2010 Most Valuable Players (Position Players)

Here are the most valuable position players in the leagues, according to my estimates. Pitchers here.

AL
Rank	Player		Team	$-Value (MRP)
1	Jose  Bautista	TOR	$21.11
2	Josh  Hamilton	TEX	$19.43
3	Miguel  Cabrera	DET	$18.65
4	Shin-Soo  Choo	CLE	$18.00
5	Evan  Longoria	TBR	$17.67
6	Robinson  Cano	NYY	$17.03
7	Adrian  Beltre	BOS	$16.01
8	Daric  Barton	OAK	$15.28
9	Carl  Crawford	TBR	$15.11
10	Ichiro  Suzuki	SEA	$13.48
11	Austin  Jackson	DET	$12.48
12	Joe  Mauer	MIN	$12.38
13	Nick  Swisher	NYY	$12.35
14	Nelson  Cruz	TEX	$12.04
15	Vernon  Wells	TOR	$11.98
16	Justin  Morneau	MIN	$11.93
17	Nick  Markakis	BAL	$11.93
18	Billy  Butler	KCR	$11.93
19	Paul  Konerko	CHW	$11.91
20	Torii  Hunter	LAA	$11.83
NL
Rank	Player		Team	$-Value (MRP)
1	Albert  Pujols	STL	$21.61
2	Joey  Votto	CIN	$20.17
3	Matt  Holliday	STL	$18.04
4	Ryan  Zimmerman	WSN	$17.99
5	Adrian  GonzalezSDP	$16.64
6	Jayson  Werth	PHI	$16.13
7	Aubrey  Huff	SFG	$15.95
8	Troy  TulowitzkiCOL	$14.83
9	Carlos  GonzalezCOL	$14.02
10	Jason  Heyward	ATL	$13.97
11	Ryan  Braun	MIL	$13.81
12	Jay  Bruce	CIN	$13.15
13	Kelly  Johnson	ARI	$13.05
14	Chase  Headley	SDP	$12.19
15	Rickie  Weeks	MIL	$12.14
16	Prince  Fielder	MIL	$11.94
17	Hunter  Pence	HOU	$11.80
18	Chris  Young	ARI	$11.76
19	Chase  Utley	PHI	$11.71
20	Angel  Pagan	NYM	$11.70

13 Responses “2010 Most Valuable Players (Position Players)”

  1. Can you discuss again how you come up with these numbers. What, for instance, makes Beltre worth more than 50% more than any other position player on the Red Sox. I would have expected he was middle-of-the-pack.

  2. JC says:

    I estimate the impact of winning (via run-differential) on revenues (using Forbes’s The Business of Baseball report, various years). Then, I estimate the impact of player performance on run production (hitters) and run prevention (pitchers). These estimates are adjusted for home-park influences. I value defense based on positional importance to preventing runs and use the Plus/Minus system to adjust for defensive quality. I then convert the run-contribution estimates to dollars using the estimates of the impact of winning on revenues. Because the impact of winning on revenue is non-linear, the reported values assume that the player is added to a .500 team. Players added to teams with above (below) average records generate more (less) revenue. The estimates are also gross (not net) marginal revenue product estimates, and therefore do not account for costs such as coaching, medical care, etc.

    See Hot Stove Economics for a detailed description.

  3. I am wondering where Andres Torres was on your list. Not that he’s the greatest, but a high OPS CF with great defense, and Pagan beat him out? Maybe I don’t know how good Pagan is…

    Same with Headley, I was surprised to see him there too, looking over your description, wouldn’t the Padres low revenues hurt his value? Or am I misunderstanding?

    Also, did Torres’ many games in LF/RF hurt his overall “value” since he’s great compared with CF, but only slightly better in corners.

    Thanks!

  4. JC says:

    Torres was 23rd at $11.58 million. He’s right there with Pagan, but Pagan played more. Also, estimates are based on an average revenue function for the league, so individual team quirks don’t factor in.

  5. So are these estimates retroactive estimates for the previous year only?

    I think it would be nice to see the numbers where some specific players are compared, so we can see what is weighted how much by the algorithm. I understand you don’t want to give away the whole book, but I also don’t want to read a whole book without having some sense of what it is I’ll be learning about. I mean, there are an infinite number of algorithms one could employ.

  6. bazooka joe says:

    again on Torres – FanGraphs had him at about #7 in the NL iirc.

  7. JC says:

    Problems with Fangraph $-value estimation method:
    1) It assumes there is a constant linear relationship between wins and dollars, which is incorrect. There are clear increasing returns to winning.
    2) By taking total “wins”added and dividing them among free agent contracts, it assumes the y-intercept is 0, which biases the estimates.
    These first two problems result in bizarre estimates on the extremes: why 1/3 of the league can be worth negative dollars and Ben Zobrist can be worth $40 million (thereby, challenging the assumption used to build the model that teams are rationally valuing players).
    3) Based on UZR. I use BIS’s Plus/Minus based metric, developed by John Dewan and his organization. The method is clearly explained in two books.

  8. Sky says:

    I’m not in love with the FG dollar-value method, but I don’t fully agree with these complaints:

    “1) It assumes there is a constant linear relationship between wins and dollars, which is incorrect. There are clear increasing returns to winning.”

    I fully agree that as teams win more games, the increase in revenue goes up faster. However, why should this team effect carry over to players? A team at 85 wins is highly motivated to spend more money in order to get to 90 or 95 wins, but why should it pass on that increase in revenue to specific players? If there’s a premium on paying a stud (and having a hole at another position), why not just save some money by paying two lesser players for the same total production? I realize the better the team, the more value there is in consolidating production into one player (roster size is limited) but that effect is pretty small — even the Yankees have holes.

    (Also, the Yankees are a big outlier, in many ways — your wins vs. revenue graph in the book clearly shows five points all in the upper right corner — the Yankees. Ignoring them, it’s much less clear that the best fit curve should be non-linear.)

    2) By taking total “wins” added and dividing them among free agent contracts, it assumes the y-intercept is 0, which biases the estimates.”

    Not clear on this one — why is it bad that someone who is adding nothing to the team is worth no money? Sorry, just unclear… (Maybe it’s our likely differing of opinion of what “adding nothing” means.)

    “These first two problems result in bizarre estimates on the extremes: why 1/3 of the league can be worth negative dollars and Ben Zobrist can be worth $40 million (thereby, challenging the assumption used to build the model that teams are rationally valuing players).”

    And only about 15% of players are worth more than -$1M. That’s about three runs below what FG calls replacement level. In 100 PAs, that’s about .030 points of wOBA, or a .270 wOBA instead of a .300 wOBA from a rep level player. Certainly well within the large fluctuations we observe in player performance over small samples. Just because someone plays worse than replacement level doesn’t mean their actual talent level was worse than replacement level.

    Ben Zobrist is a bit unfair of an example. In 2009 he had as many fWAR as Albert Pujols — is it so hard to believe that Pujols’ season might have fetched nearly $40M on the open market? The problem people have with Zobrist is that they didn’t think he was actually as good as Pujols. A few reasons for that — one, he didn’t have the track record, and two, a ton of his value came from fielding which is both underappreciated and was probably overrated by fielding metrics. People were mostly disagreeing that Zobrist was as good as Fangraphs said he was, not that the conversion of his production into dollars was crazy.

    Before converting into dollars, how good does your system say Zobrist was and how does that compare to Pujols?

    “3) Based on UZR. I use BIS’s Plus/Minus based metric, developed by John Dewan and his organization. The method is clearly explained in two books.”

    Has it been shown that +/- is significantly better than UZR? Yes, it includes more things (first base scoops, for example), but the average of all players is also about +10 runs PER TEAM.

  9. Sky says:

    JC, how about listing your performance numbers in addition to the dollar values. I believe you come up with a number of runs above/below average, which then get converted. Sharing those would help people (like me) see if we disagree on production or disagree on dollars.

  10. JC says:

    1) It applies to players because they are valued according to their marginal contributions to team value. That’s marginal revenue product theory of value. If anything, my estimates underestimate the increasing returns, because the numbers assume the player plays for an average team.

    2) y= mx +b. If you simply assume b =0 then m is going to take on a value that doesn’t properly reflect the added value of x. This is basic concept in regression estimation. The estimation technique I use doesn’t make any assumptions about b, and it is estimated to be non-zero. The Zobrist comment applies to Pujols as well. To an average team, Pujols wasn’t worth $40 million either. When you draw a line to measure a curved relationship, the bias is going to be greatest at the extremes. Also, players can’t theoretically have negative MRPs, so that 1/3 do is more than random fluctuation.

    3) John Dewan has a long record of excellent work and clearly explaining the method behind it. I have seen the BIS raw data, I know where it came from, and the process that produced it. I don’t have the same level of confidence in UZR.

    Also, the performance metrics used are publicly available at the links attached to each player. I use batting runs and defensive runs saved for the 2010 numbers (both available at Baseball-Reference). In my book, I used Plus/Minus to generate defensive runs saved, as DRS wasn’t developed in time for me to use it in the book. For pitchers, I use a DIPS-ERA estimate. The performance numbers are listed in my book for hitters and pitchers. There is nothing controversial or secret about the performance measures I employ.

    If you’re interested in what I am doing, please pick up a copy of my book (it’s free through your local library). I explain all the details.

  11. Sky says:

    Thanks, JC.

    “Also, players can’t theoretically have negative MRPs”

    So you’re saying that no matter how bad the player, he will always be worth something (but perhaps approaching $0 — or league minimum — asymptotically?) If the Blue Jays gave me 500 PAs and I was 100 runs below average, I’m not worth that much less than someone who was -50 runs?

    “To an average team, Pujols wasn’t worth $40 million either.”

    This goes back to my question on Twitter. Are the numbers you’re showing (and the answer might be different for these 2010 values as for 2011 predicted salaries of free agents) estimates of free agent value (where teams pay a premium) or estimates of overall value, ignoring contract status. For example, in the FG model, each marginal win costs about $2.5M if you include every player. But if you only look at free agents (and ignore pre-arb and cost-controlled arbitration players) that number is, oh, $4.5M per win. I know you’ve mentioned before about knocking a player’s worth down if he was due arbitration, so I’m wondering if you’ve bumped any of these reported prices up to reflect the premium teams pay for free agents…?

    Lastly, am I doing this right for reading the player values from B-Ref… Take Pujols in 2010. He’s at +64 runs Rbat, -2 Rfield, and -10 Rpos. Are you using +54 runs above average as his total production? Or are you also adding in the other offensive pieces, like baserunning, ROE, and GIDP?

  12. JC says:

    If employers are rational, they should not be willing to employ inputs that increase losses.

    The estimates are based on the added dollar value to the team’s revenue. There is no aggregation of contract dollars, free agent or otherwise. The $-per-win model is really a rudimentary version of Krautmann’s free-market returns approach. I spend a good deal of time in my book discussing why the Scully revenue-based approach for estimating value is superior. I prefer a fundamental value approach over market valuation.

    Again, I used Batting Runs (aka “linear weights”) and Defensive Runs Saved. I do not use that particular fielding adjustment. I develop the value of average defensive contribution based on fielding opportunities. The adjustments are listed in my book. In fact, I use Pujols to demonstrate the components of the estimates, step by step.

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