How should the Cardinals handle three-run save situations?

On Sunday, following consecutive losses to the Cincinnati Reds, a team that the St. Louis Cardinals should have destroyed, the Cardinals carried a 5-2 lead into the bottom of the ninth inning at Great American Ball Park. Due up for the Reds were the pitcher’s spot (eventually taken by Adam Duvall), Tyler Holt, and Zack Cozart.

The Cardinals turned to their most reliable bullpen arm, Seung Hwan Oh, and while he allowed a base hit to Duvall, Oh struck out Holt and Cozart and then following a line out by Joey Votto, the game was over. The Cardinals avoided the sweep and won a critical game in their quest for the 2016 postseason. Everybody is happy, right?

It would be hard to argue that Oh was not the player who most improved the Cardinals’ odds of winning that game, unless one believes that a reliever other than Oh is the best bullpen option the team has (I have arguably ridiculous opinions about Seung Hwan Oh, but I very much believe he is the best reliever on the team).

But according to FanGraphs’s Win Probability model, hardly a perfect metric but a solid approximation of the situation in which a team finds itself, the Reds entered their half of the 9th with a less than four percent chance of winning the game. A similar situation unfolded on Tuesday night, though I’m more willing to chalk that up to the unexpected nature of the three-run lead in a game in which the Cardinals trailed entering the top of the inning.

Crazy things happen, but the Cardinals’ chances of winning the game Sunday were, on the surface, very good. But the Cardinals were also operating with a bullpen which has been much-maligned throughout the 2016 season. And while several of the available options, such as Jonathan Broxton, had been inconsistent at best over the first five months of the season (Kevin Siegrist and Zach Duke, for what it’s worth, had both already pitched in the game), Seung Hwan Oh’s company among baseball’s best relievers by FanGraphs Wins Above Replacement are perennial bullpen aces such as Kenley Jansen, Dellin Betances, Aroldis Chapman, and Andrew Miller.

Certainly, if the Cardinals had a 5-2 lead in the 9th inning of Game 7 of the World Series, going to Oh is the correct move. At that point, pitching Oh is the right move pretty much regardless of score—the team has absolutely nothing to gain by saving him. But in this case, pitching Oh against the Cincinnati Reds, who pose no threat to the Cardinals’ playoff chances aside from their ability to beat the Cardinals, meant that he would have less availability against the Pittsburgh Pirates, who are Wild Card contenders.

In 2016, there have been 14 relief appearances by St. Louis Cardinals pitchers which lasted one inning or less in which three or more runs were allowed. One of them had occurred the day before, by Jerome Williams in a blowout. Only one was in a true 9th inning save situation—Trevor Rosenthal allowed three runs, on a walkoff home run to Adam Lind, against the Seattle Mariners on June 24. But even so, 14 appearances so poor seems like an awful lot.

Among MLB teams in 2016, however, it really isn’t. Through September 4, the Cardinals were tied for 19th in such games. Twenty-six of thirty teams had at least 13. And here’s a stat for Cardinals fans wanting to feel better about the bullpen this season: the Arizona Diamondbacks have 40 pitcher games in which a pitcher allowed three or more runs in an inning or less of work. Daniel Hudson has eight of them by himself.

But not all of these appearances are created equal—several came in what amounted to mop-up duty. The Cardinals avoiding pitching Seung Hwan Oh, but that does not necessarily mean they would have to go with their lowest-leverage pitcher just because they are not going with their highest-leverage one. Matt Bowman, who warmed up simultaneously with Oh (and likely would have pitched had the Cardinals expanded their lead from three to four), was available, and while he is a less effective reliever than Oh, he has been one of the team’s better bullpen arms this season.

And while the Cardinals had 14 outings in which a pitcher went an inning or less while allowing three or more runs, entering the 9th inning on Sunday, the Cardinals had 225 outings of exactly one inning (the duration any incoming reliever would ideally go) in which two or fewer runs were surrendered.

This would imply the Cardinals bullpen had a 5.86% chance of blowing the lead, but this is only counting outings which went exactly one inning. The Cardinals had 290 relief appearances which went at least one inning with two or fewer runs allowed, boosting the odds of a blown lead to 4.6%.

But even then, this assumes the average Cardinals reliever is pitching. It assumes said reliever cannot be removed from the game and replaced with another reliever, perhaps Oh, if things starts to go haywire.

And to assume inevitable doom for a non-Oh reliever is to exaggerate the inefficiency of the Cardinals bullpen. Which is not to say that the bullpen has been great, by any means, but even Jonathan Broxton, whom I would not have pitched even with a three-run lead, had only allowed more than two runs in 4 of his 56 appearances up to that point. Matt Bowman allowed more than two runs in 3 of his 49 appearances, only allowing four runs (if he allowed exactly three runs, the Cardinals would be back to essentially a coin flip to win the game) one time.

As it turned out, Seung Hwan Oh pitching was fine, since the Cardinals won on Monday much more decisively and his appearance was more gratuitous. And while deeming Sunday’s decision the correct one on the grounds of independent results from Monday’s game is a bit shortsighted, the possibility that Oh would not be necessary on Monday was always there.

So I understand pitching Seung Hwan Oh, even if it is a bit on the overly conservative side. But Oh has already hit his highest innings total since 79 ¹⁄₃ in 2006, a mark he will likely surpass barring injury. And it would behoove the Cardinals to find spots in which to conserve him. A three-run lead against a mediocre offense leading into a critically important series would perhaps have been a good opportunity for this.