# The Cardinals Give a Lesson in Context

As a shortstop, you never want to be in this position:

You can almost see the expletives flying out of his mouth, and it gets worse: Nolan Arenado is out of frame to the right, which means that ball is ticketed for left field. How did it get to this point? Let’s back up.

When you’re fielding a bunt, decisions come at you immediately. Barehand it? Glove it? Lead runner? Take a beat and take the sure out? You have to make all of those choices in a split second. Here’s the play in the ninth inning of Sunday’s Cardinals/Royals game that left Paul DeJong lunging helplessly:

Obviously, it didn’t turn out well. But it’s not as though Paul Goldschmidt didn’t know there was a chance of failure going in. Going for the lead runner on a bunt is a high-risk, high-reward play; anyone could tell you that. How large was the risk? How valuable was the reward? Let’s find out together, because I think this situation is low-key fascinating.

We should do the standard math, the boring math, first. You know the kind I’m talking about: how often do teams win when there’s a runner on second, one out, the moon in the east, and… well, no, I just used our WPA Inquirer to get a rough sense of the probabilities.

The Inquirer isn’t perfect, but it gives us a nice baseline. With a runner on second and one out in the top of the ninth of a tie game, the home team wins 43.9% of the time (I used a 4.0 run environment). With that runner on first instead, their win expectancy ticks up to 49.8%. Preventing that extra base advancement is worth roughly 6% of a win.

On the other hand, if you don’t make the play, things get bad quickly. With runners on first and second and no one out, home win expectancy falls to 30.1%. With runners on second and third (say, due to a throwing error), that’s 17.7%. In other words, you need to be sure you’ll make the throw before you attempt it.

Let’s say that there’s a 5% chance of making the error Goldschmidt made, to pull a number out of thin air. How often does he need to get the lead runner at second? We can blend the odds of the other possible outcomes to come up with a breakeven. If you get the runner at second 73% of the time, leave runners on both bags 22% of the time, and make a throwing error 5% of the time, that blended win probability comes out to 43.9%, exactly the same as taking the sure out at first, at least in a neutral context.

That would be a tremendously boring conclusion, but we’re not done yet. You see, context was most definitely not neutral. Alex Reyes, the pitcher on the mound, has one of the most extreme profiles in baseball. He misses a ton of bats. He walks a ton of batters. The last time he allowed a ball in play was the Pleistocene era — or, fine, the single that put Hanser Alberto on first earlier in this inning, but he doesn’t allow much contact.

Those numbers I quoted up above? They use league average rates for each outcome. To figure out the breakeven on this play with Reyes on the mound, we need to consider how much the extra base of advancement affects him, not a random pitcher. The two outcomes where Reyes is most extreme — strikeouts and walks — make base positioning matter less. If he walks a batter, the advancement disappears. If he strikes the next two batters out, the advancement doesn’t matter.

To get an idea of how this works, I had to write a computer program to iterate the rest of the inning, because there’s no handy webpage for how often runners score with specifically Alex Reyes on the mound. I plugged in the frequency of each outcome that he’s gotten so far this year, then iterated out each base/out state a million times. This let me come up with the frequency that the team ends the half-inning tied, down by one, down by two, and so on, like so:

Runs Scored From Base/Out State (Reyes Pitching)
Outs Runners On 0 1 2 3 4 5 6+
1 2 69.5% 21.9% 5.3% 2.1% 0.8% 0.3% 0.2%
1 1 82.2% 9.3% 5.2% 2.0% 0.8% 0.3% 0.2%
0 12 36.7% 30.6% 16.2% 9.3% 4.2% 1.8% 1.2%
0 23 9.4% 29.6% 43.7% 9.8% 4.4% 1.9% 1.3%

With that matrix in hand, I converted each of those end-of-inning situations into a win probability, using the odds of winning as of the start of the ninth inning. I then multiplied them by the odds of each situation occurring, which gave me a win probability grid:

Win% From Base/Out State
Outs Runners On Win Prob (STL)
1 2 47.9%
1 1 53.7%
0 12 30.2%
0 23 15.1%

Using those, we can calculate the same breakeven as above. It’s now 79%; Goldschmidt needs to be even more certain he’ll make the out at second base. Even these numbers are missing context. These runners aren’t the same; the difference between Alberto on second and Jarrod Dyson on first isn’t as big as it used to be — Dyson is 37 and not at his blinding peak — but putting a stolen base threat on first isn’t exactly great either.

Was Goldschmidt 80% to make this play when he fielded the ball? You be the judge:

Oh yeah, one more complicating factor. It was raining, and the field was wet. The game actually went into a rain delay immediately at the conclusion of this play. That’s yet another complicating factor; the ball might be slippery, but Alberto would likely be slower on the basepaths. Baseball is hard, particularly at major league speeds!

I’d argue that this wasn’t a good play ex ante. Maybe Goldschmidt could have converted the out, but he wasn’t a big favorite to make such a tough play. The spin-and-fire throw is never a given, particularly without a good grip on the ball, and while there would have been some chance for a double play against a slow runner, it’s Jarrod Dyson!

There’s more. There’s always more, and when it comes to the Cardinals, that more often involves Mike Matheny. You see, Dyson didn’t have to be up there bunting. Giving Reyes a free out doesn’t seem like a wise choice to me offhand; with those elevated walk rates, every out gives the offense more chances to get on base without even having to make contact. In a tie game, that’s a big deal.

Dyson isn’t an average hitter, which makes the decision more complicated. He’s hitting a woeful .224/.257/.327 so far this year. To come up with an estimation of how he’d do against Reyes, I used a nested odds ratio method, then worked out the odds of the Cardinals winning after each potential outcome. It’s really close — by my math, the Cardinals were 47% likely to win if Dyson swung away. That’s quite close to their odds of winning if he laid down a successful sacrifice bunt. Bunt, swing away — it probably didn’t matter much in the big picture.

Of course, those odds assume the Cardinals take the out at first base. Bunting gave them a chance to go for broke, taking a shot at the brass ring of an out without advancement. It didn’t go that way, but it could have — or Dyson could have laid down a perfect bunt, or Goldschmidt could have taken the out at first. The possibilities, at the moment he fielded the ball, were overwhelming.

In the end, that play probably wasn’t the difference in the game. After a groundout to the left side of the infield (Alberto was thrown out at the plate), Nicky Lopez laced a single to right field. With two outs and Alberto going from second, he probably would have scored anyway. But none of that was set in stone when Goldschmidt fielded the ball.

Should you go for the out at second when you get a chance? Sure! But you shouldn’t decide in a vacuum. The pitcher matters. The situation matters. Even the weather matters. Baseball is full of decisions, big and small. Even a play you’ve seen a million times — a sacrifice bunt and the first baseman making a decision — has several layers to consider, variables to weigh against each other. I’m not sure Goldschmidt made the right play — but it was close, and the Royals’ decision to bunt was just as close. Against a different batter, or with a different pitcher on the mound, things might have been different. That’s one of the things I love about baseball — it feels like you’ve seen it all before, but new situations that make you think still come up every day.

Ben is a writer at FanGraphs. He can be found on Twitter @_Ben_Clemens.

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