Table of Contents

Thursday, November 08, 2007

Player Value, Part 4: Position Player Wrap-Up

To view the complete player value series, click on the player value label on any of these posts.

Let's go over the main principles we've covered thus far:

1. A run saved is worth the same as a run scored. Therefore, estimates of player value require one to consider both offense and defense.

2. We often find it useful to compare players to replacement players, who we assume will hit at 73% of league average and play league-average defense at a given position.

3. A player's total offensive contributions can be estimated using linear weights, relative to replacement player offensive production levels.

4. A player's fielding performance can be best estimated using the combined estimates of several different statistics. Because replacement players can be assumed to be league-average fielders, we simply report all fielding statistics as +-average at a position.

5. We also need to add a position adjustment to a player's fielding estimate to signify the differences in value (i.e. average difficulty) of playing one position vs. another. This should be pro-rated for the player's playing time (defensive innings).

Now, let's put it all together and look at a case study.

The 2007 Reds Position Players


While I've already posted offensive value estimates for the '07 Reds, I haven't yet posted fielding data, so let's start there.

Below I've used combined data from the Fans' Scouting Report, ZR, RZR, and the catcher statistics (C-Runs below) to estimate fielding runs saved vs. average. Methods are as described in my previous posts. ZR and RZR data are the summed values across all positions a player played. FSR data are calculated using Tango's custom weights for each position a player plays, pro-rated for his defensive innings at each position (Player innings out of 1440), and summed. I've also added a position adjustment (using Tom Tango's numbers) to the data to get an estimate of total fielding value.

Here are the data (sorry about the missing cells--nature of the beast). Fielding is the +-Fielding value relative to a player's position. TtlFldVal is a player's total fielding value, which is the sum of Fielding and the position adjustment (PosAdj). All values are reported as +-runs.
Name PriPos Inn FSR ZR RZR C-Runs Fielding PosAdj TtlFldVal
D Ross C 837 6.9

6.3 6.5 5.8 12.3
B Phillips 2B 1371 15.3 -0.8 15.1
9.2 0.0 9.2
N Hopper CF 607 0.6 4.3 11.2
6.0 0.9 6.8
A Gonzalez SS 872 2.2 3.2 5.4
3.8 2.4 6.2
R Freel CF 577 -0.7 -4.7 7.8
1.0 1.5 2.5
J Ellison RF 82
1.8 3.5
2.1 -0.2 1.8
D Wise CF 13
0.4 0.6
0.5 0.0 0.6
M Bellhorn 3B 14
0.2 -0.1
0.0 0.0 0.0
R Hanigan C 20

-0.1 -0.1 0.1 0.0
J Keppinger SS 509 -3.4 2.9 -3.2
-1.0 1.0 0.0
R Jorgensen C 34

-0.2 -0.2 0.2 0.0
J Valentin C 472 -4.4

-3.1 -3.4 3.3 -0.1
J Hamilton CF 663 2.0 2.3 -8.4
-1.8 1.6 -0.2
C Moeller C 87

-0.9 -0.9 0.6 -0.3
B Coats RF 68
0.0 -0.5
-0.3 -0.1 -0.4
P Lopez SS 93
-2.6 1.2
-0.7 0.3 -0.4
E Cruz SS 2
-0.7 -0.7
-0.7 0.0 -0.7
J Castro SS 178 0.0 1.0 -4.9
-1.5 0.2 -1.3
J Cantu 1B 112
-1.7 0.1
-0.8 -0.6 -1.4
J Conine 1B 435 -1.9 1.4 -2.8
-1.0 -2.4 -3.4
J Votto 1B 188
-0.7 -5.7
-3.2 -0.9 -4.1
S Hatteberg 1B 772 0.6 7.4 -11.1
-1.2 -4.3 -5.5
E_Encarnacion 3B 1168 -1.1 3.0 -21.9
-7.4 -0.8 -8.2
K Griffey
RF 1163 -1.0 -1.2 -17.1
-7.1 -3.2 -10.4
A Dunn LF 1189 -14.2 -4.1 -17.5
-11.6 -3.3 -14.9

According to these data, the Reds' most valuable fielders in 2007 were David Ross, Brandon Phillips, Norris Hopper, and Alex Gonzalez. Phillips was the best at his position of any Red in terms of runs saved vs. average, but Ross (who was ranked the 8th most valuable catcher in MLB) played a more valuable position, and this pushed his overall ranking to the top. Strangely, Phillips was rated as merely average by ZR, which speaks to the differences between the BIS and STATS hit location datasets.

In contrast, the Reds' worst fielders were Adam Dunn, Ken Griffey Jr., Edwin Encarnacion, and Scott Hatteberg. Dunn got hammered by all of the fielding statistics, so there's clear consensus that he's Not Good in left field. In contrast, Griffey was rated as roughly average by both Fans and ZR, but was hammered by RZR. This is largely because the latter statistic places far more weight on plays out of zone, which is where Griffey's performance really fell short. Edwin was also rated differently by the two datasets, though in his case it's not clear why RZR dislikes him so much more than ZR.

Overall, I really like how total fielding value ranks these players. Compared to rankings that are strictly relative to positions, the total fielding value rankings recognize the inherent differences in value among different positions, which results in appropriate looking boosts to guys playing hard positions (C, CF, SS) and penalties to guys playing easier positions (1B, LF, RF).

Total Value

Now, the moment we all (or, at least, I) have been waiting for: let's put together our offensive and fielding numbers and rank the '07 Reds non-pitchers based on their total value!!!

In the table below, RAR represents a player's offense (runs above replacement), while TtlFld represents a player's defensive value (+- fielding and a position adjustment). Total_Value is the combined value of offense and defense!
Name POS
B Phillips 2B 30.2 9.2 39.4
A Dunn LF 51.3 -14.9 36.4
K Griffey Jr. RF 36.4 -10.4 26.0
J Hamilton CF 25.2 -0.2 25.0
S Hatteberg 1B 26.9 -5.5 21.4
A Gonzalez SS 13.3 6.2 19.5
J Keppinger SS 17.1 0.0 17.1
N Hopper CF 10.8 6.8 17.6
EEncarnacion 3B 24.8 -8.2 16.7
D Ross C -4.6 12.3 7.7
J Valentin C 3.2 -0.1 3.1
J Cantu 1B 3.8 -1.4 2.4
J Votto 1B 7.3 -4.1 3.2
R Freel CF -0.2 2.5 2.2
D Wise CF 0.3 0.6 0.9
J Conine 1B 4.6 -3.4 1.2
R Jorgensen C 0.4 0.0 0.4
R Hanigan C 0.3 0.0 0.3
J Ellison RF -1.8 1.8 0.0
E Cruz SS -0.2 -0.7 -1.0
M Bellhorn 3B -1.4 0.0 -1.3
B Coats RF -1.4 -0.4 -1.8
P Lopez SS -3.6 -0.4 -4.1
C Moeller C -4.8 -0.3 -5.1
J Castro SS -8.2 -1.3 -9.4
Isn't that exciting? Seven long articles worth of methods just to produce this little table!!!! :)

After all of that work, I'm quite comfortable saying what many would probably have been willing to say from the get-go: Brandon Phillips was the most valuable position player on the Cincinnati Reds in 2007! He was their third most valuable hitter, and the second most valuable fielder. Overall, it was an outstanding season by the Reds' second baseman. Hopefully he can continue that success next year.

For all my concerns about Adam Dunn's defense, he still came in a close second as the Reds' second most valuable position player thanks to his tremendous offensive performance. Josh Hamilton also had a strong showing, especially when you consider that he only had 337 PA's. Just think of where he'd be if he could get 650-700 PA's next season while maintaining this level of performance. I get misty-eyed when I think about it.

Without going back to repeat the math throughout his career, Alex Gonzalez may well have had the best all-around season of his career despite getting only 430 PA's. And Hopper and Keppinger may have had what will, in fact, turn out to be the best seasons of their MLB careers (though I'm obviously hoping they have more in the tank).

On the flip side, despite early-season struggles offensively, Edwin Encarnacion did manage to come out with positive value over replacement in this analysis, which is probably an improvement over 2006. His hitting slipped a bit this season overall, but he did show some improvement in his defense. If he can continue to improve on defense, while getting his offensive production back to his '06 rates over a full season, he could be a force to be reckoned with. But if he can't get his offense back on track for a full season, or his fielding slips to '06 levels of misery, he might not keep his job much longer. The kid's only 24, but the Reds will only wait so long for him to put things together. Next season might be his make-or-break season, at least as far as the Reds are concerned.

Finally, David Ross shows up better than I expected thanks to his strong showing on defense. Nevertheless, 8 runs above replacement-level is not acceptable performance from someone who got ~350 PA's on this team. Catching was very clearly the biggest hole in the Reds' lineup, and the place where they could potentially gain the most ground via an acquisition. ... not that the free agent market for catchers is particularly rich.

Coming up next: pitchers!
Brandon Phillips Photo by AP/David Kohl
Edwin Encarnacion Photo by Cincinnati Enquirer


  1. Justin,

    I must say that I loved this series of mini research papers and analysis. It has kept me from two hours of work over the last two weeks I am sure... but that is certainly no complaint.

    I wish more people would be willing to factor defense into a players overall value. I have had many arguments lately concerning Adam Dunns value and how it may be easier to replace than a lot would like to admit with just a solid-average defender and a lesser bat, although still a good bat without having to replace his walks and HR all in 1 big swoop. Given that he plays a corner outfield position, it seems that most people think that other guys suck in LF too so defense out there doesn't matter. Obviously, as we know, thats not true.... anyways, I am rambling now becuase I don't want to go back to working, but great stuff once again.

  2. Hi,

    Thanks, glad you've enjoyed it! Next up is pitcher evaluations, though those parts should be shorter because a lot of the ground for those pieces has already been laid.

    As for Dunn, what these data indicate is that he could probably be replaced for a 30 RAR bat who plays slightly above average defense in left field (+4 vs. average to make up for the -4 LF penalty). The problem is that those players are not necessarily easy to find--the Reds only had three guys who broke 30 RAR last year, and only one of them played above average defense (Phillips)! I definitely think it was worth picking up the one year option. Whether it's worth it to try to sign him to a long-term extension is another question.

  3. Good work, Justin. I'd say those rankings are pretty much in line with what I'd expect. Hamilton's season was quite impressive given his limited playing time. Hopefully he can maintain that level next year but give us more games.

    On Dunn, it should be noted from sky's list that only 5 LF had a better total year than Dunn last year. Obviously someone could move from another position and probably handle LF, but I'm not sure it's so easy to replace 30 runs as it might seem on the surface. I'm not sure he's worth $15 million, but I'm also not sure you can replace him on the free agent market for much less.

    One last thought. There is still a part of me that wonders if these aggregate numbers are assuming too much linearity in baseball. I think what would make me see this more clearly is if you could (once you get the pitchers done) show how these numbers lead to a win-loss probability. Theoretically, if all of these runs are equal, then we should be able to reasonably predict how a team of a total value distribution would do.

    Am I right in thinking this or am I misunderstanding something? Do I even make sense?

  4. Hi Joel,

    Had a nice chat with you just now. :)

    I think our takes on Dunn are largely the same. 30 TVAR players don't grow on trees. :)

    As for the runs vs. wins issue, I keep falling back on the regression I posted in the first part of this series: variation in run differential explains 90% of variation in win totals, and runs scored tells as much about wins as runs saved. It's true that there could be some linearity problems with extreme players (e.g. Dunn, Adam), but I think we're getting pretty close to the mark with these data.

  5. Joel, I think an important offshoot to your question is the money question. If Adam Dunn is worth 15M as a 40 run player, does that make Alex Gonzalez worth 7.5 as a 20 run player?

    I think your non-linearity would really show up in payroll distribution. How much is a run worth? Is it linear? In the market, are runs consistently valued by position? Is there an exponential increase of cost per run at the player level?

  6. Payroll questions definitely take this stuff to the next level of complexity. I think Dave Studeman and JC Bradbury have done some of the best work on monetary value of production, but even with their excellent work it may be over simplified--the best players provide production that simply cannot be replaced by one player, which may mean that there's potentially a nonlinear relationship between value and price tag for those individuals that is only countered by team payroll limitations (i.e. do you pay the same for 50 TVAR if it comes from one player vs. 2 players?). Factor in ever-increasing team budgets and you have a damn complicated thing to try to understand.

    I'm not going to touch monetary player value issues for quite a while. :)

  7. Justin,

    Given roughly where Hamilton rated with centerfielders I was wondering what your rough guess would be with how he would be as a LFer. Comparable to Dunns overall value? Higher?

    Basically I have been tossing around the idea in my head of moving Dunn, replacing him in LF with Hamilton, puting Bruce in CF and leaving Griffey in RF since he will likely be more difficult to move than Dunn. I have a feeling that having a Hamilton/Bruce/Griffey outfield could out produce a Dunn/Hamilton/Griffey OF next season... just me thinking out loud and seeing what anyone else thought.

  8. Hi Doug,

    These total value ratings "try" to account for variation among positions, such that a player will retain roughly equal value wherever you put them. That's not strictly true, of course, because different positions require different skills. I have no doubt that Hamilton would be a brilliant left fielder, though his arm might be wasted a bit there.

    On average, an average center fielder (which is about what Hamilton is) would save +9 runs/season above average in left field. However, under this system, that value would be counteracted by removing a +5 runs/season bonus for playing center field, and adding a -4 runs/season penalty for playing left field.

    FWIW, I'm skeptical that Bruce can outperform Dunn, at least in the near-term. If he has a superb season, though, he might out-perform Griffey. Seems to me that a Chris Young-type season might be what we'd expect from Bruce this year though...

    Also, regarding moving Dunn--doesn't he have a no trade clause until mid-next season now?

  9. Justin,
    I don't think Bruce will outproduce Dunn next year, but given Hamiltons defense over there along with his offense (given he can stay healthy and clean) he has a legit shot at outproducing Dunn in LF. Then sliding Bruce into CF, where if I am getting correct reports, he is still slightly above average in CF defensively, he is a defensive upgrade over Hamilton for the time being and could still be an above average CFer at the plate. Griffey is still Griffey, plus bat, minus glove...

    As for Dunns contract, yes, he does have a no trade clause, but if the Reds get the right deal and tell him they aren't going to be signing him after the season, and its to a team he likes, he could always waive it and be moved.

    Really though, I have just been running a million ideas around on how to improve the run differential of this team and this is one that I come back to often considering that you will get some talent back for Dunn and likely some money to maybe get a bullpen arm or two if you so choose to go that route.

  10. Doug,

    I think you might be going the wrong route to try to improve the run differential. I think moving your second most valuable player would make it harder to improve the run diff. Your outfield plan depends a lot on both Hamilton and Griffey remaining healthy. I think if he's healthy, Hamilton could replace Dunn's production (with Bruce replacing Hamilton's), but Hamilton's injuries last season were during some less than strenuous events. It's not like he was running into walls or sliding hard into a base. I think if you want to compete in 2008, you need Dunn's durability and production in the lineup, even if he's not a great defensive player.

    I think if you're looking for bullpen help, the person to look at trading is Gonzalez. I know he doesn't have as much value as Dunn, but he should be able to pull a bullpen arm or two in a deal. Plus, his production is easier to replace than Dunn's (it shouldn't take a best case scenario to replace him) and they would still be saving some money that they could use to sign more bullpen help.

    I think trading Dunn before his no-trade clause runs out will be difficult in the sense that you'll need the perfect storm of the right team (i.e. willing to take a chance on what could be a one year rental), with the right return, that Dunn will want to play for. I think it's more likely that he will get dealt in July, when a team in contention could use a bat to replace an injured player or fill a hole in their lineup. Also, the Reds will have more options then (10 teams) that won't require Dunn to sign off on the deal.

  11. Justin,

    Very interesting. I can only imagine the amount of time you put into it. I'm looking forward to your pitcher evaluations.

    As far as Dunn goes, I'd still like to see him signed to a multi-year deal even though he's a defensive liability. I think it would be very difficult to replace his offense. Plus, Griffey's contract expires next year. I think we'd really miss Dunn in 2009 if he's traded.

  12. A friend of mine and I are having a debate of who is more valuable, Troy Tulowitski or Derek Jeter?

    He says Jeter, and I say Tulo.

    When I offered my opinion why I valued Tulo more, I was quickly rebutted with, "You cannot punish a player's value because the player has an exceeding contract, especially since the players that you are comparing to havent yet hit the market"

    I just wanted to get another persons opinion on this subject....

    Do you think a players value should have his salary factored in when determining his overall value?

    In my opinion, a player like Tulo, who is giving the same offensive production as Jeter, better defense, for a cheaper price (Tulo 5 million, 20 mill for Jeter); is much more valuable overall.

    In his opinion, they cant be compared due to Tulo never hitting the open market....which I think is ridiculous.

    Please help with this situation, if you can.

    Thank you,

    Justin - Cincinnati

  13. Hi Justin (funny--I used to go by Justin In AZ!),

    Skyking162 did a nice recap of shortstop performances last year. He had Tulowitzki producing 24 runs above a replacement player on offense (after park adjustment), and another 22 runs on defense. When you also add in a 5 run value bonus for playing a premium position, that puts him at 51 runs above replacement last season. Certainly, you have to project a bit weaker performance next year, but 40 runs above replacement isn't out of the question for the guy. He's awesome.

    In contrast, Derek Jeter was +41 RAR on offense, but a miserable -24 runs on defense. He's routinely been 1-2 wins below average on defense throughout most of his career, so this wasn't a surprise. The result was a player, after value boost due to playing shortstop, of +22 runs.

    So, by that comparison alone, Tulowitzki's about twice as valuable as Jeter. Now, add on top of that fact that Tulo's making just $31 million over the next six years, compared to Jeter's $20 million per year? My goodness, yeah, he's Tulowitki's a heck of a lot more valuable of a property than is Jeter.