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I wanted to look at how well our pitching staff did when it really mattered. I took the play-by-play information from Fangraphs and narrowed the view to 6th inning on, with either a one-run deficit, a tie game, or a 1/2/3-run lead (or four runs with two men on or five runs with the bases loaded). Basically it's a save situation, but expanded to include starters and situations where giving up a run can mean the game.
From there, I tallied up the stats for each pitcher. Any batter that reaches against a pitcher without causing a runner to be out counts as a Reach (this gathers in ROE's, no-out fielder's choices, dropped third strikes, etc.); Reach (Rch) divided by Rch + outs registered (Outs) yields Effective On Base percentage (EOB); Rch divided by Outs/3 gives us Reach per Inning Pitched (RIP).
Any run scored against a pitcher (inherited or otherwise) is just a Run; Runs divided by Outs/27 (the same formula for ERA) is Runs On Watch average (ROW). I also broke down the Runs into Gap (runs scored with the pitching team in the lead that don't tie or put the batting team ahead: ? > +1), Tie (+1 > 0), GA (go-ahead: 0 > +1), and Ins (insurance / putting the game farther out of reach: +1 > +2). I basically wanted to eliminate worrying about low-leverage runs, so if a pitcher gives up a grand slam in a tie game in the bottom of the eighth, I'm only counting the GA and Ins Runs; in the bottom of the ninth, the same situation only yields a GA Run.
The other stat I use here is Win Probability Added (WPA). You can read more about it here, but it basically starts with the idea that both teams begin with a 50% chance to win the game and that each action changes the probability of a win occurring. If Alex Rodriguez hits a 2-run HR in the eighth inning of a 9-2 game, it has virtually no impact, positively or negatively; if Albert Pujols hits a 2-run bomb to walk off an 8-7 tilt against the Reds on Easter Day 2006, it completely transforms the game. For pitchers, negative values are good; for hitters, go with positive.
Disclaimer: All of these numbers are at least relatively SSS. I'm not trying to be predictive or draw too much importance out of them, but there is some usefulness to the data.
The Bullpen Stalwarts
Trevor Rosenthal: Almost every single out he recorded met the criteria I stated before. All of his numbers were above average - good RIP/EOB & ROW (with half those Runs of limited significance, especially for a closer where the only run that really matters is the tying run), great WPA (2nd best on the team), only three blown saves (plus one blown lead of his own). He was even tougher with the tying run on base or at the plate (2nd best RIP among relievers w/15+ Outs).
Kevin Siegrist: Very similar numbers to Rosie (RIP/EOB, ROW), with very low hits and high walks & K's. His WPA was good, not great, as he was rather poor with the tying run in jeopardy (.362 EOB, 6.14 ROW, +0.561 WPA in those situations).
Seth Maness: Talk all you want about his less-than-inspiring repertoire and his middling overall numbers - he was fucking money with the game on the line. Best WPA (both overall for the season and these situations), best RIP/EOB (he's helped out by a ton of double plays, which count double towards EOB, unlike OBP), 21 Holds & 3 Saves. He was even better than Trevor with the tying run (basically same WPA in less than half the opportunities, best RIP/EOB (tied with Lackey)), so most of his Runs were less than game-changing. He had some notable blowups that pushed fairly close games into laughers, but with the contest in doubt, especially before the ninth, Seth was the Man-ess.
Randy Choate: His final WPA wasn't bad and he didn't give up a tying or go-ahead run, but his underlying numbers were less than stellar. He was actually quite effective when it mattered through the first half (24 outs, 5 Rch, -0.601 WPA), but he struggled over the next 30-ish days, then couldn't get ANYONE out after that, completely losing Matheny's trust (yay Mathenaging!).
Carlos Villanueva: Nobody expected him to be a shutdown reliever; he's there to soak up extra innings, whether they are the 4th/5th/6th or the 12th/13th/14th. His WPA looks like hell because he allowed three walk-off hits and his RIP wasn't good because he just isn't.
Jordan Walden: Would have been interesting to see what he could have done over a full season - high K's, decent enough walks, very effective.
Matt Belisle: He struggled for the time he was here, posting an EOB of .389. His ROW isn't really bad (worse than the team average), but the only things he did well were strike guys out and prevent homers.
Mitch Harris: Great story & enough velocity to be somewhat interesting, but could not put away hitters. Of the 35 outs he was credited here, only four of them were via the strikeout. The WPA was actually decent, but smoke & mirrors can only do so much.
Sam Tuivailala: Speaking of smoke, Sudden Sam can hump it up there, but he does need to rein in the walks. His only real blemish was the Alvarez shot in the 12th of Tui's 2015 debut.
Miguel Socolovich: Statistically speaking, he was basically indistinguishable from Tuivailala. Miguel didn't get the prestige innings Sam did, but he did vulture out a couple wins.
Steve Cishek: The strikeouts were nice and most of his numbers weren't BAD (and he managed to snag a Save), but a penchant for walks & big runs don't get the job done.
Jonathan Broxton: Basically the opposite of Maness - big arm (and everything else), lots of K's & BB's (including the only bases-loaded walk in these situations), most of his runs allowed were pivotal (worst ROW & WPA), and trusted more than he probably deserved.
Nick Greenwood: 14th inning, single, homer - drive home safe to Memphis.
Adam Wainwright: Definitely a SSS blip, with poor hits allowed, strikeouts, and results.
Carlos Martinez: Including his relief work, Tsunami had the best results of any starting pitcher in terms of WPA & ROW. The only runs he allowed were a 2-run HR at Colorado that only reduced the lead to one and a pair of runs in the 18th (his fourth inning of relief) against the Mets. If he can learn to cut down on the walks, he'll be elite.
Lance Lynn: Kind of disappointing, with way too many hits & walks. When Lynn comes back, Matheny (assuming he's still here as well) will need to have a hair-trigger on his hook, as Lance managed to not allow a homer (and few doubles), but was hurt by bunches of singles & free passes.
John Lackey: While not quite as impressive as Martinez, Salty John had the best RIP/EOB for the rotation (second overall to Maness). He kept the walks low and held strong with the tying run on base or at the plate.
Michael Wacha: Compared to Lynn, he was more efficient but less effective, posting the worst WPA & ROW (> 1IP). Too many HR's and awful numbers with the lead in jeopardy sabotaged otherwise solid control.
Jaime Garcia: Unlike the rest of the regular starters, Jaime didn't really strike many guys out, but relied on a 3:1 GO/FO ratio. He did give up a few runs and more than a hit per inning, but when a third of the singles don't leave the infield, you'll take your chances with that.
Tim Cooney: We're only talking about four appearances and 3.2 qualifying IP in July, but those were four consecutive starts, working into at least the 6th inning in tight ballgames, allowing just one run on a wild pitch. The walks need to come down, though.
Tyler Lyons: Even less to go on.
BTW, I plan on posting a companion piece to this on how our offense did against our opponents in the same situation.