# Pitch Type Linear Weights

The* Pitch Type Linear Weights (“Pitch Values”)* section on FanGraphs attempts to answer the question, “How well has a batter/pitcher performed against/using a certain pitch?” Pitch values make use of the changes in average run expectancy from one count to another and while the changes in run expectancy between an 0-0 count and a 0-1 or 1-0 count are obviously very small, when added up over the course of the season, you can get an idea of which pitch a hitter was best against. If they hit one pitch especially hard or they are less likely to chase on sliders, these successes will show up using Pitch Type Linear Weights. Also, if a hitter swings and misses on a specific pitch frequently, this problem will show up as well.

You’ll notice that there are two different types of Pitch Type Linear Weights: total runs by pitch (which is shown as wFB, wSL, wCB, etc.) and standardized runs by pitch (shown as wFB/C, wSL/C, wCB/C, etc.). The first category is the total runs above average that a hitter has contributed against that pitch or total runs saved by a pitcher using that pitch. However, it is tough to compare these total numbers since hitters see different amounts of each pitch. The second category corrects for this, standardizing the values on a “per 100 pitch” basis. In other words, when you see wFB/C, that represents the average amount of runs that hitter produced against 100 fastballs thrown.

**Calculation:**

You would very likely never choose to calculate pitch type linear weights or pitch values on your own, but the basic mechanisms are pretty straightforward if you want to put in the effort to customize your own values.

Essentially, there is an average run expectancy for each count (0-0, 0-1. 1-0, etc) and the change from from one to the other is the run value we use to create the pitch value. For example, if we start in a 0-0 count we begin at a perfectly average 0.0 run value (because all PA start as an average PA) and then the run expectancy of a 1-0 count is 0.04, meaning the value of taking that pitch for the hitter was +0.04 and -0.04 for the pitcher. If the next pitch is a strike, the run expectancy of a 1-1 count is about -0.02, so the batter gets -0.06 and the pitcher gets +0.06 from moving from the +0.04 world to the -0.02 world. Those run values are attached to the type of pitch thrown in each case, so if both were fastballs, the total wFB would be -0.02 for this at bat so far. Or -1.00 wFB/C, when scaling to 100 fastballs.

The numbers used above were rough estimates meant to demonstrate the concept and are not the precise values we use. Those values are included in the table below (**table coming soon!**)

Now imagine it’s a 1-1 count and the run value sits at -0.02. If the batter singles, the run value of that single is roughly 0.45, which means they will get a +0.47 for that pitch and the pitcher will get a -0.47 for that pitch. This brings the total for the three pitches (assuming all fastballs) +0.45 for the hitter and -0.45 for the pitcher. If the first two pitchers were fastballs and the third was a changeup, the wFB would be -0.02 and +0.47 wCH for the hitter.

Run values for the offensive actions vary by run environment, but this can serve as a helpful guide.

The run values of each count are based on the average offensive output in that count relative to the average offensive output in a 0-0 count and are generated using Linear Weights. These weights are averaged across all counts and are not conditional on the base-out state or the inning. A first pitch ball is a first pitch ball no matter the situation using this method. Also, the count change is the only thing that is captured using this method. A swinging strike and a called strike are the same and a ball on the corner and one way outside are identical. Additionally, a foul ball after two strikes has a run value of zero even though it is technically a “strike,” because the count did not change.

**Why Pitch Values:**

Pitch values allow you to see how “successful” each pitch has been over the course of a season. You may know that a hitter has a .350 wOBA or that a pitcher has a 3.10 FIP, but there are more fine grained details to consider. Has a particular pitch been effective for a pitcher? Do hitters struggle to produce against sliders? When the hitter puts a changeup in play, is it usually an out or a home run?

Pitch Values are an accounting method for attaching run values to each specific pitch rather than each specific plate appearance. There are reasons to be cautious, discussed below, but if you want a retrospective look at which pitches were crushed and which were effective, pitch values will provide you with some approximate totals. If you see a wFB/C of 1.50, you can generally say that hitter was successful against fastballs that year. It’s not always that simple, but that’s the basic idea.

**How to Use Pitch Values:**

Pitch Values can be a fun tool, but you also have to be careful about two major issues when using them. First, Pitch Values aren’t predictive. Looking at a pitcher’s wFB/C doesn’t tell you much about his true talent or about how he’s going to perform using his fastball in the future. Great pitchers will have better numbers, but you can’t treat pitch values as a strong measure of true talent.

Second, pitching is complicated and interdependent. Sure, you got a batter to swing and miss at a fastball, but that swing and miss didn’t occur simply because you threw a good fastball. That swing and miss occurred in part because of the quality of your other pitches, your location, and the sequencing of those pitches. In other words, when you get a +0.08 on a specific pitch, that single, solitary pitch isn’t the only reason you got a positive outcome.

If you have a great fastball, you’re going to usually have a great wFB, but if you also have a great slider, there’s a good chance it will help your wFB too. Pitch values are about the change in run expectancy against various pitches, or the production against those pitches. You can’t leap from *performance* against a pitch to the *quality* of the pitch. Baseball just isn’t that simple. Use these numbers appropriately as a reflection of what happened, not necessarily a method to explain why something happened.

**Context:**

A score of zero is average, with negative scores being *below* average and positive scores being *above* average for both hitters and pitchers. A positive outcome for a hitter is equally negative for the pitcher, but the numbers are calculated so that positive values equate to positive outcomes.

In general, pitches will generally fall somewhere between +20 and -20 runs, with the most extreme pitches touching +/-30. This is obviously conditional on how often the pitch is thrown so a very effective pitch that is thrown sparingly might look less impressive than a solid pitch which is thrown often. For example, fastballs fall into the -20 to +20 range regularly, but sliders are more typically in the -10 to +10 range. On a per 100 pitch basis, the range shrinks to around -1.5 to +1.5 runs for fastballs and -5 to +5 for other types of pitches. Again, you’ll see some extreme scores on either end of the spectrum, but that’s the range you will usually observe.

**Things to Remember:**

● This stat has limited predictive power. It can show you what pitches a hitter has had success with in the past, but you should be careful in extrapolating those results and projecting the future. It’s a descriptive statistic, not a predictive one. The year to year correlation is below 0.25.

● Beware of sample sizes! Pitches can be misclassified and a handful of good outcomes against a particular pitch can dramatically swing the outcome without sufficient data.

● Pitch Type Linear Weights can be used to evaluate hitters and pitchers. Positive values are *always* good for the player in question.

● FanGraphs has Pitch Values based on Baseball Info Solutions pitch type data and PITCHf/x pitch type data. The calculations are the same, but they draw on different pitch classification protocols.

**Links for Further Reading:**

Pitch Type Linear Weights – FanGraphs

Pitch Type Linear Weights Explained – FanGraphs

Searching For The Game’s Best Pitch – Hardball Times

Steve is the editor-in-chief of DRaysBay and the keeper of the FanGraphs Library. You can follow him on Twitter at @steveslow.

Does a positive linear weight for a hitter mean he has more success against it, or will these results be the inverse of the pitching? Judging by Khalil Greene’s large negative value against sliders and Pujols large positive values on all pitchers, I’m guessing the former. Would probably be helpful to put that somewhere in the explanation.

On July 8th 2012, San Diego Padres outfielder Will Venable will hit a homerun at 2:17:04 PM PST. He will trot around the bases and will fart while he crosses home plate approximately 19.56 seconds later.