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# Spring Cleaning - Tale of Two Players: Adjusting wRAA Value for Lineup Position and Team Quality

In 2008 Grady Sizemore and Josh Hamilton had similar seasons Grady played in 157 games with and 0.384 wOBA and Josh played in 156 games with a 0.385 wOBA. Grady had a wRAA (link) of 34.4 and Josh's was 33.1. Even though they played in the same number of games, Grady's wRAA was higher because he had 41 additional plate appearances during the season.

The reason a player can have additional at bats while playing in nearly the same number of games is:

1. The place in the batting order for the player. The first position in the lineup will get an additional 11% more at bats then someone that always bats second

2. The offensive nature of the team that the player is on determines a player's at bats. A good hitting team will give the players on the team more chances to hit.

The problem is that some players might be considered inferior for these two reasons when they should have the same results (same wOBA in same number of games). wRAA is a component to to the WAR value on Fangraphs. The two players could have produced the the same output if they had been higher in the lineup or on a different team. Looking at Josh and Grady's numbers, Grady's additional 1.3 wRAA would lead to a WAR increase of 0.13 (wRAA/10). If a person is using a previous season's WAR to compare players, the team quality and batting order position needs to be taken into account.

If a person wants to adjust a player's wRAA for batting order and team ability, here is the procedure.

Batting Order adjustments (2008 Data) - I took the total number of at bats at each position. Then I decided to adjust all batters as if they were in the number 5 spot in the lineup. For 2008, here are the at bats at each position along with the lineup position adjustment.

 Position PA Multiplier for #5 spot Batting 1st 22946 0.9100 Batting 2nd 22416 0.9316 Batting 3rd 21862 0.9552 Batting 4th 21382 0.9766 Batting 5th 20882 1.0000 Batting 6th 20364 1.0254 Batting 7th 19790 1.0552 Batting 8th 19286 1.0828 Batting 9th 18686 1.117

The lineup positional adjustment is found by dividing the at bats at that position by the number of at bats in the 5th position.

The problem, with just these numbers, is that players can bat at several positions over a season. I plotted the 9 points and created a regression line to help quickly determine the adjustment value.

Adjustment = 0.0255(average batting position) + 0.8783

r-squared = 0.9943

Team Offensive Adjustment (2008 Data) – Some teams just have better hitters and those hitters lead the entire team to have more plate appearances. To adjust for this, I took the 2008 league average in PA per game. Then I divided the Team PA/game by the League Average PA/game. This value can then be multiplied time the wRAA to adjust for team hitting ability.

Multiplier for batting position = 0.0255 * Average Position + 0.8783

So for the above equation, Josh get a multiplier of .961 and Grady get one of .904

Then I found the multiplier for the PA/G for each team.

For Cleveland the number is 0.9930 and Texas = 0.9656

With these values we adjust the player's wRAA

Josh = 33.1wRAA * (0.0255 * 1 + 0.8783) * 0.9656 = 30.71Adjusted wRAA

Grady 34.4 wRAA * ( 0.0255 * 3.24 + 0.8783) * 0.9930 = 30.87 Adjusted wRAA

It can be seen that both Mr. Sizemore and Hamilton both got some help from hitting high in the lineup and being on better than league average teams.