May 20, 2013

Baseball Therapy

Would the Astros' Piggyback Starters Model Work in the Majors?

by Russell A. Carleton

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A few weeks ago, I wrote an article in which I suggested that teams might benefit from going to a model that gets rid of the traditional starting pitcher. Instead of having five men who are expected to go 6-7 innings over 100 pitches, I suggested a model in which three pairs of pitchers each throw 50 pitches, and on the third day, they would pitch again, in fulfillment… I should stop there. I argued that a team that committed to that model could leverage a group of (cheap!) pitchers who were good for a couple innings, but not for six. In this way, a team could get the same sort of results that they might expect from having a bunch of pretty good starters, but for a fraction of the (David) Price.

Three days later, Houston Astros GM Jeff Luhnow announced that his organization would be using a similar model in their minor league affiliates. Luhnow said at the time that the goal was to allow the team to get a good look at eight pitchers (in four pairs, with one member of the pair throwing 75 pitches and the other 50, and the two switching after three days) rather than five in the traditional model. Coincidence? Actually, yeah. On both ends.

The Astros have quietly abandoned the idea at the Triple-A level, seemingly because several key members of their “rotation” were called up to the big club. If we take the Astros at their word, this arrangement makes perfect sense. A tandem starter model does allow for the team to get a good look at more than five guys, and the outcomes of minor league games don’t matter much. Luhnow stated that the Astros have no desire to do this at the major league level.

But what if they did?

Warning! Gory Mathematical Details Ahead!
One of the first things that I did with this was to fire up a sim game and play within these rules, just to see what strategic situations popped up that I hadn’t expected. I started as a National League team with no DH, figuring that I could leverage the fact that I could pinch hit in the middle of the game for the pitcher’s spot sometimes. While this happened in a couple of games, I often found myself in a situation where it was the sixth or seventh inning of a close game and the second pitcher in the tandem had thrown 30 pitches (20 short of his allotment). Should I pinch hit?

This sort of decision happens in the traditional starter model as well. The manager must make a decision between the value of the extra inning that the starter might give him versus the increased probability that a pinch hitter might help to score a desperately needed run. But in the traditional model, the manager does it with the luxury of a six- or seven-man bullpen. If there are eight “starters,” a team could really carry only four relievers, meaning that the relative cost of pinch hitting, even in a high-leverage at-bat, just went up. Who would have thought that teams would miss having those two extra lousy relievers?

In the American League, this wouldn’t be an issue because of the DH, so I think an AL team would be much more likely to adopt this model. And as I have to keep reminding myself (and others), the Astros are now in the American League. But that four-man bullpen is still an issue. The problem with a small bullpen is that using a reliever not only affects today’s game but tomorrow’s. Use a guy for too long, or for too many days in a row, and suddenly he can’t pitch the next day and you’re down to a two- or three-man micro-bullpen. It did lead me to consider a variation on the Astros model in which the “starting” staff consisted of seven pitchers (rather than eight). Each pitcher started on a day of the week (for example, Monday) and threw 75 pitches, then rested for three days (Tuesday-Thursday), pitched on the fourth day (Friday) in relief, throwing 50 pitches, rested for two days (Saturday and Sunday), and then started the cycle again on Monday. This could allow for a team to gain a fifth man in the bullpen, but that’s still a big handicap. Or is it?

It’s easy to hear “five-man bullpen” and assume that the plan wouldn’t work. We are all creatures of our age, and we’ve been trained to think about bullpens in a specific way. The average number of relievers used in a game has gone up over time. We live in the era of the LOOGY and the one-inning closer. We’ve been trained to believe that you need a lot of bodies in the bullpen. Maybe the problem is that we’re thinking about the way things are now, rather than what they could be.

Let’s first look at what could be gained on the starting end of such a plan. In my original piece, I identified 15 pitchers (Carl Pavano, Jake Arrieta, Tommy Hunter, Colby Lewis, Justin Germano, Drew Hutchison, Brandon Beachy, Bud Norris, Hisashi Iwakuma, Charlie Morton, Ryan Vogelsong, Vance Worley, Jered Weaver, Joe Kelly, and Mike Minor) who, in 2012, had an xFIP in their first 50 pitches that was at or below 3.75 but got significantly worse after that. Since we have one pitcher throwing 75 pitches, and the other 50, let’s look only at what might happen during the first 50 pitches of the “starter’s” 75 and the 50 pitches of the first “reliever’s” tenure. Even if they made it only to the original cutoff of 3.75, the average starter ERA in 2012 was 4.19. I estimated that 100 pitches bought a team about six innings’ worth of pitching. That’s worth 47.5 runs. Call it four and a half wins over the average starting pitcher.

Now, let’s talk about what happens between pitches 50 and 75 for the “starter.” Those 15 pitchers had a combined xFIP of 4.41 between those two points. Now, those 25 pitches are pitches that are thrown by one of our piggyback starters, because they are working in tandem. In a real game, they’d probably be thrown by a seventh-inning reliever. If we make the assumption that the reliever was league average, he would have an ERA of 3.64. Figure that 25 pitches would buy an inning and a half, and our “starter” is at a 20-run disadvantage over the standard league-average reliever over 162 games. Still, we assume that over those 125 pitches, our tandem starters clear about 2.5 wins worth of value over and above what we might expect from those 125 pitches as thrown by starters and middle relievers.

Then there’s the matter of the cost savings that a team would get from relying on pitchers whom the market has devalued. That money could be invested in upgrades elsewhere on the team, perhaps in the bullpen or for the hitters. If a team invested well, it might squeeze out some extra runs from the extra money it saved by going to the tandem model. But let’s for a moment assume that they derive no extra value. This is strictly a cost-saving move on their part.

Can we show that having a smaller bullpen would have a penalty of more than 25 runs over the course of a season? First, let’s look at how much work the bullpen will need to take on per game. I found that in 2012, the average start lasted 17.4 outs, which is almost six innings. I also estimated that 50 pitches would get a starter through about three innings. Running the same sort of analysis, we see that in 75 pitches, a pitcher got through a mean of 13.7 outs, and a median of 14 outs. Call that 3 2/3, for something just shy of seven innings. Our tandem model means that we have fewer guys in the bullpen, but fewer innings for them to pitch.

In fact, while only 127 complete games happened in 2012 (about four per team, roughly three percent of games), judging by the distributions of what starters were able to accomplish in 50 pitches, and then in 75 pitches, a team could expect the two tandem buddies to record 27 outs in about 10 percent of games. So, there would be more nights in which the bullpen wouldn’t need to pitch—assuming, of course, that a manager would stick with the second pitcher into the late innings of a close game. And this brings up another issue: in order for a small bullpen to work, a team would need to allow their second starter to throw his 50 pitches, even if it means that he’s throwing pitch no. 43 in the eighth inning of a close game with runners on.

The way the modern game has evolved, this is when managers start deploying seven-pitches-and-out specialists, mostly to gain the platoon advantage. With a lot of bodies down in the bullpen, there’s always someone new to bring in. And in a high-leverage situation, a fresh pitcher with the platoon advantage is going to at least look a lot more enticing (and often, be a better option) for this particular batter. Especially compared to the failed starter in his third inning who doesn’t have the platoon advantage. And double especially with everyone watching because it’s now the eighth inning.

If we assume that gaining a platoon advantage is worth 20 points of OBP, and the cost of turning an out into a time on base is roughly .75 runs (very back of the envelope here), then over about 60-70 PA in which a team was not able to gain a platoon advantage (but would have otherwise), it surrenders back one of those wins. In 2012, pitchers had the handedness advantage against 39 percent of hitters in the first inning, 41 percent in the second through fourth inning, 44 percent in the fifth inning, and 46 percent in the sixth. In the seventh, it jumped to 52 percent, followed by 53 percent and 49 percent in the eighth and ninth. It looks as though bullpen maneuvering gains the platoon advantage for the pitching team (roughly) an extra 10 percent from the early (starter) innings to the later innings. If a pitcher faces 4.5 batters per inning, he will face an extra 73 batters without the handedness advantage that otherwise would have been handled by a LOOGY or ROOGY. Not only that, but they are high-leverage situations, which means their influence is outsized. There goes at least one win.

To gain the 25-run advantage that I mentioned above, and to even begin to think about allowing a team to survive on a small bullpen, a manager would have to (most of the time) skip playing match-up ball in the seventh or eighth inning. It’s easy to see that a manager is handling a particular decision differently than all the other managers when the situation is highly emotionally charged. It’s not as easy to see the runs that didn’t score in the top of the fifth. One comfort of the modern bullpen is that it’s built to handle high-leverage situations through the sheer number of guys out there, while providing cannon fodder for low-leverage situations. The tandem starter model, because it requires so many roster spots to be burned on starters, doesn’t offer many of these comforts. Sometimes you have to let the second “starter” handle a high-leverage, late-inning situation, and sometimes you have to pitch your closer in mop-up duty because there’s no one else left.

There’s also a hidden assumption that a guy who has been a starter his whole career can pitch just as effectively in the third inning as he can in the eighth inning, even if it’s just his third inning of work. That’s a big assumption. We’ve been trained to believe that only special pitchers can handle those situations, but we know so little about what actually happens in those situations.

Then there’s the matter of extra innings. One nice thing about a six- or seven-man bullpen is that if a manager sees the game careening toward extra frames, he can switch to using his relievers for an inning or two, rather than as matchup artists. That way, if it becomes a war of attrition, he can last longer before #weirdbaseball starts happening. The manager of a tandem starting team has to be more careful in using his relievers to go multiple innings because he doesn’t have that many, and he may need to keep one or two at least serviceable for tomorrow.

Now, for what it’s worth, there’s a cost-benefit analysis to be done here. Yes, the tandem-starter team will lose a game in the 12th with their fourth outfielder taking the loss because he had to pitch, while the other team has three guys sitting out in the pen eating sunflower seeds. But then again, a 12-inning game doesn’t happen all that often. The point of the game is not to avoid having your fourth outfielder pitch, it’s to win more games. If the strategy that you choose means that you gain more on the front end, and the cost is a couple of comic moments on the highlight reel and a smaller number of wins surrendered through these extra-inning games, then it’s a good strategy.

Would it Work?
Let’s look at both sides of the ledger. We can estimate that the tandem starters in an Astros-style system would contribute 2.5 wins over the course of a season in the pitching department, if staffed right, and represent a significant cost-savings to the team, which could be invested in bringing in more wins from other corners. The extra amount would depend on the savvy of the front office, but in theory, a team could realize some real value.

There would be a cost to be paid in the form of not being able to play match-up ball, particularly in gaining a platoon advantage, as much in higher-leverage situations with relievers. This would probably be worth 10 runs, but the situations would be higher leverage and might actually cost more than one win. There may also be a penalty for a “starting” pitcher who is not trained to pitch in late-inning, high-leverage situations, but is attempting to do so anyway (this has never really been tested). Further, the team will lose some extra-inning games through bullpen attrition (and if you figure that with a “normal” bullpen, a team has a 50/50 shot in an extra-inning game, but having a position player pitch is essentially giving up, every game lost to attrition is half a win lost) and some fraction from having to rely on a lesser reliever because the closer had to pitch a lot recently.

So, now we’re down to some unknowns. The success of the piggyback starter model that the Astros have introduced in the minors would probably depend on how good a front office is at spending extra cash on offensive talent. In fairness, that can have two effects, both driving up a team’s runs scored numbers and leading to fewer tense close-and-late situations. But there might be a penalty for asking the second “starter” to pitch in a role to which he is not accustomed.

So, which do you believe is more powerful? Is it the ability of a front office to invest a significant cost-savings in offensive and bullpen talent to produce value elsewhere? Is it the penalty to be paid for asking a pitcher to fill a role that just hasn’t really existed much before? And there’s still the matter of finding actual pitchers who would take part in such a crazy scheme, not to mention the health aspect.

There is a set of circumstance in which you could argue that this system could actually turn a profit. But is that profit worth restructuring the entirety of how a pitching staff is conceptualized?

Russell A. Carleton is an author of Baseball Prospectus. Follow @pizzacutter4
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