When the pitcher’s spot in the Cardinals’ order came up in the ninth inning of Tuesday’s loss to the Diamondbacks, the Cardinals’ win expectancy was around 71.3%, according to Fangraphs.com (72.6% according to Walkoffbalk). The bases were loaded with one out, and the score was tied. Given the options of Brendan Ryan and Ryan Ludwick, Tony La Russa then decided to pinch-hit with the Flyin’ Irishman.

What happened after that was of course important but not the concern of this post. Rather, we’d like to analyze the wisdom of the decision-making that went into the choice of Ryan over Ludwick, who, after all, created 8.2 runs per game last year. One of the reasons that TLR gave was that he was concerned with the batter hitting into a double play, and rightly so: "I felt good about him [Ryan] putting the ball in play, he wasn’t going to be doubled." Indeed, a GIDP would’ve killed the rally and sent the game into the bottom half of the ninth, giving the Diamondbacks a roughly 66% chance of winning.

One problem with this logic is that it was Ludwick and not Ryan who offered a better chance of avoiding a double-play grounder. While Ryan is a speedier runner, his rate of actually hitting into double plays so far in his MLB career — 1.6% — is higher than Ludwick’s — 1.1%. But it’s possible that those numbers contain some noise. After all, how many chances has each player had at grounding into a twin killing? Let’s attempt to normalize those by using their splits with runners on base in a GIDP-possible situation (runner on first, on first and second, on first and third, or bases loaded):.

This, of couse, makes sense, given that Ryan hits nearly half of his balls in play on the ground (48.9% GB rate), whereas Ludwick does so less than a third of the time (30.1 GB%).

So Ludwick, since he is less of a GIDP risk, is the clear choice, right? Not so fast. Another bad outcome, though not quite as bad, is the strikeout. In this, Ryan has the advantage, striking out only 12.3% of his PAs, whereas Ludwick is nearly twice that at 23.9%. So what is a manager to do?

Probably make a quick decision, based on a combination of intuition and anecdotal memory. After all, managers don’t have the luxury of Baseball-Reference when they’re in the dugout like we in the scribbling class do. But in his free time, he or one of his assistants might use those percentages along with win-probability numbers and try to come to a reasoned conclusion. Assuming that the chance of all other events is equal (a big assumption, granted), who is a better bet to win the game: a player who strikes out seldom but is a more likely DP candidate, or a player who is strikeout-prone but unlikely to hit into a double?

Let’s do a probability exercise. According to Fangraphs, a strikeout would result in a 53.2% win expectancy for the Cardinals, whereas a GIDP would be 35.6%. If we multiply each of those by each player’s likelihood of achieving them, then add them together with the chance of something else happening– anything other than a strikeout or GIDP — we can figure out who would’ve been the better bet. A couple of big assumptions: First, as we mentioned, we’ll set the "other" value the same for each player, and, second, we’ll set that value at 60.0%:

As Mel Allen would say, how ’bout that?! Strictly based on their rates of striking out and grounding into double plays, Ryan and Ludwick were equal chances for success in the ninth inning last night. Whether Ludwick represented a better chance at succeeding in one of those "other" events is another question, but La Russa certainly didn’t need to apologize for his decision, at least based on the concern about putting the ball in play. Moreover, the higher one estimates the WE of the "other" value, Ryan improves in comparison.

Of course, as providence would have it, Ryan — you guessed it — struck out. The lesson? Perhaps it’s that neither TLR nor the hypercritical fans and media should get too bent out of shape over it, especially without at least considering some numbers.

This entry was posted by Pip on Wednesday, April 15th, 2009 at 10:30 pm and is filed under analysis. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.