Command Post February 29, 2008
Locational Run Values

In the last couple of weeks there have been several great articles written about the run value of different pitches. These articles have explored how much every pitch in baseball is worth on a per-pitch basis, and while some of the math behind the scenes might be slightly different from article to article, the general idea is the same. You need to find out how much every event is worth in a given environment (based on the count, pitcher, stadium, or any other type of environment you're working with), and then multiply those weights by the number of events caused by a given pitch to find the total number of runs above average that the pitch saved. One thing that none of these articles have discussed is exactly how location impacts the value of a pitch. Clearly the location of a pitch matters in determining it's value, but how big is the impact?

I split up the strike zone (and the surrounding area) into bins, and in each bin, I found the number of runs above average that were saved per pitch thrown to that area. Below is a chart showing the value of different regions for right-handed pitchers throwing fastballs against left-handed hitters. My calculations are based on the hitter's perspective, so negative values are saving runs compared to an "average location" and are good for the pitcher, while positive ones are the opposite.

The most obvious thing I noticed on the graph is the value of the strike zone. Eight of the nine regions prevent runs from being scored compared to an average location, which initially seems high. This actually makes sense though, if you think about how often batters get out and the fact that when a batter doesn't swing at a pitch in the strike zone, it always puts him in a less advantageous position to hit from. In this chart, which is from the pitcher's perspective, you can see regions where, as a group, left-handed hitters are more vulnerable to a right-handed pitcher's fastball. The idea that left-handed hitters like the ball low and inside seems to be backed up a little bit, as the bins in that region of the strike zone have a higher value than the rest of the zone. Using rigid bins isn't the best method for looking at the strike zone because you run into problems with deciding where to put the edges of bins, and a continuous approach is probably the ideal way to do this in the future.

Even with this limitation, what else can we learn from this chart? One thing to notice is that left-handed batters are either swinging at pitches low and outside, or umpires are calling this pitch a strike against lefties. Either way, it appears to be an area that pitchers can possibly exploit. Looking at all fastballs thrown by a pitcher-batter grouping is interesting, but exploring how the count and location impact an at-bat is more interesting. The chart below has the same group of batters and pitchers, but is now showing the linear weights per pitch of each section in an 0&2 count (this includes all pitches, not just fastballs).

When reading this chart, you need to remember that the weights used to calculate the value of each region are based on an 0&2 count. The middle region being .154 runs means that compared to an "average" location on an 0&2 count, that area allows .154 runs per pitch more. This isn't saying that overall, a pitch down the middle is worth .154 more runs than an average pitch, just on an 0&2 count. With this in mind, the chart makes a ton of sense. You can see the expansion of the strike zone, as virtually all the regions around the strike zone now allow fewer runs than average.

The increased ability for a pitcher to work outside the strike zone makes any miss into the strike zone hurt that much more. Using the same logic that a hit in a 0&2 count hurts the pitcher more than giving up the same hit in an 0&0 count, throwing a pitch right down the middle in an 0&2 count is a worse idea than doing the same thing in an 0&0 count. The idea is reversed on a 3&0 pitch, which is plotted below. A pitch outside the strike zone is now a tremendous advantage for the hitter, so the pitcher is forced to throw a strike. Somewhat counter intuitively, even though hitters "know" a strike is coming, pitches thrown in the strike zone in 3&0 counts still favor pitchers. This just speaks to how hard hitting actually is.

One other point I wanted to mention is the magnitudes of the impact of location. Using 50 pitches to a type of batter as a rough cutoff point, I found that the best and worst pitches range from roughly -.07 runs/pitch for the best to .07 runs/pitch for the worst. The spread between the best and worse locations varies, and depends on the count, but it can be as large as almost 1 run/pitch. Obviously this will have a huge impact on the value of a pitch, and potentially could negate any value a pitch has. You could have the best pitch in baseball, but if you can't locate it very well, it won't do you any good. Creating these plots for every pitcher could give a good indication of how much location actually helps and hurts a pitcher, depending on the situation.

## Comments

Just wondering: if left handed hitters like the balls low and in, why do all those locations lead to negative run expectations? Wouldn't pitches in locations that batters "like" lead to positive expectations for the hitters? Or is it that they have no restraint on those pitches, especially those pitches out of the strike zone?

I'm wondering how the numbers would change if you only took into account pitches on which the batter swung? One would assume that all strikes would have a negative expectation (the only way to get the batter out without swinging) reduced by the chances of the batter hitting the ball successfully, and thus all balls would have a positive expectation, since walks lead to runs a lot better than do strike outs, less the chances that batters would swing at them. So the negative expectations on the low inside swings for left handed hitters have to be substantial in order to overcome the fact that that pitch is a ball and thus good for the batter.

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