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It’s the 2015 trend that no one is talking about. The Rays are at it again. Even with Joe Maddon in Chicago, they’re still getting all inventive on us. It’s easy to miss if you don’t watch Rays games every night (indeed, Tommy Rancel of Rays blog The Process Report tipped me off to this one) but the Rays have apparently figured their #NewMoneyball. It used to be signing Evan Longoria, or turning Ben Zobrist into a resonance structure, or trading for Wil Myers, or trading Wil Myers, but this year, the Rays are trying something different.

They don’t do it every night, but see if you can pick up on the pattern here:

· April 14Matt Andriese starts, faces 18 batters (72 pitches). 2 runs, 5 hits, 1 walk, 2 strikeouts, pulled after 3.2 IP with runners at first and third with two out.

· April 19 – Andriese again, faces 18 batters (63 pitches), 4 runs, 8 hits, 2 walks, 1 strikeout, pulled after giving up an infield hit with a runner at first and one out. He lasted 3.1 IP

At this point, there’s no pattern other than noting that Andriese is a rookie who was pitched himself into a jam in the first game and just wasn’t having a good game in the second. Nothing to see here.

· April 24Drew Smyly starts, faces 18 batters (79 pitches), and gives up 2 runs on 4 hits (5 K/1 BB). Pulled in the middle of the fifth inning with two outs… which were the result of Smyly retiring the first two hitters in the inning. (Andriese gets the save with three innings of relief!)

· April 25Erasmo Ramirez starts, faces 16 batters (58 pitches), allows one run on 4 hits, 1 walk, and 2 strikeouts. Pitches four innings and doesn’t come out for the fifth. His fourth inning had been three uneventful grounders, all to Logan Forsythe at first.

Ramirez was making a spot start, and 10 days earlier, he had thrown 91 unspectacular pitches (and didn’t make it out of the fourth), so maybe the Rays just didn’t want to tempt fate. Smyly’s outing was his first of the year, coming back from a Spring Training injury. I get that it may have always been scheduled as a five-and-fly, but Smyly’s pitch count wasn’t super high and had he gotten one more out, he would have been eligible for the most important pitching stat of all – a win. Why pull him then?

· April 27Nate Karns faces 19 hitters (87 pitches), only gives up a run on three hits, but two walks. He does strike out five. He leaves after 4.2 IP after pitching himself into a jam in the fifth. I’d assume that this was just Kevin Cash going to get a kid in trouble, except…

· May 1Alex Colome starts, faces 18 hitters (60 pitches), gives up no runs on three hits, with no walks and six strikeouts in five fantastic innings. Huh?

· May 3 – Nate Karns again, faces 18 hitters (66 pitches), gives up no runs two hits, with one walk and four strikeouts in five fantastic innings. Double huh?

· May 6 – Alex Colome again, faces 20 hitters (79 pitches), gaves up 2 runs on 4 hits, no walks and four strikeouts in five-plus innings. This one isn’t as suspicious as he leaves so that a lefty can face David Ortiz.

· May 9 – And just to bring everything full-circle, Matt Andriese pitches to 17 hitters (65 pitches), giving up 2 runs on 5 hits, (1 walk, 2 K’s). He leaves with two out in the fourth, after giving up a two-run home run and a double.

Regular readers of Sabermetric writing will probably pick up on the pattern. The Rays are being very careful about letting certain starters go through the lineup a third time. It’s not every night (Colome pitched last night and faced 29 batters… giving up eight runs), but there are nights when they’re being rather obvious about it, taking pitchers out mid-inning who aren’t in trouble and pulling pitchers who are throwing shutouts. Taken individually, many of these cases might just be the result of a quick hook on Kevin Cash’s part. But the number 18 has come up enough that it makes me wonder.

Mitchel Lichtman has written extensively about the issue, pointing out that as the pitcher turns the lineup over another time, particularly the third time, he suffers a penalty. Even controlling for how well their seasonal stats say that they should hit, the hitters have a decided advantage their third time around. Jon Roegele has shown that the more of a specific type of pitch that a batter sees from the pitcher (i.e., he’s seen five fastballs from Smith today), the more bonus he is likely to pick up. Lichtman also found that pitchers who have more pitches in their repertoire seem to have less of a penalty as the game wears on.

A question. There’s naturally something else that happens as a pitcher turns over the lineup for the third time. At the very least, he’s throw a few dozen more pitches than when he went through the second time. The magic behind the third time through the order penalty might just be that the pitcher is tired. If the Rays really are asking how many hitters a pitcher has faced, rather than staring at his pitch count, are they looking at the right number?

Warning! Gory Mathematical Details Ahead!

I used data from 2010-2014 and using the log-odds ratio method calculated how likely it was that a given batter-pitcher matchup would end up in a strikeout (min 250 PA for both pitcher and batter, limited to starters only in the first three times around the lineup). I put this control into a logistic regression. I added in the pitcher’s pitch count at the beginning of the plate appearance and which trip around the lineup this was (entered categorically, for the super initiated.) I made similar regressions for walks, HBP, etc. I made the regression a stepwise regression, specifically so that the two variables could fight it out and we could figure out which one was more important.

The results depended on the outcome and it was something of a mixed bag. For strikeouts, times through the order was a better predictor, and as expected they became less frequent relative to expectations. Walks, on the other hand, were more pitch count dependent, but their frequency went down as the game went on. Singles and home runs were tied more to pitch count, but extra-base hits (doubles/triples) were more tied to times through the order. All went up as the game wore on. Outs in play were more dependent on times through the order, but as the pitcher turned the order over, he became more likely to induce an out in play (but remember, less likely to induce a strikeout).

It’s not entirely clear which factor drives more of the equation. In no case did both variables enter in simultaneously. That is, once the regression decided that pitch count was the stronger predictor, there was no variance left over for times through the order. It seems like they are both picking up a lot of the same variance. But they do tell a rather interesting story combined. As the game wears on, outcomes in which the batter doesn’t hit the ball (strikeouts, walks) go down (again, relative to expectations), while outcomes where the ball is put into play go up. Expected BABIP and OBP go up (best predictor is pitch count).

So, strikeouts go down, outs in play go up. Walks go down, hits go up. In fact, I ran a regression predicting whether an at-bat would end in a “contact event” (not a walk, strikeout, or HBP), again controlling for batter and pitcher rates and sure enough, there was a big difference between the first, second, and third times at bat. Hitters really do put it in play more often as the game wears on. Not only that, but I dug deeper.

At the individual pitch level, again controlling for pitcher and batter tendencies on this sort of thing, we see that in the first time through the lineup, we see fewer swings, less contact when the batter does swing, and when he doesn’t swing, it’s more likely to be a called strike. As the game goes on, we see more swinging, more contact, and less likelihood of taking a called strike. Plate appearances were also longer in terms of pitches seen. What’s interesting, is that when I limited my sample to batters who are having their third time at bat and then looked at whether they were facing the starter or a reliever, when the batters were facing a reliever, these effects disappeared.

If there is a times through the order effect, I think we’re misinterpreting what’s going on to cause it. The increased contact the third time around could be that pitchers are giving pitchers better offerings to hit. Or perhaps the hitters are taking a different approach. Maybe both. If hitters are doing better, it might not be because they have learned more about the pitcher through repeated interactions with him. It might just be that at the beginning of the game, hitters are taking bigger swings, and waiting more patiently for their pitch. By the third time up, when the starter is a little more tired, they might think a more pro-active approach is better. (“He’s more tired, he might give me something to hit.”) Plus it’s probably his last chance to do some damage against this guy. The different approach seems to be a better one or at least it works better with a tired pitcher.

This Isn’t My First Time Around
But with that said, I don’t see conclusive evidence that the 19th batter is specifically cursed. It’s much more to do with the fact that by batter 19, a starter is beginning to get gassed, and batters seem to change their approach. If there’s a message to be drawn here, it’s actually not about how teams should deploy their starters, but what they should tell their hitters. If it works in the sixth inning, it might work in the second. But as far as pitchers go, it seems like the evidence points to the boring conclusion that a pitcher should pitch until he is tired and there is a better replacement available in the bullpen.

In defense of the Rays, it’s entirely possible that they’re not being completely dogmatic about the “third time around” rule. They might be using the 18-batter rule as a way to say that they want to keep a short leash on some nights or with some pitchers. There are advantages to using fresh pitchers when they are available and conserving a guy’s innings. It might be easier to say to a pitcher “We’re sending you out there for 18 batters” than to give some sort of vague “until you look tired.” But now that you’ve been shown it, you’re going to watch a couple of Rays games, aren’t you. Maybe that was the New Moneyball all along.

Thank you for reading

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I'm confused about your conclusion: if we're nor certain whether the effects seen are a result of pitch count or times through the order, how do we know it's related to batter approach? You cite the vanishing effects when a reliever enters, but if the reresults are tied to pitcher tiring wouldn't we also expect that vanishing? As in, isn't it inconclusive that the effects go away when a reliever comes in?
There are two possible theories as to what's happening. One is that I do better against the pitcher the third time around because his pitch count is at 80 and he's been working for an hour and a half, vs. back in the first inning when his pitch count was 10. The other is that I've now seen him three times and have a better feel for him. Of course, the two are going to be conflated. The lack of a clear victory for either theory in my initial set of regressions suggests that there's a certain amount of conflation.

What surprised me though was that the results weren't "strikeouts and outs in play go down, everything else goes up." It was strikeouts and walks go down, everything involving the ball being hit into play goes up. The difference isn't that hitters are universally better, just that they are putting the ball into play more often (and are getting better value for doing so).

The reliever issue was telling. The starter vs. reliever was "guys in their third AB of the game", so if it was just a matter that as the game went on, guys got more contact happy, we'd see no difference for starter vs. reliever. But there was one. I guess my argument is that batters treat a third time against a starter differently. In essence, that the batters become (somewhat) different hitters and that's actually what makes them better.

There is some magic to the 19th batter....

You accept that the expected sequential increase in wOBA per batter accelerates typically when a pitcher is passing through a line-up a 3rd time (whether due to pitch count or batter experience/strategy we cannot say)

We can also reasonably assume that for most line-ups the largest sequential increase in wOBA is from the #9 batter to the #1 batter

Therefore, an optimum point to remove a starter would be after the 18th batter as the sequential move from the 18th to 19th batters suffers the greatest increase in expected batter wOBA due to the combination of the factors above....
There is and there isn't. My analyses control for the fact that the #1 hitter is likely better than the #9 hitter. All of this is relative to seasonal expectations. If there is magic to the 19th batter, or if there is some preventive power in pulling the starter at that point, it's in that it possibly stops the offense from adopting a more potent strategy (more focus on putting the ball in play). There's no specific reason why the offense can't do that at other times, but these numbers suggest that for whatever reason, they don't. So, putting in a reliever would keep them in sub-optimal mode.
If this really is a strategy than it should fit in with going to a four-man rotation. Might we see some evidence for that?
If a team wanted to really go deep into this, they would probably have to adopt a four-man rotation, if only because they'd need more bullpen arms. They might also try something more along the lines of having more relievers who are "longer" rather than the 58 tactical relievers that most pens have now.
I disagree with your thesis and conclusions. My research made it pretty clear, at least to me, that the times through the order penalty is about familiarity and not fatigue. In other words there IS magic to not facing the 19th batter. That is easy to test though and I'm surprised you did not.

Simply look at the results of the 18th and 19th batters in all games against the starter. If there is no magic then we should see a blurred line between the performance of the two. If we see a bright line, which I think we will, then that strongly suggests it's all about familiarity.

I also don't know why you ascribe some magic to the third time through the order. There isn't. The penalty from one time to the next is pretty constant other than the huge first time penalty for the road team.

As far as the penalty having to do with pitcher and batter approach and not so much familiarity per se, that is possible. However, I doubt that. If it were, as you imply, that would mean that batters or pitchers are using a suboptimal approach either at the beginning of the game or as the game goes on. Plus, I have shown evidence that the more pitches a batter sees in his first AB, the better he performs, by a lot, in the second AB. Again, that suggests that the effect is one of familiarity.
I actually ran (but did not report on) number of pitches previously seen in this game from this pitcher as a potential predictor, but it never poked its head above significance and never beat out either times through the order or pitch count overall. It got left on the cutting room floor for that reason. Because it would be conflated with overall pitch count and times through the order, it makes sense.

You are correct that there's generally a stair-step pattern to times 1 then 2 then 3 on the outcomes, although the steps that I saw were a little steeper for the transition from 2 to 3 than from 1 to 2. That could just be "fatigue is not linear" or it could be that on the second PA, guys are a little more contact happy, but by the third, they are fully invested in the approach, for whatever reason.

I focused on 2->3 because no one takes the starter out after 9 batters. The tell for me was that it wasn't hitters taking the same approach and just getting better at everything. Strikeouts go down, but outs in play go up. In some sense, we're just changing how the outs are made. On top of that, we have the evidence about the changing of the approach.

It doesn't shock me that baseball players would use a sub-optimal strategy. Isn't that why we all have jobs writing this stuff? ;) You could say that early in the game, guys are being too picky, or they're too invested in the idea of running up the pitch count and they are taking too many pitches. Maybe it's not sub-optimal given where the pitcher is at the time. When the pitcher is fresh, it pays to take bigger, riskier swings and be more picky. When he's more tired, it makes sense to just go up there and hack.
I am not disputing that pitcher and batter approaches change as the pitcher cycles through the order. I am simply highly doubtful that the increasing advantage by the batters is due to a sub optimal approach by batters early in the game or a sub optimal approach by pitchers later in the game. There is just no way that we would see such a drastic penalty each time through the order.

As far as fatigue versus familiarity that should not be too hard to figure out without doing regressions (of which I am not a fan of unless they are absolutely necessary). I mean if fatigue is a driving factor and familiarity was not the driving factor we would see at least 2 things. One, the bottom of the order would show a larger advantage than the top. And two, if we simply look at 2nd and 3rd time deltas while holding the pitch count constant we should see very little difference if it were all about or even mostly about fatigue.

For example if we look at second time penalties at 80 pitches versus 3rd time penalties at 80 pitches that should give us some idea as to whether the overall effect is mostly fatigue, familiarity or some combination of nearly equal parts.

Have you looked at those 2 things?
I would question whether there's any signal in all that noise... a pitcher who is at 80 pitches the 2nd time through the order likely has some bigger problems than hitters getting a 2nd look at him.
I was just using that as an example. It could by any number. As long as you held pitch count relatively constant.
I think you're making this more complicated than it is. One, batters perform better as they face the same pitcher more and more. Any baseball player will tell you that that is the case. Two, when you are unfamiliar with a pitcher, even if you have seen him before in previous games, you take many more pitches simply because you are more tentative. So of course you will walk and K more early in the game. And as you become more familiar with the pitcher, you are more aggressive, you get fooled less, and you hit the ball harder. It's really not complicated or mysterious.
But the question becomes, would there be a benefit to trying to be at least a bit more aggressive earlier? Hitters might get fooled more, but would the aggressiveness pay off enough to offset it? The first step was confirming that the change in behavior was real. The next step will be figuring out if it can be better optimized.
We have no idea as to the answer to that question, but my educated guess is no.
I love that you are trying to quantify what many are simply taking for granted.

It was those efforts that formed the basis of sabermetrics and lead us to really reconsider many of the baseball myths.

Keep up the analysis of macro trends. I love it.
Did you or MGL (or anyone else...) ever look at times-through-the-order effects in long relief appearances? Using the approach of this article, one could see whether or not the changes in approach are due to growing familiarity with the pitcher or related purely to inning.

Maybe there aren't enough >9 PA relief appearances to get a useful sample, but I'd think the mechanisms under discussion are endemic enough to baseball/human nature that going back farther than 2010 wouldn't be unreasonable.