Bonus Intentional Walk Math: The Big Bang Theory

Yesterday, I wrote about the intentional walk heard ‘round the world. It was mostly reflex, really. When someone issues a strange intentional walk, I can’t help but dig through the numbers. But this one, I was quite sure from the start, was bad. The math was just a way of rubbernecking, staring at a baseball accident from across the highway and saying “Wow, I wonder how that happened?”

But in doing so, I didn’t engage Joe Maddon on his weird, hipster-glass-wearing turf. Maddon didn’t say he was trying to minimize run expectancy (though he should have been). He didn’t say he was trying to maximize his team’s chances of winning the game (though he should have been). He said he was trying to “avoid the big blow,” or prevent a big inning in other words.

Bad news, Joe! Using the same simulation I used to estimate run and win expectations, I can work out the chances of a “big blow” for some arbitrary definition of big. Take my initial simulation. I estimated that the Rangers stood to score roughly 1.75 more runs in the inning when Corey Seager came to the plate, before any intentional walk shenanigans. We aren’t limited to looking at that in terms of average runs, though. It can also be expressed as some likelihood of scoring zero runs, one run, two runs, etc:

Run Matrix, Pre-Seager Walk
Runs Likelihood
0 24.7%
1 30.2%
2 16.5%
3 11.3%
4 10.3%
5 4.4%
6+ 2.6%

What’s your definition of a big inning? For me, it’s three runs. One run had already scored in the inning, but Maddon presumably wasn’t counting that. Thus, to meet my definition of a “big blow,” the Rangers would have to score three more times. That happened in 28.6% of the simulations all told.

Next, I had the computer walk Seager intentionally and re-ran the data. All the other batters remained unchanged, a run scored, and then the simulation continued from there until the end of the inning. This time, the Rangers scored roughly 2.6 runs in the rest of the inning on average. Again, I broke it down by frequency of run scoring:

Run Matrix, Post-Seager Walk
Runs Likelihood
0 0.0%
1 29.8%
2 28.7%
3 15.6%
4 9.4%
5 10.0%
6+ 6.2%

You’ll never believe it: giving a team a one-run head start increases their chances of scoring multiple runs in an inning. They scored three or more runs in 41.2% of my simulations. That’s hardly a surprise, to be honest. There are two ways you can get to a big number when you start with the bases loaded: a series of small cuts or one big blow. Walking Seager increased one path while leaving the other mostly unchanged.

A series of small cuts? That one is pretty clearly a loss when you walk a run in. At this point, if Mitch Garver reaches base safely, a “big inning” is more or less assured. Even if he reaches on a walk or a single, that’s two runs in (from the time Seager came to the plate) with only one out. From there, the Rangers score three or more runs quite frequently.

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One big blow? Seager and Garver have roughly equal extra-base-hit rates in their career. Maddon is somewhat in the right here – Seager both projects for a higher rate of extra-base hits going forward and had the platoon advantage in the game – but not by nearly enough to offset the series of small cuts channel.

Here, you can look at Maddon’s decision from the standpoint of how much the Rangers’ odds of scoring each possible number of runs in the inning changed when Seager walked:

Change in Scoring Post-Walk
Runs Change in Likelihood
0 -24.7%
1 -0.4%
2 12.2%
3 4.3%
4 -0.9%
5 5.6%
6+ 3.6%

I particularly enjoy the fact that the Rangers score four runs less frequently after an intentional walk. Why is that? A grand slam by Seager leads to the Rangers scoring four runs — but no more than four — almost all of the time. Force him to drive in one run with a walk, and an exact four becomes less likely. What is Garver going to do, hit a bases-clearing triple and then fail to score? Clean the bases with a double and get stranded? Those are the most likely ways for it to happen, but they’re still less likely than the grand slam/no further scoring combination.

Perhaps I’m being unfair to Maddon’s decision-making. Perhaps what he actually meant to say was “I wanted to decrease the odds of the Rangers scoring exactly four more runs in this inning, other outcomes notwithstanding.” He absolutely did that with the walk. But if you, like me, think of a big blow as lots of runs scoring, it should come as no surprise: gifting the opponent a run is not a good way to lower the likelihood of runs scoring, even if you couch it in terms of “big blows” and crooked-number innings instead of run and win expectancy.





Ben is a writer at FanGraphs. He can be found on Bluesky @benclemens.

21 Comments
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Mahoney
4 years ago

At this point, I’m beginning to think Maddon was testing his rookie pitcher to see if he’d push back on an obviously wrong idea. Once he went along with it, Maddon was probably like “oh #@!$, I can’t back off now.”

Jack
4 years ago

If you were watching the game in real time, it was pretty obvious that this was a “overturn the tables” move of emotional annoyance. Warren had just pitched around the previous batter and walked him, to load the bases. Madden then sort of spontaneously came out of the dugout and seemed to essentially communicate “You want to just throw this game away and walk the bases loaded? I’ll show you how to really throw this game away, we’re gonna walk a run in and blow up your ERA! Let’s see how you get out of this jam now!”

Essentially, it seemed obvious that Madden intentionally made the wrong move as a way of showing up his own pitcher that “I’ll show you what happens when you <something> a stranger in the <something>” (wait… wrong reference).

So the probabalistic proof provided by Ben only reinforces that this was indeed a bad move, which was sort of the managerial intention. (As weird as that sounds! Joe Madden likes weird, as we’ve witnessed many times.)

crocb3
4 years ago
Reply to  Jack

I, personally, am very excited for the Evil And Spiteful Joe Maddon character arc

CC AFCMember since 2016
4 years ago
Reply to  Jack

Do not fight a stranger in the Alps. It never works out the way you hope.

Last edited 4 years ago by CC AFC
South DetroitMember since 2020
4 years ago
Reply to  Jack

I think there’s some backing to this idea in Maddon’s own quote “I thought by walking Seager, it would avoid the big blow. And just to stir up the group, quite frankly. It’s not something you normally do. I thought by going up there and doing something like that, the team might respond to something like that,” I think the next analysis is how well players respond after being showed up. but given Warren’s two walks and hit allowed in 2/3 of an inning in his first game since, I am thinking this rationale for the intentional walk didn’t work out too well either.

bndj88Member since 2017
4 years ago

Seems like he took a page out of the Michael Scott theory of management:
“Like a bunch of fourth graders. Sometimes what brings the kids together is hating the lunchlady.”

LenFuegoMember since 2025
4 years ago

Is it at all possible that Madden ordered the walk simply because he mistook how many runners were on base — i.e., he thought it was, say, first and third rather than based loaded — and decided the fallout from pretending he meant to walk in a run was less than the fallout from admitting he mistook how many runners were on base?

Last edited 4 years ago by LenFuego
shortstop
4 years ago

Ben, I’m curious to see how Maddon’s logic plays out if you buy his false assumption that Seager was more likely than not to drive in at least two runners with a hit. In other words, if you assume Seager had a 50% chance of getting a hit, what would the run expectancy have been? How high would that xBA have to be to have that logic check out?

PhilMember since 2016
4 years ago
Reply to  shortstop

If you assume Seager had a 50% chance of getting a hint, then you must work for Apple TV+.

shortstop
4 years ago
Reply to  Phil

Maybe ol’ Joe is better suited for a broadcasting career at this point.

Jason BMember since 2017
4 years ago
Reply to  Phil

Or maybe he’s one of those that thinks all either/or propositions are 50/50.

Seager gets a hit? 50/50. Either he gets a hit or he doesn’t.
Win the lottery? 50/50. Either you win or you don’t…

Lunch AngleMember since 2016
4 years ago

What if: bottom of the ninth, you’re up by four runs. Two outs, bases loaded, Juan Soto at the bat. On deck: Alcides Escobar. How about now?

Dave Stewart
4 years ago
Reply to  Lunch Angle

Impossible. Escobar’s a lead off guy, no way you have Juan Soto batting ninth.

Ruben Amaro Jr.
4 years ago
Reply to  Dave Stewart

Dumbass.

Lanidrac
4 years ago
Reply to  Dave Stewart

Soto could’ve had the day off and was brought in to pinch-hit for the #9 hitter.

cf467
4 years ago
Reply to  Dave Stewart

Looking at the Nats’ depth chart…if one of Keibert Ruiz, Nelson Cruz, or Josh Bell gets hurt and another is getting a day off, it’s not inconceivable that Escobar would get penciled in as the cleanup hitter…I mean, everyone on the team except Ruiz, Soto, Cruz, and Bell is projected for an OPS between .600 and .700

sadtromboneMember since 2020
4 years ago

Bad news Joe! If you need to complete Step 1 (which is bad) before moving on to Step 2 (which is worse), completing Step 1 makes you more likely to complete Step 2!

I mean, seriously. What the tarnation.

hopbittersMember since 2020
4 years ago

I’m pretty sure this all started with a drunken argument about analytics sites that devolved into a bet about how many times Joe could get them to reference Mitch Garver in the next three days. You can trash him all you want, but his diabolical scheme worked and the man got paid.

Well, not really. It’s hard to collect from drunks. But it’s still a moral victory.

cowdiscipleMember since 2016
4 years ago

Mitch Garver has a projected RoS wRC+ of -100, so it makes sense to me!

(not sure why everybody has a RoS -100 wRC+ right now)

Jon L.Member since 2016
4 years ago

So this article claims that intentionally walking a batter with the bases loaded is *always* the wrong move – yet, if you go ahead and crunch the numbers, every team that’s attempted this strategy under the new CBA agreement has eventually won the game.

Okay, okay, I’ll admit I get a kick out of Joe Maddon’s unconventional managerial decisions. I like the way this article addressed his “big inning” theory, and testing the other part of Maddon’s explanation seems… elusive. All in all, I’d say the author has convinced me that intentionally walking in a run is probably not always the best strategy.

montrealMember since 2022
4 years ago

Madden is a bonehead. That was an embarrassing move for an MLB Manager. It was stupid. Corey Seager ?? Not Babe Ruth but Corey Seager ?? Regardless it is a dumb move. There are too many managers trying to show off and look cool. Try to win the bloody ball games. It is so annoying. Even if it worked, it was a bone head idea.