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  1. With regards to point 3, surely this is an artefact of the Winner’s Curse: – and part of the reason that these players are not getting re-signed may be that their original club has more complete information on them (e.g. they expect them to age badly) in the first place?

    Additionally, there’s also the fact that players may be giving discounts to their current club because they’re deriving utility from staying put – both in terms of their personal lives (not moving family etc.) and also from a personal-marketability perspective.

    Comment by Aaron (UK) — February 14, 2012 @ 11:12 am

  2. If you want to get technical, we probably didn’t outproduce Zito. Speaking only for myself I know that I haven’t been a replacement level baseball player since high school jv.

    I like the article though, and am wondering if you could go a step further with point number three: break the sample into players who have not switched teams since team control expired, and players who have. See what kind of “hometown discount” there actually is.

    Comment by ussdavidprice — February 14, 2012 @ 11:16 am

  3. I recommend you get yourself a copy of the 2012 THT Annual where you can find Matt’s article on the topic.

    full disclosure – I write for THT and have an article in that Annual.

    Comment by Brad Johnson — February 14, 2012 @ 11:32 am

  4. Good article – I look forward to more on the free agent market.

    Has anyone done research into allocation of total payroll to free agents vs. players not yet eligible? It seems odd to say that a 3 WAR season is “worth” $15 million when plenty of pre-free agency players contribute as much war, but much cheaper.

    Comment by tz — February 14, 2012 @ 11:33 am

  5. Why can’t all articles be like Matt Swartz articles?

    Comment by Matt H — February 14, 2012 @ 11:42 am

  6. Good stuff…

    Comment by AL Eastbound — February 14, 2012 @ 11:44 am

  7. Good article but unfortunately sabermatics does not equate economics. A players contract is for a players worth, not WAR (or ability). A players worth can be skewed a thousand different ways (merchandise, attendance, etc, etc). Though this good start for pricing a win, should also look into how much of a players contract is for peripherals?

    Comment by Thomsawyer — February 14, 2012 @ 11:56 am

  8. Just a question, not sure what the methodology is, on point number 4:
    Does the value of the draft picks considered present value and time value of money? I just ask because on a non-analytical thought track the first thing that came to mind was yes these draft picks may offer more value over their lifetime, but you have to wait as many as 4 years or so for them to start producing. I would rather have a 2 win player for this season than a 5 win player 4 seasons from now (im sure there is a more exact valuing if you did the math (ill try it out) but this is my rough offering). Especially when you consider that the people making the moves know they have their job now but not in 4-5 years you would think this would add a little more value to the FA who can produce sooner…

    Comment by zbelair — February 14, 2012 @ 11:57 am

  9. Agreed. Excellent article with lots of food for thought.

    WRT the $5M per WAR figure, it only applies to free agents because you can’t price players who are not available on the market.

    Comment by Craig — February 14, 2012 @ 12:00 pm

  10. That’s one reason it’s not really “$ per win”, but rather “$ per win that we can’t get out of cost-controlled options”. An imaginary awesome team with cost-controlled players (second/third year guys, all at least good players) might only be able to upgrade a couple of wins with 20 million a year to one premium free agent. A terrible team full of useless players might only need to spend 10 million/year to get the same benefit in wins spread out over 3-4 roster spots. It comes out in the wash in the end, I suppose, but team-specific dynamics make it a blunt tool for single acquistion analyses.

    Comment by test — February 14, 2012 @ 12:00 pm

  11. Amen!

    Comment by Baltar — February 14, 2012 @ 12:01 pm

  12. I believe all the rest of us are interested in the player’s value to the team, not his value to the employee who signs him.

    Comment by Baltar — February 14, 2012 @ 12:05 pm

  13. can we PLEASE banish the notion (however joking it is) that by not playing the game, us basement occupying bloggers and mouth breathing blog readers have accumulated 0 WAR? i’d be fucking thrilled if i were as good of a ballplayer as kosuke fukudome or edinson volquez were in 2011.

    Comment by gcm — February 14, 2012 @ 12:17 pm

  14. I wonder how much of point 4 is an artefact of “hometown discounts”

    Comment by Dave — February 14, 2012 @ 12:32 pm

  15. *point 3 sorry

    Comment by Dave — February 14, 2012 @ 12:35 pm

  16. dude, the point is not that we’re *as good a ballplayer* as, or better than, a player posting a negative or zero WAR…. the point is that *by not playing at all* we have helped the team more than a player posting a negative WAR.

    Comment by Richard — February 14, 2012 @ 1:10 pm

  17. Value, much like beauty, is in the eye of the beholder. While it seems ideal to assume that all decisions should be made in the best interests of the “team” (however you define that word) its simply non-sensical to ignore that fact that real, live human beings, with unique emotions and motivations, are the ones making the decisions. It is certainly likely that a GM, team president, or team owner will apply their own personal perspectives (biases, maybe) when determing the value of a prospect or a FA.

    Bottom line: while we’d like value to be spit out of an exacting formula; value is not a one-size fits all commodity. Its ruled not by our formulas, but by the individual perspectives of those attempting to behold it.

    Comment by SeaWolf — February 14, 2012 @ 1:17 pm

  18. The term is “above replacement”… that should not be confuse with NEGATIVE value. Replacement level does produce some value, similarly a replacement player is not paid $0; yet because the way the construct is done 0WAR = $0.

    An all replacement team does not generate 0 wins. It generates something in the 40’s… so to say 0 WAR players are worth zero dollars is just another reason why baseball stat folks should not play internet economist or internet CPA. Last I checked even replacement players get paid more than 0 (or at least that’s what the CBA says)

    Similarly 4.5MIl is the PRICE (or if you prefer, cost) of a win on the free agent market (assuming you agree with how this is calculated). It is not the VALUE of a win…. yet this constantly is used interchangeably. Is the value of a win from Strasburg next year less than the value of a win from Werth. The price is obviously different and you can look at “ROI” , but people continue to use a free agent cost of a win as the generic value of a win.

    Comment by Joe — February 14, 2012 @ 1:47 pm

  19. Do you think you could show a comparison to the “fan’s” projections (as well as Tango’s survey’s). I’m hoping to use those for my play time projections.

    Comment by bcrossman — February 14, 2012 @ 2:19 pm

  20. Anyone with 0 PA has accumulated 0 WAR, no matter how talented they are, right? I accumulated 0 doctor WAR, 0 lawyer WAR, and 0 teacher WAR in 2011, because I spent no time as a doctor, lawyer, or teacher. This is not to say I’d be better at surgery than the worst doctor in 2011 was.

    Comment by Chris — February 14, 2012 @ 2:20 pm

  21. I would really like to see this. I’ve read Dave Cameron chats where he alludes to studies indicating that the non-baseball value of superstars is negligible, but I’d like to see them.

    Comment by Chris — February 14, 2012 @ 2:22 pm

  22. It really shouldn’t make a difference who you are measuring value for, the team or the management, Wins in Baseball are the same as Dollars in Finance: one today is worth more than one tomorrow…
    It really comes down to the fact that you can’t measure value to a team in such a general sense. What is the goal of the “team”? Would anyone argue that you would prefer to win the World Series this year vs winning it 10 years from now?

    Comment by zbelair — February 14, 2012 @ 2:49 pm

  23. This article is the Albert Pujols of FG pieces.

    Comment by david — February 14, 2012 @ 3:31 pm

  24. I think the playing time issue is complicated by injuries. Over a 5 year contract, at least 1 year is likely to be a down year due to injury. That’s one reason multi-year deals are discounted, but maybe they are not discounted enough.

    There are a number of high profile players who have had free agent years bought out with extensions with below free market rates, so the over pay for free agents is even worse.

    I think the reason for the overall overpay is that for those teams who spend the most of free agents, a win is worth more than those who don’t. So while the average incremental W might be valued at 5 million or less by the Nationals, that W’s value is worth more to the Red Sox, Yankees and Phillies with higher potential revenues and more to lose by not fielding a contender. And worth more to teams who are close to being a playoff team but need a bit more like the Tigers (post V-Mart) and Angels

    The other reason for the “apparent” overpay is revenue figures are too low. With many teams owning regional stations like the Yankees and Red Sox, revenue from NESN and YES are part of the equation, and indeed, revenues for the Red Sox and Yankees may be understated to minimize revenue sharing..

    Comment by pft — February 14, 2012 @ 4:23 pm

  25. What it means is the patient would be better off with your as doctor (and saying, “I’m not really a doctor! Get any real doctor to do this”) than having the world’s worst surgeon, who would kill them on the operating table.

    Comment by Rally — February 14, 2012 @ 5:54 pm

  26. You are complete correct Joe. What they really mean to say is “Average cost of a win on the open market.” I think it is kind of comical to really use that as the basis to say contract A is bad, contract B is good. After all if everyone started paying only the average cost of a win to FAs the average cost would start to drop. The problem is that player talent is not perfectly distributed into the same amount of 1,2,3,4,5 WAR players. Therefore the higher WAR players are very likely to get more than their fair share of the FA dollars available because generally speaking teams perfer WAR density vs. WAR balance.

    As to the value of a win if you took the reported MLB revenues for 2009 and divided by the total number of regular season wins you would come up with a number very close to $3mil. Two caveats with that figure.

    1) That is the REPORTED revenues so who knows how much those numbers have been fudged and it doesnt take into account the sweetheart deals with sister companies where vendors and other services are banking money and paying the team pennies on the dollar all while being own by the same owner as the team.

    2) The total above assumes that all wins are equal and doesnt include the post season at all. So regular season wins are gonna be worth less. Also on a team basis vs a league basis we all know that the extra wins that get you into the postseason are much more valuable in terms of revenue than going from 50 wins to 60 wins. So 5 wins for the Tigers might equal 50 mil, while 5 wins for the Astros might equal 10 mil.

    Comment by Ronin — February 14, 2012 @ 6:09 pm

  27. I also think it’s kind of ridiculous that somebody thinks $18.5 million is a lot of money. That’s only about a third of what you’d need to buy a decent townhouse in Manhattan.

    Comment by JimNYC — February 14, 2012 @ 7:06 pm

  28. Matt, did you look at the pitching numbers split by starters and relievers?

    Comment by Colin Wyers — February 14, 2012 @ 8:34 pm

  29. Look at this article.. it seems all you need is a copy of THE CREATIVE MIND” and a bunch of signs in your room to tell you how wonderful you are! Ask Barry what the hell happened to him?
    Did his creative mind get sidetracked and loose focus?

    Comment by Zito's Conscience — February 14, 2012 @ 9:11 pm

  30. I explored this in a lot of detail in this year’s THT Annual. I don’t know that the Winner’s Curse is the whole explanation, because if players knew this, they would hold out more and switch. So at best it’s a coupling of Winner’s Curses plus hometown discounts.

    But a very important finding I had was that pitchers actually fell short of projections significantly when they switched teams and beat them pretty handily if they stayed put. The best market imperfection explanation is probably that players who switch teams are Akerlof Lemons:

    Comment by Matt Swartz — February 14, 2012 @ 9:13 pm

  31. In the THT Annual piece, I break it down in a lot of detail, but basically I think the hometown discount affect seems like it would at best explain half of the effect, and probably a good deal less.

    Comment by Matt Swartz — February 14, 2012 @ 9:15 pm

  32. The fraction of dollars above league minimum that goes to free agents is under 70%, but it was closer to 80% a few years ago. The flat economy plus arbitration raises continuing the grow in a non-market environment is the culprit there.

    Comment by Matt Swartz — February 14, 2012 @ 9:18 pm

  33. This is 100% true and a very essential fact to know about understanding the market for baseball players. From Marvin Miller’s wikipedia:

    “As an economist, Miller understood that too many free agents could actually drive down player salaries. Miller agreed to limit free agency to players with more than six years of service, knowing that restricting the supply of labor would drive up salaries as owners bid for an annual, finite pool of free agents.”

    Comment by Matt Swartz — February 14, 2012 @ 9:20 pm

  34. Very good idea. Of course, without free entry and exit, Major League Baseball will not have anywhere near the same market pressures as other sports, so you can get mispriced assets in the baseball labor market like you’d never imagine in markets where bad businesses disappear.

    Comment by Matt Swartz — February 14, 2012 @ 9:22 pm

  35. Check out the link on the present value of draft picks linked above. Teams appear to act as though they value wins and dollars about 10% less next year than this year.

    Comment by Matt Swartz — February 14, 2012 @ 9:24 pm

  36. Joe, I must have liked the idea of playing an economist on the internet so much that I spent a decade at Penn getting a bachelors, masters, and Ph.D. in economics. Try playing a guy who uses Google on the internet and you might have checked out my background a little.

    So it shouldn’t surprise you that I valued all contracts is by considering opportunity cost– relative to using the roster spot on a 0 WAR player playing for to the league minimum. Since we’re dealing with a labor market with finite vacancies, we need to focus on the opportunity cost of employing a worker at the expense of employing another.

    And of course, the reason that the market price of a win is treated as the value of a win is that we are making a rational expectations assumption. Of course, without free entry and exit, this assumption can be seen as limited, but if one assumes an increasing marginal revenue product of wins, the approximation seems more than defensible. Add in the fact that teams that increase their spending appear to stay just as profitable and teams that decrease their spending don’t seem to become more profitable, it seems quite likely that the marginal revenue product of free agent labor approximately equals the marginal cost. The value of a win for teams that spend money on them (disproportionally on the cusp of playoff contention) tends to be particularly high.

    Comment by Matt Swartz — February 14, 2012 @ 9:44 pm

  37. Ronin, what you’re missing in just dividing wins per dollar is that you’re explicitly assuming that the marginal revenue product of a win is equal to the average revenue product of a win. This is particularly unlikely when you consider that the marginal revenue product of a win increases as you approach the playoff cusp, and because players actually signed represent the highest value that any team placed on them.

    Comment by Matt Swartz — February 14, 2012 @ 9:47 pm

  38. I’ll look into this. Thanks.

    Comment by Matt Swartz — February 14, 2012 @ 9:48 pm

  39. Coming soon!

    Comment by Matt Swartz — February 14, 2012 @ 9:49 pm

  40. Could the playing time overestimates also be an artifact of the decreasing run environment? Playing time for hitters = PA, so fewer runs (probably) derives mostly from fewer men on base, which by extension means fewer PAs.

    That effect wouldn’t be as pronounced with have much effect with pitchers, at least league-wide, since IP is pretty much fixed but for extra inning games, and pitcher IP is generally overprojected much less than hitters…

    Comment by Pat Folz — February 14, 2012 @ 10:05 pm

  41. This is a very good example of the difference between zero and null. A replacement level ballplayer has 0 WAR; you and I have a NULL instead.

    Comment by Colin Wyers — February 14, 2012 @ 10:07 pm

  42. Apologies for the butchered grammar, im commenting from a phone.

    Comment by Pat Folz — February 14, 2012 @ 10:07 pm

  43. An interesting idea, but the average change in PA vs. the previous year is only 0.3% less than the previous year. Creative thinking though.

    Comment by Matt Swartz — February 14, 2012 @ 10:12 pm

  44. Hypothetically assuming 4.5mil/win cost)
    3 WAR player is paid 13.5 mil
    2 WAR player is paid 9mil
    1 WAR player is paid 4.5mil
    0 WAR player is paid 0.5 (rounding from 480K league min)

    –> from this hypothetical we conclude all players are paid fairly

    – the upgrade from 0 to 1 is at a cost of 4mil (4mil/win)
    – the upgrade from 1 to 2 is at a cost of 4.5mil (4.5mil/win)
    – the upgrade from 0 to 2 is 8.5mil (4.25mil/win)
    – the upgrade from 0 to 3 is 13mil ( 4.33mil/win)

    Or to put it differently if a team wants to upgrade by a win and has the option to upgrade a 0WAR player or a 1 WAR the net cost is different. Going from a 0WAR player to a 1WAR player is an extra 4mil in payroll (assuming the players are priced efficiently); going from a 1 WAR player to a 2 WAR player is an extra 4.5 mil (again assuming players are priced efficiently). For a given team that 1 extra win has the same value but it comes at 2 different costs.

    Comment by Tom — February 15, 2012 @ 2:21 am

  45. rWAR and fWAR have different replacement level. Team full of rWAR replacement players would produce several more wins than team of fWAR replacement level players (I believe it’s 54 to 50, but I’m not sure). So, there is less less WAR, around 4 per team, in rWAR than in fWAR. So, $/WAR should be higher, maybe 10% or so.
    Players on the free market often sign for the highest bidder and almost always for one of 2-3 highest (they may decline PIT or someone like that, but most of players don’t take way smaller contract than 2nd best). So, team that has signed them is generally most optimistic. When you pay people according to 60th or 70th percentile projection (specially considering injuries) instead of 50th, over large enough sample you have to lose. For example, NYY valued Burnett at something like 4/60. But when ATl started bidding, they had a choice between paying him 5/82.5 or losing him, even though they knew that 5th year was lost money, maybe even 4th. But they got WS win out of that.

    Comment by Davor — February 15, 2012 @ 6:41 am

  46. Matt – not sure you noticed but I was responding to Richard.

    Sorry if you took the stat guys line as a shot directed at you it was directed at a lot of these commenters who shout dumb move or great move because they hear 4.5mil = 1 win and maybe are ‘advanced’ enough to apply a 5% inflation rate and an aging curve and think that’s all there is to it. Or think a guy off the street provided more value than a below replacement level player.

    Though I do have issues with your rational expectations assumption and using pretty much unknown/unconfirmable profitability vs payroll to validate a marginal revenue assumption… it may be true, but we really have no way of knowing what the profitability of these teams are. We just don’t have enough insight into their books and detailed cash flow analysis to understand where money is going/not going and what the true profitability of these teams are.

    I think the market is too small (and it gets even smaller with some players) to make some of your market assumptions. I’m not sure you can apply a rationale expectations market assumption when this may not be a market at or near equilibrium, has different levels of knowledge among the participants and the motivation of the market members are not all the same.

    Is each owner trying to max profitability? Are some trying to win at all costs? Are some trying to get a stadium built? Are some trying to assuage the commish’s office and MLBPA and take on enough payroll so they stop threatening them? Similarly players’ motivations may also not be about max money as well and lead to a less than rational expectations market. If Oswalt signs for 5-6 mil in Stl or Tex is that the real rational market demand or is it a somewhat artificial one as he has made clear there are only a few places he wants to play. Are some players applying location, team strength, personal concerns (wife/family), etc to the decision process which might significantly impact what that player signs for and how much he gets paid…

    Comment by Joe — February 15, 2012 @ 3:31 pm

  47. Quick clarification, someone. Is rWAR Baseball Reference WAR?

    Comment by Ben Hall — February 15, 2012 @ 9:02 pm

  48. Playing time using Tango’s community forecasts is over-projected too. For 2011:

    IP over-projected 7.5% (103.7 vs. 96.5)
    PA over-projected11.9% (415.5 vs. 371.3)

    Comment by Matt Swartz — February 15, 2012 @ 10:34 pm

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