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# An introduction to per-pitch run values

An introduction.

I'm about to start on a long process of pitching analysis that I hope will be interesting and insightful, but that definitely at times may not be. Before getting to that, though, I need to set some groundwork.

The following is not my research, but it sets the table for what I'd like to write about. Credit goes to Joe Sheehan (2008), Dan Farnsworth (2014), and Dan Meyer (2015). I've set it to the 2014 run environment.

#### The Count Matters

Let's begin with something we "know" about baseball.

We know that a double with no outs and the bases loaded leads to more runs than a double with two outs and the bases empty, but to calculate linear-weights-based offensive metrics like wOBA, we give both doubles the same value—namely, the average run value of all doubles in all situations.

Sometimes it doesn't make sense to be completely context-independent. Sometimes the context might tell us real and important things about what's going on in an at bat.

For instance, we know that pitchers tend to pitch differently in an 0-2 count than they do in a 3-0 count. and batters change their approach as well. And while 0-2 and 3-0 are extremes, there are probably still real and different effects of most counts on the batter-pitcher relationship.

So while it may still make sense to ignore who's on base, when trying to analyze pitching, there's likely value in looking individually at the count.

Luckily, we can do that pretty easily. And even more lucky for me, Dan Meyer has already done that.

In that article, he presents the average wOBA for all plate appearances that pass through a certain count. There we can see that at the beginning of a plate appearance, league average wOBA in 2014 was .310. But when hitters got ahead 3-0, those at bats proceeded to end up with a whopping .622 wOBA. Alternately, down 0-2, hitters ended up with a .196 wOBA. And then there's much range in between.

 Situation wOBA 3-0 0.622 3-1 0.470 2-0 0.436 3-2 0.384 1-0 0.355 2-1 0.352 0-0 0.310 1-1 0.293 2-2 0.273 0-1 0.262 1-2 0.223 0-2 0.196

There's obviously some selection bias in here, because hitters who are often ahead in the count are probably better hitters in other ways too, but let's move on.

One great thing about wOBA is that you can easily translate it into runs. Those runs are called Weighted Runs Above Average, or wRAA. All that you have to do is subtract the league average and divide by a scaling constant. So if we know the wOBA of a count, and if we know the wOBA of the count after one more pitch, we can assign a run value to that single pitch based on how that pitch changed the count.

Here's that data. Note that we've assigned the wOBA of a walk (or .689) to a four-ball count and the wOBA of a strikeout (or 0) to a three-strike count. Also note that these are runs above average. So a negative number is not negative runs. It's just a below average expectation of runs.

 Situation wOBA WRAA/PA Value of Strike Value of Ball 3-0 0.622 0.239 -0.117 0.051 3-1 0.470 0.123 -0.066 0.168 2-0 0.436 0.097 -0.062 0.143 3-2 0.384 0.057 -0.294 0.234 1-0 0.355 0.035 -0.035 0.088 2-1 0.352 0.032 -0.069 0.064 0-0 0.310 0.000 -0.037 0.032 1-1 0.293 -0.013 -0.054 0.048 2-2 0.273 -0.028 -0.209 0.085 0-1 0.262 -0.037 -0.051 0.024 1-2 0.223 -0.067 -0.171 0.038 0-2 0.196 -0.087 -0.150 0.021

#### Balls in Play—Two Approaches

That first part was pretty straightforward, but what to do with balls that are put in play is a more difficult question.

One approach is to just go ahead and give the hitters and pitchers credit for what happened. Call a single a single. Shoot straight, shoot first, and ask questions later.

 wOBA R/PA 1B 0.892 0.446 2B 1.283 0.746 3B 1.635 1.016 HR 2.135 1.400

That's fine, cowboy, but you can do all that and still adjust for count.

That's potentially important because a pitch that results in a single off of an 0-2 count is a much more disappointing for the pitcher than a pitch that results in a single off of a 3-0 count. Here are the numbers on that.

 Situation wOBA WRAA/PA v1B v2B v3B vHR 3-0 0.622 0.239 0.207 0.507 0.777 1.160 3-1 0.470 0.123 0.324 0.623 0.893 1.277 2-0 0.436 0.097 0.350 0.650 0.919 1.303 3-2 0.384 0.057 0.390 0.689 0.959 1.343 1-0 0.355 0.035 0.412 0.712 0.982 1.365 2-1 0.352 0.032 0.414 0.714 0.984 1.367 0-0 0.310 0.000 0.446 0.746 1.016 1.400 1-1 0.293 -0.013 0.459 0.759 1.029 1.413 2-2 0.273 -0.028 0.475 0.775 1.044 1.428 0-1 0.262 -0.037 0.483 0.783 1.053 1.436 1-2 0.223 -0.067 0.513 0.813 1.083 1.466 0-2 0.196 -0.087 0.534 0.834 1.104 1.487

Of course, if you're more the quiet, introspective type, you might think that maybe a pitcher shouldn't get all the credit or all the blame for what happens to a ball in play, and you might be more interested in the types of balls in play that a pitcher gives up.

Dan Farnsworth is apparently the quiet, introspective type, as he's already done this. Here are his numbers.

 wOBA R/PA GB 0.213 -0.074 LD 0.681 0.285 FB 0.346 0.028

And when adjusted for count, you get this:

 Situation wOBA WRAA/PA Value of GB Value of LD Value of FB 3-0 0.622 0.239 -0.314 0.045 -0.212 3-1 0.470 0.123 -0.197 0.162 -0.095 2-0 0.436 0.097 -0.171 0.188 -0.069 3-2 0.384 0.057 -0.131 0.228 -0.029 1-0 0.355 0.035 -0.109 0.250 -0.007 2-1 0.352 0.032 -0.107 0.252 -0.005 0-0 0.310 0.000 -0.074 0.285 0.028 1-1 0.293 -0.013 -0.061 0.298 0.041 2-2 0.273 -0.028 -0.046 0.313 0.056 0-1 0.262 -0.037 -0.038 0.321 0.064 1-2 0.223 -0.067 -0.008 0.351 0.094 0-2 0.196 -0.087 0.013 0.372 0.115

Most interesting here is that a ground ball is almost always a below-average outcome. The only time when a hitter should be happy with a ground ball is if he hits that grounder in an 0-2 count, when the expectation was much worse.

#### Wrapping Up

There isn't really a point in this article other than to say, "these are run values."

Right now, as people gain access to more Statcast data, we can expect analysts to make more and more advanced buckets to drop pitching results into. But there's already a lot of good work that's been done by some very fine baseball researchers and writers, and that means that when you or I want so analyze pitching, we don't have to reinvent the wheel.

To make the wheel more accessible, I've put it together in a google doc, and in an excel spreadsheet: Run Values

Please check these numbers (and tell me if you think I've done something wrong). Furthermore, please use these numbers (like, for instance, in a FanPost), and please come back and read what I hope will be far more interesting articles based on run values.

Up next, I will use this data to look at which pitchers get the most value out of working ahead the count, and which succeed by avoiding being hard to hit, regardless of count.