John Gibbons is losing the bullpen battle

Playoff narratives are extremely silly. Despite what some people would have tried to tell you before Tuesday's game, Clayton Kershaw can definitely pitch in high-pressure situations, and so can David Price, even if he hasn't displayed it yet this fall. The skills that make you a good baseball player in April make you a good baseball player in October.

The same isn't true of managers, though. Bullpen usage is the most obvious thing that changes from the regular season to the playoffs, as the rosters are bigger, the margins are smaller, and there's much more rest between games. Like I said last week, there's a thriving cottage industry of manager criticism for their bullpen usage. This October, there haven't been any high-profile meltdowns yet, or moves that everyone has agreed were terrible, so I decided to take some deeper looks, to see who deserves accolades and who should be relentlessly mocked. (Or intelligently and constructively criticized, I guess.)

I started broadly, looking merely at the average number of batters faced by starters of each team. The "times through the order" (TTO) penalty is well understood now; first laid out in The Book, and discussed here by one of the authors, Mitchel Lichtman, the core concept is that starting pitchers generally perform worse as they seem the same batters multiple times. It's not totally clear what drives that trend -- batters doing a better job of recognizing or predicting pitches, pitchers getting more fatigued, something else entirely -- but a starter on their third time through the order, even a good one, is probably a worse option than a decent reliever.

In the playoffs, each individual game matters more, and using relievers is easier, meaning the smart move is often to turn the ball over to the bullpen before your starter has to face the top of the order a third time. That doesn't mean it's a move that's often made, however. What managers have had the quickest hook this playoffs?

Apparently Mike Matheny, by a pretty large margin. The difference between St. Louis and the Mets is eight batters, or practically a whole loop through the order. The Cardinals' average is pulled down, though, by three bad starts, in which practically any manager would have removed his starter quickly, and one John Lackey start which was so efficient that, despite throwing 7.1 innings, still covered only 23 batters. Terry Collins has let his starters go deeper, but again, that might be a function of simply having better pitching performances, rather than awareness of the TTO penalty. Perhaps more meaningful: two Toronto starters, Price on the 8th and Stroman on the 9th, have seen more than three full loops of the order (28 and 29 batters, respectively). No other team has more than one start over 27 batters faced, which might suggest John Gibbons is a little lacking in this respect.

This, clearly, is too broad of a measure to communicate much meaning over four games each, given how much goes into a single start. To get a better sense for management of the pitching staff of each team, I turned to leverage index. If you aren't familiar, there's a great primer over at FanGraphs, but what it basically does is measure the importance of a given at-bat. Up by ten in the seventh? Very low leverage index, since there's just not much that batter can do to change the outcome of the game. Tie game in the ninth? Very high leverage index! A leverage index of 1.0 is precisely average, and it is a useful stat to see how managers have deployed their relievers. Are they using their best relievers in the most important spots, or saving them for save situations that may never arrive?

To answer that question, I looked at each pitcher used in relief through Tuesday's games, and multiplied their total batters faced by the average leverage index in those at-bats. This results in a measure of the total impact of that reliever. A pitcher who faced two batters, both at a leverage index of 0.5, had about the same total impact as a pitcher who faced one at 1.0, or four at 0.25.

Then, for each pitcher, I took their regular season FIP-, and divided it by the best FIP- of the bullpen. A pitcher with a team-scaled-FIP of .5 is roughly half as good as the best reliever available to the manager. Then, I multiplied those figures by their total leverage figure, summed that score for each team, then divided by the sum of the total leverage for each reliever. Confusing! Basically, a team that concentrates its high leverage plate appearances (and its plate appearances in general) among their best relievers will have a higher score, while a team that sends out mediocre or bad relievers at important times will have a lower score.

Another suggestion that John Gibbons has struggled when it comes to deploying his relievers in an intelligent fashion. Given that this "leverage concentration" stat is completely and totally made up, it's hard to say what's a meaningful difference, but the gap between Toronto and the Mets (second-lowest) is roughly the same as the gap between the Mets and the Cubs (second-highest). The injury to Brett Cecil was unavoidable, and means he hasn't been used as much as he probably would have, but the Jays' best reliever by FIP- in 2015 was Liam Hendriks, and he's only been used for two batters in below-average LI situations. Aaron Sanchez, on the other hand, who has the worst FIP- among the relievers used thus far, has faced 12 batters in roughly average LI situations. To be fair to Gibbons, Sanchez has performed well, and he had limited options in the 14-inning game against the Rangers. Still, when combined with the above indication that he's perhaps leaving starters in longer than is ideal, and his utterly baffling use of David Price on Monday, Jays fans would be justified in feeling some nervousness going into Game 5 Wednesday afternoon.

The Dodgers, on the other end of the spectrum, grade out surprisingly well, given Mattingly's reputation. Kenley Jansen facing five batters yesterday, in a very high-leverage 8th and 9th, is a move this index is a big fan of. Similarly, the options that seem decidedly sub-par, like Joel Peralta or Luis Avilan, have only been used sporadically, and in very low-leverage situations.

The postseason functions as a crucible of sorts for managers, given how much every single decision is scrutinized, but usually, they only get called out when a decision leads to a disastrous result, regardless of the process behind it. John Gibbons hasn't seen anything blow up yet, and neither has anyone else, but it's only a matter of time if he keeps using his bullpen like this.

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Henry Druschel is a Contributor at Beyond the Box Score. You can follow him on Twitter at @henrydruschel.