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.