Using a Monte Carlo Simulation to Propose a Radical Four-Man Rotation


Much has been made of the ‘bullpen revolution’ over the past couple of years. Andrew Miller and Chris Devinski represent relievers on the forefront of the revolution, on teams at the forefront of innovation. The Astros routinely use Devinski in the middle innings, and for multiple innings. Devinski, a skilled pitcher who could close on many teams, provides a bridge to the ‘high leverage relievers’ , and affords the Astros bullpen flexibility that is usually unseen with conventional bullpen management. Conventional bullpen management calls the starter to pitch at least 6 innings, with high leverage relievers then entering to close the game. However, as pointed out in recent articles by Russel Carleton at Baseball Prospectus, starting pitchers often fail to reach the sixth inning. Starters are pitching less every year, and real evidence has been found of starters performing considerably worse towards the end of outings.

Carleteon, and others around the baseball community, have examined different possible rotations constructs that would make starters more efficient. Rotation ideas include tandem starters, four-man rotations, six-man rotations, and others. What I propose is something slightly different and more radical.

My method proposes a group of seven pitchers capable of handling a starters workload. The goal of these 7 pitchers is to maximize the amount of games the team enters the 7th inning with a lead. The traditional model would have the 5 best pitchers pitch every fifth day, and if they are unable to complete six, they are relived, usually by a mediocre reliever. Instead, my system proposes a tandem-type method where decisions are made based on the leverage of the game in different innings. If your goal is to reach the 7th inning with the lead, having a good pitcher available to bridge the gap and conserve the lead makes sense. Specifically, my method calls for a four-man rotation, with each starter going anywhere from three to give innings, rarely six. Here’s the kicker; the ace is not one of the 4 starters. Instead, the ace will often relieve a starter in the fourth, fifth or sixth innings in high leverage situations.

I believe this simulation hones in on one important question. How valuable is a pitcher throwing 6 innings of two run baseball, but doing so once every five days? Is he more valuable pitching three times a week, two important innings at a time, with his runs allowed more likely spread over three games? Many will say that a starter who can go deep into games and keep the your team in games is indispensable. It keeps the bullpen fresh and gives your team a great chance to win. I don’t disagree. But I think the notion that this is the most efficient way to manage a whole rotation is short sighted. By having the best starter available to come in in the third, fourth, fifth, or sixth of almost any game, you’re creating the opportunity to win games you might otherwise lose had you let the inferior pitcher remain in the game. I propose that it’s likely that six innings pitched over three games provide no disadvantage when compared to 6 innings pitched in one game.

And finally, the question of if pitchers can pitch on four days rest if they are only going three-five innings at a time is important to consider. Russel Carleton showed here that pitchers going on three days of rest are largely unaffected in their performance. Previous game pitch count has a much greater effect on current game performance than days of rest. However, the effects of pitching a couple innings every other day or every three days could catch up to a pitcher over the course of a season. Then again, it could be beneficial to the pitcher by allowing them more opportunity to work on their craft. The truth is, a a strategy that calls for pitching 3 innings at a time multiple times a week hasn’t been seen in decades, and the exact effect it would have on todays pitchers is unknown.

Simulation Specifics

I created a Monte Carlo simulation in Python with the ultimate goal of seeing if two teams, comprised of the same exact pitchers, may achieve different results using different pitching management strategies.

I started by gathering pitcher data from FanGraphs. I got ERA data for starters and relievers who qualified over the past three years. Then, using random sampling in Python, I randomly sampled 150 times from the starter data. These 150 samples represent the 150 starters in my simulation, and each starter was placed on one of 30 arbitrary teams. I did the same for relievers, generating seven per team.

Now, with 30 teams, each of differing skill levels, I could simulate a season. While each team had high leverage relievers, for the sake of this model, I only looked at the five starters and the 2 worst relievers ( the mop-up men) for each team. I also insured that the two mop-up men always had worse ERA’s than any starter on their team.

I first simulated the season using traditional rotation management. Each pitcher went as far as he could, and was removed based on simplistic criteria that relied on the amount of runs he had given up and the amount of innings he had pitched. Of course, more goes into deciding weather to pull a starting pitcher, but for the sake of this simulation, I kept the criteria simple. Innings were simulated all at once, with the amount of runs determined by a random number generator which incorporated the pitchers ERA. No offense was used in the run generation, only the pitching talent level was considered. After each game is simulated through six innings, the winner and loser is recorded; in the event of a tie, the away team gets credited with a win.

For the second simulation, the starting rotation is made up of the number two, three, four and five starters. The ace never starts!!

In the second simulation, the starter always pitches at least three innings, regardless of his performance. He goes out for the fourth inning only if he’s given up less than 3 runs and he pitched less than 5 innings in his previous start. He goes out for the fifth inning only if he’s given up less than 2 runs and he pitched less than 4 innings in his previous start. He goes out for the sixth inning only if the ace and the two mop-up men are not available. If the starter is pulled, either the ace or one of the mop-up men is brought into the game, depending on the leverage of the situation.

The criteria above is one instance in which the starter is removed due to rest or runs given up. There is another instance in which the starter can be removed. If the Leverage Index is greater than 1.1 heading into the fifth or sixth innings, and the ace is sufficiently rested (determined by other criteria), the ace will be brought in.


For each of the thirty teams in my fictional league, I simulated 100 seasons where that team used the new pitching strategy, and every other team used the old pitching strategy. On average, teams added .6 wins a season. The max wins added was 1.32, the min wins added was -.666. There does seem to be a very slight advantage to be had from saving your ace for the big moments.


The future of the five-man rotation is in question. As teams and analysts explore alternate strategies, the question posed by this project will certainly be raised. Through this analysis, it seems the value of a start by an ace once a week can be matched, and beaten, by 2 or 3 separate two inning high leverage outings by that same ace. Furthermore, it is known that pitchers moving to the bullpen perform better because they are able to exert more energy per outing, since they pitch less than starters. A question remains, however, on whether pitching less per outing but pitching in more games allows pitchers to exert more energy per outing, despite pitching the same amount over a given time, say a week.

The practicality of this simulation is lost a bit in simplicity and in the unknown. Runs are modeled using a random number generator, and pitching changes are ruled by a small series of if-and-elif statments. Not to mention the simulation only allows pitchers to be subbed before an inning starts. Certainly, real baseball is more complex. Regardless, I believe the simulation provides a framework to understand different pitching strategies. Future work could involve an examination of other pitcher management strategies as well as added complexity.

All in all, a strategy such as the one proposed here calls for very short rest and short outings throughout the year, something that hasn’t been seen in decades. Furthermore, a team moving their ace to the bullpen to add marginal wins would face an uproar from the fans, the media, and the ace himself. It’s fun to imagine aces pitching this way in a simulation, but the reality of a strategy like this is a little far fetched. Nonetheless, as starters start to pitch less, good pitchers are going to be needed to bridge the gap to the late innings. There is value to be had in shortening outings and insuring good pitchers pitch in important situations.

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6 years ago

This is a phenomenal article and a very hot topic. I would be curious to see what the results would be if the 3rd or 4th starter was moved to the bullpen. Great research again! Mixing this with statcast data could give us a great answer to this.

6 years ago

I like it. I am a bit surprised by the low number of extra wins added. perhaps the solution is to organizationally develop relievers who can go 3 innings and build a rotation/bullpen of guys who can dominate for 3 innings at a time with your “ace” or “aces” giving you 7 innings every 4 days.

6 years ago
Reply to  yojiveself

Glasnow is perfect for this role

6 years ago

The ace (turned glorified reliever) would find another team to play for. You can’t take into consideration the mindset of the pitchers involved.

Captain Tenneal
6 years ago
Reply to  Jim

I’m not so sure. Vulturing wins like this might give you a shot at being the first 30 game winner in 50 years.