David Bote and the Maximum Swing

There are certain highlights in baseball you like to watch, but most people don’t care about. Baseball really is a regional game, or a tribal game, and, more often than not, people in Denver don’t care much about what happens in Boston. But then there’s the rare highlight that transcends the tribalism, that sends chills down the spine of anyone who chooses to look it up. You don’t have to like the Cubs to enjoy watching David Bote’s walk-off grand slam. Rian Watt already wrote about Bote a few hours ago, but for the second time on today’s front page, let’s see the clip in all of its glory:

I’m sure you hate that if you’re a Nationals fan. I’m sure you hate that if you’re a fan of the Cardinals, or a fan of the Brewers. But, most baseball fans are none of those things. Most baseball fans can simply appreciate the latest ultimate grand slam — a two-out, walk-off grand slam to erase a three-run deficit. Bote hit exactly the home run every kid dreams about hitting. The only difference, I suppose, is that Bote didn’t win the World Series. (Yet.)

In recorded history, there have been 15 walk-off grand slams, with two outs, to erase a three-run deficit. Before Bote, the most recent had been hit by Ryan Roberts, in September of 2011. For the same reasons I embedded the Bote clip above, I’ll embed the Roberts clip below:

Everyone should be able to enjoy that one — even Dodgers fans, by now, given the passage of time. A walk-off grand slam basically sells itself. You don’t need to get bogged down in the details to understand why that’s one of the coolest things that can ever happen on a baseball field. But, what the hell, this is FanGraphs. Let’s get bogged down in some details anyway.

This is a link to our win expectancy glossary page. Unlike a walk-off grand slam, win expectancy isn’t always the easiest sell, in part just because “expectancy” is an awfully clunky word in a sentence. The idea, though, is really quite simple, and intuitive, and — dare I say — fun! Using math, and what’s happened in baseball in the past, it’s possible to estimate a given team’s odds of winning at any point in any game. From there, it’s hardly a leap from win expectancy to win probability added. Say a batter comes up when his team’s odds of winning are 50%. He singles, and the odds go up to 60%. The batter’s win probability added, for that at-bat, is +10%. In the end, it gives you an idea of who did the most to contribute to a win (or a loss).

The actual math behind win expectancy is kind of complicated. But the output should be familiar to anyone who’s read FanGraphs for any length of time. Here is the win-expectancy graph for Sunday’s Nationals/Cubs game:

Here’s the win-expectancy graph for that 2011 game between the Dodgers and Diamondbacks:

This follows what you’d expect. This explains what makes the Bote and Roberts grand slams so electrifying in the first place. With one swing of the bat, a team goes from an almost-sure loser to a sudden winner. It’s just putting in words, or in graph form, what any observer feels in their heart. Bote and Roberts swung the win expectancies about 90%. You couldn’t really ask for more from any swing. It’s about the maximum swing that could exist.

Here is our WPA Inquirer. It’s an under-utilized tool, and I can say that because I’ve worked here for years and I’d never even seen it before. Let’s plug some situations into that tool, using the standard 4.5 run environment. According to those numbers, here are the biggest possible swings of the bat, and swings of win expectancy as a consequence:

The ultimate grand slam is actually a somewhat surprising second. Realistically, though, these differences are more or less negligible. They’re all within a single percentage point, and these are just mathematical estimates. Still, if the numbers are our guide, the actual biggest swing is a walk-off three-run homer with two outs and runners on first and second, in a two-run ballgame. Let’s file that away for a minute.

And let’s return to the Bote grand slam. It turns out Bote faced an even higher degree of difficulty. See, win expectancy is calculated and published on the per-plate-appearance level. It assumes certain chances of outcomes from the plate appearances. But, of course, it can get more granular than that. Bote fouled off the first pitch he saw. He took the second pitch, which was close, but which was called a ball. He took the third pitch, too. This was called a strike:

At that point, after the borderline call, Bote was behind 1-and-2. The next pitch was low, evening the count at 2-and-2. Now, 2-and-2 is certainly more hitter-friendly than 1-and-2, but at the same time, 2-and-2 is still a pitcher-friendly count. Here are the league-average wOBAs this season through each of the 12 possible counts:

Bote was in the fourth-worst count possible. Even though we don’t have the numbers, that means the Cubs’ chances of winning would’ve been even lower than they were when Bote first came up. Roberts’ grand slam was great, but that came against the first pitch. Bote was down to the last strike. The 2-and-2 pitch wasn’t even that bad; Bote simply made perfect contact:

That’s how the Cubs won the game. There is a limit as to how much of a difference is ever possible to make with one swing of the bat. Bote just approached that limit. He achieved the event with the second-highest win-expectancy swing, and he did it in a pitcher-friendly count, which only makes it all the more remarkable. Baseball can hardly get more extreme, more dramatic than what Bote just did. Maybe that goes just as well without saying, but by saying it, at least we all get to sit and think about it longer.

Now, in closing, let’s leave Bote behind. Here’s a win-expectancy chart from April of 2007:

As per the earlier table, the only possible play bigger than the ultimate grand slam is the two-out, walk-off three-run homer to erase a two-run deficit. And as per the earlier plot, of course, a count doesn’t get more pitcher-friendly than 0-and-2. Count data only exists going back to 1988, so I can’t speak to the whole of baseball history, but on July 10, 1994, Tony Phillips hit that exact three-run walk-off homer off Tom Henke in an 0-and-2 count. And then on April 15, 2007, Marco Scutaro did the same. With the A’s trailing the Yankees 4-2 in the bottom of the ninth, Scutaro came up with two outs and runners on first and second. Scutaro quickly found himself in an 0-and-2 hole. The opposing pitcher: Mariano Rivera.

I don’t know if it can get more amazing than that. Just on a single-game basis, forgetting about seasonal context, that might be the most that win expectancy has swung on one play. David Bote didn’t get all the way there, but he came close enough. It’s a highlight he’ll remember for as long as he lives, because it’s almost literally impossible for a single-play highlight to be more dramatic.