The key component in a WEZ score calculation is the standard deviation (SD) of the population of data being referenced. A smaller (“tighter”) SD indicates that the league scores were generally bunched closer to the league average, making outlier performances rarer and that much more “special.” A larger (“looser”) SD indicates that the league scores were spread out further from league average, making outlier performances more common. So in dividing by SD we are effectively grading how special a pitcher’s performance was relative to his league that season.
The first step in calculating a pitcher’s seasonal WEZ score (sWEZ) was to collect the league-wide WE scores for all starting pitchers from a particular season into one bin, then calculate the mean (average) and standard deviation (SD) from those WE scores. Each pitcher’s sWEZ was then calculated according to the formula below:
Each game’s WE (shown as WEi above) is subtracted by the league average for that particular season. The differences were added for the entire season, yielding a “net sum” which was then divided by the number of starts. The result was divided by the league SD.
Here are three simple scenarios to demonstrate. In all cases, consider the league mean as 0.600, and league SD as 0.300.
Scenario A: Pitcher makes ten starts, with every start having a WE score of 0.800.
Scenario B: Pitcher makes ten starts, with five WE scores of 0.800, and five WE scores of 0.400.
Scenario C: Pitcher makes ten starts, with every start having a WE score of 0.400.
In Scenario A, the pitcher’s average delta with the league over the entire season can be expressed as ∑(0.800 – 0.600) / 10 = 0.200. Dividing by the league SD results in an sWEZ value of +0.667. This number states that the pitcher performed at a level two-thirds of a standard deviation above the league average.
In Scenario B, the pitcher’s average delta with the league over the entire season will result in a net score of 0.000 because the five positive differences will cancel out with the five negative differences. Dividing by the league SD results in an sWEZ value of +0.000. This number states that the pitcher performed at a level equivalent to the league average.
In Scenario C, the pitcher’s average delta with the league over the entire season can be expressed as ∑(0.400 – 0.600) / 10 = -0.200. Dividing by the league SD results in a WEZ value of -0.667. This number states that the pitcher performed at a level two-thirds of a standard deviation below the league average.
