Command Post October 26, 2007
Pitch Frequency

There are many variables that impact what type of pitch a pitcher will throw on any given pitch. The type of hitter, the count, if there are runners on base, what the score is, what pitch was just thrown, as well as the different types of pitches a pitcher has in his arsenal all play a big part in what pitch will be thrown next.

Given any situation that a pitcher is in, be it close game or blowout, facing Ryan Braun or Ryan Freel, in a hitter's count or pitcher's count, there is a certain frequency that he should throw each of his pitches for optimal results. These frequencies are dependent on the situation and pitcher, and even though we don't know exactly what they may be in each situation, they do exist. A pitcher can't let a hitter get too comfortable in any situation, so even if the pitcher has an amazing slider, he is still going to have to occasionally throw a fastball to keep a hitter honest.

Last week I looked at the sequencing of pitches in an at-bat and used the overall percentage that a pitcher threw his fastball as a proxy for his true rate of throwing a fastball on any particular pitch. Prompted by these two threads on The Book's website, I went back into my database, and for every pitcher with at least 100 pitches, I found out how often they threw their fastball. I've created lists like this before, but this time I created splits based on the count the pitch was thrown in, either hitter's counts, pitcher's counts, or neutral counts. Using the overall percentage of pitches that were fastballs (FB%) for a pitcher as their true rate of throwing fastballs, I then looked to see if pitchers were throwing a significantly different amount of fastballs in each type of count. I used the frequencies of fastballs thrown because it is the easiest pitch to look at. Every pitcher throws a fastball and while they all don't move the same, fastballs have much more in common across different pitchers than any other pitch does.

I have 421 pitchers in my sample, and in hitter's counts 299 of them threw significantly more fastballs than their overall average, while only 4 threw significantly fewer. In pitcher's counts, 286 pitchers threw significantly fewer fastballs, while only 9 threw significantly more. This is pretty much what we would expect to happen. One reason why hitter's counts are considered advantageous to hitters is because they see lots of fastballs (more than the overall average), which are generally easier to hit than breaking balls.

Results like that also make me think that the overall fastball frequency of a pitcher isn't a good substitute for his frequency in different counts. In my article last week I looked at Josh Beckett, C.C. Sabathia and Greg Maddux and their pitching patterns. Splitting their fastballs by count yields this chart, which shows the number of pitches thrown by each pitcher and the percent that were fastballs, both overall and in hitter's counts. (Hitter's counts are 3-0, 3-1, 2-0 and 2-1. Pitcher's counts are 0-2, 1-2, 2-2, and 0-1. The other counts are considered neutral counts.)

```Name            Total Pitches   FB%     Hitter's Counts   FB%-hitter's counts
Josh Beckett    1122            0.68    108               0.81
C.C. Sabathia   1232            0.62    136               0.71
Greg Maddux     1137            0.65    105               0.62
```

All three pitchers throw a lot of fastballs overall, and two of them throw more fastballs than their overall average when in hitter's counts. This pattern holds true for almost all the pitcher's in my sample, with the average FB% going from 55% overall to 68% in hitter's counts. In light of this difference, using the overall FB% doesn't seem like the best proxy for the true FB% in hitter's counts.

One way to estimate the true amount of "skill" involved in an act is to regress it toward the population mean. In this case, I'm looking to estimate the true level of decision making that impacts the FB% in hitter's counts (basically finding the amount of "skill" for a measurement given the observed frequencies, random standard deviation, population average and population standard deviation). Once the regressed FB% are found you've got a much more accurate idea about what to expect in a given count from a pitcher. The overall FB% of a pitcher doesn't really matter to a hitter because a hitter will always find himself in a situation that alters the base frequency. Here's a table showing the eight pitchers who throw the most and least fastballs in hitter's counts.

```Name            Hitter's Counts   FB%-hitter's counts
Scot Shields    87                0.96
Daniel Cabrera  68                0.94
Jose Valverde   50                0.94
Brian Fuentes   65                0.94
Derrick Turnbow 75                0.93
Sean Green      82                0.93
CJ Wilson       71                0.92
C. Wang         77                0.91
----------------------------------------------------------------
Mark Buehrle    134               0.36
Ubaldo Jimenez  167               0.36
Jamie Moyer     162               0.35
Doug Davis      74                0.35
Andy Pettitte   93                0.29
Mike Maroth     63                0.26
Julian Tavarez  69                0.25
Kenny Rogers    88                0.20
```

The first thing I noticed about the list is that the top group are almost all relievers, while the bottom group is almost all starting pitchers. There are other starters besides Cabrera and Wang at the top of the list, but for the most part, relievers are more likely to throw a fastball in a hitter's count. This is probably because they don't usually have a good second or third pitch that they can throw strikes with. Fastballs for relievers are also usually faster than those of starters, so even if the batter knows the pitch is coming, they might not be able to do anything with it. Starters generally have more pitches than relievers, so they become less reliant on one pitch in any count, although as Cabrera shows, this isn't always the case.

I wouldn't take too much from that list as there are good and bad pitchers at both ends of the list. However, if you were to take absolute difference between the FB% in hitter's counts and the FB% in pitcher's counts, you would get a list of pitchers who are throwing their fastballs equal amounts in both counts.

```Name             FB%-hitter   FB%-pitcher   Difference
Curt Schilling   0.50         0.50          0.00
Andy Pettitte    0.29         0.29          0.00
Livan Hernandez  0.44         0.44          0.00
Julian Tavarez   0.25         0.25          0.00
Mark Buehrle     0.37         0.36          0.01
-----------------------------------------------------
Jake Westbrook   0.82         0.39          0.43
Jack Taschner    0.89         0.45          0.44
Frank Francisco  0.91         0.45          0.46
Rafael Perez     0.74         0.27          0.46
Derrick Turnbow  0.93         0.43          0.51
```

The guys at the top of this list usually have the reputations for being "smart" or "crafty", willing to throw any pitch at any time. Without looking at their other pitches, I can't verify that they will throw anything in any count, but according to this list, they don't alter the amount of fastballs they throw based on the count, which means at least that they throw the same total frequency of off-speed pitches in the different counts. The bottom of the list is populated with pitchers who drastically change the amount of fastballs they throw depending on the count. Someone like Lidge, who just has two pitches, primarily throws fastballs in hitter's counts and sliders in pitcher's counts. Even if Lidge is throwing his fastball and slider at their optimal frequencies in these counts, the difference between frequencies gives hitters very good information about what pitch is coming.

Comparing the pitch frequencies for the same pitcher in two different time periods, like Fausto Carmona in the regular season vs. the playoffs, is another interesting application of these frequencies. Using his regressed regular season pitch frequencies as his true frequencies, you can see if he significantly changed his style of pitching in the playoffs. I looked at this briefly before, but here are the FB% for Carmona and Sabathia in the playoffs compared to how they usually pitch. For whatever reason, both pitchers threw significantly more fastballs in hitter's counts in the playoffs than in the regular season.

```Name             Count type    True FB%   Playoff FB%   Playoff N
Fausto Carmona   Hitter        0.83       0.91*         44
Fausto Carmona   Pitcher       0.58       0.73*         80
-----------------------------------------------------------------
C.C. Sabathia    Hitter        0.71       0.89*         35
C.C. Sabathia    Pitcher       0.46       0.47          118
*-significantly different from true FB% (alpha=5%)
```

This is more of a backwards looking analysis that explains what happened rather than why it happened or what will happen in the future. Even still, it's fun to look at.

I think of the frequencies that pitches are thrown like the slices on a circular spinner. Making the correct decision about what pitch to throw is easy for a pitcher, just spin the Wheel-of-Pitches and throw whatever comes up. Knowing how big to make the slices for each pitch in different situations is much harder than actually deciding what pitch to throw. I didn't really look at this, but I'm curious how much the catcher contributes to setting the frequencies and spinning the wheel. At the top of the list of pitchers who throw fastballs in any count (the "smart" pitchers) were two pitchers on the Red Sox, with a third, Dice-K, just missing the cut. Jason Varitek generally gets credit for calling a good game, so I'm curious about his level of contribution to pitch selections.