Mathemadage: The Inevitable Reliever Blowup Theory

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:

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. That’s much bigger than the standard deviation of pitcher talent or pitcher form. Sometimes you scatter five hits; sometimes they stack up. For comparison, one standard deviation of form is worth about 0.09 runs per inning in expectation. Whether you’re having a good day or a bad day matters a little for how many runs score in a given inning, but how the cookie crumbles matters more. That’s why all of these numbers are about the same, even though the effect points in the direction we would expect.

Second, relievers are more likely to be in good form, too. Six arms means six chances to draw someone who turns in a clunker, but it also means six chances to draw someone who’s red-hot. And while we think of blowups as largely driven by pitchers not having it, the converse is true too. A pitcher who’s really locked in on a given day is less likely to allow a blowup.

Okay, that’s a simulated version of reality. What about actual reality, though? I’m pretty sure that John Smoltz, a big proponent of the Inevitable Reliever Blowup Theory, isn’t going to read this section of my article and be convinced. I didn’t even use any real baseball players! So let’s fix that problem by taking actual starter and reliever performances.

For this version, I switched over to wOBA allowed in each inning. I produced an expectation for each fresh half-inning (ignoring mid-inning entries) thrown by every pitcher in baseball in the regular season or postseason from 2015 to 2026. The expectation uses regressed pitcher talent and regressed hitter talent, so a scrub facing the Dodgers projects to do much worse than a closer facing the Giants. I then compared the expectation to the actual wOBA allowed in that inning:

I added an annotation to the spike on the left part of the graph; lots of innings go 1-2-3, so there’s a big chunk of data points there. The distribution tails off to the right just like you’d expect something random to do, with 7.2% of observed innings that were 300 or more points of wOBA above expectations. I picked 300 points because it’s a nice round number and really does indicate a blowup, but different thresholds produced similar results.

I wanted to compare that to random chance, so I came up with a test: Instead of using real innings, I constructed innings by sampling randomly from actual results that pitcher had that year, grabbing one result at a time until I hit three outs. In other words, I got rid of daily form completely by picking arbitrary groupings of plate appearances rather than all the plate appearances from a single day. That’s the black line here:

As you can see, blowup innings (300 wOBA points or more above expectations) happen more frequently than you’d expect from chance alone. That’s evidence that pitcher form moves from day to day; we observe more days with a concentration of bad results than you’d expect if everything was pure randomness. But 7.2% isn’t that much more than the 6.5% we’d expect from pure randomness – again, lots of blowup innings just come down to sequencing luck and random chance in a game that features a round bat hitting a round ball. Next, let’s look at how starters compare to relievers using the same standard:

Frankly, these distributions look incredibly similar. Starters also have more blowup innings than you’d expect by chance, though they have marginally fewer than relievers, and their odds of blowing up are closer to random chance than that of relievers. That’s the intuition that led to this question in the first place, and the effect is here. It’s just incredibly small.

For completeness’ sake, I ran the same test using runs instead of wOBA. This time, I didn’t do any adjusting for expectations. I just counted how many runs scored, and then did the same random-chance reshuffling from above to compare it to a baseline. There isn’t much of an effect here, but it’s worth noting that relievers had fewer innings where two or more runs scored. That’s because relievers had better results than starters in our voluminous sample:

I think this provides good evidence that there’s no real bullpen blowup issue to worry about. But just to be safe, I decided to go a little bit further. First, I took all the playoff games from 2015 to 2026 and split out starter and reliever innings by wOBA allowed. I didn’t do this one “against expectation” since I think it’s a bit less clear what that means in playoff games; this is just the distribution of actual inning-level wOBA allowed for both groups:

To me, those are compelling charts. But this article isn’t about convincing me; I’d have had a much easier time writing it if so. It’s about convincing people who didn’t just do 10 hours of research from a bunch of angles. So while this last test isn’t as statistically rigorous as the rest thanks to its small sample size, I did one more check: I just looked at actual bullpen games in the playoffs.

To do this, I split every team-game since our playoff database started in 2002 into one of four buckets: bullpen games started by a short-stint reliever (think Daniel Espino this year, or Trevor Megill and Louis Varland last year), bullpen games started by some type of improvised bulk pitcher (think Ray Kerr or Hagen Smith this year), regular games started by an ace (the starter with that team’s highest regular-season WAR), and regular games started by a non-ace starter. Then I just counted up how many runs were allowed in each, as well as what percentage of the time the team allowed five or more runs in a game (here I’m using all nine innings, not just the first six), and what percentage of the time the team allowed three or more runs in a single inning:

Bullpen games have been almost exactly equivalent to non-ace starter games in our sample, with 4.20 runs allowed compared to 4.25, and 42% of games allowing five or more runs as compared to 41%. Meanwhile, 34% of bullpen games contained a three-plus run inning; 36% of games with conventional starters had one of those. The sample size for bullpen games is minuscule, and I wouldn’t consider this scientific proof or anything. But it’s what I expected to see after all the other data. It sure doesn’t seem like there’s much difference between bullpenning the whole game and using anyone other than your very best pitcher to start.

There are a few caveats to this. I wouldn’t read too much into my splitting of each group; it’s not like my view of who was a short-burst reliever and who was a bulk guy in 2016 is perfectly accurate. Likewise, ace vs. non-ace is a pretty blurry distinction, and it gets blurrier the further back we go. But there’s just really nothing to see here. If the Inevitable Bullpen Blowup Theory held water, you’d expect to see much different numbers between these two groups, not tables that look pretty indistinguishable from top to bottom.

Do I think that this deep dive will convince the most ardent proponents of the Inevitable Reliever Blowup Theory? Most certainly not. Its most ardent proponents probably aren’t people who read FanGraphs, or care about statistics. Many of them actively dislike statistics, in fact; seeing statistical evidence that runs contrary to their belief might make them more sure they’re right. But I’m still happy I did this, because like I said, the theory has intuitive merit, and if I didn’t investigate it, I’d still be in the dark about whether it exists or not. As it turns out, there’s some evidence suggesting that reliever form is real and that guys have good and bad days that have an impact on their run prevention. There’s just no evidence that it matters at the game level, because there are a million offsetting effects, and various probabilistic effects – sequencing, batted ball luck, and so on – swamp the variance in pitcher form.