Re-Examining WAR’s Defensive Spectrum
The defensive adjustment for the DH and the DH hitter penalty offset each other. (via spablab)
Wins Above Replacement (WAR) attempts to measure all the aspects of a player’s total value. For position players, that encompasses hitting, fielding, base running and a positional adjustment. Today, I am going to look at the last aspect of the equation, positional adjustments, to see if the values need a little tweaking.
The reason for the investigation is based on the actions of major league teams. They don’t value—or don’t seem to value — players the same way as do the writing and researching public. It seems teams put more emphasis on the corner guys, while the public sees players up the middle as having more value. I had an idea that teams may know a little more than the general public and decided to dig into the values.
The values used for the position adjustments we use currently come from this thread at the old Inside The Book blog. In the end, the following values were agreed upon and are the ones used by our sister site, FanGraphs:
Catcher: +12.5 runs (all are per 162 defensive games)
Shortstop: +7.5 runs
Second Base: +2.5 runs
Third Base: +2.5 runs
Center Field: +2.5 runs
Left Field: -7.5 runs
Right Field: -7.5 runs
First Base: -12.5 runs
Designated Hitter: -17.5 runs
Do these values need some tweaking? It has been a few years since these were established, and it’s always good to refresh our research, even if nothing really changes. To start with, I will look at the infield position adjustments used in WAR and ignore the DH for a bit. I am going to examine differences two separate ways—by defensive and offensive numbers. Let’s start with the defensive values.
For the defensive values, I used all the non-catcher UZR data from 2002 to 2014 and compared the defensive runs saved per 162 games by using the harmonic mean in innings played. We end up with four columns.
- Position 1: One position compared
- Position 2: The other positions are compared
- Innings: Total number of innings are compared
- Difference: The runs saved or lost when moving from Position 1 to Position 2
Here are the data ordered by the most matched innings:
| Infield Defense Comparison, 2002-2014 |
|---|
| Position 1 | Position 2 | Innings | Difference |
| LF | RF | 138,722 | 0.7 |
| LF | CF | 102,871 | 8.8 |
| CF | RF | 97,933 | -9.4 |
| 2B | SS | 81,092 | 3.0 |
| 2B | 3B | 77,715 | -0.1 |
| SS | 3B | 56,493 | -2.8 |
| 1B | 3B | 52,190 | 6.9 |
| LF | 1B | 41,452 | -5.5 |
| RF | 1B | 39,141 | -9.3 |
| LF | 3B | 24,951 | 1.6 |
| LF | 2B | 20,367 | 2.3 |
| 1B | 2B | 18,086 | 4.2 |
| RF | 3B | 16,516 | 1.1 |
| RF | 2B | 14,044 | 1.5 |
| CF | 2B | 12,713 | -2.1 |
| LF | SS | 9,091 | 5.9 |
| CF | 3B | 8,843 | -4.2 |
| 1B | SS | 7,726 | 11.2 |
| CF | 1B | 5,493 | -6.4 |
| CF | SS | 5,377 | 6.2 |
| RF | SS | 5,099 | 0.7 |
So, a couple of ground rules for creating this positional spectrum. First, I am going to concentrate on the values that contain the most innings. These are the pairs with the most data since players make this transition the most. Also, I am going to concentrate and give more weight to the positions where players are most likely to move from. No first baseman is going to be asked to play shortstop. Instead, they will likely be moved to a corner outfield spot (see Moss, Brandon) or to third base (see Cabrera, Miguel). Players usually move up or down the defensive spectrum one spot.
With that in mind, let’s go through the values from center field to first base.
With the outfield, we have the most opportunities of players playing different positions — this is where we find the top three innings totals. Players moving from center field see a 9.4 run bump when moving to right field and an 8.8 run bump going to left field. In addition, the difference between right field and left field is 0.7 runs. With these data points, it can be said that center field is just over nine runs harder than right field and left field.
Next, we move down to the eighth and ninth spots, where the corner outfielders move to first base. The differences aren’t really that close, with left fielders seeing a 5.5 run increase and right fielders seeing a 9.3 run increase. If we take a weighted average of the two, we get 7.3 runs gained from moving from left or right field to first base.
In between, we have the infield, where the third-highest total is moving from shortstop to first base. The fourth-highest innings total is between shortstop and second base, and the difference is 3.0 runs. From shortstop to third base (sixth-highest total), the difference is 2.8 runs. Finally, the second and third base (fifth highest) difference is basically zero (-0.1). With these points, we get that shortstop is three runs harder than second and third base.
Moving on to first base from the rest of the infield gets murky. The top innings total is third to first (seventh-most innings) with a difference of 6.9 runs. The second to first (12th-most innings) is 4.2 runs. I am going to split the difference (more or less) and go with 5.5 runs here.
So, here is the defensive spectrum using just defensive numbers:
- Center field: 7.5 runs harder than…
- Shortstop: 1.5 runs harder than…
- Right field and left field: 1.5 runs harder than…
- Second Base and third Base: 5.5 runs harder than…
- First base
OK, these values contain three big differences from the original list. The total spread is only 16 runs for these positions instead of 20 runs. Shortstop is no longer the hardest position, with center field moving above it. Finally, second and third base are less difficult than left field and right field, instead of being 10 runs apart. Here are the run value differences between just the outfield and infield positions (very limited sample):
- Third base is 1.6 runs harder than left field
- Second base is 2.3 runs harder than left field
- Third base is 1.1 runs harder than right field
- Second base is 1.5 runs harder than right field
Now, I am getting to the part of the process where things get murky and these results somewhat contradict the previous values. The positions are close to the same difficulty, but it seems the infield positions may be a bit tougher. I could see moving second base and third base together with left field and right field, but for now I will lean on the larger samples and keep them separated. Let’s move on to the hitting differences between positions.
Using offensive values to find the defensive spectrum is quite a bit easier. Why offense to find defense? What is this, the Gold Glove Awards? Well, the idea here is that major league teams will find the best hitting players they can and then put them as high up on the defensive spectrum as possible. Then they take the next best hitter and do the same thing, and so on and so forth.
I summed the offensive runs produced over for each position over the same time frame as the UZR information used above. From there, I took the average runs produced per team for each position. Here are the results with the differences between each category:
| Difference in Offensive Production per Position, 2002-2014 |
|---|
| Position | Weighted Runs Above Avg (wRAA) | Difference |
| C | -14.0 | — |
| SS | -11.1 | 2.9 |
| 2B | -7.6 | 3.5 |
| 3B | -4.0 | 3.6 |
| DH | 2.9 | 6.9 |
| CF | 3.0 | 0.1 |
| LF | 5.9 | 2.9 |
| RF | 6.8 | 0.9 |
| 1B | 8.9 | 2.1 |
Some notes on the list before I morph it with the defensive values. The range from shortstop to first base is now 20 runs instead of 16 runs. Catcher is easily the worst hitting position, with shortstop coming in second-worst, rather than center field. Center field actually makes a jump past second and third base, and is fairly close to the other outfield spots, and being on par with the designated hitter. The DH has really been a production sink compared to its potential these past 13 seasons.
Now, let’s compare the two rankings. Truthfully, I would not have a problem with a person using either list, but do I think the answer lies somewhere in between. If people want to use their own weighting of the values, go at it. As long as they use the basic frame work, they won’t be “wrong.”
- Center field: six runs harder than…
- Shortstop: three runs harder than…
- Second base, Third base, right field and left field: seven runs harder than…
- First base
Now, let’s seek some level of agreement between the offensive and defensive runs differences. Starting with the outfield:
- Center field is nine defensive and three to four offensive runs harder than right field and left field.
- Right field and left field are seven defensive runs and two to three offensive runs harder than first base.
Now to the infield:
- Shortstop is three defensive runs and 3.5 offensive runs better than second base
- Second base is 0 defensive runs and 3.5 offensive runs better than third base
- Third base is 5.5 defensive runs and 13 offensive runs better than first base
Taking an average of the defensive and offensive values, the scale becomes:
- Shortstop: 3.25 runs harder than…
- Second base and center field: 1.75 run harder than…
- Third base: 4.5 runs harder than…
- Right field and left field: 4.75 runs harder than…
- First base
Still with me? OK, then let’s perform a little clean-up of our values:
- Shortstop: three runs harder than…
- Second base, center field, third base: six runs harder than…
- Right field and left field: five runs harder than…
- First base
You might notice that the catcher was missing from all of that. Let’s add it in. We found it to have the lowest offensive production by threeruns over shortstop and therefore should get the highest positional adjustment. Originally it was five runs, but three runs is within reason. So without the designated hitter, the final defensive adjustments for WAR are:
| Final Defensive Adjustments (No DH) |
|---|
| Position(s) | Runs/162 Games |
| C | 7.75 |
| SS | 4.75 |
| CF, 3B, 2B | 1.75 |
| RF, LF | -4.25 |
| 1B | -9.25 |
The biggest change I can see is a shrinking of the range. The order stays the same, but players don’t get as much credit for playing harder positions. Now with all the rest of the positions done, it is time to finally move to the most controversial adjustment — the designated hitter.
With the designated hitter there are two adjustments. The first is where to put a defensive value on a player who doesn’t play any defense. The theory is that the DH would be able to field like a first baseman with minimal defensive ability, which has been historically set at -15 runs. The DH’s value then would start below that figure.
Not all the DHs would be at that -15 value, obviously. Some could have been average defensively at first base, but for a different above-average defensive first baseman also being on the team. This hypothetical DH would be overly penalized for his defense for really no reason. I think there needs to be some adjustment, but perhaps it doesn’t need to be as drastic. I could envision any value between -5 and -15. But before I settle on a value, let’s go over the second DH adjustment — the DH penalty.
The first time I was introduced to the DH penalty was in 2007, when I read The Book. It said:
We also find that players are less effective when used as designated hitters, suffering about half the performance penalty incurred when pinch hitting. Interestingly, the DH penalty does not vary significantly from player to player, indicating that the time between at-bats is something that some players are able to withstand and others are not. (Or, perhaps we’re simply seeing the effect of slightly injured players being used as designated hitters. Our data do not allow a more detailed study of this, so, we will not examine this question further.)”
Well, the information is now available. Looking at players who hit as DHs from 2002 to 2014, I found the DH penalty to be 8.4 runs per year. Now, the spread depends on whether the player is normally a DH or normally in the field. For the players who are normally a DH, the penalty is only 4.8, whereas it is 9.2 for those who normally play a position in the field. It seems to take a certain player to be a successful DH. Or does it? Players who hit as the DH and didn’t go on the disabled list during that season had a seven-run penalty compared to playing their normal position. The players who used the DH as a spot to regain their health performed 12.4 worse runs at the plate than when they were in the field. Summing up:
| Designated Hitter Penalty Conditions |
|---|
| Condition | Runs/600 PA |
| Overall | 8.4 |
| Normally a DH | 4.8 |
| Normally in the field | 9.2 |
| Healthy | 7.0 |
| Some DL Time | 12.4 |
I’m a little uneasy saying this, but I would put the DH on par with first base in terms of value, as the defensive adjustment and DH hitter penalty offset each other. The DH penalty (8.4 runs) is more than one standard deviation (eight runs) from the mean. This method gives the DH a below average defensive rating, but then takes into account how hard it is for hitters to move to the DH position. In the end, I recommend the following scale:
| Final Defensive Adjustments |
|---|
| Position(s) | Runs/162 Games |
| C | 7.75 |
| SS | 4.75 |
| CF, 3B, 2B | 1.75 |
| RF, LF | -4.25 |
| 1B, DH | -9.25 |
If a scale like this one is used, previous free agent values may need to be re-worked. Matt Swartz’s in “Bargain Hunting in the Free Agent Market” in the The Hardball Times Baseball Annual 2013 found:
The cost per WAR of 2B, 3B, SS and C was an average of $4.92 million, while OF, 1B and DH cost an average of $7.15 million per WAR. The difference dwarfs some of the findings above and suggests that the best way for teams to spend their money on the free agent market is to develop their own outfielders and bring in athletic, slick-fielding infielders from other teams.”
The WAR values for the first set of players will be less with this adjustment and higher for the second set. Sadly the writing community is probably behind the times and teams have already figured out the difference in values. In terms of next steps, I think it would make sense to go back and look at these values every few years to make sure nothing changes. Or take the information we have and look at the 2002 to 2008 time frame and then from 2008 to 2014. No matter what gets done, it seems like we are a bit behind major league front offices in giving position players too large of a range of values for playing certain positions. The range is likely much narrower.
References & Resources
- Special thanks to Peter Melgren for helping to compile the information on the position to position UZR comparisons.
- The Book: Playing the Percentages in Baseball, by Tom M. Tango, Mitchel Lichtman, Andrew Dolphin
- The Hardball Times Baseball Annual 2013, edited by Dave Studeman
it is fantastic article wow~
Title should be: David Ortiz – Hall of Famer
Great article–very well done.
Eh, even with his WAR boosted by the adjustment (not even counting his games at 1B), he’d be at 54 career WAR. That’s not HoF caliber, no matter how “feared” you are.
Edgar, however, goes up to 76 WAR. No doubt status.
What has Ortiz done that Bonds or McGwire have not done better?
Ringz
Hit very well even with the DH penalty?
There is a fairly obvious reason for the shrinking of the range in adjustments. The rise in strikeouts over recent seasons means there are fewer balls in play, thus fewer chances for fielders to affect the course of the game. Your tweaking work certainly passes that eyeball test, and I suspect breaking down the ’02-’14 timeframe will show the numbers tracking at least fairly well with the K numbers. (Also a good reason to keep following the numbers.)
Good food for thought. Thanks.
My own suspicion is that positional adjustments should be in WINS, not runs.
Convert back to runs if you must have everything in runs.
You can’t get the WAR or win value without first finding the run values. Runs are used to determine wins, not the other way around.
Yeah, but having found a positional run value, you can convert it to wins and use the win value for the adjustment for different years.
A lower run environment depresses the positional value if measured in runs, that’s EXACTLY what Jeff is observing here. Fewer runs, the value of a CF vs a 1st baseman declines, and you’d EXPECT that, and expect the decline to be about proportionate to the increased importance of a run.
Great article, seriously, but I have one question: WHY?
Are you saying “Why adjust our statistics to more accurately represent their real world values?” I would hope that answer is self-evident…
we should quickly update for the shrinking of the range in adjustments.
this article is revolution.
Awesome work! I’ve been wondering about this for a while, but I don’t have the math for it, haha.
I’d love to see someone tackle the followup study you suggested.
This was enlightening. Great work, Jeff!
I’m very interested in positional adjustments, and have (for awhile) thought that fWAR does a bit of a disservice to bat-only 1B and DH. This is a fascinating article, and a very important one.
That said, I think that as it’s currently constructed part of the problem with the positional adjustment is that it implies something about scarcity, and if I were an MLB GM trying to value players I’d much rather scrap positional adjustments altogether and instead evaluate the market relative to the quality of talent at each position in the offseason. Fundamentally, it’s an issue that you *have to* play somebody at first base–you can’t play two shortstops to maximize WAR, for example.
In other words, should we really be penalizing David Ortiz so harshly for being a DH?
Jeff, terrific work and concept.
Did you control for age at all and if not, do you think it would be at all useful to do so? If (some) people are shifting positions partially because of age I wonder if that could be a confounder.
My thoughts exactly. This could explain why it appears SS are overvalued in the current system. Once they can’t be SS then they are moved to another, easier position, thus only prime years are counted.
The data we used was separated into single seasons, so age doesn’t play a factor in these results.
So are teams better off developing catchers or signing the best FA catcher out there?
Thanks for the update Jeff. I had been wondering if the positional adjustments were still applicable over the last few years.
I do like your idea of a follow up splitting the data into 2002-2008 and 2008-2014 buckets. It seems that more teams have embraced the concept of defensive runs saved, meaning that teams are more likely to move players down the defensive spectrum to improve their overall defense than they are to move players to a more challenging position to get better bats in the lineup.
So as, say, the pool of LFs loses the Adam Dunns and adds the Alex Gordons, the difference in pure talent between the LF pool and the pool of players at tougher positions should decrease. This might be the cause of the narrowing range of positional adjustments.
One of the things I liked about Win Shares was it measured players from a hypothetical 0 value. Designated Hitters were easy. The defensive value was zero and they were worth as much as they hit. There were fielding adjustments but those were only for defensive purposes.
Not saying that Win Shares were at all superior to WAR, but that part was elegant. The assumption that a replacement player can play average defense makes things complicated.
Thanks for the support and I will get to answering you questions in a day or so. -Jeff
Such an interesting article. The positional adjustment is one of those really tricky subjects that we all like to ignore most of the time. Thanks for tackling such a messy subject so fearlessly 🙂
(Provided that WAR handles defense correctly)
“Players moving from center field see a 9.4 run bump when moving to right field and an 8.8 run bump going to left field.”
You mean that they save 8-9 more runs when making that move? Why? I think your starting assumption is that the typical CF makes a greater % of plays on comparably-sized buckets than a typical corner OF. Therefore, what is defined as saving a run above average requires a more difficult play, is that correct?
But what if a typical CF has fewer opportunities than a typical corner OF? That would also contribute to a run difference. Don’t you have to separate these two factors? Since you are looking at runs saved per innings or games, not per plays, it seems to me that this would have a significant effect on the results.
Thank you, this is much more reasonable.
I still have an issue with defensive adjustments in general since there is some selection bias in what players get moved and when (eg not all CF’ers get moved to RF just those who have the arm, and only those players who can hit well get moved to 1B), and a player may be playing a position that does not fit his talent level but fits the organizations needs (eg Machado moving from SS to 3B, and Arod moving from SS to 3B, and Papi playing at DH instead of 1B), or perhaps because a player has icon status (eg Jeter remaining at SS his entire career).
I also don’t agree with morphing offensive and defensive for the position adjustments for obvious reasons. We are using this to determine best or most valuable player, not to provide a handicap to ensure a level playing field. Leave offense out of it. If you can’t hit then defense is your game and defense value alone should determine the adjustment.
But despite the latter objections, it is progress, much needed progress. Perhaps once the various WAR’s implement the changes I will give it more consideration in comparing players in different positions rather than just for same position
Also, in your offensive approach, are you using batting runs above average, or all offensive runs, including baserunning, above average?
Awesome job. A couple thoughts:
Is it possible that infield play (except first) requires a skill set that is less correlated with the underlying abilities required for hitting than outfield play? If so, the findings from the offensive component of this analysis could underrate the difficulty of outfield play.
In an different vain, is there a potential selection bias when comparing the play of players who have been asked to switch positions? Perhaps those players were particularly versatile, which might reduce the overall range of difficulty that you would see in the total population of players.
Just pondering here, curious to know your thoughts!
Great article, it echoes a lot of what I’ve thought about positional values. I do have some questions, though maybe I’m just thinking out loud here…
Is ‘defensive value’ potentially subject to selection bias? As in the players that are changing positions in the data set are representative of those at the edges of the spectrum. E.g. Players who moved from second to short were only the best second basemen, not indicative of group performance or expected performance of an average second basemen. The data set is unlikely to include many innings from the worst second basemen. Does using the harmonic mean negate this?
Also this raises another issue. When looking at SS -> 2B and assigning one value we are really talking about shortstop defense because we are only talking about players who can play shortstop. These defensive values assume that positional adjustments are equal going both ways. It assumes that a second basemen going to first will save 4.2 runs and a first basemen going to second will cost 4.2 runs. This seems counter intuitive as it implies that you can arrange players on the field however you want with little consequence. The data set in this case must be made up entirely of second basemen going to first base, and few if any first basemen going to second. Runs saved and lost is also a function of opportunity, a first basemen playing second will have far more opportunities to lose value when playing second base than the second basemen has to gain value playing at first. This is the main reason we see the offensive difference so much higher than the defensive. 4.2 significantly underrates a second basemen’s abilities compared to first.
This leads to my next point. You end up with two different sets of values. A defensive positional adjustment, and an offensive adjustment. Using 2B -> 1B again you have 4.2 and 16.5 respectively. You had trouble reconciling these differences and ultimately you end up averaging them, but in reality you are getting two measurements of two different things. The 4.2 is the defensive value gained of a 2B playing 1B. 16.5 is the defensive value lost (in the opinion of GM’s and managers deploying resources to the best of their knowledge and ability) when playing a 1B at 2B. 12.3, or the difference between the two, is the tactical, inherent difference between the two positions on the field defensively. In other words that is the value gained / lost by virtue of correctly / incorrectly deploying your resources.
Ultimately you average the two numbers, and settle on a number close, but a little lower than the 12.3 (11). I am not totally sure what makes sense mathematically, but I feel like both numbers should be included in the WAR calculation in some way.
I agree with your thoughts on the DH, as the position has been undervalued for years. While I think your number is much more correct than FGs current solution, I’d like to see something a bit more elegant. I think ultimately a more correct positional adjustment will be in some way tied into pitcher hitting in the NL … which is another value that is glaringly omitted from WAR calculations.
Lastly, this is great work, and it should open up some eyes to the value of some sort of rolling adjustments made for historical data based on league wide trends. The sports is constantly adjusting to itself, and part of the fun of statistics is looking back at long gone players and comparing them to todays. I think this study hints at some potential issues with looking at WAR for players through different eras.
When comparing defense between two positions, was the runs value fixed for a specific number of opportunities? Part of the defensive spectrum is that the up the middle positions get more chances than the others. The very best 1B might be +5 per season, while the very best SS is +25, in part because the SS might get twice as many competitive chances.
Great article! Not only do increases in strikeouts affect the impact a defensive player can have on the game, but reduced offense (fewer runs scored per game), whether that reflects strikeouts or other factors, mean that the range of defensive value should be less to reflect that. In fact, I wonder if the new standard ought to be expressed as a percentage of league-wide offensive production, rather than a static number of runs adjusted for each position?
Fascinating stuff, as usual.
I’m thinking though, that the weighted average may not be the best way to adjust for sample size differences, here. A sample of 100,000 innings for example, isn’t anywhere near twice as accurate as a sample of 50,000. The unweighted average actually ends up closer to being properly weighted than the weighted average does.
Just taking unweighted averages of how each position compares to all others in that 2002-2014 defensive data, I get this:
-5.0 SS
-4.1 CF
-0.5 2B
-0.4 3B
+0.5 RF
+2.3 LF
+7.3 1B
Perhaps there’s some way to adjust for sample sizes from there, but the adjustments shouldn’t be that large.
A couple of thoughts about using offensive levels to calculate defensive spectrum:
1. At times there are clusters that would skew the data. 20 years ago there were a number of great-hitting shortstops. Calculating the defensive spectrum then would have led to the conclusion that playing shortstop was not that difficult.
2. There is an additional scarcity at second, third, and shortstop, since only right handed people can play those positions. Lefthanders who could handle the position otherwise are forced to play first base or the outfield. That means that the outfield and first may be more difficult than the offensive levels would imply.
I suppose you could include catchers in the scarcity category too, although the refusal to play left-handed catchers seems to be more tradition than the ability to handle the position (a new inefficiency to be exploited?). Catcher is a unique position anyway, since despite being at the top of the defensive spectrum, very few catchers move to shortstop or second base.
Turtles all the way down…
I was wondering how much interleague play affects the DH values. Often, the NL team will keep their 1B in the field and just use a bench player as DH. But maybe that’s already included in the “Normally in the Field” category of that one table.
I used to think that replacement levels were determined independently by position based on how well AAAA types do at that position. Why wouldn’t this work? Then you wouldn’t have to worry about hypothetical positional adjustments. Each position would have it’s own baseline.
One thing I wonder about if there’s a general skill difference with players who shift between infield and outfield. For instance: If it’s more likely that true-talent infielders can play passable outfield than that true-talent outfielders can play passable infield, then the players who switch between infield and outfield will be more likely to be playing in their natural position in the infield than in the outfield. That would mean that the switching measures make the outfield positions look harder than they really are. For instance, if your average 2B can play RF equally well, and your average RF can’t play 2B at all, then 2B-RF switchers would come out even even though 2B should be higher on the defensive spectrum.
“The cost per WAR of 2B, 3B, SS and C was an average of $4.92 million, while OF, 1B and DH cost an average of $7.15 million per WAR. The difference dwarfs some of the findings above and suggests that the best way for teams to spend their money on the free agent market is to develop their own outfielders and bring in athletic, slick-fielding infielders from other teams.”
A few factors we should take into account here:
1. Players tend to decline offensively and shift rightward along the defensive spectrum as they get older.
2. It is in the team’s interest to back-weight contracts (i.e. pay more in the later years rather than the earlier years, due to the time value of money).
3. On long-term contracts, we shouldn’t expect the distribution of annual salary to match up with the distribution of value from year-to-year. In fact, due to the first two points, we should expect the salary to go up while the value is going down and as the player is moving rightward across the defensive spectrum.
This doesn’t necessarily mean that teams are overvaluing 1B/OF/DH types — if they are accurately forecasting a player’s future value and movement across the defensive spectrum, it just means that they are deferring some of the compensation for his earlier performance until later in his career. For example, when Joe Mauer signs for 8 years, $23 million per year, he’s obviously going to get paid more $/WAR when he’s playing 1B/DH then when he’s playing C, but that doesn’t mean the Twins value that production more.
I haven’t read the book – does Swartz try to account for this at all?
Jeff, I wonder if a more accurate view of the replacement batting level for the different positions would be found if you excluded starters. I suspect that some positions are a little “deeper” than others, but perhaps I’m incorrect. Obviously, its quite difficult to determine who qualifies as a starter and who does not, but I might suggest using all players who spend any time in the minor leagues (excluding rehab assignments). That should identify the replacement population as well as anything.
Jeff: Would your offensive production comparison change at all if you looked at median performance (or 20th percentile performance)? Mean levels can be distorted by a few great hitters at a position, which isn’t really relevant to your purpose here. In effect, we’re trying to measure the differences by position of replacement-level players. While mean and replacement level offense must track reasonably well, you might see non-trivial differences in a few cases.
He used the harmonic mean for his calculations. This will give a result that gives less weight to outliers.