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If you’ve watched a postseason game in the last decade, you’ve heard the theory. Honestly, if you’ve watched a postseason game in the last decade, you’ve probably thought of the theory yourself. When a team eschews a regular starter and instead uses a string of relievers, surely one of those relievers is bound to be a little bit off. There are just so many of them. What, they’re all going to have it? C’mon, man. Be reasonable. And what happens as a result? Well, that reliever is going to give up a bunch of runs. You know, like pitchers do when they don’t have it. Obvious!

Hello, and welcome to another edition of Mathemadage. This time, we’re hot on the trail of what I like to call the Inevitable Reliever Blowup Theory. There isn’t one specific adage to point to here, but I’ve always wondered about this effect myself, and last week Other Ben (Lindbergh) forwarded me this tweet:

I hear this every bullpen game that the risk is law of averages says one of the relievers wont have it.

I have not seen any actual study anyone has done about this. Seems like it is just passed around as conventional wisdom.

— JJ Cooper (@jjcoop36) October 3, 2026

That was a good enough excuse for me to dig in – like I said, I’ve had this on my mind for a while, and the playoffs are the perfect time for a deep dive. But before I started cracking open my spreadsheets and coding agents, I did a literature review, because I knew I couldn’t be the first person to have investigated this. Back in 2015, Henry Druschel found that starters had more “disaster” outings than relievers, though he didn’t delve into the stacking aspect of using multiple relievers in a single game. I also found former colleague Kevin Goldstein’s investigation into the subject, which focused on the Rays’ ability to avoid reliever blowups. But those didn’t settle the debate for me, so I pressed on.

One of the hardest parts of this problem is defining it. How ineffective does a pitcher have to be for it to count as a blowup? What does “not having it” mean? How about counterfactuals? I spent a long time thinking about what I was even trying to measure here – in this day and age of everyone having tremendous analytical power at their fingertips, it’s easy to make a bad experimental design look quite shiny indeed. I came up with a few definitions of the problem and investigated each to see if they agreed with each other.

I began by measuring “blowups” in two ways: runs allowed in an inning, and wOBA allowed in an inning. On the runs side, I used a few different blowup thresholds; you’ll see me refer to two runs in an inning, three runs in an inning, or five runs in the first six inning of a game. On the wOBA front, I considered wOBA both unadjusted and relative to expectations, with those expectations based on the regressed seasonal lines of the pitchers and hitters. I picked a ton of different options so that no definition would be load bearing; if our different blowup measures are saying different things, that’s a sign that we need to dig further.

Using runs as a measure of blowups is self explanatory. Why also add wOBA? If a guy walks four hitters in an inning, sprinkles in a double play, then gives up another single to get chased, I think it’s a blowup even if only one run scores. On the other hand, surrendering a single and then suffering three straight errors isn’t a blowup to me. I also care about the whole inning, not just the length of time that a pitcher was in. Why? Because one key benefit of bringing in a reliever is that if he doesn’t have it, you can just bring in another reliever. If reliever A loads the bases with no one out and then reliever B comes in and wriggles out of the jam without a run scoring, well, the jam was wriggled out of. Can’t charge the bullpenning strategy with a blowup if there was no blowup.

As for whether a pitcher does or doesn’t have it, we need to understand how big the difference is between a good and bad day for them – in other words, what is their volatility? My first attempt at working out pitcher volatility was to model it from actual performance. To do that, I gauged pitcher form through a big old covariance matrix comparing within-outing variance to overall variance. I did this for starters and relievers separately. I found that reliever form varies quite a bit; the spread in a single reliever’s form from outing to the next was about as big as the spread in talent between relievers. Starter form varies a bit less, but there’s a meaningful spread there too. Pitchers just pitch differently on different days – that’s hardly surprising. This effect was concentrated in whiffs and strikeouts, and likely related to velocity; I found a clear relationship between pitcher velocity relative to their own average and pitcher effectiveness relative to their own average. If you’re looking for a rough order of magnitude, I found that a league average reliever having a one-standard-deviation good form day pitches to a 3.60 RA9, versus a 5.20 RA9 for a one-standard-deviation bad form day. That’s meaningful.

With all that in hand, I ran a simulation. I constructed two different pitching plans. In one, I created a starting pitcher, gave him league average true talent, and then selected his daily form randomly from the distribution of starter form that I’d built up above. I built some simple relief pitcher rules based on actual managerial decisions – the more runs allowed and the later in the game, the more likely that a starter’s bad inning gets him pulled and replaced with a string of league-average relievers. I also tested one where a starter always got pulled after three runs, and one where he always stayed in for six innings, just to establish some bounds. I also built in a times-through-the-order penalty; starters do a little better than their overall line the first time through, and a little worse than their overall line the third time through.

To model the reliever side of things, I created six relievers, each with the same league average true talent I gave the starters, and then selected each reliever’s daily form randomly from the distribution of reliever form. I didn’t model any hooks here; each pitcher who started an inning finished it. Then I used a Markov chain, the details of which I’m happy to discuss on the side if you’re the kind of person who wants to discuss Markov chains on the internet, to figure out the distribution of run scoring under each plan:

Modeled Runs Allowed in Innings 1-6, Three Strategies

Strategy	Avg. Runs	P(5+ Runs)	P(any 2+ run inning)
Six Relievers	2.93	22.5%	55.0%
Starter, Real Hooks	2.90	22.3%	54.4%
Starter, No Hook	2.93	22.7%	54.6%
Starter, Hook at 3+R	2.88	21.9%	54.5%

If there’s any effect here, its size is tiny. The odds of a two-plus run inning were pretty much identical across the board, as were average runs allowed and the odds of a blowup game, with five or more runs in the first six innings (we’re leaving out innings seven through nine because that’s where relievers will typically pitch regardless of your bullpen strategy). That’s despite the fact that the six-reliever plan really does end up with a pitcher having a bad day more often. I know that to be the case because I literally specified it in the model.

Why? It comes down to two things. First, sequencing luck and the inescapable fact that baseball has a lot of randomness in outcomes are the main drivers of run scoring. Take the distribution of actual runs allowed per inning across the entire season; the standard deviation is about a run per inning....

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