An Update on Positional Adjustment

Positional Adjustment has always been a point of contention about WAR. While most understand the principle of positional adjustment, I doubt that anyone has really scrutinized the process behind the values for positional adjustment. The established values for positional adjustment were developed by Tom Tango using UZR data for players who switch positions over multiple years. He took some liberty with the numbers, and adjusted the values based on relation to offensive value and his own intuition. I have always wondered why so few people questioned these values and accepted them as they are, so I decided to verify these values on a slightly different methodology.

The methodology is not as difficult as it seems at first glance. The data that follows are taken from 2003, the first season where both DRS and UZR are available, to 2013. The defensive rate stats used are DRS and UZR per 162 games or 1458 innings. First, I look at every combination of two positions, excluding catcher. I look at all players who played both positions during a single season. Each player’s difference in defensive numbers at the two positions is weighed by the harmonic mean of their innings played at the two positions (I repeated the study weighing by the lesser of the innings played and the results remained almost identical). Each pair of positions created an equation such as CF – LF = 12.74. This means that players who played both CF and LF during a single season perform better in terms of DRS/UZR by 12.74 runs per 1458 innings in LF than CF on average, so the positional adjustment for CF should be 12.74 runs higher. After every pair of positions is completed, I perform a weighted linear regression with the weights being the total number of the harmonic mean of the innings between the two positions. This means that the difference for common position switches, such as LF and RF, are weighed much more heavily.

What are the results for my calculation on the positional adjustment compared to the established values?

POS	DRS	UZR	Est	Est Adj
CF	8.0	7.9	2.5	4.3
SS	4.7	3.6	7.5	9.3
2B	1.9	1.6	2.5	4.3
3B	-0.9	0.5	2.5	4.3
RF	-1.0	-1.7	-7.5	-5.7
LF	-4.4	-3.8	-7.5	-5.7
1B	-8.3	-8.1	-12.5	-10.7

The standard errors for the values calculated are around 2 runs.

Another question I have always had with the established positional adjustment values is that the values, even considering catcher and DH, do not add up to 0. I have adjusted the established values so that the positions excluding catchers and DH add up to 0, so we are comparing apples to apples.

What can we gather from the results?

Firstly, UZR and DRS differ only slightly in terms of the values, and the orders of the positional spectrum are identical. So where do they differ from the established values? The major difference is the order of CF and SS. While Tango had SS ahead of CF by 5 runs with CF getting the same value as 2B and 3B, my methodology has CF ahead of SS by about 4 runs and way ahead of the other infield positions. Another major difference is that RF and LF are much closer to the infield positions than established. All the outfield positions are undervalued and all the infield positions other than 1B are overvalued according to this methodology.

Some of this is attributed to the handedness issues addressed by Tango. While all players can play the outfield and 1B, the other infield positions are limited to right-handed players. He estimated this effect to add 3 runs to the infield positions other than 1B and to subtract 3 runs from the outfield positions. This conclusion is largely based on defensive stats of left-handed SS from the 19^th century, so I don’t know if that can be trusted at all and decide to bypass the handedness issue.

Clearly catchers and DH have to be added to complete the positional adjustment spectrum. I would suggest basing the catcher’s positional value on both their batting and baserunning value such that the average catcher has the same WAR as the average position player. From 2003 to 2013, the catchers have been collectively 3617 runs below average in terms of offensive value. Pro-rating it to 690 PA, which is roughly 162 games during this period, the catcher would receive a boost of 11.7 runs from the positional adjustment.

The process for estimating the value of DH is much more difficult. I took a look at all the players who accumulated more than 100 PA at DH in a single season from 2003 to 2013 and how they fared at 1B defensively. Either weighing it by their PA as DH (which should be unbiased but highly imprecise, since the players weighed more heavily have very few innings on the field) or (which should overestimate their defensive ability, since the players weighed more heavily are occasional DHs), DRS has the DHs about 7 runs below average at 1B and UZR has them about 5 runs below average. The DH penalty has been revisited by MGL last year and he found that a player loses around 14 points in wOBA as DH. That would translate to about 7.7 runs over 162 games. So, overall, this implies that DH should receive a positional adjustment higher than 1B, simply because their disadvantage hitting wise outweighs their shortcoming in the field. Of course, this seems implausible, and the reason can likely be attributed to the overestimation of DHs as fielders. Changing the minimum number of PA at DH to 200 or 300 lowers their fielding value slightly, to around 10 runs below average by DRS and around 6 runs below average by UZR. However, this does not change the fact that DHs appear to deserve a higher positional adjustment value than 1B. The fact that these players are put at DH implies that their defensive abilities are clearly below the average 1B, so that does not make sense. These players should be held accountable for some of the DH penalty due to their inability to play any of the positions at the league average level. Arbitrarily, I decide that DHs should only receive 50% of the DH penalty. This means that DHs are valued at 4.4 runs below 1B, receiving a boost of 3.8 runs from the DH penalty and treated as a 1B who averages 8.2 runs (average of DRS and UZR estimate) below average in the field.

Averaging the estimates from DRS and UZR and readjusting the values so that the center is back to 0, the final positional adjustment is as such:

POS	Runs
C	11.7
CF	7.2
SS	3.4
2B	1.0
3B	-0.9
RF	-2.0
LF	-4.8
1B	-8.9
DH	-13.3

While all of the positions are affected by less than 5 runs compared to the established values, I think it’s imperative to get the estimates as precise as possible. WAR, the central metric for player evaluation, is highly dependent on positional adjustment values. A potential change of 0.5 WAR can change the perception of a player’s value significantly, and over a player’s career, that difference can add up to a substantial amount. It’s time to improve our estimates of positional adjustment, so that our estimates of player value can be as precise as possible, and that there is one less opaque aspect about the framework of WAR.