Using Three to Make Two

Photo courtesy of David Banks-USA TODAY Sports

As the Cubs’ rotation stands right now, they’ve got three (sorry Edwin Jackson) back-end starters on the roster in Kyle Hendricks, Travis Wood, and Tsuyoshi Wada. With conventional usage, Hendricks and Wada are traditional starting pitchers who will be expected to toss at least six innings before turning things over to the bullpen. Wood becomes a situational reliever, who you might expect to throw an inning every other day.

Suppose instead of expecting the back-end starters to go six-plus innings, the expectation was that Hendricks and Wada would instead go through the batting order exactly twice, then turn the ball over to Wood, a reliever with back-end starter ability who was expected to go through the order exactly once. Then Wada, who was brilliant last year in his first two times through the order, wouldn’t have to face a lineup the third time through, where he was simply awful. Wood was a league-average starter his first time through the order, and much worse afterwards. Hendricks’ pattern is unusual—decent the first and third times through, very good on the second time through opposing lineups.

Here is some data on the three Cub starters in 2014-15. These numbers show how each pitcher performed on their first, second, third and sometimes fourth trips through the opposing batting order.

1st PA in G as SP 19 171 1.00 0.320 0.721 123 3.52
2nd PA in G as SP 19 161 0.28 0.239 0.506 40 3.16
3rd PA in G as SP 18 114 1.18 0.360 0.754 165 3.46
4th+ PA in G as SP 3 7 0.00 0.143 0.286 -17 1.14
1st PA in G as SP 38 342 0.95 0.317 0.707 106 4.06
2nd PA in G as SP 38 338 1.07 0.336 0.761 114 4.02
3rd PA in G as SP 36 247 1.71 0.396 0.919 145 5.65
4th+ PA in G as SP 9 14 1.29 0.286 0.747 118 2.54
1st PA in G as SP 13 117 0.38 0.250 0.528 56 1.99
2nd PA in G as SP 13 116 0.62 0.313 0.690 95 3.52
3rd PA in G as SP 11 56 1.77 0.429 1.249 226 8.35

A few quick notes before some analysis. R/9 PA is essentially the number of runs the pitcher allowed on average in that particular turn through the order. sOPS+ represents the OPS allowed by each pitcher relative to league average for that particular split. This is estimated by plate-appearance weighted average for Wood and Hendricks who have had appearances in both 2014 and 2015. Also, FIP reported here is not perfectly accurate because it isn’t easy to completely account for outs made on the basepaths, so Innings Pitched used to calculate FIP is estimated as (AB-H+GDP+SH+SF)/3.

The Cubs’ other three starters, Jon Lester, Jake Arrieta and Jason Hammel, are all better than league average in their third trip through the order, so there’s no reason to limit them to two turns through. Wada and Wood, however, should never see a hitter for the third time in a game. Wood allows a .919 OPS on his third trip through, while Wada’s FIP is an astronomical 8.35.

I’m not sure which two pitchers would be best-suited for the scheduled starter role and which pitcher would be suited for the scheduled long relief role, but the Cubs have sent Wood to the bullpen, so we’ll go with that. How would the below rotation work?


The first thing to examine is workload. This approach is predicated on an assumption that Wood can pitch to nine batters with two days’ rest in between, and that there are enough off-days in the schedule to juggle the rotation accordingly. It’s also plausible to skip a planned relief turn and use Jackson or a committee in a pinch. Wood would see more frequent usage than a typical starter, with longer outings than a typical reliever. There aren’t very good contemporary comparisons for this sort of usage, but it was common among bullpens prior to the rise of the modern closer. As for the starters, they would pitch with the same frequency but less intensity, which should help with wear and tear as the season goes along.

An examination of the chart shows that each pitcher made it through the lineup at least twice in nearly every single start. In 70 combined starts totaling 398 innings pitched, there were just five games in which the starter didn’t at least begin the third trip through the order. On average, these three starters tossed 5 2/3 innings and faced about 6.5 batters after the second time through the order, including a few outings where the starter pitched into the fourth time around.

If the Cubs adhere to the plan strictly, with the starters (Wada and Hendricks) facing the first 18 hitters and the reliever (Wood) facing the next nine, then, we can estimate how deep in the game these pitchers might expect to go. In Wada’s first two trips through the order, we can expect him to record approximately 13.15 outs, while Hendricks records 13.04 outs. Wood, meanwhile, notches 6.23 outs in his first trip through the order.  That’s a little better than 6 1/3 innings every time out, and because we’ve gotten rid of Wada and Wood’s third trip through the order, they’re 6 1/3 better innings than the 5 2/3 we used to get. We’re replacing Hendricks’ sOPS+ of 165 and Wada’s sOPS+ of 226(!) with Wood’s sOPS+ of 106.

That extra 2/3 of an inning makes it hard to do an apples-to-apples comparison of run expectancies between the traditional approach and the approach outlined here, but we can make some back-of-the envelope calculations. If we look at runs per nine plate appearances for each of the splits in the table, we can get a good approximation of how much each pitcher might allow in each turn of the lineup. Hendricks allows one run in the first trip through, 0.28 runs in the second trip through, and 1.18 in the third. Replace that 1.18 with 0.95 runs allowed by Wood in his first trip through the order, and we’ve allowed 0.23 fewer runs. With Wada, we get to replace 1.77 runs in the third trip through the lineup with 0.95 runs, a savings of 0.82 runs in Wada starts.

Over 60 starts in a season, the three-headed monster might reasonably be expected to work two outs deeper into games and allow about a half a run less than Hendricks and Wada holding down traditional roles. They also can be expected to toss 40 more innings in those starts, but they also use up one more roster spot that could go to a relief specialist. These 40 innings are essentially coming from Wood at the expense of the last reliever in the bullpen.

In 2014, the average National League club threw about 1450 innings over the course of the season. If Lester, Arrieta and Hammel are good for 210 apiece, while Hendricks, Wada and Wood contribute 380 in total, that leaves 440 innings to be covered by six or seven bullpen slots. Last year’s Cub bullpen tossed a National League-high 536 1/3 innings with seven or eight bullpen slots, and the median bullpen usage was 479 bullpen innings. Joe Maddon’s Tampa Bay Rays tossed 509 relief innings. It would seem, then, that this approach would not be overly taxing on the bullpen.

A strategy like this has some interesting and potentially innovative implications for roster composition. This arrangement would have been perfect for Greg Maddux’s swan song with the Cubs, where he was essentially a five-inning pitcher by design. Roger Clemens was similar in his last year. Steven Strasburg’s rookie campaign might have been regarded very differently had he had his innings spaced out in this way, rather than simply shut down before September.

It also has the potential to free up a host of 4-A starters and talented but flawed prospects. Maybe they have two major-league quality pitches but not a third. They may have starter durability, no major platoon splits, and good command, but without the third pitch, they’re exposed the third time through the order. Or maybe they have the repertoire, but not quite have starter durability. C.J. Edwards’ slight frame might not project as such a problem if he only has to throw 75 pitches. How would Kerry Wood’s career have looked if he didn’t have the pitch count problems in the middle innings that came with missing so many bats in the early ones?

I am sure that part of the reason a strategy like this hasn’t been employed is that it relies to some extent on off-days to keep the rotation on schedule, and that’s a potential problem, but it’s a solvable one. Roster-juggling to push back Wada/Hendricks starts would lead to 2-3 more Lester/Arrieta/Hammel starts over the course of the season, not a bad thing. And if you can’t avoid a situation where Hendricks and Wada have to pitch with just one day of rest between them, you can ask the starter to go an extra inning or two, something their arms should be well-rested for.

I worry, though, that a big part of the reason a strategy like this hasn’t been tried is because of the Pitcher Win stat, which requires the starter to toss five innings, or its evil twin, the Quality Start, which requires the pitcher to go six. Wada and Hendricks aren’t likely to be happy with a baseball card that shows, say, four wins in 30 starts despite strong (and improved!) advanced metrics and an increase in team success, but smart fans would know better.

Wood, on the other hand—he’d probably become an odds-on favorite to break Roy Face’s record for relief pitcher wins in a season (18),  and might even have an outside shot at 30.

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4 comments on “Using Three to Make Two”


I’ve been interested in this general concept since Earnshaw Cook’s “Percentage Baseball”. An added advantage is that it gives you a semi-DH in the N L. The drawback is roster spots and bullpen recovery rates, in particular the latter.

Michael Wenz

Haven’t read the book, thanks for the tip. I don’t know what the right recovery time would be for a 35-pitch outing would be, but two days off seems about right to me. The roster spot issue I don’t think is a problem. In the article I argued you get two starter workloads plus 40 IP from the the third spot, but I think you could do a bit better than that. Sometimes the starter will find themselves in a low-leverage spot with one or two outs in the fifth as the lineup flips. Like if last night’s game was 3-0 instead of 3-2 when Wada was yanked. The same may be true for the reliever innings. On those days, let him throw to an extra hitter or two. I’d bet you could pick up an extra 20-40 outs that way over the course of a season, so it would be more like 50 extra innings, not 40.

Al B.

A four-headed monster, Wada/Jackson and Hendricks/Wood would seem even better, assuming Jackson could be counted on for even that. By alternating handedness in each piggyback arrangement, lineup construction becomes more complicated for opposing managers. Having Wood pitch twice in a cycle seems like it’s asking for unforseen (negative) consequences.
If Jackson can’t be counted on for even that, and assuming the DFA would soon follow, CJ Edwards would seem like a perfect counterpart to Wada, and might ease the transition into a big league season (4 months of 70 pitches every 5th day).


4 guys is too many roster spots I think, but I do think C.J. Edwards would be perfect for a role in this. Jacob Turner maybe too.

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