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March 31, 2006

What is Manny Really Worth?

© Mitchel Lichtman

Note: The following article is original content written for this website.

There is little doubt that Manny Ramirez is a whiney, malcontent...um, one of the premier hitters in all of baseball. In fact, he may be the best hitter not named Bonds, although Pujols and A-Rod might have something to say about that. Rather than cite a whole bunch of statistics (e.g., OPS, EQA, MLVR, VORP, RC) to “prove” that Manny indeed has been and is projected to be an outstanding hitter, I'll use what I consider to be the gold standard of hitting metrics, MGL's offensive linear weights. Before I take any credit for inventing the formula, let me give the proper citation for linear weights in general. For those who have not read Palmer and Thorn's The Hidden Game of Baseball (and I suggest that if you haven't, you go right down to your local library or onto eBay and pick up a copy), a linear weights formula for computing a player's (or team's) theoretical run contribution above or below average, based on their component stats, was first presented and aptly explained in that landmark tome (as far as I am aware). My linear weights formula is simply a more rigorous version of the original one. There is virtually nothing that is better at quantifying a player's marginal run value within a lineup of average players.

MGL's offensive linear weights

offLwts = .48 * (S–ifS) + .4 * ifS + .77 * D + 1.07 * T + 1.4 * HR + .32 * BB + .51 * ROE – outval * (AB–H),
where “ifS” is “infield singles” and “outval” for a RHB is .288 * SO/outs + .274 * Flyouts/outs + .308 * Groundouts/outs.

The exact coefficients for each of the offensive components (especially the out values) above vary according to the overall run environment, the specific personnel in a team's batting order, and the player's batting slot. In fact, the coefficient for the “outval” term is set each year such that each league has a total combined linear weights of exactly zero. I keep the rest of the coefficients more or less constant from year to year.

The following numbers in runs per 630 PA (around 150 games) are the top 11 players in park and opponent-adjusted offensive lwts, according to the above formula, for 2003, 2004, and 2005, along with a projection for 2006. The projection is essentially an age-adjusted, weighted average of the last 4 years' lwts with the appropriate amount of regression towards the mean thrown in for good measure (a very necessary part of a good projection, especially for players with limited histories).

2003200420052006 (projected)
Bonds 76Bonds 91Lee 62Bonds 89
Pujols 69Pujols 64Ortiz 54Pujols 56
Helton 58Helton 57Pujols 57Cabrera 39
Sheffield 56Edmonds 51A-Rod 57A-Rod 38
Manny 50 Beltre 49Ortiz 55Manny 36
Delgado 50 Drew 49Teixera 51Helton 34
Lopez 48Berkman 47Manny 48Ortiz 34
A-Rod 45Mora 44Hafner 46Texeira 34
Giambi 45Abreu 41Delgado 44Dunn 34
Thome 39Guerrero 41Bay 43Hafner 33
Edmonds 39Manny 38Giambi 41Giambi 32

So while Manny only cracks the top 5 in one of the last 3 years, he is indeed the fifth “best” hitter in baseball (as defined by their current projected lwts rate).

Fielding

Now that we “proved” what most of us already knew (that Manny is a great hitter—one of the best in baseball), let's turn out attention to something a little more controversial—Manny's defense.

There has been much ballyhoo concerning modern defensive metrics lately, culminating in an excellent treatise by John Dewan and Bill James, The Fielding Bible. According to the Bible, over the last 3 years, Manny caught “69” (I put the number in quotes because that is the “enhanced” number which adjusts for the expected run value of each batted ball) fewer line drives and fly balls in OF than an average left fielder “would have” based on the location, speed, and type of batted ball hit in and around Manny's fielding area. That corresponds to around 52 runs “cost” (each batted not caught by a fielder that would have been caught by an average fielder, or vice versa, is worth the value of a hit, in the case of Dewan's “enhanced” plus/minus rating, a single, or .47 runs, minus the value of an out, around - .28 runs) by virtue of Manny's poor fielding, in a total of 409 games played (actually around 396 defensive games based on his fielding “opportunities”), or -20 runs per 150 defensive games.

The other thing that Dewan measures for outfielders is the value of their arm, in terms of throwing out baserunners and preventing them from advancing or not. Although Dewan does not express that in any currency that can easily be transposed into runs saved or cost, Manny appears to be around the middle of the pack in “arm value,” according to his 3-year numbers.

Unfortunately, Dewan, as far as I can tell from a quick read of his book, does not tell us how, if at all, he handles park adjustments. Since even an average left fielder in Fenway Park would appear to be well-below average without a park adjustment, I suspect that Dewan is in fact using some kind of park adjustment. In other words, based upon UZR and other advanced and not-so-advanced defensive metrics, it appears that Manny is at least as bad as Dewan suggests, after adjusting for his home park. So I suspect that if Dewan were not using any park adjustments at all, Manny would look even worse.

In addition to the park adjustment question, The Fielding Bible, also as far as I can tell, does not explain how it handles errors, either ROE errors (allowing the batter to reach safely on a batted ball), or other types of errors, such as on a throw from the OF.

According to the methodology in The Bible, over the last 3 years Manny has cost the Red Sox around 20 runs per year by virtue of his poor defense. Let's take a look at what a couple of those other metrics have to say about Manny's defense.

UZR

One of those metrics is UZR. It is a play-by-play based defensive metric designed by yours truly around 15 years ago and inspired by STATS ZR. It has gone through many incarnations (and presumably gotten better along the way) since its inception. The current (2006) version of UZR measures range, error rate (all errors), and arm value for outfielders (and “turning the DP” value for infielders) in a very similar manner to the Fielding Bible, although it uses a different database (STATS Inc.). (Technically UZR is just “range plus errors,” and I have separate categories for OF arm and IF DP.) According to UZR, Manny was -58 runs in range plus errors over the last 3 years, which is an average of -22 runs per 150 games, or only around 2 runs per year worse than Dewan's numbers.

His arm, according to UZR, was above average and contributed an extra 6 runs to his defense in 2003 to 2005. So his total defensive contribution over the last 3 years was -52 runs, or -20 per year (150 games). That takes a serious bite out of Manny's overall value.

The other metric we can compare Dewan and UZR to is BP's DFT's, which are an integral part of the Pecota player evaluations and projections. According to Pecota, Manny was -30 runs in defense in 03 to 05. Because Pecota does not use PBP data to compute a player's defensive rating, their numbers will tend to be somewhat conservative. Given that, -30 runs is well in accord with the -50 something (Dewan and UZR) generated by two PBP-based systems.

In 2002, Manny's (park adjusted) UZR per 150 was -19 (in 60 games). If we do a weighted average of the last 4 years, age adjust, and regress toward the mean, we get a UZR projection of “only” around -16 per 150. Combine that with a projected arm value of +1 and we get -15 in total estimated defensive value/performance for Manny in 2006.

Between the ages of 22 and 34, an average fielder will lose around 10 runs in UZR. That would imply that Manny's defense was around 5 or 6 runs worse than average in his “prime.”

Overall

Now that we have a pretty good estimate of his defensive value over the last 3 or 4 years and hence his 06 projection (and beyond), we can combine this with his offensive linear weights historical value and future projection, throw in a few odds and ends (like baserunning), and voila, we get Manny's total past and projected future value (in marginal runs or wins) as a left fielder. From that, we can estimate his $ value in the FA market, and we can compare his salary to other Sox players to determine who are the better values.

First let's compute Manny's total value as a player and eventually convert that into a projection for 2006. We've already seen that Manny was worth 136 total runs in offense (hitting) in 2003-2005 over and above the average ML player, or 46 runs per 150 games (630 PA). However, the “average ML player” includes light hitting SS, catchers, etc. The average left fielder posted an offensive linear weights of a little less than 10 runs per 150 games over the last 3 years. So Manny was only 36 runs, or around 3.3 wins (using 11 runs per win) better than the average left fielder, which is still not too shabby, and easily rates him as the best-hitting non-megacephalic left fielder in baseball.

However, when we add in his -15 runs in defense (range, errors, and arm), Manny becomes only 21 runs better than the average left fielder (remember that by definition, the average left fielder has a UZR of zero), all of a sudden not too earth-shattering. In fact, at 21 runs better than average he moves from the undisputed Prince (not King) of left field to around 5th among full-time major league players who played left field for at least one of the preceding three years! Once we throw in his baserunning and propensity to hit into double plays, his 3-year total run value is reduced by another 8 runs or almost 3 runs per 150 games, which puts him at only 18 runs above average (again, for a left fielder), or a little less than two marginal wins.

Now let's compare Manny's salary over the last 3 years to that of the 7 or so “left fielders” who rank ahead of him in total runs per 150 games. We'll only consider those players who averaged at least 500 PA per season. In the last column, we are defining “replacement” as 20 runs per 150 games below an average player, a typical replacement level for most positions.

PlayerTotal runs per 150 (runs above replacement)Average salary per yearDollars per run over replacement per year
Pujols *69 (89)6.3 mil$71,000
B. Giles40 (60)8.6$143,000
Mora *36 (56)2.6$46,000
C. Jones32 (52)14.9$287,000
Ramirez28 (48)21.5$448,000

* Not yet FA

So, Manny made almost twice as much per marginal run produced (above replacement) as the next highest paid player, Chipper Jones. He also made more than two and a half times what the average FA in baseball makes (around $175,000 per marginal run over replacement).

Red Sox

What about some of the other Red Sox players? Since the Sox are a large market team with a very large revenue base, and are a perennial post-season contender, they can presumably pay their players more than most teams. Let's see if Manny is overpaid as compared to some of his teammates. Remember that while Manny is 28 runs per 150 in total linear weights, he is only 18 runs per 150 better than the average left fielder. So his total value over replacement, adjusted for position, is plus 38 runs and not 48 as in the table above (there he is compared to other left fielders). 21.5 mil divided by 38 runs is $566,000 per run.

Johnny Damon was a total of 38 runs better than the average CF'er, or 11.6 runs per 150 (31.6 runs above replacement). He made an average of 8 mil per season over the last 3 years, which is $253,000 per marginal run over replacement. So Manny made over twice what Damon made, given the same production, after accounting for their positional value.

Jason Varitek was a total of 77 runs better than the average catcher, or 31 runs per 150 (51 runs above replacement). He made an average of 5.3 mil over the last 3 years, which is $104,000 per marginal run over replacement, more than 5 times less than Manny, and quite the bargain to boot, as compared to the average FA.

Trot Nixon was 31 runs better than the average RF'er, or 16.3 runs per 150, 36.3 over replacement. He earned 5.4 mil per year, or $149,000 per marginal run, almost 4 times less than Manny.

(Note: Varitek would not have been a FA until 2004, and Nixon, 2005, so presumably they would have been paid more as FA's for the entire 3 years.)

Back to Manny

So it does appear as if Manny was grossly overpaid as compared to his actual 3-year value as a left fielder, even for a large market team like the Red Sox, at least as compared to some of his teammates, not to mention the league as a whole.

So what is Manny worth now (in 2006)? For that, we have to “jump ship” a bit and focus on his projection. As I said earlier, a projection is basically a weighted average of a player's historical stats adjusted for age and regressed toward the mean. Without going through the actual computations, which can be a little messy, I'll cut to the chase. Manny is projected at only around 9 runs per 150 games above that of the average left fielder. That includes his projected offense, defense (including arm), baserunning, and propensity to hit into the DP—in other words, the whole “ball of wax.” Why is his projection 9 runs less than his 3-year average? The short answer is that last year was the worst defensive year of his career (last year carries more weight than any other year), and he is two years older than his average age over the last 3 years.

How does that stack up with other full time left fielders? Here are the players who have a better 2006 projection as left fielders than Manny, along with their total projected linear weights per 150 games.

Bonds73
Cabrera26
Bay19
C. Jones18
Dunn18
Manny9

Now let's look at all of these players' 2006 salary so we can see whether Manny's current salary is commensurate with that of his competition.

Bonds18 mil
Cabrera.472
Bay.75
C. Jones11
Dunn7.5
Manny19

Again, we can see that Manny's current (2006) salary is as out of line with his current projected value as his salary over the last 3 years has been out of line with his historical value over the same period of time. Manny is earning almost twice what every player above him is making, save Bonds. (Again, not all of these players are presently under free agent contracts.) His $ per projected marginal run over replacement (29) is $655,000, almost 4 times the going rate for FA's.

What about some of the other Red Sox players? Here are their 2006 position-adjusted projected runs over replacement and salaries along with Manny's.

Varitek359 mil
Lowell179
Nixon316.5
Ortiz456.5
Manny2919

Once again, Manny is making over twice what these other teammates are making and his position-adjusted projection is worse than all but one, Lowell.

Position

Finally, is left field really the best position for a player like Manny or would the Red Sox (or some other team) be better off using him at first or as a DH? Well, that is not an easy question to answer. It depends on the personnel that the team already has and what options they would have in terms of picking up an additional player. Generally a player who is less than around -10 or -15 runs (per 150 games) in defense should be moved to a less demanding position if they are capable of playing that position substantially better.

Given that Manny projects to be worse than -15 runs on defense in LF, he is a prime candidate to be playing first base or to DH (although there is evidence that when players DH, their offensive production drops considerably, as compared to when they play the field). Certainly if the Sox had or were interested in acquiring a reasonably competent left fielder (one who could hit and field well), moving Manny or Ortiz (and having Manny DH) to first would not be a bad idea. Without a doubt, if he were traded to another team, his value would be much higher as a DH and slightly higher as a first baseman (he would lose some offensive value and gain some defensive value). As it stands, given the current personnel on the Red Sox, he is probably “stuck” in LF, even though his overall (position-adjusted) value is not nearly what most fans think it is, and he is grossly overpaid for that value, even by large-market team standards.