Archive for Mathemadage

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. Read the rest of this entry »

You want your ace on the mound when all the marbles are in the fire. When the stakes are high, the big cheese needs to have his hands on the wheel. Are those real metaphors? No, but I bet you knew what I was talking about in each case, because the playoffs are a perfect time to discuss the importance of star pitchers. But do you want to deploy them as early in the series as possible? Or do you want them for the decisive game? Does it even matter?

In our game chats and article comments — across the internet really — it’s hard to find a consensus. When I wrote about Chris Sale earlier this week, there were comments to the effect of “It’s a bummer he pitched out of the ‘pen in the Wild Card, now he won’t get to pitch in NLDS Game 5,” as well as “Don’t save Sale for Game 7 of the NLCS, there might not be a Game 7!” Those are exact opposite opinions, and yet they both make a lot of sense when I hear them. But they can’t both be right, so let’s do some math. Even though there’s no real adage to prove or disprove here, this feels like a job for Mathemadage.

Here’s the question, as I see it: For a given set of pitchers making postseason starts, which way would you like those starts arranged in a seven-game series? In other words, if you have an ace, a second banana, and some bullpen games, would you prefer to have your ace for Games 1 and 5 or Games 3 and 7? There are good intuitive reasons to prefer either. Games 1 and 5 happen in almost every seven-game series; Game 7 is a much less frequent occurrence. More innings for my best guy, please! But the stakes can also never be higher than they are in a decisive game. In a big spot? Why wouldn’t I want my best guy in? Read the rest of this entry »

It’s time for another installment of Mathemadage, where I investigate time-honored baseball sayings using whatever data I can get my hands on and explore whether there’s any validity to them. If you’re new to my writing, I would describe my method as a semi-rigorous blend of math and intuition, with a rigorous amount of skepticism applied on top. If you’re not new to my writing, hi, hello! Welcome back. Today, we’re investigating a saying that was both my top candidate for this article and the one that came up most frequently in the comments of my last one. Yes, it’s time to talk about outs at third base. Oh, and if you’re looking for Five Things, it will return next Friday – Pete Alonso’s return to Citi Field was my favorite thing this week, and Jay Jaffe already covered it.

“Don’t make the first or third out at third base” was one of the rules that got hammered into me most frequently as a kid. It’s so ingrained that the last time I played rec league softball, I bonded with teammates over how we reflexively repeated it every time we coached third base. (I’m a big nerd, OK? I’ll take whatever bonding I can get.)

The logic behind this one makes good sense, too. With no one out, two productive outs could drive you home from second – why risk erasing yourself heading to third? With two outs, most plays that score you from third would score you from second as well – why risk erasing yourself again? But with one out, getting to third base is a big deal, because then a sacrifice fly or well-placed groundout can bring you home. From that angle, the logic is incontrovertible. Read the rest of this entry »

Welcome to Mathemadage, a new series where I investigate time-honored baseball adages using whatever data I can get my hands on and explore whether there’s any validity to them. I’ll apply my normal Ben Clemens mixture of a bit of math, a bit of intuition, and plenty of healthy doubt in declaring strong solutions to complicated problems. I hope to demonstrate that some of these true and others false, but I’m sure that many will end up in a suggestive but unprovable middle ground. And true to the premise of the series, we’re starting off with a fun adage that resists easy conclusions.

If you watch a baseball game from start to finish, you’re pretty much guaranteed to see a hitter get tied up on an inside fastball. “Got jammed,” the announcer might say, or maybe, “He just couldn’t get around on that one.” It’s a visual reminder of one of the pitching truisms that I learned as a kid and haven’t forgotten since: hard in, soft away.

I intuitively look for this pitching pattern when I’m watching a game. Hitters look incredibly uncomfortable when they’re trying to get their bat around a fastball in on their hands. Now that we have a few years of bat tracking data, though, I can do better than just vaguely searching for this effect. So this week, when I saw someone get jammed, I winced in sympathy and then started furiously downloading spreadsheets. Read the rest of this entry »