-squared for 2 models. I set the intercept at zero.

    http://deepcenterfieldmlb.files.wordpress.com/2013/12/2014-war-value.gif

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  21. pft says:

    So 7 million per WAR should be used in the Fan Graph calculations on the player pages for a given years value. Right? Hasn’t the average always been used n the past?.

    The NPV number is based on long term projections are so uncertain and a players long term deal is influenced by a multi-year discount to hedge against risk, and it starts with 7 million as the single year free agent value in any event.

    The 7 million is certainly skewed by elite players which is why the median is so much lower at 6 million.

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  22. Patrick says:

    http://i.imgur.com/TSxhBaI.png

    Looks like there’s a pretty strong relationship showing the better you are, the more per WAR you get paid. (I excluded contracts expected to produce <1 war).

    In otherwords it looks like it's better to to have 1 Robinson Cano than 2 Carlos Beltrans.

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  23. hk says:

    With none of the Phillies 3 signings listed among the top 25, can we surmise that maybe the analytics guy they signed is having some impact or just that they got lucky this off-season?

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    • Jason B says:

      I think their situation dictated many of their signings, or their approach to this offseason – they didn’t want to do a total teardown and rebuild, with an eye on their upcoming TV deal and keeping butts in the seats, but at the same time realized that they’re not just one huge signing away from being considered favorites, so they opted for shorter-term, lower-cost, lower-risk deals which look pretty good on paper and don’t hamstring them going forward, a la Ryan Howard.

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  24. Travis L says:

    The McCann contract looks a lot better in light of the Baseball Prospectus catcher framing/blocking analysis from this week. In it, they found that McCann’s framing skills have been worth about 2 WAR per year. Although we don’t know how well that skill ages (it may not decline at all, since it seems to be less based on physical tools), I think we can include another 1 WAR/year to McCann over the life of the deal.

    That would change his value from 13.5WAR to around 18 WAR, meaning the Yankees might have gotten the steal of the offseason with him.

    (For those who haven’t read the BP piece, I highly recommend it — it’s the first framing analysis I’ve seen that I would take seriously.)

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