Re-Examining WAR’s Defensive Spectrum

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