**Note: “Guy,” a frequent participant on The Book Blog, pointed out an error I have been making in calculating the expected RA9 for starters. I have been using their season RA9 as the baseline, and then adjusting for context. That is wrong. I must consider the RA9 of the first 6 innings and then subtract that from the seasonal RA9. For example if a group of pitchers has a RA9 for the season of 4.40 and they have a RA9 of 1.50 for the first 6 innings, if they average 150 IP for the season, our baseline adjusted expectation for the 7th inning, not considering any effects from pitch count, TTOP, manager’s decision to let them continue, etc., is 73.3 (number of runs allowed over 150 IP for the season) minus 1 run for 6 innings, or 72.3 runs over 144 innings, which is an expected RA9 of 4.52, .12 runs higher than the seasonal RA9 of 4.40.**

**The same goes for the starters who have gotten shelled through 6. Their adjusted expected RA9 for any other time frame, e.g., the 7th inning, is a little lower than 4.40 if 4.40 is their full-season RA9. How much lower depends on the average number of runs allowed in those 6 innings. If it is 4, then we have 73.3 – 4, or 69.3, divided by 144, times 9, or 4.33.**

**So I will adjust all my numbers to the tune of .14 runs up for dealing pitchers and .07 down for non-dealing pitchers. The exact adjustments might vary a little from these, depending on the average number of runs allowed over the first 6 innings in the various groups of pitchers I looked at.**

Almost everyone, to a man, thinks that a manager’s decision as to whether to allow his starter to pitch in the 6^{th}, 7^{th}, or 8^{th} (or later) innings of an important game hinges, at least in part, on whether said starter has been *dealing* or getting banged around thus far in the game.

Obviously there are many *other *variables that a manager can and does consider in making such a decision, including pitch count, times through the order (not high in a *manager’s *hierarchy of criteria, as analysts have been pointing out more and more lately), the quality and handedness of the upcoming hitters, and the state of the bullpen, both in term of quality and availability.

For the purposes of this article, we will put aside most of these other criteria. The two questions we are going to ask is this:

- If a starter is
*dealing*thus far, say, in the first 6 innings, and he is allowed to continue, how does he fare in the very next inning? Again, most people, including almost every baseball*insider*, (player, manager, coach, media commentator, etc.), will assume that he will continue to pitch well. - If a starter has
*not*been*dealing*, or worse yet, he is achieving particularly*poor*results, these same folks will usually argue that it is time to take him out and replace him with a fresh arm from the pen. As with the starter who has been*dealing*, the presumption is that the pitcher’s*bad*performance over the first, say, 6 innings, is at least somewhat predictive of his performance in the next inning or two. Is that true as well?

Keep in mind that one thing we are *not *able to look at is how a poorly performing pitcher might perform if he were left in a game, even though he was removed. In other words, we can’t do the *controlled *experiment we would like – start a bunch of pitchers, track how they perform through 6 innings and then look at their performance through the next inning or two.

So, while we have to assume that, in some cases at least, when a pitcher is pitching poorly and his manager allows him to pitch a while longer, that said manager still had *some *confidence in the pitcher’s performance over the remaining innings, we also must assume that if most people’s instincts are right, the *dealing *pitchers through 6 innings will continue to pitch exceptionally well and the not-so *dealing* pitchers will continue to falter.

Let’s take a look at some basic numbers before we start to parse them and do some necessary adjustments. The data below is from the AL only, 2003-2013.

** **

** ****Pitchers who have been dealing or not through 6 innings – how they fared in the 7^{th}**

Starters through 6 innings |
# of Games |
RA9 in the 7^{th} inning |

Dealing (0 or 1 run allowed through 6) |
5,822 |
4.46 |

Not-dealing (3 or more runs allowed through 6) |
2,960 |
4.48 |

First, let me explain what “RA9 in the 7^{th} inning” means: It is the average number of runs allowed by the starter in the 7^{th} inning extrapolated to 9 innings, i.e. runs per inning in the 7^{th} multiplied by 9. Since the starter is often removed in the middle of the 7^{th} inning whether has been *dealing *or not, I calculated his runs allowed in the entire inning by adding together his actual runs allowed while he was pitching plus the run expectancy of the average pitcher when he left the game, scaled to his talent level and adjusted for time through the order, based on the number of outs and base runners.

For example, let’s say that a starter who is normally 10% worse than a league average pitcher allowed 1 run in the 7^{th} inning and then left with 2 outs and a runner on first base. He would be charged with allowing 1 plus (.231 * 1.1 * 1.08) runs or 1.274 runs in the 7^{th} inning. The .231 is the average run expectancy for a runner on first base and 2 outs, the 1.1 multiplier is because he is 10% worse than a league average pitcher, and the 1.08 multiplier is because most batters in the 7^{th} inning are appearing for the 3^{rd} time (TTOP). When all the 7^{th} inning runs are tallied, we can convert them into a runs per 9 innings or the RA9 you see in the chart above.

At first glance it appears that whether a starter has been *dealing* in prior innings or not has absolutely no bearing on how he is expected to pitch in the following inning, at least with respect to those pitchers who were allowed to remain in the game past the 6^{th} inning. However, we have different pools of pitchers, batters, parks, etc., so the numbers will have to be parsed to make sure we are comparing apples to apples.

Let’s add some pertinent data to the above chart:

Starters through 6 |
RA9 in the 7^{th} |
Seasonal RA9 |

Dealing |
4.46 |
4.29 |

Not-dealing |
4.48 |
4.46 |

As you can see, the starters who have been *dealing* are, not surprisingly, better pitchers. However, interestingly, we have a reverse *hot and cold *effect. The pitchers who have allowed only 1 run or less through 6 innings pitch worse than expected in the 7^{th} inning, based on their season-long RA9. Many of you will know why – the times through the order penalty. If you have not read my two articles on the TTOP, and I suggest you do, each time through the order, a starting pitcher fares worse and worse, to the tune of about .33 runs per 9 innings each time he faces the entire lineup. In the 7^{th} inning, the average TTO is 3.0, so we *expect* our good pitchers, the ones with the 4.29 RA9 during the season, to average around 4.76 RA9 in the 7^{th} inning (the 3^{rd} time though the order, a starter pitches about .33 runs per 9 worse than he pitches overall, and the seasonal adjustment – see the *note* above – adds another .14 runs). They actually pitch to the tune of 4.46 or .3 runs better than expected after considering the TTOP. What’s going on there?

Well, as it turns out, there are 3 contextual factors that depress a *dealing* starter’s results in the 7^{th} inning that have nothing to do with his performance in the 6 previous innings:

- The batters that a
*dealing*pitcher is allowed to face are 5 points lower in wOBA than the average batter that each faces over the course of the season, after adjusting for handedness. This should not be surprising. If*any*starting pitcher is allowed to pitch the 7^{th}inning, it is likely that the batters in that inning are slightly less formidable or more advantageous platoon-wise, than is normally the case. Those 5 points of wOBA translate to around .17 runs per 9 innings, reducing our expected RA9 to 4.59*.* - The parks in which we find
*dealing*pitchers are not-surprisingly, slightly pitcher friendly, with an average PF of .995, further reducing our expectation of future performance by .02 runs per 9, further reducing our expectation to 4.57. - The temperature in which this performance occurs is also slightly more pitcher friendly by around a degree F, although this would have a
*de minimus*effect on run scoring (it takes about a 10 degree difference in temperature to move run scoring by around .025 runs per game).

So our *dealing *starters pitch .11 runs per 9 innings better than expected, a small effect, but nothing to write home about, and well within the range of values that can be explained purely by chance.

What about the starters who were *not dealing*? They out-perform their seasonal RA9 plus the TTOP by around .3 runs per 9. The batters they face in the 7^{th} inning are 6 points worse than the average league batter after adjusting for the platoon advantage, and the average park and ambient temperature tend to slightly favor the hitter. Adjusting their seasonal RA9 to account for the fact that they pitched poorly through 6 (see my *note* at the beginning of this article), we get an expectation of 4.51. So these starters fare almost exactly as expected (4.48 to 4.51) in the 7^{th} inning, after adjusting for the batter pool, despite allowing 3 or more runs for the first 6 innings. Keep in mind that we are only dealing with data from around 9,000 BF. One standard deviation in “luck” is around 5 points of wOBA which translates to around .16 runs per 9.

It appears to be quite damning that starters who are allowed to continue after pitching 6 stellar or mediocre to poor innings pitch almost exactly as (poorly as) expected – their normal *adjusted* level plus .33 runs per 9 because of the TTOP – as if we had no idea how well or poorly they pitched in the prior 6 innings.

Score one for simply using a projection plus the TTOP to project how *any* pitcher is likely to pitch in the middle to late innings, *regardless of how well or poorly they have pitched thus far in the game*. Prior performance in the same game has *almost no bearing* on that performance. If anything, when a manager allows a *dealing *pitcher to continue pitching after 6 innings, when facing the lineup for the 3^{rd} time on the average, he is riding that pitcher *too long*. And, more importantly, presumably he has failed to identify *anything *that the pitcher might be doing, velocity-wise, mechanics-wise, repertoire-wise, command-wise, results-wise, that would suggest that he is indeed *on *that day and will *continue* to pitch well for another inning or so.

In fact, whether pitchers have pitched very well or very poorly or anything in between for the first 6 innings of a game, managers and pitching coaches seem to have *no *ability to determine whether they are likely to pitch well if they remain in the game. The best predictor of 7^{th} inning performance for any pitcher who is allowed to remain in the game, is his seasonal performance (or projection) plus a fixed *times through the order penalty*. The TTOP is approximately .33 runs per 9 innings for every pass through the order. Since the second time through the order is roughly equal to a pitcher’s overall performance, starting with the 3^{rd} time through the lineup we expect that starter to pitch .33 runs worse than he does overall, again, regardless of how he has pitched thus far in the game. The 4^{th} time TTO, we expect a .66 drop in performance. Pitchers rarely if ever get to throw to the order for the 5^{th} time.

**Fatigue and Pitch Counts**

Let’s look at fatigue using pitch count as a proxy, and see if that has any effect on 7^{th} inning performance for pitchers who allowed 3 or more runs through 6 innings. For example, if a pitcher has not pitched particularly well, should we allow him to continue if he has a low pitch count?

**Pitch count and 7 ^{th} inning performance for non-dealing pitchers: **

Pitch count through 6 |
Expected RA9 |
Actual RA9 |

Less than 85 (avg=78) |
4.56 |
4.70 |

Greater than 90 (avg=97) |
4.66 |
4.97 |

** **

Expected RA9 accounts for the pitchers’ *adjusted *seasonal RA9 plus the pool of batters faced in the 7^{th} inning including platoon considerations, as well as park and weather. The latter 2 affect the numbers minimally. As you can see, pitchers who had relatively high pitch counts going into the 7^{th} inning but were allowed to pitch for whatever reasons despite allowing at least 3 runs thus far, fared .3 runs worse than expected, even after adjusting for the TTOP. Pitchers with low pitch counts did only about .14 runs worse than expected, including the TTOP. Those 20 extra pitches appear to account for around .17 runs per 9, not a surprising result. Again, please keep in mind that we dealing with limited sample sizes, so these small differences are inferential suggestions and are not to be accepted with a high degree of certainty. They do point us in a certain direction, however, and one which comports with our prior expectation – at least *my* prior expectation.

What about if a pitcher has been *dealing* and he also has a low pitch count going into the 7^{th} inning. Very few managers, if any, would remove a starter who allowed zero or 1 run through 6 innings and has only thrown 65 or 70 pitchers. That would be baseball blasphemy. Besides the *affront* to the pitcher (which may be a legitimate concern, but one which is beyond the scope of this article), the assumption by nearly everyone is that the pitcher will continue to pitch exceptionally well. After all, he is not at all tired and he has been *dealing!* Let’s see if *that *is true – that these starters continue to pitch well, better than expected based on their projections or seasonal performance plus the TTOP.

**Pitch count and 7 ^{th} inning performance for dealing pitchers: **

Pitch count through 6 |
Expected RA9 |
Actual RA9 |

Less than 80 (avg=72) |
4.75 |
4.50 |

Greater than 90 (avg=96) |
4.39 |
4.44 |

Keep in mind that these pitchers normally allow 4.30 runs per 9 innings during the entire season (4.44 after doing the seasonal *adjustment)*. The reason the expected RA9 is so much higher for pitchers with a low pitch count is primarily due to the TTOP. For pitchers with a high pitch count, the batters they face in the 7^{th} are 10 points less in wOBA than league average, thus the 4.39 expected RA9, despite the usual .3 to .35 TTOP.

Similar to the *non-dealing* pitchers, fatigue appears to play a factor in a *dealing *pitcher’s performance in the 7th. However, in either case, low-pitch or high-pitch, their performance through the first 6 innings has *little bearing *on their 7^{th} inning performance. With no fatigue they out-perform their expectation by .25 runs per 9. The fatigued pitchers under-performed their overall season-long *adjusted *talent plus the usual TTOP by .05 runs per 9.

Again, we see that there is *little value *to taking out a pitcher who has been getting a little knocked around or leaving in a pitcher who has been *dealing* for 6 straight innings. Both groups will continue to perform at around their expected full-season levels plus any applicable TTOP, with a slight increase in performance for a low-pitch count pitcher and a slight decrease for a high-pitch count pitcher. The biggest increase we see, .25 runs, is for pitchers who were *dealing* and had very low pitch counts.

What about if we increase our threshold to pitchers who allow 4 or more runs over 6 innings and those who are pitching a shutout?

Starters through 6 |
Seasonal RA9 |
Expected RA9 |
7^{th} inning RA9 |

Dealing (shutouts only) |
4.23 |
4.62 |
4.70 |

Not-dealing (4 or more runs) |
4.62 |
4.81 |
4.87 |

Here, we see *no* predictive value in the first 6 innings of performance. In fact, for some reason starters pitching a shutout pitched slightly worse than expected in the 7^{th} inning, after adjusting for the pool of batters faced and the TTOP.

How about the holy grail of starters who are expected to keep lighting it up in the 7^{th} inning – starters pitching a shutout *and *with a low pitch count? These were true talent 4.25 pitchers facing better than average batters in the 7th, mostly for the third time in the game, so we expect a .3 bump or so for the TTOP. Our expected RA9 was 4.78 after making all the adjustments, and the actual was 4.61. Nothing much to speak of. Their *dealing* combined with a low pitch count had a very small predictive value in the 7^{th}. Less than .2 runs per 9 innings.

**Conclusion**

As I have been preaching for what seems like forever – and the data are in accordance – however a pitcher is pitching through X innings in a game, at least as measured by runs allowed, even at the extremes, has very little *relevance* with regard to how he is expected to pitch in subsequent innings. The best marker for whether to pull a pitcher or not seems to be pitch count.

If you want to know the most likely result, or the mean expected result at any point in the game, you should mostly ignore prior performance in that game and use a credible projection plus a fixed *times through the order penalty*, which is around .33 runs per 9 the 3rd time through, and another .33 the 4^{th} time through. Of course the batters faced, park, weather, etc. will further dictate the absolute performance of the pitcher in question.

Keep in mind that I have not looked at a more granular approach to determining whether a pitcher has been pitching extremely well or getting shelled, such as hits, walks, strikeouts, and the like. It is possible that such an approach might yield a subset of pitching performance that indeed has some predictive value within a game. For now, however, you should be pretty convinced that run prevention alone during a game has little predictive value in terms of subsequent innings. Certainly a lot less than what most fans, managers, and other baseball insiders think.

[…] A fascinating read from MGL on taking out, or leaving in, pitchers who are “dealing.” The short version? It appears that there is no predictive relationship between how a pitcher pitches in the first six innings and the seventh. In other words, just because a guy has cruised for six innings, that doesn’t mean he’s any more likely to pitch well in the seventh than he would otherwise. That feels wrong, given that guys admittedly have better stuff/command/control on given days (maybe they simply feel physically better), but the numbers are the numbers. This is why we have sabermetric analysis: sometimes the data simply doesn’t support the things we “know” to be true, and we have to re-examine what we think. That’s a good thing, whether you’re wearing a jock or not. […]

I especially liked the point about the quality of the batters faced. In the 7th a pitcher probably is facing the bottom of the order the third time through. If he has a perfect game going, it’s the top of the lineup, but if you’ve allowed 1 baserunner per inning, it’s 7-8-9. Trying to control for the quality of the batters does make sense.

Interesting. I didn’t look at the average lineup slot in the 7th. It is also true that the manager is more likely to leave the starter in if he has the platoon advantage for the batters he faces in the 7th. When I did my “batter adjustment” I also adjusted for the platoon advantage. It is also possible that managers are more likely to leave in a starter who IS facing the bottom of the order.

[…] most of the game, that has no extra predictive value going foward, based on real-world results? http://mglbaseball.wordpres… and […]

thank you