It’s been a tough September in San Francisco. That even-year magic that should have been carrying the Giants to their fourth World Series title in the last seven years seems to have left AT&T Park (our own Rob Mains has all the gory details).

We now hop into our time machine and travel back to September 4. The Giants were playing a day game at Wrigley Field, trying to salvage a split of a four-game series with the Cubs. Holding a 2-1 lead going into the bottom of the ninth, manager Bruce Bochy turned to Santiago Casilla, who had saved his 30th game the previous day. Casilla allowed a double to left field by Addison Russell, uncorked a wild pitch sending Russell to third, and then gave up a game-tying single to Jason Heyward.

Casilla escaped the ninth inning with no further damage, but the Cubs were eventually able to fly the “W” flag over Wrigley by virtue of another RBI single by Heyward in the 13th inning. It wasn’t unheard of for Casilla to blow a save. Even the best closers cough up a ninth-inning lead about 10 percent of the time, and for Casilla it was his sixth blown save of the year. But three nights later, Casilla couldn’t hold a two-run lead in the ninth in Colorado.

On September 13, the Giants entered the top of the ninth of a game against the Padres with a 4-1 lead, and walked out with a 6-4 deficit. This time, Hunter Strickland was victimized. On the 17th, Sergio Romo and Casilla couldn’t hold a 2-1 lead against the Cardinals in the ninth. On the 19th, Derek Law, Javier Lopez, and Strickland politely allowed the visiting Dodgers to delight the home fans with a ninth-inning, come-from-behind, walk-off 2-1 win.

The panic that gripped the baseball world on behalf of the Giants was palpable and the damage done to the Giants’ playoff chances was obvious, but was this a run of horribly-timed bad luck or something bigger? There’s always been a bit of unease with questions like this among Sabermetricians. There’s the well-known XKCD comic which attributes all of sports analysis to narrative pasted atop a random number generator. Relievers pitch in small samples and small samples are subject to huge amounts of variability.

It’s possible that the Giants just had some horribly-timed luck. Or maybe there’s something to it. The narrative around the Giants during the month of September is that no one in the bullpen has any confidence any more. Is it possible that, after coughing up that many ninth inning leads, there was a contagion effect? Everyone got so nervous about closing down a game that the anxiety fed back on itself and, suddenly, Bruce Bochy had a bullpen filled guys who were “pitching scared”?

If the “random variation” hypothesis is right, then we wouldn’t expect to see one pitcher’s struggles impact others on his team. But if the effect does spread, we ought to be able to find evidence of that.

Warning! Gory Mathematical Details Ahead!

I used data from 2003-2015. First, I looked up traumatic blown saves, which I defined as a team that entered its pitching half of the ninth inning with a lead, but then lost the game (whether there or in extra innings). I looked at various indicators of how recently a team had experienced one of these ninth-inning meltdowns, including whether they had experienced one in their previous two games. I also looked at how many they had endured during the last 5, 10, and 30 games. I also did a raw “it’s been X days since we had a ninth-inning meltdown” count. I looked at performances by relievers only. I controlled for the talents of the hitter and pitcher overall using the log-odds ratio method, and I looked into a number of outcomes including strikeouts, walks, singles, etc.

If a team had suffered a bullpen meltdown within the previous couple of days, did the relievers who pitched in a subsequent game feel the effects? The answer turned out to be yes. If a team had suffered a blown save in the previous day or two, their relievers were more likely to give up a walk than we would otherwise have predicted from the overall seasonal stats of the pitcher and batter. The number of games since the last meltdown was also similarly predictive, with a more recent meltdown leading to more walks. However, the number of blown saves in the last 5, or 10, or 30 games didn’t make much difference. By that point, maybe a week of games makes it stop smarting.

To make sure that I wasn’t just getting random Type I errors from running so many regressions, I looked specifically at circumstances in which a team was once again trying to protect a save-worthy lead (three runs or fewer) in the eighth inning or later. If there’s a situation that’s going to make them blanche after a blown save, it would be being back in that same situation. And in that case, the effects continued to hold.

Now, it was just walks. Nothing else really shook out on a consistent basis. But that tells us something. Walks are often a sign of nibbling. The effect wasn’t that relievers start walking everyone after their team blows a save, but the walk rate does tick up, and for pitchers, that’s a bad thing. And most importantly, the effect was bullpen-wide, not just restricted to the pitcher who blew it. To give some idea of what sort of effect we’re dealing with, if we had a situation in which a league-average hitter from 2016 was facing a league-average pitcher (both had a walk rate of 8.2 percent on the season), then the day after (or two days after) a blown save, we would actually expect that plate appearance to end in a walk about 9.1 percent of the time. That’s pretty impressive.

We can’t immediately chalk this up to being sad about the blown save (although that’s a decent guess). One thing that might be happening here is a blown save leading to an extra-inning game, and the next day, the bullpen is just more tired than usual. But we can’t rule out the idea that the bullpen takes the loss kind of hard, and takes it kind of hard as a group.

The Cascade Effect and the Value of a Closer

Let’s take stock for a moment. Here we have evidence that the bullpen might actually move as a unit. That they are more than just a group of individuals. When someone blows a save, it hurts across all the members of the corps. That maybe the whole team chemistry thing has real effects on real players. Neat.

But let’s play this out a bit. A couple of weeks ago, I meditated on the Cy Young case of Zach Britton, closer extraordinaire for the Orioles. In that piece, I noted that while Britton’s value, when you strip out all of the context, doesn’t compare to a starter’s value, the entire point of Britton’s job is that he comes in for a very specific context. Here, we see that we need to put a few more pennies in Mr. Britton’s basket.

A good closer (by definition) will save more of his chances than a bad one, and we see from this that if he does so, he actually prevents his teammates from suffering an increase in their walk rate. And yeah, it seems like the effect only lasts for a game or two, but every little bit helps. And it’s worth pointing out that we’re looking at the “average” effect. In specific cases, the effect might be bigger (or smaller). A blown save might beget another blown save, which in turn begets another blown save. The cascade effect could torpedo an entire team’s season, even if they have even-year magic.

There probably are places where we are too quick to see a pattern in randomness in baseball (and life), and there are probably things commonly chalked up to “team chemistry” that are just the random number generator having its way with our emotions. But we need to be careful not to dismiss all of them out of hand. In this case, there’s likely something to be said for some sort of systemic effect. If this sort of chemistry effect is out there, are there other ones that we don’t know about yet?

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Thought this was a great article. Very interesting. Russell Carleton is always worth reading, but this in particular was an interesting question. Still hoping he will address some of the questions he raised earlier in the season regarding "priming" effects and sequencing.
All in good time.