Last weekend's MIT Sloan Sports Analytics Conference featured a multitude of insiders and big names, but not all of the thought leaders on hand were as well-know and influential as Mark Cuban, Malcolm Gladwell and Jeff Moorad. The conference also included research paper track presentations, which gave MBA candidates like Greg Rubin an opportunity to display their analytic skills and ideas. Rubin, who attends New York University’s Stern School of Business, sat down with BP to give an overview of his paper, “Paired Pitching: How to Avoid an Arms Race.”


“If you look at the past 25 years, starting pitchers in a five-man rotation are throwing fewer and fewer innings than they used to. I think that’s primarily because of the Moneyball effect where batters are working pitch counts and you get to 100-110 pitches much more quickly. The bullpens, who are less-efficient pitchers than the starters, are now responsible for more of the game.

“The idea here is to cut your losses by saying, OK, our starters aren’t as effective as they used to be and we’re still paying them a lot of money, so instead of having a five-man rotation we’ll have a four-pair rotation where two pitchers each throw four innings per game. The first guy throws innings one through four and the second throws innings five through eight. Then you have four bullpen spots who can take the ninth inning and any extra innings.

“The reason this works is twofold. One is that if you only throw four innings, you’re only facing each batter twice on average. If you look at the data, you’ll see that the more times you face a batter in a game, the better the batter is going to do against you. In 2009, which is the data I used, pitchers averaged 5.8 innings per start and faced each batter 2.8 times.

"Let’s assume that the [first] four innings of statistics — the by-inning statistics — are representative of what a pitcher would throw in innings five through eight. He’s coming in fresh, and if you look at how pitchers perform over their first four innings, you’ll see that it’s much better than how they perform over the successive innings.

“83 starters threw over 150 innings in 2009, and in my study I took the eight most average pitchers. These are mostly guys in third and fourth rotation spots. Going with what those average pitchers were averaging, if you run it out over the course of the season, you would actually save 96 runs using this system. I used the Pythagenpat formula for this. What you would gain is about nine wins per season.

“There are a lot of factors that go into it, but pitchers will say they don’t throw their best stuff every pitch. They wait until they need to, to throw 100 percent. That might be part of why a pitcher might improve over the course of a game: he doesn’t want to use his best stuff early. Pitching only four innings could act as an incentive to throw your best stuff earlier in a game.

“I didn’t quantify what would happen if you pulled a guy who had thrown four perfect innings — whether he was more likely to throw another three, four or five perfect, or near perfect, innings. Would he be better than the next guy? That’s definitely a follow-up piece of research.

“Of course, you would never see a no-hitter, let alone a complete game with this system You’d never see a lot of the things that a pitcher likes to have on his resume, and that his agent wants in order to garner him a larger contract. Because of that, you’d end up saving a lot of money by virtue of the fact that aces wouldn‘t be the same as they are now. Data shows that the average team spent 28 percent of their payroll on their five-man rotation, which constitutes 12.5 percent of the roster. A paired-pitching system would have an economic benefit as well as saving runs.”

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I don't see a link to the paper here, but there just feels like a lot missing with his analysis from the quotes here. It feels like a high-school analysis of a topic that should require doctoral level work.

For example, why does everyone assume that if a pitcher can pitch a certain way for his first four innings, that those innings can happen at anytime of the game?

This feels like a consultant-type analysis in a business where there are far more variables to track than are taken into account here.
"Let’s assume that the [first] four innings of statistics -- the by-inning statistics -- are representative of what a pitcher would throw in innings five through eight. He’s coming in fresh, and if you look at how pitchers perform over their first four innings, you’ll see that it’s much better than how they perform over the successive innings."

That just feels like regression towards the mean. Let's say you have a pitcher who randomly gives up 1 run every other inning(his true ERA is 4.50). He also is always yanked if he gives up 4 runs. If you were to look only at his starts where he pitched 8 innings, then almost by definition they were starts where he outperformed(was lucky) in innings 1 thru 4, that's the only way a guy like that gets to pitch 8 innings. So, while it may look like his performance declines in later innings, it's really just a bias in how the data was selected.

The other thing that strikes me is that any team that tries to implement such an approach will be severely handicapping themselves in terms of talent acquisition. Just because one team decides to use starters this way doesn't mean that all teams will, and doesn't mean that starters will be paid according to this new usage pattern vs the established makrers like ERA, IP, Wins, etc. In other words, which top free agent pitchers would choose to pitch for a team employing this strategy? Which homegrown pitchers would choose to stay with a team employing this strategy instead of demanding a trade or leaving via free agency ? It seems that the costs in terms of talent acquisition would surely be high, but the returns on this strategy are hardly guaranteed, so I can't imagine anyone ever trying it.
Regarding whether or not innings 1-4 can be applied to innings 5-8: I haven't seen anything empirical suggesting otherwise, so until there's even something qualitative to the contrary I think it's an ok assumption to make.

Regarding the distribution of runs allowed: I'm not totally sure how it applies here. If the above assumption is valid, then using data from innings 1-4 should be valid. To your point, that is why I didn't use ERA or WHIP, or something that smooths the data over the entire appearance. Perhaps you could elaborate if I'm not understanding a nuance.

Regarding the cost of talent acquisition: The payment structure would definitely change. I'm not suggesting that this system is easy to implement, or even practical. That said, one nice side effect of this system is that because of the limitations in the cost of talent there is no way all teams would implement this system. So yes - agreed that the marginal cost of talent would change as the number of teams implementing this system changes.

I'm a proponent of tandem pitchers. 96 runs would seem to be a huge exaggeration. I'd be happy to review Greg's research if he wants to email it to me: tom~tangotiger~net
The paper was more detailed than what we covered in a five-minute conversation, so I have invited Greg to jump in here to both clarify and elaborate. Hopefully he will find the time to do soon.
Yeah, due to blowback, you'd be building your pitching exclusively through pitchers you can control: pitchers drafted in the mid-rounds or later. Free agents would never come there, but also high draft picks in the amateur draft would go back to school, most of them. So, really, you'd be building this staff with 5th and 6th starters, not 3rd and 4th.

That said, starting pitching is where a lot of money gets wasted in free agency and the draft, so that might be a place where the "loss" is actually a gain.

IfI were the Pirates, I'd try this out during the inevitable August and September snooze period, as they'll be mathematically eliminated. September rosters seem particularly suited to this.

Also, the author should account for what would happen when they hit the playoffs and lacked anything resembling an ace.
Yeah I didn't really account for what happens in the playoffs.

Other teams that might be in a position to try it (in my opinion): Indians, Blue Jays, A's
Hi all-

I wrote the paper, and thank you for your feedback. I'd be happy to send the full paper to anyone who would like a more in-depth discussion of how I got to the results I did. Email me at gjr250 (at) stern dot nyu dot edu

I'll have more time tomorrow to cover some of the issues raised.

Also, this paper by no means was meant to cover every aspect of tandem pitching...only the most transparent ones. There are a number of analyses that I would have liked to do if given the data.

If you let the starters go 5 innings rather than 4, they could still get the official 'W'. And with 40+ starts per year, you'd again get 20-game winners. I think that would effectively address the political issues. You'd also transfer some innings from your 5-8 'best' pitchers to your top 4.
Yessiree, the '4-Day Richie Rotation!!!' (you can tell how good it is by the extra '!'s) Your top 3 throw 45 starts a year averaging 5 IPs per start. (an occasional efficient 6, occasional pulling after 3-4 when they're already down by a decent amount)
First, I wish you and all Stern grads named Greg unbridled success, as I myself am one.

Now then, I have always seen a few problems with real-life tandems, despite their handiness in sim games like Hardball Dynasty:

1) Invalid assumptions about performance: "Let’s assume that the [first] four innings of statistics -- the by-inning statistics -- are representative of what a pitcher would throw in innings five through eight." I don't think that's a valid assumption. Starting pitchers are accustomed to set pre-game routines based on a known starting time (not quite - obviously some variation for the visiting pitcher - but less variation than when the 5th inning will begin). I think altering that routine would noticeably degrade performance, largely b/c it would hamper the type of fine tuning in the bullpen that is important for starters, resulting in higher BB rates and poorer command of secondary pitches. I say this largely given my own experience and not based on statistics, but I suspect there aren't enough examples of starters moving into a tandem role to create a meaningful sample anyway.

2) Workload management: There is some leverage in starting pitching - a starter's going to be throwing long toss, maybe flat ground, plus 30-40 pitches in the bullpen before entering a game, and he has to do that every time no matter whether he throws 60 pitches or 100. When he throws 60 in-game pitches every 4 days a higher percentage of arm wear is being allocated to warm-up than if he throws 100 in-game pitches every 5 days. In other words you aren't maximizing the wear on your staff's arms, which I think would be costly over the course of a long season. In the shorter term, a strict 4x2 tandem would leave only 4 bullpen arms, only 1 of which could be a long man, so if one or both tandem pitchers can't make it through 4 innings the bullpen will get gased very quickly.

3) tbwhite's last point above, which is dead on, echoed by others. Sure, it could be cheaper, but every free agent knows he won't get paid. I think you'd attract long men who can't find a job as a starter, and the rest of your pitchers would be youngsters not yet eligible for free agency. As soon as they are free agents they will leave, as they won't earn fair value in arbitration. And draftees other than college seniors probably will not sign with a team that employs that strategy either, as they also know they won't get to be a regular starter, with the associated money and glory.

I don't mean to be outright dismissive. Over time you could see some experimentation with tandems. Perhaps teams will experiment with the 5th slot in the rotation, particularly those like the Twins who are long on mediocre starting pitching (though not the Twins themselves as they would never try something unorthodox). But I don't think a full-on 4x2 tandem rotation will ever happen, nor do I think it would work nearly as well in practice as theory might suggest.
1) As I replied to tbwhite - I think it's a valid assumption to make given that we don't have data suggesting otherwise. Feel free to convince me otherwise.

2) I asked a scout for the D-Backs about this and he said that pitchers can do whatever you train them to do, and that he didn't see the reduced "recovery" time as a limiting factor. The trick would be to model the likelihood of a tandem pitcher not being able to go his 4 innings. My sense is that it's either Poisson or Erlang distributed - in which case you could plan your bullpen accordingly.

3) Totally agree in that you'd attract young guns and veterans who just want to pitch somewhere on anything but a minor league contract. I see this system as more of an "ace factory" in that young guys would come in, pitch in tandem for a couple years, then you could trade them (from a position of power) to a standard rotation team.

4) Yeah I think if at all, you might see a team experiment with a 5th rotation spot (though it might mean carrying an extra bullpen pitcher).
I posted a reply to Greg's paper on my blog, as well as posting his paper there.
Interesting idea.

What happens when starter #1 gets bombed in the second inning? You can't use the other 7 starters or your "closer". I guess you also propose having 2 mop-up men on your staff? Seems a shame to use your worst pitcher in the second inning down 4-0, effectively giving up the game.
The Leverage Index of that situation is 0.4. No reliever has an LI as low as 0.4 for the season, meaning that that IS the situation in which you would want to use your mopup reliever.

And, it's hardly "giving up the game". How is putting in a reliever that gives up 5 runs per 9IP a huge drop compared to a reliever that gives up 4 runs per 9IP? It's a drop, but it's not giving up the game.
I think this could be an interesting idea, though the idea that the team would pitch better seems very unlikely.

I think the idea is interesting based on the concept that money saved on starting and short relief pitching could be spent on offense and defense, perhaps more than offsetting the pitching losses.

However, I don't think the idea has much merit, at least as presented above, as a way to enhance a team's pitching performance. The biggest flaw in the data, as I see it, is going with the average starting pitcher. In the scenario presented, a team would be using eight "starting" pitchers. Yet the data used was for the most "average" starting pitchers among the 83 with the most innings pitched. If I'm reading this correctly, that means the data for roughly the 42nd best starting pitcher in 2009 was used to compute what would happen with a four-man rotation and tandem starts. With 30 MLB teams -- and acknowledging that this team would purposefully not be focusing on the top pitchers, either in free agency or the draft -- this seems to be a wholly unreasonable assumption.

Instead, this seems to advocate taking innnigs from the top 1-5 starters and top (non-closing) short relivers and giving them to the 5-8 starters. As I said, I can see the merit of the idea in that this should reduce pitching costs, allowing the team to spend elsewhere (perhaps more efficiently) but I cannot see how the data supports that this would be a more effective pitching staff.

That's absolutely true if we consider "average" to be determined by how the pitchers' respective teams rank them. In that context the 83 pitchers would have been ranked by rotation spot and then yes, the average would have been the 1.5 rotation spot (or thereabouts).

However, my definition of average was from a RA per Batters Faced standpoint. In this context the 83 pitchers don't perfectly correlate to rotation spot. In fact, the 8 "average" guys I picked from a RA per BF standpoint average a rotation spot of 3.9.

Yes, this is still a touch higher than what would be ideal for the runs and cost savings, but it is much more achievable than trying to get the 2nd guy in some team's rotation to come pitch for you.