Bonus Intentional Walk Math: The Big Bang Theory by Ben Clemens April 19, 2022 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. 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.