Have you researched any other type of data that concludes a changeup being more effective than a fastball when repeatedly thrown? Really interesting what you have here.

For some reason, the charts did not come through for me. However, had to laugh. . .nice W reference.

Very intersting research. Could you add confidence intervalls around your data points? That would give us a better idea about how relevant the averages are.

Without looking at any numbers, I'm willing to guess that for most pitchers

a) fastball velocity decreases throughout a game
b) smaller differences in fastball velocity versus other pitchers leads to decreased effectiveness (within range & reason)

Maybe including this as a variable will help discern how much of the difference is fatigue versus pitch selection?

Lou,

He's studied this before, if you look back at some of the older articles. And good luck disentangling that from the effect of the batters getting used to the pitches.

Jeremy,

This is absolutely fascinating work. It's incredible to see what you've come up with over the last few weeks... And it makes me shudder to think what others, working for teams full time, are coming up with. Imagine if this were your full time job. :)

Good stuff!

Danny, I'm not sure what you mean by type of data. This is the first time I've done research in this type of pitch sequencing.

Mark, I don't know what's up with the charts not coming through for some people, or why Google Reader doesn't show Google Charts. I don't know what to do about that.

Bjoern, I don't have the raw data handily available to calculate confidence intervals. But I wouldn't trust the results too much whether they're statistically significant or not.

Patrick, thanks for the comment.

Jeremy,

Can you tell us a bit more about the delta method?

I assume each point shows us the change in expected runs for the 1st and 2nd pitch, including only data for which hitters saw two pitches. But I don't believe the numbers. Are you sure your not normalizing by something? That is, are you sure the Y axis is expected change in Runs expected per 100 ABs?

Chris,

I'm not entirely sure what you're asking. I'll do my best to explain what I did.

For all batters who saw at least two pitches, I found the average run value for the first and second pitches and multiplied by 100. For all batters who saw at least three pitches, I found the average run value for the second and third pitches and multiplied by 100. And so on. The charts express the accumulative deltas. So the first point represents the difference between pitch one and pitch two, and the second point represents that difference plus the difference between pitch two and pitch three. That's it.

Thanks Jeremy,

I'm just trying to interpret the delta plots, and I find that I can't. I think two things that I can't reconcile with the graphs: (1) I would expect the derivative to be smaller than the values in the plots above them; (2) the plots of RV/100 show positive and negative slopes, so the derivative should have both positive and negative values.

The method you described sounds right. Are you sure there isn't a small glitch somewhere in the analysis that produced the delta plots? Or am I missing something?

Chris, here's what my numbers showed:

Batters who face at least three changeups have a rv100 of 0.2 on the third changeup, but they only have an rv100 of -1.1 on the second change. This is a delta of 1.3 runs. Meanwhile, batters who face at least four changeups have an rv100 of -1.3 runs on the third change and 0.3 on the fourth, another huge delta of 1.6 runs. So the first graph shows the average run value on the third and fourth changeups to be 0.2 and 0.3 runs. That's a small derivative. The second graph shows the change in run values to be 1.3 and 1.6 runs. Those are very large. I think the reason I didn't get any negative values is that pitchers stop throwing a pitch type once they get burned by it. So if a batter hits a homer off a slider, the pitcher probably wouldn't give up a homer if he threw another slider, but he's become scared to throw it, or he's been pulled from the game. Anyway, that's the theory I'm working with. I tried to express that I don't have much confidence in the results due to the sampling problems, but I am confident that the numbers I produced are accurate.

Hi Jeremy,

Batters who face >=3 changeups:
second: -1.1
third: 0.2

Batters who face >=4 changeups:
third: -1.3
fourth: 0.3

Since batters who face >=4 changeups is a subset of the batters who face >=3 changeups, in order for >=4 to average to -1.3, the batters who face exactly 3 changeups must have a crazy high run value associated with that third changeup. Hence your explanation that they are getting hammered on that pitch. What is the distribution of outcomes for that 3rd change-up for batters that see exactly 3 change-ups (HR, 1B, OUT, etc)? I assume thats how you calculated RV/100?

Chris, here are the numbers I have for 3rd changeup for batters that see exactly 3 change-ups. Let me know if you want the distribution for any other pitch types/counts.

Ball	38.20%
Strike	42.26%
Out	12.05%
Single	4.76%
Double	1.51%
Triple	0.17%
Homer	0.84%

I use the methodology outlined by John Walsh and Joe P. Sheehan to calculate run value. I then multiply that by 100 to scale it to 100 pitches.