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 righthanded 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 lefthanded 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. Prorating 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.