Recently, Mitchel Lichtman posted two excellent articles (here and here) on the *times through the order* *penalty* (TTOP). For those unaware, the TTOP demonstrates that as a game advances, hitters progressively gain an advantage over the starting pitcher. The more times a batter faces a pitcher during a game, the better he does. TTOP is typically measured by looking at the pitcher's performance using wOBA-against. It might be expected that a pitcher's wOBA would remain consistent throughout his start. But that is not what is found. This is critical information, of which managers should be aware.

Lichtman's work demonstrates a number of other important aspects of the TTOP. For example, for batters, the number of pitches seen makes a large difference. If a batter sees more than four pitches in his first plate appearance, he is on average 25 points in wOBA better in his next plate appearance. In addition, the number of pitches in a pitcher's repertoire makes a difference. The fewer pitches a pitcher has in his repertoire the more quickly a batter becomes familiar with him; leading to a larger jump in the TTOP.

Finding that the number of pitches in a pitcher's repertoire influences the TTOP made me wonder if the pitch-*types* in a pitcher's repertoire matter. There is good evidence for differences in platoon splits across pitch types, with changeups and curveballs relatively neutral to batter handedness while sliders show high splits. Does something similar exist for the TTOP? Perhaps pitchers that use a changeup (or curveball) as their predominant secondary pitch (after the fastball) do not incur as large a TTOP as pitchers that use a slider. This would be important information for teams to consider.

To examine this I examined times through the order splits for starting pitchers between 2008-2013. This period was selected because it represents the period for which reliable PITCHf/x data are available. Any pitcher that did not have at least 100 batters faced (BF) for each of the three splits (1^{st} PA, 2^{nd} PA, 3^{rd} PA) was removed from the dataset. Data for 4^{th} PAs were included as long as the pitcher had 100 BF for the split. PITCHf/x pitch-type data were obtained from FanGraphs. Pitches are categorized as fastballs (fourseam, two-seam, cutter, split-fingers and sinkers), changeups, curveballs, sliders, knucklecurves, eephus, screwballs and knuckleballs. Data from pitchers whose primary pitch (largest percentage of pitches thrown) was not a fastball were removed. This removes R.A. Dickey, Tim Wakefield, Jesse Litsch and Kenny Rogers.

Before digging into the pitch specific analysis, 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 | 248,307 | 0.315 |

2 | 233,433 | 0.329 |

3 | 177,823 | 0.345 |

4 | 13,858 | 0.327 |

As expected there is an evident trend in wOBA. Batters get better each time through the order, gaining on average 14 points in wOBA from their 1^{st} to 2^{nd} PA, and then 16 points from their 2^{nd} to 3^{rd} PA. The return to 2^{nd} PA performance levels for the 4^{th} PA is likely a small sample and selection bias issue. Few starting pitchers remain in the game to face a batter for a 4^{th} time (evident from the reduction in total BF for this split) and if they do it is likely because they are pitching well. For the remaining analyses, data for the 3^{rd} and 4^{th} PA are collapsed.

Now that we have an idea of the TTOP for this sample we can examine differences in TTOP as a function of pitchers' pitch-type repertoire. First, we will examine TTOP as a function of the predominant secondary pitch that a pitcher uses. Pitch type percentages were used to categorize pitchers secondary pitch (i.e., highest percentage use after the fastball). Recall that all pitchers in this dataset use the fastball (broadly defined as fourseam, two-seam, cutters, split-fingers and sinkers) as their primary pitch (average % thrown = 62.4, std. deviation = 7.9).

Here are some relevant statistics for the developed secondary pitch categories.

Secondary Pitch | N (Pitchers) | % fastballs thrown | std. deviation | % secondary pitch thrown | std. deviation |
---|---|---|---|---|---|

Slider | 144 | 62.4 | 8.3 | 20.7 | 5.9 |

Changeup | 106 | 62.1 | 7.4 | 19.7 | 5.4 |

Curveball | 79 | 62.8 | 8.0 | 19.1 | 4.7 |

Note: 1 pitchers' predominant secondary pitch was the knucklecurve. He is not included in this analysis for obvious sample size reasons.

As is evident from the table pitchers in these categories throw their fastball at roughly the same rate, and also use their predominant secondary pitch at roughly the same rate. There are more pitchers whose main secondary pitch is a slider (account for 43.5% of batters faced in the dataset), than there are pitchers whose main secondary pitch is a changeup (32.4% of batters faced) or curveball (24.0% of batters faced).

Now let's examine the TTOP for each of these categories.

Secondary Pitch | BF | Overall | 1st PA | 2nd PA | 3rd/4th PA | Second - First Penalty | Third/Fourth - Second Penalty |
---|---|---|---|---|---|---|---|

Slider | 290,801 | 0.327 | 0.314 | 0.328 | 0.344 | 0.014 | 0.017 |

Changeup | 217,113 | 0.328 | 0.315 | 0.329 | 0.343 | 0.014 | 0.017 |

Curveball | 160,344 | 0.329 | 0.318 | 0.330 | 0.342 | 0.013 | 0.014 |

There is remarkable consistency here. I will admit I was hoping to find that one of these groups exhibited a difference in their TTOP, but as is evident each group of pitchers has essentially the same TTOP. The curveball pitchers show a slightly lower penalty but the difference is not really something with which managers should be overly concerned.

Despite the lack of difference for secondary pitches we can carry on and examine if a pitchers' predominant third pitch matters for the TTOP. To some extent this is just re-arranging the deck chairs, but there might be something interesting.

First, here are some relevant statistics for the third pitch categories.

Third Pitch | N (Pitchers) | % fastballs thrown | std. deviation | % third pitch thrown | std. deviation |
---|---|---|---|---|---|

Changeup | 133 | 63.0 | 7.8 | 11.7 | 4.2 |

Curveball | 103 | 62.7 | 7.8 | 11.3 | 3.9 |

Slider | 92 | 61.0 | 8.3 | 13.1 | 3.9 |

Note: 1 pitchers' predominant third pitch was the knucklecurve and 1 pitcher did not have a true third pitch. They are not included in this analysis for obvious sample size reasons.

Again, pitchers in these categories throw their fastball at roughly the same rate, and use their main third pitch at roughly the same rate. The distribution of third pitch types differs slightly from secondary pitches. Now, there are more pitchers whose main third pitch is a changeup (accounting for 38.1% of batters faced in the dataset), than there are pitchers whose main secondary pitch is a curveball (35.6% of batters faced) or slider (26.3% of batters faced).

Finally, the TTOP for these categories.

Third Pitch | BF | Overall | 1st PA | 2nd PA | 3rd/4th PA | Second - First Penalty | Third/Fourth - Second Penalty |
---|---|---|---|---|---|---|---|

Changeup | 255,605 | 0.331 | 0.318 | 0.332 | 0.347 | 0.014 | 0.017 |

Curveball | 239,210 | 0.324 | 0.311 | 0.325 | 0.338 | 0.014 | 0.016 |

Slider | 176,263 | 0.330 | 0.318 | 0.331 | 0.345 | 0.013 | 0.016 |

Again there is remarkable consistency with these data. Each pitch-type group incurs about a 14-point penalty in wOBA as they progress through the order. While the categorization does not map on perfectly, these results fit well with Lichtman's analysis of the TTOP for 3-pitch pitchers. As he demonstrated, having three pitches in one's repertoire (> 10%) results in 13- and 15-point wOBA penalties. The analysis here compliments that finding by demonstrating that it does not really matter *which* pitches are in the repertoire. While it is possible to examine differences in TTOP as a function of the combination of secondary and tertiary pitches (e.g., changeup-curveball v. changeup-slider), that gets into much smaller samples that may not be reliable.

Further analysis could focus on individual differences within these categories. Perhaps pitch quality (as measured by standardized run values) rather than pitch frequency is a better predictor of the TTOP. This could be an interesting line of inquiry, however, recall that Lichtman found good and bad pitchers have around the same TTOP, so this form of analysis may not lead to any demonstrable difference. Another approach could be to look at when pitchers are using their secondary and tertiary pitches. Do they use them at a consistent rate throughout the game, or are they holding back their use of certain pitches for certain points in the game? Joe Roegele conducted an analysis along these lines last year. This is an interesting question to consider.

In the end it seems that managers and front offices should not be too concerned with the types of pitches their pitchers are throwing when considering the TTOP. While the number of pitchers in a repertoire may matter, it appears that regardless of *what* a pitcher has in his arsenal, batters will have a distinct advantage in the third PA against a starter.

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**Update (Jan. 19/2014):**

*Data were updated from the original publication to reflect the more appropriate analysis (Delta Method) suggested by Mitchel Lichtman in the comments. This analysis lead to slightly larger penalties for each of the pitch-type groups, particularly for the Third/Fourth-Second penalty. There are no systematic penalty differences as a function of pitch-type arsenal and therefore the new analysis did not affect t**he conclusions suggested in the original article.*

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*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.*