Save your Ace by Shifting Your Pitching Rotation

Sabermetrics and baseball analytics are all about questioning traditional wisdom with data. We challenge traditional wisdom, long held beliefs. This is precisely why sabermetrics are often so controversial. This time we’re going to look at the pitching rotation in baseball. Specifically we want to look at pitching rotations in playoff series.

The traditional wisdom is that you start your ace game 1. Then in game 2 you start your #2, followed by your third guy before rotating back through again. Sometimes there is a fourth pitcher in the mix, but generally this is the approach.

Is it right, though? If both teams do this, then you might waste your best guy going against their best guy. If your ace is outclassed by theirs, are you just wasting them? Maybe it is better to shift your pitching rotation to create more matchup advantages while sacrificing a game.

We’re going to explore this problem. Why do we think there might be an advantage to shifting your pitching rotation? What is the traditional wisdom we’re going against? And, most importantly, what does the data say?

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Standard Pitching Rotation Wisdom

Everything we’re talking about revolves around the baseball playoffs. In the regular season, pitching rotations don’t matter nearly as much. Things tend to even out over the course of a 162 game season. But for a 5 or a 7 game series, the order matters a lot more.

If you use a 3 man pitching rotation, the first guy gets to have three starts in a 7 game series. The other two pitchers only get two. The traditional wisdom says that you put your best pitcher first so that you get an extra game out of your best pitcher.

This makes sense both intuitively and mathematically. You want to minimize the runs your team gives up over the series. One way to do this is to maximize the innings of your best pitchers. More innings by good pitchers = less runs allowed overall.

It is a really solid strategy, but the whole point of baseball analytics is to challenge conventional wisdom. For example, in certain settings intentionally walking in a run is better than letting Barry Bonds hit. As another example, using an opener instead of a closer is sometimes a winning strategy.

The numbers often tell us more about the game than our gut instincts. So what about alternate pitching rotations?

An Alternative Strategy: Saving your Ace

The idea here is simple. If we start our best pitcher against theirs, it kind of negates any advantage they might give us. What if we pitch our #1 against their #2? And our #2 against their #3? While we’re basically throwing game one, this strategy gives us an advantage in games 2 and 3.

The graphic below is meant to explain this philosophy when there are four pitchers in the pitching rotation.

Notice how this strategy gives one team an advantage in 3 games while basically throwing game 1. Winning a series is all about winning games. It doesn’t matter if we lose by 10 runs in game 1 if we win games 2, 3, and 4.

Drawbacks to The Shifted Rotation Strategy

If I stopped the argument after the above graphic, it might seem obvious that the shifted pitching rotation strategy is a good one. However, there are some complications that muddy the waters.

• In games 2, 3, and 4 above we are getting only a small advantage. In game 1 we’re giving up a huge advantage. In fact, it might be the case that trading a near guaranteed loss for 3 65% chances of winning is a net-negative trade.
• The other main reason for starting your ace in game 1 is that they will get as many starts as possible. If we play our ace in game 2, then they might get fewer starts. The further we push our ace, the more likely it is that they miss a start they may have otherwise had.
• The other team can change their strategy in response to ours! Finding a different pitching rotation that works better requires knowing the rotation the opponent will use. If we come out with some wild rotation that gives an advantage, the opponents can change their order in response.

Now that we’ve listed the pros and the cons of this method, let’s move on to actually studying it.

Simulation Methodology

We want to study how pitching matchups change probabilities of winning games. By shifting the pitching rotation around and saving our ace, we might be able to move the winning probabilities in a favorable way.

To do this, we’ll use a cool stat: WPA or win probability added. WPA looks at a player’s actions and asks how much they helped their team win. If a closer comes into a 1-run game and strikes out the side, maybe they take their team’s winning percentage from 85% to 100%. They would be credited with +15% of WPA.

If our starting pitcher has a +10% WPA against an opponent’s average pitcher, that means our team should have a 60% chance of winning the game (assuming offense’s are equal-strength). However, if our +10% pitcher goes against their +10% pitcher, it cancels out and the game is back to 50/50.

Our simulation methodology takes the WPA of the pitchers in the pitching rotation, combines it with their opponents, and comes up with a probability of one team winning. Then, we try all possible pitching orders to see which are more or less effective. For us, we measure pitching rotation effectiveness by measuring the probability of winning either a 5- or 7-game series.

Let’s start by looking at the 2023 World Series matchup to get a sense for whether our theory works or not.

2023 World Series Simulation

The Diamondbacks are facing the Rangers in the 2023 world series. Though the Rangers are likely to employ a four man rotation, we’re going to simulate it assuming both teams only use three. The data for our simulation was obtained by dividing total season-long WPA by the number of starts. This gives us a “per start” win probability added.

The data is as follows:

• Starter 1:
  • Diamondbacks: Gallen, 9.4%
  • Rangers: Eovaldi 8%
• Starter 2:
  • Diamondbacks: Kelly, 6.1%
  • Rangers: Montgomery 6.1%
• Starter 3:
  • Diamondbacks: Pfaadt, -8%
  • Rangers: Scherzer 5.2%

We simulated 100,000 series with every possible order of Diamondbacks pitchers. We counted how many times the Diamondbacks won with each pitching rotation. And…

Our theory doesn’t work.

The best pitching rotation for the Diamondbacks is still Gallen, then Kelly, then Pfaadt. The second best order is Gallen, then Pfaadt, then Kelly which is only about 0.1% worse. In either case though, deviating from the traditional pitching rotation is not ideal for the Diamondbacks.

To hammer this home, if the Diamondbacks do the backwards order and switch Pfaadt and Gallen, their chance of winning the series drops by nearly 5%. This is good evidence that the traditional pitching rotation order is in general good.

This isn’t always the case, though. We did find a setting where this idea worked pretty well.

When Does Changing the Pitching Rotation Work?

Switching the order of your pitching rotation only works when your ace is absolutely outclassed by an opponents’ ace. For example if your best pitcher is roughly a 5% but is going up against a +20% juggernaut, then it actually can be beneficial to wait to start your ace. The idea is that you basically throw the game against the juggernaut and take the advantages everywhere else.

We simulated a 7 game series with four man pitching rotations. Team 1 has the juggernaut ace and the win probability of their rotation goes +25%, +0%, -10%, -20%. Team 2 has the much-less-good ace and their rotation has WPA +10% ,+8%, -10%, -20%.

By switching the first two pitchers, the second team’s probability of winning the series jumps by almost 3%. This kind of advantage is huge and is something worth looking at.

In 5 game series, it becomes even more attractive to change the pitching rotation because the ace doesn’t get to pitch three times. We simulated yet another example where one team has a bona fide ace and the other has more average pitchers. By intentionally matching up our worst guy against their best, we were able to increase our odds of winning the series by nearly 10%.

To play around yourself, check out our Github for the code we used to run our simulations.

Extending to Other Sports

While this idea didn’t prove that valuable in baseball, it might be a lot better in many other sports. In certain golf or chess tournaments, teams play against each other by doing a series of “head to head” matches.

Here, the idea of throwing one game for the benefit of the rest is actually a really good idea. Typically all competitors play the same number of matches and the team that wins the most matches wins. Sacrificing one game for an advantage in all the rest is all of a sudden very attractive.

We did a simple simulation with two teams of three players. Each team has a +25%, +0%, and -25% player. Obviously if both teams match up in order, the outcome of the match is 50-50.

However, if one of the teams can change the matches so THEIR -25% guy plays against the other team’s +25% guy and then have advantages in the other two, this is a beneficial trade.

Doing this shift changes a 50-50 matchup into a 55% advantage for the team that uses the clever ordering!

More on Simulation Methodology

Previously we said that we “combined” the two pitchers’ win probability added to estimate the probability of one team winning. The specifics of how to do this is a bit complicated. One way you could do this is by just taking the difference between the two WPA.

For example, if one pitcher was 8% WPA going against a 4% opponent, then the team with the better pitcher should win 4% more than normal (or 54% of the time overall). This works pretty well, but runs into some weird edge cases. For example, if we had a 25% WPA guy going against a -25% WPA opponent, using this combination method would imply a 100% chance of winning. This obviously can’t be correct.

We use a model that doesn’t run into this problem. Let W be a pitcher’s WPA. We introduce a new variable \delta with the formula W=\frac{1+\delta}{2+\delta} . This \delta represents the % increase in overall team quality. Notice this is different in change in win probability because \delta can be any number and still make sense. This is the key change.

Then, for two pitchers’ with WPA W_1, W_2 and associated values \delta_1,\delta_2 , the probability that team 1 wins the game is \frac{1+\delta_1}{2+\delta_1+\delta_2} .

This model retains nice properties like if two pitchers have the same WPA, then the matchup between the two of them is 50-50. This model is a standard application of the ideas present in the Bradley-Terry model for sports analytics.