Times through the order revisited: GB and FB pitchers

About two months ago, I investigated the times through the order penalty (TTOP) as a function of a pitcher's pitch-type arsenal. The basic conclusion was that we should not be too concerned with the types of pitches a pitcher throws when considering the TTOP. The number of pitches in the repertoire may matter, but regardless of what a pitcher has in his arsenal, batters will have a distinct advantage with each additional PA against a starter in a given start/game. Here I am revisiting the TTOP, but considering differences between ground ball and fly ball pitchers. There is probably a joke here about a writer taking another turn through examining the TTOP but I will leave that to the reader.

The lack of influence of a pitcher's arsenal on the TTOP made me wonder if a broader category of pitcher-type was important. For example, we know that pitchers have a tendency to give up more batted balls on the ground or in the air. Ground ball (GB) pitchers tend to give up more batted balls on the ground and fly ball (FB) pitchers tend to give up more batted balls in the air. There are many good pitchers that are ground ball pitchers and many good pitchers that are fly ball pitchers. This is also true for bad pitchers. Thus, we can ask if the tendency to be a ground ball or fly ball pitcher has an impact on the TTOP. Perhaps ground ball pitchers do not incur as large a TTOP as fly ball pitchers. This would be valuable information for a team to consider as they monitor the progress of their starter during a game.

I used a similar dataset as used for my previous TTOP analysis to examine this question. I obtained times through the order splits for starting pitchers between 2008-2013 using the Baseball-Reference play index. Unfortunately, I am not yet using play-by-play data, which would have allowed me to control for pitcher and batter quality. To be included in the dataset, pitchers had to have at least 100 batters faced (BF) for each of the three splits (1^st PA, 2^nd PA, 3^rd PA). Three hundred and thirty-three pitchers met this requirement. Data for the eighty-one pitchers that had at least 100 BF for a 4^th PA were added to their 3^rd PA data.

Here are the TTOP data for the sample considered here. wOBA-against was calculated using the linear weights given in The Book.

Times Through the Order	Total BF	wOBA
1	251,087	0.315
2	236,064	0.329
3	194,241	0.343

As expected there is a trend in wOBA as times through the order increases. Batters gain an advantage with each PA, gaining on average 14 points in wOBA each time. For clarity I will note that the 3^rd PA wOBA-against is 0.345 if the 14,163 4^th PAs are removed the analysis. The 0.002 lower wOBA-against observed when including the 4^th PAs is likely a result of the fact that pitchers getting to a 4^th PA in a game are better pitchers to begin with. Although this difference is minimal, it is present. Given this, and the comments concerning the 4^th PA data on my previous TTOP article, I decided to remove them for the remaining analyses.

Now we can examine TTOP differences as a function of batted ball type tendency. Batted ball data was obtained from FanGraphs (2008-2013 seasons). GB/FB was used to assign a pitcher to the tendency categories (i.e., GB/FB > 1 = GB categorization). Here are some relevant statistics for the groups:

Tendency	N (Pitchers)	GB%	std. deviation	FB%	std. deviation
GB	236	46.72	4.47	33.23	4.12
FB	97	36.40	2.95	43.29	3.10

Average batted ball rates match the group category assignment. There are significantly more GB pitchers in this sample (accounting for 75.4% of the batters faced in the dataset). While 97 FB pitchers and their 166,331 BF is a reasonable sample with which to work, this presents an issue to consider before making strong conclusions.

Here are the TTOP data for these categories.

Tendency	BF	wOBA	1st PA	2nd PA	3rd PA	Second-First	Third-Second
GB	502,856	0.328	0.316	0.329	0.343	0.014	0.015
FB	164,373	0.328	0.315	0.327	0.349	0.012	0.023

These results are interesting. GB pitchers follow the typical trend for the TTOP, losing 14 and then 15 points of wOBA as they progress through the order. FB pitchers on the other hand, start with a near-typical penalty of 12 points of wOBA from 1^st to 2^nd PA, but then get hit hard with a 23-point wOBA penalty from the 2^nd to 3^rd PA. At first I suspected that as the game progressed, FB pitchers were having more of their fly balls end up as home runs, and that this was driving the larger penalty. However, this was not the case. HR/PA rate remained consistent across the 3 times through the order (~3% of PAs were HRs).

Perhaps this result is an artifact of the simple method used for defining the categories (i.e., GB/FB ratio). I went back and re-assigned the group categories based on z-scores for GB% within this sample (M = 43.8, SD = 6.2). From this I created 4 categories:

• GB% less than 34.5% (i.e., z-score less than -1.5)
• GB% between 34.5% and 43.8% (i.e., z-score between -1.5 and 0)
• GB% between 43.8% and 53.1% (i.e., z-score between 0 and 1.5)
• GB% greater than 53.1% (i.e., z-score greater than 1.5)
• Note: the categories did not overlap.

Here are some relevant statistics for this new assignment:

GB% Category	N (Pitchers)	GB%	std. deviation	FB%	std. deviation
Greater than 53.1	21	56.18	2.34	25.18	2.16
Between 43.8 and 53.1	146	47.52	2.48	32.43	2.57
Between 34.5 and 43.8	146	39.68	2.56	39.98	2.90
Less than 34.5	20	31.58	2.51	47.58	3.48

Again, average batted ball rates match the group category assignment, and as would be expected, there are fewer pitchers in the extreme categories. Of interest is the distribution of the previous GB and FB assignment numbers within these categories. They are as follows:

GB% Category	N (Pitchers)	N (GB)	N (FB)
Greater than 53.1	21	21	-
Between 43.8 and 53.1	146	146	-
Between 34.5 and 43.8	146	69	77
Less than 34.5	20	-	20

Here are the TTOP data for these new categories:

GB% Category	BF	wOBA	1st PA	2nd PA	3rd PA	Second-First	Third-Second
Greater than 53.1	46,460	0.331	0.317	0.332	0.350	0.015	0.018
Between 43.8 and 53.1	326,599	0.326	0.315	0.327	0.341	0.012	0.015
Between 34.5 and 43.8	261,949	0.331	0.318	0.331	0.348	0.013	0.018
Less than 34.5	32,221	0.322	0.298	0.324	0.353	0.026	0.030

We see that the extreme low GB% pitchers (less than 34.5%) show atypically large penalties. This could be due to the smaller sample of batters faced, but also could have contributed to them facing significantly fewer batters. It looks like letting these pitchers face the lineup once would not be a terrible idea as their 1^st PA wOBA is a fair amount lower than the other groups. But then the penalty is evident in the 2^nd and 3^rd PA and they start to look more like the other groups, which could be regression to the mean. The other group that has FB pitchers (between 34.5 and 43.8 GB%) also shows a larger than typical penalty from the 2^nd to 3^rd PA (although it is the same as that observed for the extreme GB% pitchers, and again, the smaller sample caveat applies). Note that this is the only new grouping that contains pitchers from both categories of the initial categorization. Here is the data for only this group separated by the previous category assignment:

Tendency	BF	wOBA	1st PA	2nd PA	3rd PA	Second-First	Third-Second
GB	129,797	0.332	0.317	0.334	0.348	0.017	0.015
FB	132,152	0.330	0.319	0.328	0.348	0.009	0.021

This represents the majority of the FB pitchers in the sample, so it is not surprising that we see a large increase in wOBA from the 2^nd to 3^rd PA. However, it is interesting that these GB pitchers (those with lower than average GB%) show larger TTOPs than the GB pitchers with higher than average GB%. So, again, it seems as though we are picking up on something with this analysis of GB or FB tendency and the TTOP.

Overall, GB pitchers are not immune to the TTOP, but they seem to show a more typical penalty of 14-15 points in wOBA each time through the order; typical referring to the pattern observed across the entire sample (of which they represent the majority). This penalty is a bit higher than the 8-10 point increase that Mitchel Lichtman has reported when more appropriately controlling for pitcher and batter quality. Nevertheless, the observed penalty for GB pitchers is still lower than the penalty observed for the FB pitchers, specifically for the 2^nd to 3^rd PA.

Generally, it is difficult to know exactly what to make of these data. While there appears to be something interesting here, correlating GB% with times through the order penalties (i.e., Second-First; Third-Second) reveals very little relation (rs ≈ 0.05). This is cause for hesitation in making firm conclusions about the results presented above.

In the end it seems that teams may want to be aware of the batted ball tendencies of their pitcher when considering how long to leave them in a game. Batters will have a distinct advantage in the third PA against a starter. This is true regardless of the pitcher's GB or FB tendencies, but the batter's advantage may be greater when facing a FB pitcher.

. . .

All statistics courtesy of FanGraphs and Baseball-Reference.

Chris Teeter is a Contributor to Beyond the Box Score. You can follow him on Twitter at @c_mcgeets.