## Using Z-Scores to Evaluate Pitch Effectiveness

We are yet to establish a truly effective method of measuring the effectiveness of a pitch and comparing pitches. One of the main problems with attempting to evaluate a pitch on it’s own is nearly impossible. If a pitcher has an exceptional fastball, that is going to elevate his slider. Another pitcher may have a slider with more “stuff,” but it will not rank as well without the other effective pitches in his repertoire.

I will attempt to create a method here that will allow us to measure effectiveness in an improved way, although there is no guarantee here that I will succeed.

Let’s start with the main things a pitch has to be effective. In theory, a perfect pitch would be thrown in the zone and generate whiffs, while allowing weak contact when it is put in play. Obviously, it is unreasonable to expect a pitcher to generate lots of whiffs inside the zone against major-league hitters, so throwing outside the zone is a necessity in baseball to get swings and misses.

So, I used two evaluators for pitch effectiveness. I formed my own measurement, Swing%+Whiff% (Sw+Whf%). Since many pitches are meant not to be thrown in the strike zone, I did not include Zone% or Strike%. The Sw+Whf% should evaluate the ability of a pitch to get swings, and swings and misses. That evaluator covers the “stuff” component of the pitch. For the second evaluator, I used xwOBA (expected OBA), which gives a “true” wOBA based off exit velocity and launch angles. This covers the contact management component of the pitch. These are not all weighted for the part they play in run scoring, so it is not perfect, but they should give us a solid idea of what a pitch could do.

Obviously, different pitches will have different average values for these evaluators. A breaking ball is going to create more whiffs than a fastball. Fastballs are easier to hit, and thus will have a higher xwOBA. These evaluators themselves can not be used to compare different types of pitches. This is where the Z-Scores come in to play.

A Z-Score measure how much something deviates from average. First, we take the standard deviation and mean of a data sample. Then, for the Sw+Whf%, we subtract the mean from the individual’s Sw+Whf%, and divide that number by the standard deviation. We have our Z-Score! If the Sw+Whf% is higher than average, the Z-Score will be above zero, which means it is better than average. If the Sw+Whf% is lower than average, the Z-Score will be below zero, indicating the pitch is worse than average. It is the same thing for xwOBA, except for xwOBA lower is better. So instead of subtracting the mean from the individual’s xwOBA, we subtract the individual’s xwOBA from the mean. Add the two Z-Scores together, and we have our total Z.

Example:

The average Sw+Whf% on four-seam fastballs, for pitchers with a minimum of 500 four-seamers thrown, is 63.78. The average xwOBA allowed on these is .347. Chris Sale owns an 85.89 Sw+Whf% and .238 xwOBA on his four-seam fastball. The Sw+Whf% STD is 7.14 and the xwOBA STD is .038.

Sw+Whf% Z-Score: (85.89-63.78)/(7.14) = 3.08

xwOBA Z-Score: (.347-.238)/(.038) = 2.86

Total Z-Score: 3.08 + 2.86 = 5.94

Sale’s 5.94 is an incredible score, with second-place Jacob deGrom sitting at 4.81, over 1 below Sale. After that, no one else even reaches 3.5. The Z-Score has no unit, so it can be slightly confusing. It is a measurement of how many standard deviations above or below average something is.

A few things to be careful of here. These numbers are not predictive. They are simply meant to measure the effectiveness of a pitch and allow us to compare different types of pitch in a more simplified way than run values. It is just a fun statistic to look at, not something used to project the future. We also have the same problem as run values. It is impossible to look at a pitch by itself, as a good fastball will elevate a good slider. I am attempting to determine something that will allow us to better differentiate a player’s specific pitches from each other, but for now, we have this. I will be posting all the specific pitch data and tables for each pitch for starters and relievers and doing some analysis in the next few days. This is just the introduction.