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  1. Maybe general managers are indirectly allocating greater $ to players at positions that carry less injury risk. I’m throwing it out there as a hypothesis.

    Comment by Detroit Michael — June 21, 2012 @ 11:16 am

  2. I think the component you’re missing is the injury factor. Take two players who project to the same WAR over the next five years. One is a catcher and one is a first baseman. Which is more likely to realize the projection? Catchers take a hit in pay because they take hits at the plate. As we’ve seen with Buster Posey and Joe Mauer, those can lead to significant time missed.

    Comment by David Pinto — June 21, 2012 @ 11:21 am

  3. Basemen…

    Comment by Ryan — June 21, 2012 @ 11:22 am

  4. I would suspect that infielders are “undervalued” because there seems to be a higher turnover rate. Just anecdotally, it seems there are more outfielders who can keep playing for a long time than 2nd basemen (feel free to dispute–I’m writing with no hard evidence in mind). Even superstar 2nd basemen (just to pick a position that the GMs are “underpaying”) have a tendency to hit a wall in their early 30s. The overall production for the position might be more, but the players who are contributing the most toward the positional production change more rapidly. The money flows toward the more predictable production (in theory). Players don’t get contracts or produce as position groups; they get contracts or produce as individual players.

    Comment by Edwin — June 21, 2012 @ 11:24 am

  5. To be clear, these are NOT projection-based. These are actual dollars spent for actual WAR in 2007-11. I agree with you that there are issues with projections and playing time, which is why I do backwards-looking stuff like this.

    Comment by Matt Swartz — June 21, 2012 @ 11:27 am

  6. Real minor irk. Cabreras extension was signed before the 2008 season, he was signed as a 3rd basemen. He was moved to 1st party way through the season

    Comment by J6takish — June 21, 2012 @ 11:27 am

  7. Maybe first basemen are less likely to decline offensively (and don’t have much to decline defensively) than middle infielders and catchers, so GMs are more comfortable giving them long term, big-money contracts.

    Comment by YanksFanInBeantown — June 21, 2012 @ 11:36 am

  8. They don’t though– this is based on past performance, so they are declining more or just starting at lower $/WAR.

    Comment by Matt Swartz — June 21, 2012 @ 11:37 am

  9. A few issues that should be considered: injury risk, consistency, and marginal value.

    Comment by Anon — June 21, 2012 @ 11:38 am

  10. I’d argue that this is a not-so-minor irk, actually. It’s not at all uncommon for an aging player, already overpaid by the back end of his contract, to get moved to first base, which really drives up the $/WAR calculation. There’s a difference between players like Votto or Fielder who sign long contracts to play first base the whole way and players like Mauer or Cabrera who sign long contracts with the understanding that they’ll be playing out the back end at first base.

    Comment by Ian R. — June 21, 2012 @ 11:38 am

  11. He may have played 3B prior to the contract, but I think it was signed with the full knowledge that the majority of the contract would be spent with him manning 1B.

    (Until Martinez got hurt, they signed the Prince, and things changed…)

    Comment by Jason B — June 21, 2012 @ 11:46 am

  12. Consistency? *Perks up.* I like the cut of your jib. Tell me more…

    Comment by Joe Morgan — June 21, 2012 @ 11:47 am

  13. Actually, this was something I checked before here:

    The first-year-only contracts had the same distribution. All hitters had $4.1 million per WAR their first year, but 1Bs had $6.1 million per WAR.

    Comment by Matt Swartz — June 21, 2012 @ 11:47 am

  14. The cost per WAR for a catcher might be lower because a lot more players have the opportunity to play catcher over the course of the season. That in turn allows for a greater chance that a cheaper player produces as much as an expensive player. Whereas an expensive first baseman may play 155 games at first, an expensive catcher may only play 120 games. That’s 7 “cheap” games for 1st base and 35 “cheap” games for catcher. If the drop off is not dramatic, then catcher will naturally be cheaper per WAR

    Comment by dan — June 21, 2012 @ 11:52 am

  15. Any analysis on the subject should be sure to mention how the inept management of the Yankees and Red Sox infalte these values. Red Sox give $154 million to a washed up Adrian Gonzalez who is hitting .257/.312/.396 and Yankees give a $180 mil to Mark Teixeira who was OPSing .700 until a month ago.

    Comment by everdiso — June 21, 2012 @ 12:00 pm

  16. I did something called “Have Second Basemen Been Underpaid?” It is at

    Comment by Cyril Morong — June 21, 2012 @ 12:00 pm

  17. Two complaints, one minor, one major.

    1) Jeff Bagwell does not provide much context, because a dozen years ago he was 32, while Votto is only 28. Yes, I realize Bags didn’t make it twelve years from his age-28 season, but you’re pointing out a player whose already been on two HOF ballots as your “context” for Votto’s lifetime value, when even if Votto followed Bagwell’s career path the Reds would get much more out of him than the Astros got from Bagwell from 2000 onward.

    2) While you say your study looks backwards at how the positions have performed relative to the contracts they received, you still don’t really cover how much teams price risk into those contracts. Sure, the decline might be baked into league-wide WAR numbers, but for any individual catcher or first baseman (especially one at the FA stage), the catastrophic risk on a catcher is going to be much higher than that on a first baseman, so teams are going to be unwilling to give catchers longer deals. Further, if the catcher does survive intact a four-year deal (say from his age 28-31 seasons), he’s still not going to get as much on his next deal because teams won’t feel the need to overpay for his decline as they would if they were getting it packaged with his prime.

    Comment by Kevin S. — June 21, 2012 @ 12:01 pm

  18. Actually, the Red Sox and Yankees are fine at $/WAR. In Table 3A of this article (

    I found that the Red Sox were 10th LOWEST in $4.90 million per WAR, and the Yankees were 16th at $5.60.

    Comment by Matt Swartz — June 21, 2012 @ 12:03 pm

  19. To the first point, I’m not saying that Votto will decline like Bagwell. I’m just saying he’s going to be better now than in 12 years so he’s worth more now than his average annual salary through his contract.

    To the second point about risk, what you are saying is that it is better to have a players who is going to produce somewhere from 2-4 WAR than a player who is going to produce 1-5 WAR, even if both players have expected 3 WAR. Why would this be? Financial institutions and individual investors value lower risk conditional on expected value, but there is no reason for teams to do so. Most teams actually would do better to increase the variance in their expected win total.

    Put it this way: is it better to have a team that is expected to go 81-81 but with a confidence interval of 74 to 88 wins, or one that is expected to go 81-81 but with a confidence interval of 68 or 94 wins. The first team almost never makes the playoffs, but the second team makes the playoffs more often. The values of being 68-94 and 74-88 are similar, but the values of being 88-74 or 94-68 are very different.

    Comment by Matt Swartz — June 21, 2012 @ 12:08 pm

  20. It’s also probably worth considering whether GMs are simply placing the highest value on the aspects of the game they can best measure. There’s still a lot of disagreement about fielding stats. Some players look like gold glovers under one system, but are merely average, or even below average, under another.

    Comment by Jason461 — June 21, 2012 @ 12:13 pm

  21. @Matt, though your analysis is backward-looking, a GM’s analysis is forward-looking at the time he offers a contract to a player. So the risk of the forward-looking WAR projection is relevant in considering what to pay someone in a multiyear contract. Shortstop WAR could rationally be less valuable than 1B WAR, if the risk of maintaining that production is higher for a shortstop than a 1B. I don’t know that it is, but this is at least a theoretical justification.

    I also wonder if the relative positional salaries are skewed by various subtle biases, such as the timing of free agent contracts at various positions. 1B, LF, and DH might be inflated compared to 2B, SS and 3B because of which top-level players happened to become free agents in the period examined. One Carl Crawford may skew the positional results pretty significantly. It might be worth examining.

    Comment by mcbrown — June 21, 2012 @ 12:13 pm

  22. There is a flaw in the DH evaluation. The -17.5 adjustment already has the difficulty of hitting off the bench accounted for.

    Comment by butcher — June 21, 2012 @ 12:15 pm

  23. Really interesting stuff, Matt. I dig the article.

    I was thinking that you might want to remove some outliers if you want to speak on behalf of GMs. Don’t you think a single terrible contract can skew the adjustment for a position?

    Comment by Evan — June 21, 2012 @ 12:15 pm

  24. Why do left fielders get paid so much?

    I think there’s a big small sample issue here. Five years just isn’t that many. How many contracts at each position are we talking about? How did perceived supply and demand affect the market in give years? How did the particular needs of one rich club affect the price of one premium free agent in 2007? How does that albatros affect that rich club’s ability to spend in the future, and what effect does that have on supply and demand? How does one albatross contract, like Alfonso Soriano’s, affect these results?

    Comment by philosofool — June 21, 2012 @ 12:23 pm

  25. the basic issue here IMO is that the fielding component of WAR is extremely, extremely unreliable, while the hitting component is not.

    GMs will pay more for sure things than they will for iffy things. And the few GMs who have gone out of their way to pay for those iffy things in recent years seem to have been burned pretty dang badly – think Crawford in BOS or Figgins in SEA.

    Comment by everdiso — June 21, 2012 @ 12:24 pm

  26. Oh, and since I believe you are looking at all salaries, not just free agent contracts or extensions, you are including the bias of the arbitration process, which we all know exists. To really get a read on how GMs think about the value of WAR by position we probably need to exclude any player that isn’t playing under a contract that involved a valuation decision by a GM.

    Though I’m inclined to think there is an inefficiency behind this (see Howard, Ryan), I’m open to the idea that GMs know something we don’t, either consciously or unconsciously, about the value of certain positions. It could be both, actually – GMs are ahead of the curve in some ways and behind in others. We certainly see that in football, where excessive contracts to interchangeable RBs continue to exist alongside a seemingly rational allocation of salary among the offensive line positions.

    Comment by mcbrown — June 21, 2012 @ 12:25 pm

  27. I’m not sure there’s a major sample size issue if you’re looking at every dollar paid versus every win earned per position–that means looking at every person at every position for five years. However, I think there’s a good point here about the age of the contracts. Inflation hasn’t been kind to baseball, so if an inordinate number of 1B have signed there contracts in the past three years, that could be an issue.

    Comment by Evan — June 21, 2012 @ 12:26 pm

  28. nah, everdiso jr., the yanks have spent their money just fine.

    Comment by everdiso — June 21, 2012 @ 12:28 pm

  29. GM’s have several other variables to look at when building a team. One of which is can this guy be an anchor to the offense. If a GM needs a 3 or 4 hole hitter, they will spend what they have to for that hitter regardless of defense and position. I enjoy seeing the breakdown by position, and I believe that any position that produces a hitter that can anchor a team offensively will see that player paid well.

    Comment by Zigs — June 21, 2012 @ 12:29 pm

  30. I think there could be some truth to this. GMs will pay for saves, but they won’t pay for fielding, at least not if you’re only average with the bat.

    Comment by Evan — June 21, 2012 @ 12:29 pm

  31. @Matt, I actually agree with this analysis of risk, but centuries of observed behavior and mounds of psychological studies tell us that humans view risk as a cost rather than a benefit, and demand lower prices for purchasing riskier assets, all else being equal.

    Comment by mcbrown — June 21, 2012 @ 12:30 pm

  32. Not necessarily, because those aren’t their expected ranges for each year, but rather over the lifetime. On a team level, high variance might be a good way to maximize the number of times you make the playoffs, but that’s assuming your team’s true talent is .500. I would argue instead that player salary is instead weighted towards teams that either are contending or are expecting to contend at the time they sign the contract. For a ninety-win true-talent team, a confidence interval of seven wins each way still leaves them in the playoffs most of the time, but a confidence interval of thirteen wins each way would have them missing the playoffs much more often (the added utility of the 98-103 win possibilities is much less than the lost utility of the 77-82 win possibilities). Further, I wonder if your study looks just at FA $/WAR or total $/WAR. I would posit that a much more significant chunk of catcher playing time comes from cost-controlled catchers. Catchers tend to have a shorter shelf life, so their 0-6 years make up a larger portion of their career. When they do last, they often move to other positions later in their careers, making their 0-6 years an even larger portion of their catching career. Finally, backups tend to be 0-6 players more than starters do, and backups represent a larger chunk of the playing time at catcher than at any other position.

    Perhaps I am focusing on the catcher/first base dynamic too much, but I feel these concerns are relevant for the other positions as well.

    Comment by Kevin S. — June 21, 2012 @ 12:33 pm

  33. So much this.

    Considering that there are sabermetricians who question UZR, I think it’s expecting a lot of GMs (many of whom still measure value in ribbies) to take dWAR seriously.

    Comment by The Foils — June 21, 2012 @ 12:35 pm

  34. Are these numbers just for free agent years? If not, couldn’t the differences be explained by the fact that players tend to move down the defensive spectrum as they age, so a higher percentage of middle infielders are in their arbitration years compared to other positions?

    Comment by AF — June 21, 2012 @ 12:35 pm

  35. Since I am looking at all players in the aggregate, the total UZR at each position is close to 0. So GMs placing a low value on fielding won’t matter.

    Comment by Matt Swartz — June 21, 2012 @ 12:35 pm

  36. FAQs:

    1) This is only players who reached free agency.
    2) The average age at each position is similar.
    3) Fielding runs are pretty close to zero at each position on the aggregate, so whether UZR is good or terrible, it shouldn’t matter for the total $/total WAR for each position.
    4) These are based on 2007-11 salaries, so there is no projection in here.

    Comment by Matt Swartz — June 21, 2012 @ 12:37 pm

  37. Nice work, one thing on your note on Rollins: sometimes factors other than the market come into play. When you say:

    “Teams didn’t outbid the Phillies went they offered Jimmy Rollins a three-year deal for $11 million per season. Apparently, league-average batting ability is what they expect shortstops to produce for $11 million, despite the fact that the average shortstop produces 5.8 runs below average on offense. This evidence suggests that shifting money from first base to shortstop would probably help teams get more bang for their buck.”

    The Brewers offered Rollins more– substantially more, in fact– but most people said there was no way he would leave Philadelphia and that turned out to be true. Not saying that shortstops are more likely in general to take less than their value on the market, but you can run into trouble when you assume that GMs consider his value to be $11 million when you use a specific player.

    Comment by Jordan M — June 21, 2012 @ 12:38 pm

  38. McBrown, I believe I addressed your concerns in my FAQs but let me know if I did not.

    Comment by Matt Swartz — June 21, 2012 @ 12:39 pm

  39. This is a good point. But even if you ignore defensive stats, it’s clear that a SS is more valuable than a 1B with the same offensive numbers. As I understand the article, Table 3 ignores defensive WAR and still finds that GMs gives strangely small positional adjustments to middle infielders.

    Comment by AF — June 21, 2012 @ 12:40 pm

  40. Kevin S:
    The average contract is given out to a team with about 85 wins the previous season last I checked it, so this is probably not an issue. Regardless, there are very few teams with >50% playoff odds at the beginning of the season, so I don’t think the risk factor will work this way.

    Comment by Matt Swartz — June 21, 2012 @ 12:41 pm

  41. But can a great defensive 1B generate the same # of wins with his glove as a great defensive SS can? The price/WAR becomes a systematic bias if fielding is underpaidfor.

    Comment by Evan — June 21, 2012 @ 12:48 pm

  42. Thanks. This is a very interesting study. Clearly, however, there is something going on in the numbers such that they do not measure GMs true positional adjustments. It simply isn’t possible that, all else equal, GMs would pay a 2B less than a 1B, LF, or RF with the same offensive numbers, or that they would pay a SS less than a LF with the same numbers.

    Comment by AF — June 21, 2012 @ 12:49 pm

  43. Humorously, table 1 is almost an exact opposite of the defensive spectrum; except for a juxtaposition of 3B and CF. Therefore, defense is still undervalued, or offense is overvalued, or something.

    Comment by Jason B — June 21, 2012 @ 12:53 pm

  44. Ah, very good. The salaries might still be subjected to bias from outliers, but nothing structural.

    The backward looking/forward looking bit is not quite on-point I think. What I believe most people including myself are saying by bringing up the risk to WAR projections is that while you are measuring what GMs actually paid in hindsight, the contracts were awarded with foresight, and all else being equal GMs may perceive performance from certain positions as inherently risky compared to other positions. It may have turned out with the benefit hindsight that those riskier positions were in fact cheaper per WAR, but that doesn’t mean that it was the wrong decision a priori to discount them for perceived risk, or to continue doing so in the future.

    As a non-baseball example, equities have historically outperformed government bonds. That they have done so does not mean that they were mispriced in the past, as they are inherently riskier by any reasonable metric and it is rational to discount their expected future performance more heavily than that of government bonds.

    Likewise, if catchers are inherently riskier than first baseman in some way then it may be rational to discount their production more heavily for the same reason, both in prior periods and going forward.

    Comment by mcbrown — June 21, 2012 @ 12:57 pm

  45. Matt, cool article. I’m a little confused and the nuts and bolts, though. How many years did you use to generate the average offensive totals? What’s to prevent a series of very good players- say CF over the last couple of years with Kemp, Ellsbury, Hamilton etc…- from throwing off the results.

    Comment by Burton Guster — June 21, 2012 @ 1:03 pm

  46. This, plus the historical bias of valuing offense over defense. In addition, although it’s difficult to measure, offensive players are more likely to increase attendance and viewership. Teams probably have internal metrics for that.

    Comment by Keith — June 21, 2012 @ 1:04 pm

  47. I used 2007-11 and only players with six years service time. There were 797 hitters in the sample. Outliers are an issue worth looking into as time goes on (though Kemp, Ellsbury, and Hamilton aren’t included since they have <6 years service time).

    Comment by Matt Swartz — June 21, 2012 @ 1:07 pm

  48. free agents only– or, potential free agents really. This is for 797 player-seasons with >=6 years service time between 2007-11.

    Comment by Matt Swartz — June 21, 2012 @ 1:08 pm

  49. The -17.5 run adjustment means you subtract from their offensive production, so it reflects very high expectations of DHs. You have it backwards, I think.

    Comment by Matt Swartz — June 21, 2012 @ 1:11 pm

  50. I hear what you are saying, but to be clear, you are arguing that glove-first positions have all been areas where players have historically declined more or at least should have been expected to decline more– but that this group just held up historically better than should have been expected? I could buy that for one or two positions, but I have trouble thinking that all of these glove-first position players just happened to surprise GMs and retain value well.

    On top of that, here is the table of $/WAR in millions for FIRST YEAR of contracts only from the previous article:

    C: $3.1
    1B: $6.1
    2B: $2.5
    3B: $3.9
    SS: $3.0
    LF: $4.9
    CF: $6.3
    RF: $4.4
    DH: $4.6

    So, they would need to be declining right away.

    Comment by Matt Swartz — June 21, 2012 @ 1:17 pm

  51. Could also be a recognition that offense is more of a scarce resource than defense. GM’s seem to think that is the case (and realistically, it’s true), so offense is overvalued.

    It’s intuitive if you think about it. An athletic person who practiced enough could probably play LF for an MLB team, but very few individuals are good enough to hit at an MLB level, much less hit well.

    I know the caveat is runs = runs, but there’s measurement issues there.

    Comment by bill — June 21, 2012 @ 1:17 pm

  52. Good article – I might just go back and read in depth what I skimmed ;). Anyhow, my sense is that while defense and baserunning might have been undervalued before WAR came around, WAR might have gone too far the other way and overvalues them, losing sight of the bread-and-butter of position player value, which is the bat. Take, for instance, two players:

    Player A: 510 games, 12.8 WAR
    Player B: 2060 games, 30.7 WAR

    Translating to 155 games, Player A is worth 3.9 WAR, and Player B worth 2.3 WAR. In other words, Player A is a borderline star and Player B a quality regular. Now where it gets tricky is when you look at their hitting stats:

    Player A: .274/.345/.351 (.319 wOBA)
    Player B: .284/.360/.503 (.369 wOBA)

    That’s a pretty drastic advantage for Player B. Obviously the difference in WAR is in fielding and baserunning:

    Player A: 22.7 Fld, 22 Bsr
    Player B: -25.6 Fld, -53.3 Bsr

    Player A’s defense and baserunning abilities are significantly more valuable, even more so considering that we’re talking about four times as many games on Player B’s part.

    Any guesses as to who these two are? Here you go: Elvis Andrus and Paul Konerko. Now I personally have a hard time saying that in an average season, Andrus has been fully 1.6 WAR better than Konerko. I could live with equally valuable, although the .173 difference in OPS is rather hard to swallow. But +1.6 WAR for Andrus? Not buying it.

    Part of the problem with WAR, in my opinion, is that it asks every player to be well-rounded, and puts too much emphasis on defense and baserunning for players (like Konerko) for whom it is such a minor part of what they bring to the table. Remember how good Frank Thomas was in the early to mid-90s? Big Frank never had a WAR higher than 7.8 – in other words, as good as Ian Kinsler was last year (7.7). I for one don’t think that Kinsler’s 2012 was better than all but two of Frank Thomas’ seasons (’91 and ’92).

    To put it another way, who cares if Konerko is a crappy baserunner? Should his defense be such a factor? For Andrus these factors are far more important, especially fielding. Of course it would be nice if Konerko was a better fielder and runner, but to be so negatively impacted for not doing something well that isn’t all that important for him to do well just doesn’t make sense.

    I think that WAR would be more useful if it was less impacted by shoddy defense and baserunning. Maybe instead of a positional adjustment for WAR, there should be some kind of “positional impact quotient” that would be a multiplier depending upon position. So, for instance, let’s say a 1B has -10 Fld runnings over his career, but because he played 1B only 25% of that counts to WAR (-2.5), whereas if he was a SS maybe all of it would. The same would go for positive numbers. Or perhaps it would be more meaningful to have a WAR version of triple-slash line of Offense/Fld/Bsr.

    In summary, I think the problem here is sort of the downside of WAR being such a comprehensive stat: by taking everything into account there is no differentiation. Right now there are two players worth 2 WAR, one of whom is hitting .268/.289/.430 and the other .308/.366/.533. Go look it up – you’ll get a chuckle when you see the names. All things tolled, is there really anyone who would take the former over the latter?

    Comment by Angelsjunky — June 21, 2012 @ 1:21 pm

  53. If point 3 is true, does that mean that the results from Table 2 remain the same even if you ignore defensive WAR and only focus on offensive value? Can it really be that 1B get paid more than 2B and LF get paid more than SS with the exact same offensive stats?

    Comment by AF — June 21, 2012 @ 1:23 pm

  54. Just one thought I had while reading this (very good work by the way).

    If I’m a GM proposing to pay $X to player Y, I also have to gain the approval of the financial half of my organization. By that I mean the owner and his accountants that are budgeting for future marketing costs and the ROI associated with those costs. Signing a shortstop that gains a significant amount of WAR via defense may not provide the same marketing pop that signing Prince Fielder would provide. As Sabermetricians we can pare the game down to performance stats, but we have very little access to the behind-the-curtain numbers game that most front offices face. This might help explain some of the mentioned discrepancies.

    Comment by Adam G — June 21, 2012 @ 1:26 pm

  55. The other elephant in the room is that nobody knew what any of these players’ WAR was going to be when they signed their contracts. Could this be a failure of projection rather than valuation?

    Comment by AF — June 21, 2012 @ 1:26 pm

  56. Well, why do we have an assumption teams should pay a fixed amount per WAR. In fact the relationship between expected WAR to $ paid is probably not a linear relationship for most teams, nor should it be. I won’t go into why, I leave that as an exercise.

    And since there are more truly elite players at 1B (probably generally and especially over the last couple of years) it shouldn’t be surprising then that 1B have been paid at a higher $$ per WAR rate.

    I think there are other reasons this occurs as well (injury/aging patterns of 1B versus other positions/value of oWAR over dWAR), but other posters have highlighted these well I think.

    Comment by Bobby — June 21, 2012 @ 1:29 pm

  57. Thanks Matt. Regarding the first point, when you say “reach FA,” do you mean players with >= 6 years of service time, or are you excluding players who signed extensions that have bought out FA years during the study (i.e. Joe Mauer has never been a free agent, although he has more than six years of service time). If the former, I wonder if there are biases in the type of player teams seek to lock up significantly before free agency (and subsequently their salaries past six years are discounted because they took the early security). If the latter, I would wonder if there is a related bias to my first supposition, wherein only players at positions teams allow to reach FA can get a true free-market price. Either way, this effect would likely skew the results significantly since you have one type of player earning free market value at the elite levels.

    Other concerns would be what portion of a contract the five-year window gives us a snapshot of. While I know 2012 is not part of this sample, Albert Pujols just began a heavily-backloaded contract in which he is expected to deliver the majority of his value when he costs the least. Likewise, Jason Giambi would have been included in the final two years of his contract when he was making the most but not producing nearly at his average value. Basically, teams don’t price contracts so that returns to salary are even across all years of the contract. In a window that doesn’t capture the entirety of the contract, this can skew results.

    I don’t mean any of this to rebuke your work, and even my earlier criticism was meant as a specific complaint to a largely excellent piece of research. I’m just curious how these things are accounted for here.

    Comment by Kevin S. — June 21, 2012 @ 1:31 pm

  58. AF, it’s implying that 1B get paid more for the same performance relative to their position than other positions do. A second baseman who his .300/.400/.500 in 150 games is going to get paid much more than a first baseman with the same line, but that’s because that line is significantly higher than the average second baseman while there’s less of a gap between that and the average first baseman. The implication is more that a first baseman who provides (avg. 1B offense + x) will get more than a second baseman who provides (avg. 2B offense + x), even for the same value of x.

    Comment by Kevin S. — June 21, 2012 @ 1:35 pm

  59. I see this assumption that 1B carries a lower injury risk than other positions all the time, but I have never seen any evidence to support it.
    Unless there’s a study I’m unaware of that proves this injury risk assumption, could everybody please just prove it or drop it.

    Comment by Baltar — June 21, 2012 @ 1:41 pm

  60. I’m sorry, but I disagree with the premise of your argument. Why shouldn’t we value Konerko’s failure to score from second on a two-out single? Those are real runs that affect real games and teams have missed the playoffs because a lumbering 1B has gotten throw out at home in a couple crucial games over the course of the season. Just because you don’t expect his baserunning to be good, that doesn’t mean you don’t need to price the effect he has on runs scored in ALL of the ways he affects runs scored.

    Comment by Matt Swartz — June 21, 2012 @ 1:45 pm

  61. Of course it matters if Konerko is a crappy baserunner. Last year he hit 107 singles and 25 doubles, compared to 31 home runs. The fact that he is considerably less likely to score after those singles than Andrus* is a real negative: those non-scored runs are just as real as the ones he contributes through dingers.

    Likewise for defense – if Andrus gets to a ball and makes a play that your average shortstop wouldn’t have made that’s real value – the difference between the opposing hitter going 1-for-4 or 2-for-4, if you like. Sooner or later those plays add up to real runs too.

    *Andrus hit 129 singles, 27 doubles, 3 triples and 5 homers.

    Comment by Aaron (UK) — June 21, 2012 @ 1:46 pm

  62. You’re absolutely right that the dollar value of a 9-8 win vs. a 3-2 win might be different, but I don’t know how much different. I suspect it’s not that big of a deal relative to the value of winning 3-2 vs. losing 9-8, but I don’t know for sure. If so, then the price isn’t for wins and playoffs, but instead on entertainment. I do plan to check this one day…somehow.

    Comment by Matt Swartz — June 21, 2012 @ 1:47 pm

  63. Wow, Edwin, you make some whoppers of unproved assumptions.
    I think the explanation is much simpler than that.
    GM’s, just like the vast majority of fans, overvalue HR’s and RBI’s. 1B is where those stats are high, therefore 1b’s are overvalued.

    Comment by Baltar — June 21, 2012 @ 1:47 pm

  64. I think the obvious answer is that GMs could not care less about $/WAR. GMs care about winning baseball games, and having the greatest $/WAR probably has little relationship to actually winning games.

    GMs want a hitter that hits 35 homeruns and gets on base 40% of the time. Because hitting and fielding aren’t related skills, these players happen to be concentrated at the easiest defensive positions. Because all teams need elite offensive performers, most teams will end up paying a lot of money for first basemen.

    The problem is that there do not exist shortstops to pay more money to. There is no factory that produces 35 homerun shortstops. The only one in existence right now is Troy Tulowitzki. There are only two or perhaps three second basemen alive that can be considered elite offensive players. These are real limitations that GMs have to contend with. They can’t just order the $5.05M/WAR model from the factory. They need a big hitter and big hitters happen to play first base.

    Comment by Jason H — June 21, 2012 @ 1:51 pm

  65. I’ve checked linearity before– the linearity assumption holds true.

    Here’s the relevant table:

    All players : $5.4 million per WAR
    $15-20MM players: $5.6 million per WAR
    $10-15MM players: $6.5 million per WAR
    $5-10MM players: $5.2 million per WAR
    $0-5MM players: $3.6 million per WAR>

    It’s really very linear.

    Also, the fraction of elite 1B is similar..10.6% of all the 1B in the data had >=4 WAR, but 8.6% of all other hitters did.

    Comment by Matt Swartz — June 21, 2012 @ 1:53 pm

  66. ….optimal $/WAR, not greatest….

    Comment by Jason H — June 21, 2012 @ 1:55 pm

  67. Your first statement is flat out false, as well as irrelevant.
    Defensive stats may not be as reliable as offensive stats, but the difference is not nearly as great as you say.
    Yes, I know UZR varies a lot year-by-year, but what stat doesn’t?

    Comment by Baltar — June 21, 2012 @ 1:57 pm

  68. This includes extensions– it’s everyone with >=6 years service time.

    There are definitely biases– players locked up early get paid much less per WAR. BUT I checked and the same structure existed separately for re-signed players and newly signed players, where re-signed players at bat-first positions were paid a couple million more per WAR than re-signed players at glove-first positions, and similarly for newly signed players.

    The backloaded issue was something I checked on, but it mostly cancelled out since there were about as many longer contracts that were at the tail end in 2007 as longer contracts just starting in 2011.

    Comment by Matt Swartz — June 21, 2012 @ 1:58 pm

  69. Kevin, that’s not how I read the numbers. Table 2 removes positional adjustments from WAR and provides the “numbers [that] would need to be applied to each position’s WAR to clear the market at $5.05/WAR average for each position in the past five years.” Table 2 shows that the implied positional adjustment for 2B is actually lower than for 1B — in other words, that 2B get paid less per WAR than 1B even after you eliminate any positional adjustment to the offensive numbers.

    Now, WAR includes defense, so based on Matt’s numbers alone, we can’t rule out the possibility that 2Bs do get paid more than 1Bs with equivalent offensive numbers, but get paid less per WAR because their defense (as measured by UZR) is undervalued. Matt reports, however, that “[f]ielding runs are pretty close to zero at each position on the aggregate, so whether UZR is good or terrible, it shouldn’t matter for the total $/total WAR for each position.” I interpret this to mean that the differences among the positions in $/WAR cannot be explained by differences in defensive value as measured by UZR. It seems to follow 2B are, in fact, getting paid less than 1B with equivalent offensive numbers.

    Comment by AF — June 21, 2012 @ 1:58 pm

  70. In 12 years Votto won’t be among the best first basemen, but the best first basemen will be making more than 22 million a year.

    Comment by DavidCEisen — June 21, 2012 @ 1:59 pm

  71. GMs who care about winning baseball games most certainly do care about $/WAR, even if they don’t have it calculated the same way Fangraphs does. You see, there are these things called budgets and opportunity costs, and even Brian Cashman has to operate with them. Further, they understand the value of things such as position scarcity. At best, you could argue that teams proprietary metrics produce different defensive values than UZR and that they have different weights on events than the components of fWAR do, but this doesn’t change the fact that competent GMs do actually care about maximizing the impact of the dollars they spend and that they do consider position and defense along with offense when evaluating talent.

    Comment by Kevin S. — June 21, 2012 @ 2:00 pm

  72. Is it possible that a lot of “Big Names” play 1B and GM and owners sometimes desire a big splash for purely marketing reasons. The Tigers could have easily spent 114 Million more wisely then on prince Fielder…but, look how many tickets they sold…as soon as they made that signing. Look at the excitement. So, your study makes total sense, which is why, IMO, baseball is a sport that pre-season hype is so different then actual results. That being said..despite understanding the things you have written about, I was very excited when we signed Fielder.

    Comment by Chris — June 21, 2012 @ 2:00 pm

  73. You can’t use WAR to check if the proportion of elite players is the same at each position, because WAR is adjusted by position. Of course it is going to be relatively similar. You want to use statistics that are relative to the leauge here.

    Comment by Jason H — June 21, 2012 @ 2:00 pm

  74. Alright. Good to know that the study stands up to these types of issues.

    Comment by Kevin S. — June 21, 2012 @ 2:05 pm

  75. Yes, the positional adjustment for 2B seems to be similar to 1B. So, 2B are getting paid about the same for comparable offensive production as 1B!

    Comment by Matt Swartz — June 21, 2012 @ 2:05 pm

  76. Wow, you’re amazing, Matt. Not only do you write great articles, but you put a lot of effort into participating in the discussion in a very positive way.
    You’re my guy.

    Comment by Baltar — June 21, 2012 @ 2:06 pm

  77. You don’t need 35 home runs. You just need more runs than your opponents. They should only consider the value of spending the money at 1B for the free agent and staying internal at 2B, or spending the money at 2B and going internal at 1B. This strongly suggests that they are making the same mistake as you too often.

    Comment by Matt Swartz — June 21, 2012 @ 2:07 pm

  78. Of course GMs care about spending money wisely. Nobody thinks anything else.

    What GMs likely don’t care about is 1) the defensive component of WAR and 2) the crazy positional adjustments in WAR.

    GMs that are successful (I’m excluding the ideologues like Jack Z.) definitely care about absolute numbers. They need home runs. In the real world, they can’t necessarily make up the difference in production that they’d need to cover if they sign a shitty first baseman by getting better players at short, second and catcher. Those players dont exist. Also, the necessary roster flexibilty doesnt exist. So they do the smart thing and pay for real production.

    Comment by Jason H — June 21, 2012 @ 2:09 pm

  79. Jason:
    That’s true. If WAR systematically underestimates 1B, I won’t be able to prove that completely. All I did was show the variance of WAR is similar for each position, but it could be that replacement level 1B is closer to replacement level 2B than average 1B is to average 2B. I’m looking into that in my replacement level research now…article may take a few weeks though.

    Thanks! I’m off work today, so I’m going to town on this discussion because I seriously love this topic!

    Comment by Matt Swartz — June 21, 2012 @ 2:11 pm

  80. No, you don’t want to use the league, because the opportunity cost for signing a first baseman is the availability of other first baseman. If there were thirty first basemen with a wRC+ of 150 and no other hitter had a wRC+ over 120, how much would you pay for your first baseman? League minimum, because there’s no differentiation between the first and the thirtieth.

    Comment by Kevin S. — June 21, 2012 @ 2:11 pm

  81. Matt, the idea of outlier contracts skewing the results has been brought up, but if I may frame it in a slightly different way, is it possible that the skew is actually the point? For example, at first base, it’s easy to name half a dozen high WAR players/slam dunk All-Stars. And then there are the run-of-the-mill “someone has to catch the throws from grounders” guys. At SS or C, it’s harder to do that. At those positions, value tends to bunch together a little bit more. (At least it seems to… I’m doing this without checking my facts… I call mulligan rights if I’m way off.)

    As a GM, I want to maximize production per roster spot, and if one of those mega-high WAR guys is out there, and the next closest available replacement good (note: not replacement level… replacement good in the economic sense) is 3 wins behind him, the mega-high guy is more valuable and I might pay a premium for him. It’s not that teams consciously pay a premium for one position over another, just that this set of circumstances is more likely to happen when the distributions are differentially skewed.

    Comment by Pizza Cutter — June 21, 2012 @ 2:11 pm

  82. Matt,

    Yours is a recipe for losing a lot of games. Just look at the Mariners and A’s. You can’t win games -1 to 0. You do have to score more runs than your opponent as you say.

    How can they put money into a shortstop to make up the difference in run production when none actually exist?

    Comment by Jason H — June 21, 2012 @ 2:14 pm

  83. The logical implication of this statement is that there is no defensive differentiation between players and that replacement-level offense is the same at each position. Why would we believe this to be so?

    Comment by Kevin S. — June 21, 2012 @ 2:14 pm

  84. 1st basemen have the highest wOBA, and also the highest “old” numbers like HR, RBI ect. WAR, defensive value and positional value aren’t universal, but production at the plate is easy to recognize. It is also easy to convince an owner to shell out the big time paper for a slugging 1st baseman.

    Comment by West — June 21, 2012 @ 2:20 pm

  85. Hey, Pizza! Good to hear your thoughts :)

    The outliers could be skewing this in some way– effectively, teams may be overpaying for these guys when they’re available. However, I’ll tell you why I don’t think so. Firstly, the table I commented above said that the $MM/WAR for all players is $5.4, while for players with $15+ million, it’s $5.6 million. So, it’s not that great players are getting paid more $/WAR in the first place. Also, there is only some evidence of great players being more available at 1B/OF/Dh than elsewhere.

    Here is the fraction of player-seasons with >=4 WAR for each position.

    All players:
    C: 2.6% (3/116)
    1B: 10.6% (14/132)
    2B: 5.0% (4/80)
    3B: 14.7% (16/109)
    SS: 9.2% (8/87)
    LF: 6.6% (7/106)
    CF: 9.8% (5/51)
    RF: 15.6% (12/65)
    DH: 5.1% (2/39)

    Of course, it’s a little more common for players signed elsewhere to be in the outfield.

    Signed elsewhere:
    C: 0% (0/57)
    1B: 4.7% (3/64)
    2B: 3.1% (1/32)
    3B: 8.8% (5/57)
    SS: 4.1% (2/49)
    LF: 4.3% (3/70)
    CF: 12.8% (5/39)
    RF: 12.2% (6/49)
    DH: 3.7% (1/27)
    Overall: 5.9% (26/444)

    But I think that it’s still not going to be a big deal just because the top contracts are getting paid similar $/WAR as the mid-level contracts. If nothing else, I think that some of those 3Bs should have been pounced on (i.e. Beltre in both 2010 & 2011, A-Rod, Huff, Glaus).

    Comment by Matt Swartz — June 21, 2012 @ 2:29 pm

  86. Matt, I’m glad I interpreted your work correctly. That’s an amazing result. It would be interesting to see that shown directly, using only offensive numbers. As you see from comments, many people believe that the differences in $/WAR among positions are due to positional adjustments and UZR. Eliminating the WAR formula’s built-in positional adjustments, as you do in Table 2, is very illuminating. If you could eliminate UZR as well, and replicate Table 2 using only unadjusted offensive numbers, I think that would really get the point across.

    Comment by AF — June 21, 2012 @ 2:31 pm

  87. A) A team of replacement-level hitters will still score a couple runs a game, so yes, one could theoretically pitch and defend well enough to allow fewer runs than they score. The Mariners and As aren’t bad because of their model, they’re bad because in Oakland’s case they won’t spend any money on talent and in Seattle’s case the money they’ve spent has been on players who’ve severely underperformed expectations. The Nationals are 27th in baseball in runs scored, yet they have the fourth-best record and the seventh-best run differential.

    B) The average team has gotten roughly 3.3 Batting Runs above average out of its 1B this year, while it has gotten -3.9 Batting Runs from its shortstops. The As would gain about 4.5 runs by swapping their shortstops for league-average SS performance, and the Mariners would gain over 10 runs. Conversely, the As only gain about two runs by upgrading their 1B to an average offensive 1B, and the Mariners only gain about eight runs. In both cases, there’s a greater improvement by going to an average shortstop than by going to an average 1B.

    Comment by Kevin S. — June 21, 2012 @ 2:32 pm

  88. Jason, would your concerns be alleviated if I compared:

    Backups at 1B vs. Other Backups

    and found that the gap was similar to

    Average 1B vs. Average Other Players?

    That’s what I’ve been working on lately. I can’t say for sure it’s true until I do a lot more tests, but it looks like it so far.

    Comment by Matt Swartz — June 21, 2012 @ 2:32 pm

  89. Easy answer: Chicks, and GMs, dig the long ball.

    Comment by NEPP — June 21, 2012 @ 2:34 pm

  90. Of course. I am just saying it is known like you mentioned that hitting off the bench impacts performance in a negative way. And this is accounted for in the -17.5. Dont hold me down to it but out of the top of my head I think otherwise the pos. adj. would be near or at -20 runs. If you like evidence I would start digging for the exact numbers.

    My point is that you cannot use it as an argument in favor of GMs since it’s already accounted for in WAR.

    But does not mean that this article is not excellent anyways.

    Comment by butcher — June 21, 2012 @ 2:37 pm

  91. Kevin S.,

    The problem is that those most certainly are not the logical implications. You are assuming that WAR is actually a good approximation of what it tries to measure. It almost certainly is not.

    If we are talking about WAR as a concept, and not as its realization, than yes, GMs want to be spend money efficiently with respect to “WAR”. This article is not dealing with WAR as a concept, but with fWAR, which is not so great.

    Of course GMs value defense, the problem is the measurement of defense. It’s a complete nightmare. Does any GM truly believe he would, in the real word, win as many games with Brett Gardner as with Ryan Braun?! Of course not. They value defense, but certainly they value it differently than fWAR.

    Also, the problem is not so much the availability of replacement players, which, by definition, should be ubiquitous. The problem is the availability of non-replacement players. The actual market for players is extremely limited.

    During the actual games, we don’t prorate the value of runs that a first baseman produces. Thus, GMs need real world production from where ever it is available. Teams that have elite offensive players elsewhere often times don’t have high priced first basemen (e.g. Texas). But teams definitely covet elite offensive players (elite relative to the league, not the position). Is there any evidence that they are wrong for doing so?

    Comment by Jason H — June 21, 2012 @ 2:37 pm

  92. Of all the positions, it seems like common sense (to me, anyway) that 1B would have the least injury risk. They hardly every throw the ball hard. They hardly ever make running, diving plays. People rarely slide into first base. I can’t think of any position that would seem to have a lesser injury risk. So if it bothers you so much, why don’t you prove that common sense is wrong in this case?

    Comment by vivalajeter — June 21, 2012 @ 2:41 pm

  93. Great idea, AF! I’m going to do that now.

    Comment by Matt Swartz — June 21, 2012 @ 2:41 pm

  94. Thanks to a great idea from AF above, I’m going to post a new table. This is the $/WAR for each position if positional adjustment was zero and defense was set to zero. So all this uses is (1) batting runs (2) baserunning runs (3) replacement level same for every position equal to league average. I’m going to use the same adjustment for draft pick values that I normally use to avoid any bias.

    $/positionless_WAR in millions:

    C: $9.5
    1B: $3.8
    2B: $3.7
    3B: $4.9
    SS: $5.2
    LF: $4.8
    CF: $6.0
    RF: $3.5
    DH: $3.7
    All: $4.5

    So, basically GMs aren’t paying anymore to a 2B who has a .350 wOBA than they are to a 1B who has a .350 wOBA. They clearly value the same production from C/3B/SS a little more, but not all that much more.

    Comment by Matt Swartz — June 21, 2012 @ 2:45 pm

  95. Keep trolling, guy. For the record, I’ve never been anti-Yankee or anti-Red Sox, I just think the Red Sox in particular get praised around here no matter what they do. The Rays are really the team the commenters overrate.

    Comment by everdiso — June 21, 2012 @ 2:46 pm

  96. I think total WAR of the position matters as well. You look at the teams that signed first basemen to huge contracts and most are large market teams (cinci is the exception). as a large market team, $$ matter less than roster spots. they would rather concentrate a large amount of WAR in one position than spread it out. that is why the positions that typically post huge WAR (1B, LF, RF) are some of the highest paid per WAR. A player that can put up 7+ WAR is a scarce commodity, and if he plays a less injury prone position, even better.

    Comment by alex — June 21, 2012 @ 2:46 pm

  97. Matt, I think you’re overcomplicating Jason’s point. As I understand Jason’s hypothesis, it is that the differences in $/WAR among positions can be explained by three things: (1) the positional adjustments built into the WAR formula, (2) the defensive stats built into the WAR formula, and (3) the non-linearity of $/offensive value. You have rejected all three of these hypotheses in comments, but the only one that you have actually addressed in your study is (1) (as Table 2 eliminates the postitional adjustments from the WAR formula).

    To address (2), I’d like to see a measure of the amount paid per unit of unadjusted offensive value (VORP?), by position. According to what you have stated in comments (ie, that UZR doesn’t affect the results), the results should be essentially identical to those in Table 2, but that is such a counterintuitive result that I’d like to see it shown directly.

    To address hypothesis (3), it would be interesting to see a measure of whether $/unadjusted offensive value is linear. You show that $/WAR is linear (though it actually seems to increase steadily between 0 ad $15M), but it’s not clear whether that result is itself a product of positional adjustments and defensive stats.

    Comment by AF — June 21, 2012 @ 2:46 pm

  98. I’m not really arguing it, just positing a possible explanation.

    In any case your point on the year 1 salaries is taken. However I don’t think it refutes the thesis. If the idea is that GMs pay less for WAR at premium positions because of the risk of FUTURE declines, then underpaying in year 1 is exactly what you would expect to see, since that is when the player in question is most likely to still be playing the premium position, with minimal loss of playing time due to injuries. I think we need to look at values in the out-years of the contracts rather than the initial years to see if this might be going on.

    Your point on surprises is more damaging to the thesis. Despite my example, 1B and SS aren’t as different in kind as equities and bonds, so it is probably unreasonable to expect to see significant risk premiums across positions.

    Comment by mcbrown — June 21, 2012 @ 2:48 pm

  99. Whether or not the assumptions are true, that doesn’t really matter. What matters is whether the GMs believe them. I’ve heard people say many time that 2B decline earlier than other positions. There have been some great, athletic 2B that lost it early recently (Alomar, Utley). Now maybe that’s a case of a few high-profile players tainting perception of 2B, when the reality is that they age just like everybody else – but if the GM thinks they age early, and they’re the ones giving out the contracts, then they’ll take that into account (whether they’re right or wrong).

    Comment by vivalajeter — June 21, 2012 @ 2:48 pm

  100. I think Edwin is on to something. What is the average age at the skill positions? Like NFL running backs, I bet players at up the middle positions age faster and fewer remain productive past their arb years.

    Thus 1B make more money becuase more of them make it to free agency as productive players.

    Comment by Jason — June 21, 2012 @ 2:50 pm

  101. Hmmm Matt looking at the numbers you gave the relationship doesn’t look linear. I mean the difference between 10-15M contracts and 0-5M contracts in $/WAR is 6.5-3.6=2.9. That’s huge!

    I must say I’m surprised the trend of increase in $/WAR does not extend all the way up to the most elite players. It just doesn’t seem to jive with the narrative of the overpaid contracts for Fielder/Pujols/etc. Two possible explanations: 1) The elite players get overpaid b/c they get deals for much longer than the team reasonably expects them to produce or 2) For the truly elite players there are only a handful of teams that can afford them. I’m more inclined to think 1 is the real reason.

    Thanks for the reply and the thoughts tho.

    Comment by Bobby — June 21, 2012 @ 2:50 pm

  102. Adding to this, here is the $/WAR for each position with fielding set to zero for all positions.

    C: $4.0
    1B: $6.1
    2B: $3.3
    3B: $4.7
    SS: $3.8
    LF: $6.6
    CF: $5.8
    RF: $4.4
    DH: $7.1
    All: $5.0

    So it looks very similar to the results above. The only position the moved much at all is RF, where a disproportionate number of good fielders hadn’t reached free agency and a disproportionate number of bad fielders were included in the study.

    Comment by Matt Swartz — June 21, 2012 @ 2:51 pm

  103. Kevin,

    “A team of replacement-level hitters will still score a couple runs a game, so yes, one could theoretically pitch and defend well enough to allow fewer runs than they score.”

    If they score a couple runs a game on average, and their scoring is normally distributed, then they score zero runs in as many games as they score four or more runs. That means they have zero chance to win in a massive number of games. No a team cannot realistically pitch and defend well enough to win a lot of games like that.

    “The Mariners and As aren’t bad because of their model, they’re bad because in Oakland’s case they won’t spend any money on talent and in Seattle’s case the money they’ve spent has been on players who’ve severely underperformed expectations.”

    I think they actually value talent wrong and that is why the moves the do make rarely work out for them (especially the Mariners, who are the worst in baseball). Let’s agree to disagree here though.

    “The Nationals are 27th in baseball in runs scored, yet they have the fourth-best record and the seventh-best run differential.”

    The Nationals have absurdly good pitching. If your model for success includes having to have extreme outlier, best in MLB pitching you probably aren’t going to be successful very often.

    Comment by Jason H — June 21, 2012 @ 2:52 pm

  104. The problem with using the $0-5MM is that I can’t perfectly identify all of the costs. Those contracts are littered with poorly reported incentives that I can’t know and can’t include in the total cost, and that probably explains the gap. The fact that $5-10MM, $10-15MM, and $15+MM are all comparable suggests the relationship is linear.

    Comment by Matt Swartz — June 21, 2012 @ 2:54 pm

  105. This was my thinking too. IMO, fans are more eager to pay money to see Ryan Howard mash home runs than to see Jimmy Rollins flash the leather. Chicks dig the long ball, or something.

    Comment by Brian — June 21, 2012 @ 2:55 pm

  106. I should probably add that even if the thesis is correct that certain positions carry more of a risk premium than others, it would probably only explain a portion of the variation in value between positions.

    Comment by mcbrown — June 21, 2012 @ 2:58 pm

  107. Awesome, thanks!!

    Comment by AF — June 21, 2012 @ 3:00 pm

  108. Good point about $/WAR and year one. Here is the $/WAR for all players NOT in the first year of their deals at each position:

    C: $7.0
    1B: $6.4
    2B: $3.7
    3B: $4.4
    SS: $3.8
    LF: $9.4
    CF: $5.7
    RF: $6.9
    DH: $11.8
    All: $5.8

    Comment by Matt Swartz — June 21, 2012 @ 3:04 pm

  109. Average age at each position:

    C: 34.4
    1B: 33.8
    2B: 33.8
    3B: 33.5
    SS: 32.9
    LF: 33.8
    CF: 32.8
    RF: 33.4
    DH: 35.8
    All: 33.8

    So there isn’t much difference in ages here.

    Comment by Matt Swartz — June 21, 2012 @ 3:06 pm

  110. Jason, do we have any reason to believe WAR has so severely misvalued defense beside “duh!” and “obviously!”? I mean, I’m certainly not married to UZR, but in the aggregate, UZR, DRS and TZL do tend to produce similar outcomes using different methods. They aren’t bad as rough guides.

    Of course we don’t pro-rate the runs within games, but seeing as we use 162-game seasons to evaluate performance, there’s really no reason to. As for where teams get their offense, let’s model two scenarios. Assume, for argument’s sake, that league averages in batting runs are the negative of Tango’s position adjustments, i.e. average C is -12.5 RAA1B 12.5, 2B -2.5, 3B -2.5, SS -7.5, LF 7.5, CF -2.5, RF 7.5, DH 17.5. Consider two teams that have completely average defenders at each position.

    Team A:
    C: -2.5 RAA
    1B: 22.5
    2B: 7.5
    3B: 7.5
    SS: 2.5
    LF: 17.5
    CF: 2.5
    RF: 17.5
    DH: 27.5

    Team B:
    C: 10 RAA
    1B: 10
    2B: 10
    3B: 10
    SS: 10
    LF: 10
    CF: 10
    RF: 10
    DH: 10

    Your argument seems to be that the GM of Team B paid the same amount for each player, because they have the same offensive performance, while the Team A GM paid significantly more for his 1B, DH, and LF/RF. But Team B got the same offensive performance (90 RAA) as Team A without having any “elite” offense. That’s because in reality, their shortstop and catcher were incredibly valuable, providing a combined 40 runs over their positional averages despite being only 20 runs over the league average between the two of them. There might be a greater variance within the positions, but by comparing players against their positional average offensively, WAR is recognizing that there is more or less offense at that position. If the average RAA for 1B is indeed 12.5, then one should not pay very much for the 10 RAA 1B because there are plenty of 1B that can provide that level of offense, whereas there are very few SS and C who can do the same.

    Comment by Kevin S. — June 21, 2012 @ 3:11 pm

  111. Historically, does the damage from having a really bad offensive first baseman tend to doom a team, such that overpaying isn’t generally an completely terrible idea?

    Comment by Matt!Fast — June 21, 2012 @ 3:37 pm

  112. Well, now that is really interesting. So later on in contracts 1Bs and CFs still look about average, RFs and Cs have flipped from underpaid to overpaid, LFs and DHs have gotten just absolutely stupid, and the rest of the infield is still underpaid.

    Are you looking at positions at the time the contract was awarded, or in the given year?

    Comment by mcbrown — June 21, 2012 @ 3:38 pm

  113. This is performance in the 2007-11 seasons, regardless of when the contract was signed. RF were overpaid before though. Only C swapped.

    Comment by Matt Swartz — June 21, 2012 @ 3:40 pm

  114. Matt,

    “Jason, would your concerns be alleviated if I compared:

    Backups at 1B vs. Other Backups”

    I don’t think that is the appropriate test. First, backups are strange creatures. Many teams (most?) employ a player that can play many positions as a backup. But if a team does have a real backup first baseman they are likely to be either platoons or old veterans that can hit (Jim Thome) and get paid a lot for that ability.

    I think teams want to ultimately maximize the number of runs they score and minimize the number of runs they concede given their budget, and given what is actually available to them on the market. I think teams are paying money for elite offensive players (relative to the league, not the position) no matter where they play on the diamond. In theory, teams might like to behave like you want them to, but in practice the uneven distribution of elite offensive performers across positions, and the extremely limited market for talent actually available to teams at any given time for any given position means certain positions will appear over-valued. In reality, I think they are forced to pay for real production wherever it is available to them, and most great hitters are also capable of playing a passable first base.

    Comment by Jason H — June 21, 2012 @ 3:42 pm

  115. I suppose this is what I get for using vague terminology, but I believe the replacement level for offense is 3.2 runs/game in a neutral ballpark. I’m not sure how you’d calculate a normal distribution without a standard deviation, but if it was 1.65 runs (which strikes me as high), you’d expect to be shut out in roughly 5% of your games. Eight shutouts a year is not massive, and even it the SD was higher, we’re still talking about a replacement-level offense scoring a run in the vast majority of the games they play. Of course, it’s incredibly rare to actually see a replacement-level offense. Seattle scored about 3.2 runs/game back in 2010, but that wasn’t playing in a neutral ballpark, and it was the worst offense in forty years. Speaking of, unless you think Seattle signed Figgins expecting him to completely crater, I’d argue their problem was with projecting performance and not how they valued the performance they projected. Back on point, I don’t think Matt was suggesting trying to win with a replacement level offense, and my bringing it up was only to show you how absurd your -1 to 0 comment was. The Nats are the extreme example, but the Rays, Dodgers, Reds and Giants are all currently “in” the playoff slots while having below-median offenses, and the Reds, Nats, Dodgers and Angels are all in the top-ten in run differential despite having below-median offenses. None of which is to suggest that more offense isn’t good, but you’re position seemed to be that one could not win with pitching and defense, when in fact there are a number of teams doing just that.

    Comment by Kevin S. — June 21, 2012 @ 3:42 pm

  116. What I mean is, in this new table of salary per WAR for years 2+ of contracts, if a player was signed as a 1B but switches to DH in year 2, would he be counted in the DH category or the 1B category?

    My mistake on RF – still overpaid.

    Comment by mcbrown — June 21, 2012 @ 3:46 pm

  117. Based on your first table, the real questions seem to be: (1) why do 2B get paid so little, and (2) why do LF and CF get paid so much? All the other figures (including 1B) are understandable, if not necessary correctly valued.

    Comment by AF — June 21, 2012 @ 3:49 pm

  118. This really gets at what I am talking about. When you take position out, it starts to look a lot like GMs are paying for absolute offensive production except at a few spots on the diamond, where that generally isn’t even possible except in extreme outlier players.

    Comment by Jason H — June 21, 2012 @ 3:52 pm

  119. I think the title of this article could be changed to “Why Do Elite Power Hitters Get Paid So Much?” Or perhaps more simply, “Why Do Stars Get Paid So Much?”

    First Base is where very productive sluggers wind up. But they don’t always begin their professional baseball careers there. Many of the players with the $100 million plus contracts that the author listed played other infield positions when they were drafted or first signed, especially those who throw righthanded. Albert Pujols and Miguel Cabrera were shortstops. Mark Teixera was a third baseman. Joey Votto was a catcher. Jeff Bagwell, who was also mentioned in the article in a different context, was a third baseman. The one trait each of these players who were moved to first base share is the ability to hit the hell out of the ball. They were moved to first base because their teams had to find a spot for them in the lineup and 1B was either a better fit for their abilities, or there was another established player at the other position blocking their way.

    So the position of first base is populated with All-Star sluggers, the very types of players that MLB franchises will continue to shower with huge contracts. In other words, firstbase is over-represented with some of the most productive hitters in the game. I don’t know how an analysis based on positional adjustment WAR can answer any question other than whether owners and GMs overpay for stars. To be a fair piece of work, this analysis would have to eliminate the star players from each position and then determine whether GMs are still overpaying for first basemen relative to other positions.

    Comment by magdalencollege — June 21, 2012 @ 3:56 pm

  120. Well, the only 2B who produce like a 1B are Utley, Zobrist, Cano, Pedroia and Kinsler.

    Zobrist has less than 6 years and is signed to a Rays Contract anyway
    Cano signed a team friendly extension after his second full season, trading dollars for security.
    Pedroia took a hometown discount after his second full season, trading dollars for security.
    Utley was locked up by the Phillies after his second full season, trading dollars for security.
    Kinsler signed a team-friendly extension after his second full season, trading dollars for security, and his new contract doesn’t figure into this study.

    If anything, this proves GMs are smart because they locked up the elite hitting second basemen at below market rates from a young age.

    Comment by YanksFanInBeantown — June 21, 2012 @ 4:00 pm

  121. Jason, I think the original point has gotten lost in the back and forth, because what I’m saying doesn’t really seem to be relating to your original point at all. If I’m not mistaken, your two main points seem to be that there is a significantly lower spread in offense than there is in defense, and that there is a significantly greater variation in the spread of offensive performance at a position like first base as there is at a position like shortstop. On the first point, I agree, you agree, and WAR agrees – there is a lot less differentiation in defensive performance. I think you might be getting hung up on outliers like the Braun/Gardner thing. As to the second point, eleven teams have gotten shortstop production within five batting runs of the SS average, while twelve teams have gotten first base offense within five batting runs of the 1B average. Moving it up to a ten RAA either way, and we have 21 teams in the range at 1B and 22 teams in the range at SS. Although there does appear a greater spread in offensive performance at 1B, that’s largely driven by Joey Votto and Paul Konerko. Two performances don’t mean there’s systemic, exploitable differentiation that allows teams to spend more for first basemen (rationally).

    Comment by Kevin S. — June 21, 2012 @ 4:02 pm

  122. To be explicit, I want to clarify for the following reason:

    Imagine Player X, a 3B, signs a 2 year contract for 15mm per year. He puts up 5 WAR in year 1. In year 2 he switches to 1B and puts up 1 WAR. Overall, he earned 5mm per WAR and was paid fairly for his total performance. However, he earned 3mm per WAR at 3B in year 1 and 15mm per WAR at 1B in year 2. If you bucket his year 1 performance into the 3B category and his year 2 performance into 1B it will tend to bias your results towards the conclusion that 3B are underpaid and 1B are overpaid, when in fact the underpayment at 3B anticipated his future decline at a different position.

    If you are actually bucketing his entire performance into the 3B category, then this is a non-issue.

    Comment by mcbrown — June 21, 2012 @ 4:10 pm

  123. Kevin,

    The 2010 Mariners scored an average of 3.17 runs per game, with a standard deviation of 2.4 (so your guess was extremely low). They were shut out 15 times. So, they basically started the season 0-15. They scored exactly 1 run in 28 games. That is 28 games they would have had to pitch a shutout in order to win. They scored exactly 2 runs in 29 games. These are games they had to either pitch a shutout or only concede a single run in order to win.

    So in 15/162 = 9% of their games they had no chance to win

    In (28+29)/(162-9) = 37% of the remaining games they required an extraordinary pitching performance to win.

    And as you point out, this was not a replacement level team. A replacement level team would have done worse. It is simply not possible to win like that.

    It is often said that a run saved is the same as a run scored, but this isn’t quite true. You can save 30 runs in a game and still lose 1-0. Losing 1-0 is no worse than losing 31-0. If you score 30 runs, however, you almost certainly win. …saving runs don’t put you in position to win, they just put you in better position not to lose. Scoring runs put you in position to win.

    Comment by Jason H — June 21, 2012 @ 4:23 pm

  124. Excellent article Matt.

    Something that can explain why star fisrt basemen are getting paid more is because the majority of these stars are superb in “old player skills” which don’t tend to erode as quickly as offense based only in speed or high contact, which I’m guessing you find more in up the middle positions like SS and CF, giving GMs reason to overpay in years and money. Find me an average defensive SS or CF with high BB% and ISO and I’ll also overpay for him.

    Comment by chel — June 21, 2012 @ 4:47 pm

  125. Is contract duration a compounding issue here? Intuititvely (and mind you I have no actual data to back this up!) it seems that 1B and corner OF tend to get longer contracts (or 1 year ones).

    Is part of the overvaluing at 1st and say LF due to GM’s overpaying for decline years as opposed to overvaluing/undervaluing positional adjustments (this may also explain DH a little as some of those contracts may be decline years at DH for long contracts).

    Not sure if there is enough data to look at this but if you just took say 2-4 year contracts would the #’s look similar? (I;m guessing that mind render the sample size to small)

    You don’t see a lot of 5+ years to 2nd base and SS and maybe the market is just more efficiently correcting as any “mistakes” have shorter duration.

    Comment by Tom — June 21, 2012 @ 4:47 pm

  126. Kevin,


    Actually, that really isn’t my argument at all. I think I’m not explaining myself very well.

    I think teams want to ultimately maximize the number of runs they score and minimize the number of runs they concede given their budget, and given what is actually available to them on the market. I think we all agree on this. I’m just not convinced that, in practice, we should expect to see each position on the diamond approaching the optimal $/WAR. There are two reasons for this. The first, and probably least important, is that I don’t think fWAR is actually a great measure of value and I doubt many GMs do either.

    The second point, I think is more important. I think, in practice, teams are paying money for elite offensive players (relative to the league, not the position) no matter where they play on the diamond. In theory, teams might like to behave like you want them to, but in practice the uneven distribution of elite offensive performers across positions, and the extremely limited market for talent actually available to teams at any given time for any given position means certain positions will appear over-valued. In reality, I think they are forced to pay for real production wherever it is available to them, and most great hitters are also capable of playing a passable first base. It might be nice to think that you could increased value from a shortstop and a second baseman rather than a first baseman. However, when you are a real life GM and you look at the free agent market and your current roster, you see that there aren’t actually any second baseman and shortstops that exist that give the offensive production you need. You also see that you only actually have a single roster spot available in any case. You also see that the only players available on the market capable of giving the absolute offensive production you need are first basemen. You also see that every other GM in baseball has the same problem. So you are all left bidding on the same crop of hitters.

    Comment by Jason H — June 21, 2012 @ 4:59 pm

  127. Yeah, I see your point. That was why I developed the $/WAR for year-one of contracts originally. It was actually Dave Cameron’s suggestion to check for the exact issue you’re raising.

    Comment by Matt Swartz — June 21, 2012 @ 5:26 pm

  128. Tons of prospects start off as SS or CF. That’s not really relevant– what’s relevant is what they were when they were signed, which Pujols Bagwell, Teixeira all were when they signed their deals, right?

    Sure, a few people move over to 1B over time, but the fact that in the first year of contracts, 1Bs get $6.1MM/WAR but the average hitter gets $5.0MM/WAR suggests that that is a small issue.

    And also, I showed that GMs don’t pay any more for stars. They get $5.4MM/WAR overall, but $5.6MM/WAR for players that get >=$15MM per year.

    Comment by Matt Swartz — June 21, 2012 @ 5:30 pm

  129. There were a number of infielders that switched teams via free agency that had good seasons and were on free agent deals in 2007-11– Adrian Beltre (three times), A-Rod, Huff, Renteria, DeRosa, Orlando Cabrera, Glaus, Polanco. It’s not like no one existed.

    Comment by Matt Swartz — June 21, 2012 @ 5:35 pm

  130. Jason, you’re going to find tons of low-scoring games for all teams if you do the analysis like that, so you need to do that type of analysis comparatively to the rest of the league. Also, I’m pretty sure that people have looked at run distributions and winning and there really hasn’t been much there to prove the point you’re making. It could be true, but the burden is on you to prove what you’re trying to prove– which is that the value of going from 3 to 4 runs per game has a bigger effect on winning than going from 4 to 5 runs per game.

    Comment by Matt Swartz — June 21, 2012 @ 5:39 pm

  131. As I said in my comment above, years of contract is an important variable.

    If you have several old first basemen locked up in big contracts, following the premise that you overpay in the last years to get stellar production in the first years (a la Votto, Pujols, Teixeira, Bagwell, etc), you will end up with a lot of salary going to over the hill first basemen or players from other positions that have aged into first basemen.

    Comment by chel — June 21, 2012 @ 5:46 pm

  132. Interesting thoughts…I can check this pretty easily…

    Average year of deal/total length of deal for each position:

    C: 1.5/1.9
    1B: 2.1/2.7
    2B: 1.5/2.0
    3B: 2.0/3.0
    SS: 2.1/2.7
    LF: 1.8/2.8
    CF: 2.0/3.4
    RF: 2.2/2.9
    DH: 2/2.4
    All: 1.9/2.6

    Combined C/2B/3B/SS: 1.8/2.4
    Combined 1B/OF/DH: 2.0/2.8

    So it doesn’t seem to be a major issue. Most people are halfway through their deals, really.

    Looking only at $MM/WAR by position for deals of 2-4 years:

    C: $5.7
    1B: $18.0
    2B: $3.6
    3B: $3.8
    SS: $3.6
    LF: $12.1
    CF: $5.3
    RF: $9.8
    DH: $9.9
    All two-to-four year deals: $6.0

    So this actually shows a more extreme positional adjustment effect.

    Comment by Matt Swartz — June 21, 2012 @ 5:49 pm

  133. For my money, we might be best off adjusting for defense by considering the transitions that a player could go through, in terms of the real number of runs they could save by moving to a new position. As noted in the article and by just plain common sense… does moving a 2B to 1B actually save 15 runs? If so, why wouldn’t a team just sign two 2B guys and play one at 1B if they’re so undervalued?

    Position changes are asymmetric: moving a guy to an easier position gives less benefit than the harm of moving a guy to a harder position (since harder positions often see not only harder plays but also more opportunities).

    For example, a 2B sees about twice as many plays as a 1B (10k vs 5k). Let’s assume that a the 15 run split actually applies (e.g. the average switch would be 15 runs).

    If we assume this is symmetric, we’re basically saying:
    #PlaysAt1B*(Value/Play at 1B) – #PlaysAt2B*(Value/Play at 2B) ~ -15
    5000*V(1B) – 10000*V(2B) ~ -15
    V(1B) = (-15 + 10000*V(2B))/5000
    = 2*V(1B) – 0.003

    Or, in other words, for that to hold, a guy needs to be about twice as valuable at 1B PER PLAY than he is at 2B. I just don’t see how that is all that possible: the vast majority of plays at 1B are routine. On the other hand, I can easily see a 1B playing 2B being significantly worse than half as valuable per play.

    So we really have a situation more like:
    V(2B playing 1B) < 2*V(2B playing 2B)
    V(1B playing 2B) << 0.5*V(1B playing 1B)

    So both moves lose value. This makes sense. Imagine taking any team and moving the 1B to 2B and vice versa. Your worse defender is now involved in twice as many plays and your better one is now involved in half as many. It's like you switched an elite starter with a mediocre longman and vice versa. I would be entirely unsurprised to see the transitions work out to something like:

    2B to 1B: +5 Runs saved
    1B to 2B: -25 Runs saved

    (which would average to -15, but has very different implications) Clearly, the catcher adjustment is very much based on that issue as well (e.g. moving a catcher to another position adds basically no value, but the penalty for moving anyone else to catcher is absurdly high).

    So what does this mean? Well, mainly that moving a 2B to 1B isn't going to save you 15 runs but NOT moving a 1B to 2B will save you more than 15 runs. And that for value-purposes, averaging those two things is a dumb idea. I would propose that a better point of comparison would be to compare the value of a player against all other players in the league, adjusted by their one-way positional adjustments.

    Or, in other words, how good would this guy be compared to ANY other position player playing his spot. That would give a much better concept of value for a 1B or a DH. Sure, Prince Fielder is weak at fielding. But let's do a one-way adjustment about how much value anyone would give playing that 1B spot: how many players who don't already play 1B would outvalue him playing 1B? Tulo maybe? So what sense is it to give him a -12 adjustment when there's no one in the league who could actually provide that extra 12 runs in value?

    If we made a rank like that, we wouldn't need straight positional adjustments: we could do a WAR normalized by a different kind of replacement player: the replacement by anyone else on the field (adjusted for the defensive benefit/cost we'd expect out of that transition). 1B and DH benefit from this, they don't get penalized for the fact that playing them at another spot would be defensively ruinous. Because even if it is, who cares? If I sign a guy for 1B, I could care less if his UZR is -googleplex at 3B. On the other hand, when I am signing a 3B, I definitely care if a guy has -googleplex UZR at that spot.

    Comment by B N — June 21, 2012 @ 5:52 pm

  134. Okay, so now let’s take all 95 players who have over 20 batting runs in a season and look at their $/WAR but without positional adjustments. If you’re right about what teams are doing (whether it’s smart or not), then the numbers should look similar:

    C: $2.7
    1B: $2.5
    2B: $2.4
    3B: $2.8
    SS: $2.7
    LF: $3.0
    CF: $3.7
    RF: $2.7
    DH: $1.6
    All: $2.7

    So obviously the spread seems to be going way down for these players– good find.

    But the point I was making in Table 3 is that the average production is still very high for 1B/OF/DH and relatively low for C/2B/3B/SS. So it would seem that teams are better off trying to get better players at the harder positions since it will be much easier to find decent-but-not-at-all-elite hitters in 1B/OF/DH based on what Table 3 shows.

    Comment by Matt Swartz — June 21, 2012 @ 6:00 pm

  135. This is a very good point– the fewer plays at 1B means it’s tough to be an elite defender at 1B and the positional adjustment better reflects moving to harder positions for the most part. And it’s why I think the offensive difference for 1Bs (-9.6 runs) might be closer to the right approach than the full -12.5 run adjustment. But for other positions, that’s not quite true, and even for 1B, the market still gives them an even smaller adjustment than that.

    Comment by Matt Swartz — June 21, 2012 @ 6:03 pm

  136. “So both moves lose value”
    You have just found Entropy in baseball!
    I’m not kidding, it makes a lot of sense.

    Comment by chel — June 21, 2012 @ 6:10 pm

  137. Matt,

    It is not true that you find tons of low scoring games for every team.

    For comparison, the 2010 Yankees scored:

    Runs #games
    0 8
    1 9
    2 12

    So, the 2010 Yankees had little chance to win 29 games versus 72 games for the 2010 Mariners. That is a pretty massive difference when you consider the difference between the best and worst teams might be 40 games.

    The type of study you are asking from me is actually quite difficult to do given the format that the data is available to me in. I would have to write a computer program just to download all of the data to make an appropriate dataframe. I appreciate the call for rigor, but I just don’t have the time. Personally, I’d be shocked if run scoring distributions have no relation to winning. How could they not?

    Comment by Jason H — June 21, 2012 @ 6:11 pm

  138. Matt,

    Thanks for checking that. That does remove a ton of the variance. GMs are paying for hitting wherever they can find it.

    “So it would seem that teams are better off trying to get better players at the harder positions since it will be much easier to find decent-but-not-at-all-elite hitters in 1B/OF/DH based on what Table 3 shows.”

    I think the answer to this might be that these players literally do not exist. GMs probably agree with you, but these players are not available to them on the market.

    Even the Yankees and Redsox have obvious holes that they’d love to fill through the market. Hell, the Redsox haven’t had a shortstop that they’ve been happy with in almost a decade. The market just has not provided the players they need when they need them. The optimal solution is almost never actually available to the GM, so why should we actually expect the system to look optimal?

    Comment by Jason H — June 21, 2012 @ 6:28 pm

  139. Great points! It should also be noted that it is not just fielding chances that are important, but also the cost of plays not made. A second basemen that does not make a play only ever concedes a single. A first basemen that does not make a play usually concedes a single, but sometimes concedes a double.

    Center field is probably where the costliest unmade plays are. Often doubles and triples result from plays not made.

    The costs should be the same as the linear weights applied to batting outcomes.

    Comment by Jason H — June 21, 2012 @ 6:31 pm

  140. Jason, the correlation between (Actual – Pythagorean record) and runs per game is 0.03. So, this would mean that teams that have good run differentials by having good pitching are no worse off than having it by having good hitting. Runs are runs. Wherever you can add them to your side or subtract them from the other side, you do.

    Comment by Matt Swartz — June 21, 2012 @ 6:36 pm

  141. Matt, that is not an appropriate test by any means.

    Usually (in most game situations) runs saved are equal to runs scored, but not always. Because runs cannot be negative, you cannot win a game just by saving runs. If all you ever do is save runs, you lose every game. This can only really effect certain types of teams: teams that don’t score a lot of runs and teams that prevent a lot of runs through defense and not pitching. The 2010 Mariners almost certainly lost games where they saved more runs than the other team scored. They probably lost a lot of such games actually. You have a chance to win every single game you score runs in. You don’t have a chance to win every single game you save runs in. Its only once you’ve scored that saving runs means anything.

    The correlation you did is not appropriate, because it includes all teams and takes no account of defense relative to pitching in run prevention.

    Comment by Jason H — June 21, 2012 @ 7:21 pm

  142. Matt, how many are productive though? It seems like the skills that a 1B have, strength and power decline slower than speed.

    Comment by Antonio Bananas — June 21, 2012 @ 7:58 pm

  143. HR sell more tickets, 1B hit more HR. Economics. No one buys the jersey of the middle infielder who makes every play routine thus hiding his defensive ability by not diving after everything or barehanding everything (like David Wright did to swindle his way to a GG) or OBSs .400. People buy the jerseys of the mashers.

    Also, I think they get paid not relative to their position, but relative to the average major leaguer. How hard is that to comprehend? Just because there are more 1B that mash, doesn’t mean they shouldn’t be paid more. A catcher with 5 offensive WAR doesn’t hit at all as well as a 1B with it. GMs care about scarcity but they also care about ultimate production. If you have garbage at the offensive positions, your team isn’t going to score runs and not put butts in the stands.

    Lastly, maybe try running your correlation studies with more traditional stats. Using WAR or wOBA to evaluate talent would only work if that’s what the GMs were using too wouldn’t it? Pretend you ran it on something simpler like OPS, you’d find a strong correlation there. Guess what, you just found out what GMs look at.

    Comment by Antonio Bananas — June 21, 2012 @ 8:04 pm

  144. Winning puts butts in the seats more than anything. And jersey sales are paid to the league, so they don’t affect team revenue.

    And it’s not about paying players relative to the average major leaguer, but relative to the opportunity cost, which is higher offensive production for 1Bs. THAT is economics.

    I’m guessing comparing to traditional offensive stats would be able to predict salaries better, but that’s not what I’m trying to do. What I’m saying is that teams are paying for absolute offensive production more than they should, while when you look at typical opportunity costs in terms of (a) defenders switching positions or (b) offensive production at different positions, teams should be paying more to players at glove-first positions.

    Comment by Matt Swartz — June 21, 2012 @ 8:14 pm

  145. Matt, I think it is pretty clear at this point that teams do pay for absolute production. What is your evidence that teams would actually do better following your strategy, or that it is even possible given the extreme limitations of the free agent market?

    Comment by Jason H — June 21, 2012 @ 8:24 pm

  146. The evidence is simply that the average offensive production at some positions is very different than at other positions. There are frictions all over the free agent market, but however you slice it, the alternatives to spending money at 1B/OF/DH come with more offensive production than the alternatives to spending money on 2B/3B/SS/C. Once I get through with the replacement level analysis, you’re probably going to see this better.

    But suppose you had $16 million left to spend and you needed a 1B and a 2B. And suppose there is one solid-hitting average-fielding FA at 1B and one solid-hitting average-fielding FA at 2B, and both will require $15 million to sign. Are you really thinking that if we already know that teams get the same offensive production from 1B & 2B out of spending $15 million, you wouldn’t take your chances seeing what you can get out of $1 million spent at 1B vs. at 2B? You don’t think the $1 million 1B is going to add a lot more to your offense than the $1 million 2B? C’mon.

    Comment by Matt Swartz — June 21, 2012 @ 8:30 pm

  147. Matt,

    I understand your argument. But it is an argument from plausibility and it is not tested. It is a hypothesis.

    I would not be surprised in the least if your hypothesis fails because the market rarely supplies the requisite players that a GM needs to operationalize your method. Your example is very specific. A GM has two roster spots and X dollars. He needs to get the most value for dollar. He really, really wants to invest most heavily in a second baseman because value is cheaper there (as you point out). But when he looks at the market, who is actually available to him? Nick Punto. ….right, time to take a look at those first baseman again. Cano, Pedroia and Kinsler (the only living second baseman worth $15M/year in my opinion) just weren’t available this go around. Perhaps he can spread the money even further to get more players? No he doesn’t have the roster flexibility.

    Comment by Jason H — June 21, 2012 @ 8:49 pm

  148. So what you are arguing is that C/2B/3B/SS either conservatively or stupidly take below market deals too early, right? Because clearly they should be waiting around to be FA where they’ll paid handsomely if they do.

    Okay, so obviously hindsight is 20-20 but here are the infielders (other than 1B) that (1) had more than six years service time (2) have provided multiple 2-WAR seasons at some point in the 2007-11 period during which they had six years of service time and (3) changed teams via free agency.

    Adrian Beltre
    Troy Glaus

    Alex Gonzalez (twice)
    Marco Scutaro
    Miguel Tejada
    Orlando Cabrera

    Jamey Carroll
    Mark DeRosa
    Placido Polanco (twice)

    So that’s a lot of guys. Granted, some were surprises, but there were also surprises in the other direction that looked like they would do better than they did.

    Comment by Matt Swartz — June 21, 2012 @ 9:01 pm

  149. That most definitely is not a lot of players!!! Now put the expected WAR for each (and hence how much you would pay them max). Keep in mind that your hypothetical GM has a very specific dollar amount available, so the vast majority of these players wont fit his requirements. Then further consider that many if not most players do not just take the most money offered to them and may be impossible to sign in any case. I think you will find that the GM’s hands are pretty tied.

    Comment by Jason H — June 21, 2012 @ 9:18 pm

  150. wow … the league is surprisingly old. So every position is being manned (on average) by people in decline? what was your method for calculating average age?

    Comment by Jason — June 21, 2012 @ 11:45 pm

  151. This is only players eligible for FA, i.e. at least six years of service time.

    Comment by Matt Swartz — June 21, 2012 @ 11:47 pm

  152. No it’s not. If you see more of a players jerseys, sure, it’s paid to the league, but what does that tell you? It tells you that THAT player is why that person is there. So yea, it brings people to the parks to have a masher.

    Second, yea, winning does put butts in the seats, but let’s say you have a 2B, a catcher, and a shortstop that all have top WARs. That’s still not that much ultimate production.

    Third, the opportunity cost thing. Just because huge offensive numbers among 1B is more common doesn’t mean you shouldn’t pay them a lot. Think about the other opportunity cost, the opportunity cost of ultimate offensive production. Who cares if you have a guy who hits “good for a second baseman” if he’s your best hitter?

    Fourth, even though there are more 1B with big offensive numbers, there’s still not enough. There will always be a few teams bidding for that production. Combine the fact that if you don’t get that first baseman, you probably aren’t getting that offensive production AT ALL and it drives the price up even more.

    Try to not use WAR. Instead, formulate WAR not based on position, but based on league average in general (not counting pitchers) and only use offense. I think if you do that, you’ll see just how much more value offensively a 1B has.

    Also like I said again, people DO pay for names. There isn’t some nice equation that balances win% with attendance. For at least the first 3 months of the seasons, attendance is based on the fanbase’s perception of how good the team is. If a team signs a big free agent, season ticket sales go up. If a team wins a World Series, the next year’s attendance goes up. If a team comes out of nowhere during a season, it takes a while for the fanbase to believe. Look at the Orioles, Pirates, and Nationals this year. Attendance is up, but it’s not (in the Orioles case earlier and the Nats now) where you would think it would be.

    My point is that if you win without a superstar, unless you have a long history of winning, you probably won’t draw. Why do you think the As never drew? It couldn’t have just been the awful stadium or market. They were winning ugly. Attendance is based on expecations of winning. Sure in August, September, if you’re in a playoff race you’ll draw. However, if it’s April, May, June, and you are a good team but there were low expectations, you won’t draw. It’s not different than any other live performance event. People pay for their expectations. In baseball, this is based off what has happened and what people have heard. People hear about mashers, and mashers are 1B. 1B draw.

    Do something else for me. Look at attendance and see if there is a correlation between attendance and having a mashing 1B. Obviously, you’d have to try to neutralize the market size, winning %, etc. They don’t say “HR sell tickets” for no reason though.

    Comment by Antonio Bananas — June 22, 2012 @ 12:47 am

  153. There have been studies indicating greater injury risk for catchers and second basemen.

    Comment by Detroit Michael — June 22, 2012 @ 12:51 am

  154. There’s a lot of summary opinion without evidence, but I’ll try to answer.

    There have been some studies looking at revenue (not attendance because that doesn’t matter as much), and pretty much what people find is that the real value is in making the playoffs and having a good run in the playoffs. There may be some effect that’s hard to detect about HR hitters, but you don’t see Houston fill up year after year to watch Carlos Lee hit 30/100. It just doesn’t have that much of an effect. I do intend to look at some of this at some point, but the overwhelming literature suggests you really do well by winning. That 3-month-reputation thing is real– but it’s based on past winning.

    You say “combine the fact that if you don’t get that first baseman, you probably aren’t getting that offensive production AT ALL” misses the point I’m making. I’m saying that you can get more runs and wins by spending the money elsewhere. There is no rule that says you score more runs with a team wOBA of .340 if you happen to have a guy who hits 40 HRs versus if you have a team wOBA of .340 filled with guys with gap power. Seriously, you don’t get to make up sabermetrics!

    If you want to see what things might look like without WAR (or without positional adjustments), look at some of the tables I’m doing in the comments.

    Comment by Matt Swartz — June 22, 2012 @ 12:57 am

  155. Matt,

    “Seriously, you don’t get to make up sabermetrics!”

    I have to say, this really bugs me. Do we want sabermetrics to be like science? The answer is that we should. In real science you get to make up whatever you want, you just have to test it with data.

    The great irony is that you’ve described a very simple model here where teams can win more by being more efficient in the free agent market by investing in catcher and second base, but not first base. At this point, this is a simple model and nothing more. You haven’t actually tested the model. You don’t actually know that your simple model actually works in the real world. But you’ve jumped from creating the model, to assuming it is true. That is the very epitome of making things up without support.

    You did the first two steps in the scientific process. You made observations which suggest that first basemen are payed relatively more for their production than some other positions. You then formulated a hypothesis that suggests teams could do better by investing in the undervalued positions. Seems reasonable. But you jumped from the hypothesis to concluding that GMs don’t know what they are doing. You need to actually test the hypothesis, otherwise you are just making stuff up without support. Maybe the GMs know something you don’t know that your model has not considered.

    Your hypothesis makes certain testable predictions. If your hypothesis is correct you predict that teams that invest heavily in first basemen will win less relative to their overall payroll. If your hypothesis is correct you predict that teams that have a greater proportion of their payroll invested in undervalued positions will win more relative to their overall payroll. Your next step ought to be testing these predictions (actually really hard to get enough data for this I’d imagine). But until you’ve actually found support for your hypothesis, no one, including you ought to believe it.

    Comment by Jason H — June 22, 2012 @ 1:58 am

  156. Great article and discussion guys – lots of really insightful comments.

    I think what this article is showing is that it might be time to stop valuing players as SS’s, 3B, 1B, OF, etc.

    A month ago the Angels lost a game in extra innings with Howie Kendrick in left, Pujols at third, the starting catcher at 1B and probably some other nutty positioning. The point is no player is simply one thing. Every player has some specific value in terms of runs offensively and defensively at each position – and this is not some simple +/- system like WAR uses.

    In terms of WAR every time Mike Trout runs out to CF he gets a small positioning credit, and on the rare occasion he plays left he takes a much bigger hit. According to the stat Trout is giving the team less value by not playing center, but from the teams perspective it is his additional ability to play left that is being exploited to CREATE value.

    It seems that GM’s are paying for raw offensive production on the free agent market – with some other factors obviously included. I think a lot of this has to do with GM’s seeing offensive production and knowing they can find a place for it defensively – be it at DH, 1B, 3B, OF. Like we saw with Cabrera moving over to third this season to provide room for Fielder.

    If WAR is to go on I think its time for it to reconsider it’s positional valuations, or at least how they are earned. It’s fun to play with theoretical values when discussing players but we can’t get too far away from actual outs being recorded and homeruns being hit on the field.

    Comment by Erik — June 22, 2012 @ 3:07 am

  157. Thanks for the followup! Good stuff.

    It’s not surprising that there has been a fairly high level discussion, and it’s been constructive for the most part I think.

    I think that is due to:
    1) The quality of the initial post
    2) The constructive responses by you to some of the questions
    3) The lack of snarkiness in the response and your ability to entertain alternate points of view without dismissing them out of hand

    Anyways, great work… both the post and all the various comments by the community have been good reads and I wish this was more common around here

    Comment by Tom — June 22, 2012 @ 3:20 am

  158. Forgive me if someone already said this – I haven’t read all 155 comments yet – but could the different in GM valuations have to do with power? Raw power is only particularly helpful if it comes with plate discipline (or some other contribution, like fielding ability), but it’s very satisfying to the casual fan who occasionally comes to the game. Maybe this would be true of blazing speed as well, but that seems to be an even rarer commodity among MLB-capable players.

    In other words, could our metrics be evaluating on-field performance only, while GM evaluations balance on-field performance with marquee value?

    Comment by Jon L. — June 22, 2012 @ 3:31 am

  159. I see that this issue has come up a time or two above, and it’s been asserted that winning is how you put people in the stands. I’m not convinced though – people will pay to see guys Jeter and Ichiro. Admittedly, that’s star value based on past performance, but then maybe you can infer that name players are worth more to GM’s than less famous players with equivalent skills.

    I can also say that I went to a game with many fine plays, but the only on-field events that roused the people around me (and the girl I was with) were Mike Trout running around and slugging the ball, and Mark Trumbo blasting a ball off the fence. Gotta love our local Padres.

    Comment by Jon L. — June 22, 2012 @ 3:41 am

  160. But do you see how WAR insists that players be well-rounded? It negatively devalues players that are really, really good at a few things and says that a player that is average at everything is better than a player that is a great hitter but poor defender and baserunner.

    Again, I don’t see how Andrus in a given season is worth 1.6 WAR more than Konerko – that just doesn’t make sense intuitively and points to a flaw in the system (IMO). Or why Brett Lawrie (.287/.335/.419) has a higher WAR than Carlos Gonzalez (.332/.390/.617). Rather than just take that as gospel, let’s ask ourselves if that actually makes sense.

    The flaw, I think, mainly has to do with the arbitrary numbers that WAR sets for positional value. Those are arbitrary, right?

    Again, I like how WAR equalizes factors like ballpark context and brings to fore the importance of less-quantifiable factors like baserunning and fielding, but I think it goes too far.

    Comment by Angelsjunky — June 22, 2012 @ 8:16 am

  161. Well, I only checked second basemen, but DeRosa and Cabrera were both 33 after their good years, Polanco was 34 and was signed to be a third baseman, Renteria barely outperformed his contract from 2005-2008 and was 33 and terrible in 2008, Glaus was injury prone and on the wrong side of 30.

    Beltre wasn’t on the wrong side of 30, but he had underperformed his large contract from the Mariners and was signed to a below market 1 year deal by the Sox to re-establish his value, which he did, and signed a large deal with the Rangers that only counted for one year in this sample.

    Aubrey Huff is a 1st baseman.

    Comment by YanksFanInBeantown — June 22, 2012 @ 11:13 am

  162. And A-Rod is doing his best to counter-balance Longoria’s contract so that the two average out to $5/WAR.

    Comment by YanksFanInBeantown — June 22, 2012 @ 11:14 am

  163. I’m pretty sure that the defensive ranges support your suggestion. Last I looked, at many positions you see one or two outliers who provide a lot of defensive value, then a big cluster around average. Offensive ability seems to be a more even curve. So if 80% of all players at a given position will be average ±2 runs, better to spend your money trying to find a guy whose bat will be 5 or 10 runs better than average.

    Comment by JRoth — June 22, 2012 @ 12:06 pm

  164. Did you seriously just ask if positional adjustments are arbitrary? Did you read the article? I explained in detail where they come from.

    Comment by Matt Swartz — June 22, 2012 @ 12:16 pm

  165. I’ll buy that pitchers and catchers, maybe 2b’s have greater risk than 1b’s, though I’d still like to see actual research or at least be told some who and where on these studies.
    The “common sense” argument, except maybe for those 3 positions, does not hold water. I could argue the opposite, and we could both waste our time all day.
    This is far from the first time I have questioned this assumption and asked for proof and have never received a relevant reply, so I ain’t buying it.

    Comment by Baltar — June 22, 2012 @ 1:50 pm

  166. It’s kind of a two way street in my opinion. For the most part, 1B don’t have to deal with a lot of the physical ‘harms’ other positions may have to (longer/more throws, collisions, running longer distances to get to a ball, etc)
    But a lot of times, 1B seem to be in worse shape to have to do those sorts of things, so if someone like..Prince Fielder had to all-out sprint 180 feet, the chances of him pulling something would be significantly higher than someone like Elvis Andrus, who has a body built a little better for sprinting more than a few feet.

    Comment by Eric — June 22, 2012 @ 5:00 pm

  167. Matt, I’ve looked at a lot of studies at what drives attendance and revenue. You have to have the expectation that you’re going to be a playoff team for the first few months. Yea, making the playoffs the year before. I’m saying that in the context of what we’re talking about, signing a masher increases expectations and thus, attendance and revenue.

    I completely understand your argument. If I’m a salesman and I get 10% commission and I want 10,000 dollars in a month. I can sell one 100,000 dollar whatever or 10 10,000 dollar whatevers. I fully understand your point. I’m saying that A) dWAR is a LOT harder to evaluate and that B) offense is a lot easier to evaluate.

    So put that into context. You have player A who you think is 2 dWAR and you have a pretty good idea that he’s 2 oWAR. You have player B who you think is 0 dWAR, but the guy mashes and you know he’s worth at least 4 oWAR. Who do you sign?

    I’ll do an analogy. Let’s say you are buying a car. Car one is a newer model of your old car, priced at 40,000. You think that’s about right. Another car is also priced at 40,000 and despite all your research, you are still unsure about some features. Which do you think most people buy?

    I don’t think 2B are underpaid, I think it’s harder to convince people of their talents and honestly it seems harder to sustain those talents.

    I’m not making up sabermetrics, I’m questioning them. It’s a good thing, that’s how you learn.

    Comment by Antonio Bananas — June 22, 2012 @ 6:55 pm

  168. Yes, let me get to my lab and run these experiments for you.

    Comment by Heyward — June 23, 2012 @ 8:30 am

  169. Interesting article. Probably both sides can learn a little bit from each other.

    To paraphrase something Bill James said years back, positions don’t hit, hitters hit. GMs look at their 1-9 lineup and if they’re short on a major impact bat, there’s probably a better chance they’ll find one at first base where those type of hitters cluster. Yet, if the GM goes with a weaker 1B candidate so they can spend more money elsewhere, the sabermetrics crowd will start bashing on the GM claiming he needs to upgrade at 1B!

    If a team is lucky enough to have a prime A-Rod at short, then they have the ability to get a little less production out of a more traditional power position, such as first. In the end, the offensive is a collection of the hitters 1-9. It doesn’t matter where they play defensively on the diamond.

    Comment by Rob — June 23, 2012 @ 1:22 pm

  170. I’d put it this way: you win by scoring runs, and preventing them. To score runs you want guys who can hit, for power preferably. If a guy can pound the ball but defense is weak, you put him at 1B or LF. To prevent runs pitching is most important, followed by the catcher/SS/2B/CF line up the middle. So to win you maximize offense, so will sacrifice D in LF and 1B. to maximize defence teams are willing to sacrifice O at catcher, ss/2B, and CF even.

    Down the lines you build for power, up the middle defence. If you can get strong D down the lines great (Texas?). If you can get power down the middle great (Yanks?). Where D is less of a chore you want more offence, where D is hard (and crucial to victory) you need D. People may go gaga over a certain SS or catcher who hits great but has sad D, and those teams suffer for it. Nobody jumps for joy that their LF or 1B is a gold glover who can’t hit home runs.

    Comment by DSC — July 2, 2012 @ 12:00 am

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