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 14 – Matt 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 24 – Drew 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 25 – Erasmo 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 27 – Nate 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 1 – Alex 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.