Thursday, October 23, 2014

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 19th 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. 

Saturday, April 19, 2014

NBA Playoffs First Round Prediction

Pacers in 5
Heat in 5
Nets in 6
Bulls in 6

Spurs in 5
Thunder in 6
Clippers in 6
Rockets in 7

Friday, March 7, 2014

History of Pitchers as Position Players

The various projection systems are the closest we can come to predicting future. I was thinking of what they currently lack, and the first thing that came to mind was pitchers as batters. I then checked how each team did with their pitchers last season. It turns out that the spread from the best team, the Dodgers, to the worst team, the Pirates, is less than three wins. The true talent level is much narrower than that, and there does not seem to be much advantage gained by including pitcher batting in projections. Instead, I decided to look at the history of pitchers as position players.


Since the first professional league in 1871, pitchers have never hit above the league average. Their wRC+ has steadily declined over the years, all the way to negative since the 1980s. Since the adoption of the designated hitter in AL in 1973, pitchers have never had a wRC+ over 10, except for 1974.


Given their terrible performance at the plate, it is good for fans that pitchers have come to the plate less and less over the years. The sharp decreases in 1981 and 1994 are results of shortened seasons. The reason behind this is the increased usage of relief pitchers. The slight downward trend in recent years might also be a result of managers realizing the importance of each plate appearance and the diminished performance by the starter as he goes through the lineup.


Fangraphs has an opaque way of calculating WAR for pitchers as position players. While Baseball-Reference forces 0 WAR onto the pitchers as a whole no matter how well they hit, pitchers can have positive to negative WAR on Fangraphs, as long as all the position players, including pitchers, add up to 570 WAR a year. After hovering around 0 WAR from 1973 to 2001, pitchers suddenly experienced a sudden drop in value in 2002 and have not recovered since. This is where Fangraphs’ non-transparent method confuses me. From 2001 to 2002, pitchers actually improved in terms of batting (from wRC+ of -11 to -7). The majority of the difference stems from positional adjustment. While pitchers received a boost 660 runs in positional adjustment in 2001, they only gained 546 runs in 2002 in about the same number of plate appearances. It seems that pitcher positional adjustment is not constant, though there is nothing on the site that explains how it is calculated.


This is not an article that is meant to explain anything. I am simply looking at the history of pitchers as batters in a graphical and pointing out the lack of clarity behind Fangraphs calculation of WAR for pitchers.

All statistics courtesy of Fangraphs.

Thursday, March 6, 2014

Brett Gardner and Positional Adjustment: CF vs COF

Brett Gardner is the typical center fielder, with speed and range in the field. The New York Yankees just signed him for a four-year extension of 52 million dollars, but to play left field alongside Jacoby Ellsbury instead of center field. There are concerns that Gardner’s bat may not play in a corner outfield spot, that his value would be lower at LF than at CF. This is the effect of the positional adjustment. As a player’s fielding contribution is compared to other players of the same position, we have to adjust our evaluation of a player based on where he plays in the field. The established positional adjustment has a CF getting a boost of +2.5 runs over a full season while a LF or RF gets a penalty of -7.5 runs. In theory, a CF moving to LF would gain 10 runs in the field to make up the difference, as they are now compared to worse fielders. I will be testing whether this statement holds true in reality.

Predicting LOB%

In my article last week, I developed xLOB% as a descriptive statistic to estimate a pitcher’s LOB%. In this article, I will attempt to predict LOB% of a pitcher using his statistics from the previous season. Despite its fairly weak predictive results, pLOB% explains 12.7% of the variation in a pitcher’s LOB% in the following season, better than Steamer’s projection and kLOB%.

Saturday, February 15, 2014

Estimating LOB%

Luck has been the explanation whenever a pitcher has a significantly lower ERA than his FIP. There are two statistics where luck plays a huge role, BABIP and LOB%. Using Steve Staude’s pitching stat correlation tool, we can see that BABIP only has a correlation of 0.156 from one season to the next, while LOB% has a correlation of 0.205, for pitchers with a minimum of 30 innings pitched from 2007 to 2013. These numbers are much lower than the correlation of K% or BB%, suggesting that a large portion of BABIP and LOB% are subject to random variation and independent of a pitcher’s skill. However, the correlation is not 0. They are not completely random, and a pitcher can still play a small role in controlling their BABIP and LOB%. Many writers, including Steve, have tackled the issue of BABIP using batted ball data. In this article, I will be estimating a pitcher’s LOB% for the current season. This is not supposed to be a predictive stat, but a descriptive one. Think of it as FIP. While FIP estimates the pitcher’s ERA using strikeouts, walks and homeruns, xLOB% estimates the pitcher’s LOB% given his other pitching statistics for the same season. I will be introducing pLOB% in the next article, which attempts to project LOB% of a pitcher for the following season.

Tuesday, January 21, 2014

Random Thoughts from Georgetown-Marquette

(Small sample size caveat: This is the second time I have watched a Georgetown game this season)

Let me run through the last minute of regulation, with Georgetown up by four with the ball: