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Leverage and the Cardinals bullpen

A look at how many relievers a team needs for high-leverage situations

St Louis Cardinals v Chicago Cubs Photo by Jonathan Daniel/Getty Images

As I write this, the Cardinals are 5 1/2 games back in the division and a whopping 12 games back in the Wild Card. Their chances of reaching the playoffs sit at 17.8%. It bears pointing out that while the Cardinals are six games below .500, by BaseRuns, which is more indicative of a team’s true talent, they’re actually right at .500.

That doesn’t matter though. The losses have been banked. The Cards are in a hole that they have about 5 weeks to climb out of before the trade deadline. Things are dark, but rather than write about selling, I’m going to choose to continue to write about where the Cardinals can make improvements. If you’re interested, I broke down the pieces the Cardinals could sell a week and a half ago, and quantified how much value those players could bring back to the organization.

One weak spot for the Cardinals continues to be the bullpen. When adjusting for league and environment, the Cardinals’ pen has the 7th highest ERA, 13th highest FIP, and 14th highest xFIP. While the ERA is bad, the fielding independent stats point to them regressing to average. Average however, isn’t much to hope for if the Cards are going to get back into this thing.

It would be one thing if the Cards’ pen lacked depth. If they at least had a two or three strong options to rely on in close games, maybe they could just deal with the rest of the pen yielding poor results. Brett Cecil was brought in to be one of those options, but has overall been disappointing thus far. After an amazing season last year, Oh has better than average results with a 3.48 ERA, but his FIP (4.03) and xFIP (5.00) both indicate that things could have been much worse. In the offseason I warned that Oh could easily regress in 2017, but I was really hoping to be wrong on that one.

This gave me an idea. How many good relievers is ideal? OK, the answer to that is however many relievers the team carries. What I’m trying to get at though is, how many good relievers does a team need to cover all the higher leverage situations they have?

If you’re not familiar, leverage index refers to the mathematically calculated importance a situation has at any point in time. The inning, score, outs, and runners on all contribute. The quality of the hitter is not a factor. It’s scaled so that 1.0 is the average leverage. More than that is higher than average, and less than that is lower than average. For more, check out Fangraphs’ great explanation here. Relievers may pitch a lot less innings than pitchers, but the good ones get their value from locking down the close situations that occur late in games.

So here’s what I did. I took each team over the last five years, and ranked all their relievers by leverage index. There’s many types of Leverage index, but for today I’m going to use pLI, or player leverage index. That takes the average leverage index of every plate appearance the pitcher is involved in.

I took each team’s highest leveraged reliever, and from that I found an average. I also did that for each team’s second highest leveraged reliever, third highest reliever, and so on. Here’s the results:

Average leverage index.txt

leverage order average leverage average FIP-
leverage order average leverage average FIP-
1st 1.81 79
2nd 1.49 85
3rd 1.28 89
4th 1.12 95
5th 0.98 93
6th 0.87 101
7th 0.77 102

On average, teams have four relievers that overall pitch in higher than average leverage situations. Fifth place sets just below average leverage. I also calculated an average FIP- for each rank, to get an idea of what type of reliever is expected to pitch in what type of situations. With FIP-, 100 is average, and the lower the better.

100 is average for all pitchers though, not just relievers. Relievers have an advantage because they don’t go through the order more than once. Since they usually only go an inning or maybe two, they also can throw harder than they would if they had to conserve their energy over several innings. This advantage is enough to outweigh the fact that overall, relievers are weaker pitchers than starters. Since 2012, the beginning of our sample, the average FIP- for relievers has bounced around from 94 to 97. Generally, the higher the leverage, the better the reliever. The only exception is that 4th and 5th place switched spots.

Here’s the main pieces of the Cardinals’ pen this year, along with their pLI and FIP-:

Cardinal relievers.txt

Name IP pLI FIP-
Name IP pLI FIP-
Trevor Rosenthal 24.2 1.65 49
Matt Bowman 30.2 1.27 88
Seung Hwan Oh 31 2.27 94
Tyler Lyons 16.1 0.54 96
Brett Cecil 24.2 1.35 101
Kevin Siegrist 24.2 1.02 106
Samuel Tuivailala 14 1.23 115
John Brebbia 10.2 0.51 123
Miguel Socolovich 18.2 0.45 125

Trevor Rosenthal has been the best reliever by far, but has the second highest leverage. On average, the ninth has a higher leverage than any other inning - particularly the close games that the closer comes in for, though a manager that aggressively used the same reliever in all non-ninth high leverage situations might get that reliever a higher overall leverage. That might involve a trade-off between innings and leverage that doesn’t make sense overall though.

Part of Oh’s high average leverage comes from the fact that he’s often got himself into trouble. Going by gmLI - game leverage, or the average leverage just when entering the game - Oh is at 1.84, quite a bit lower but still higher than Trevor.

The Cardinals have six relievers with an above-average amount of average leverage. Maybe that’s because they’ve just played more close games than others, or maybe Matheny has had to try a lot of relievers in high-leverage situations with the team’s struggles. I don’t know, your guess is as good as mine.

Except for Trevor, no reliever meets or exceeds the expectations for their leverage rank. However, there’s reason to think that improvement will come without an addition to the bullpen. The best public projection systems - Zips and Steamer - project future performance better than a player’s current performance, and they update daily based on new information. Fangraphs averages the two together for their projections. Here’s how the members of the Cardinals’ pen projects the rest of the year:

Cardinal reliever projections.txt

Name FIP pFIP Diff. est. pFIP-
Name FIP pFIP Diff. est. pFIP-
Trevor Rosenthal 2.08 3.01 -0.93 71
Seung Hwan Oh 4.04 3.27 0.77 76
Brett Cecil 4.35 3.29 1.06 76
Matt Bowman 3.79 3.74 0.05 87
Tyler Lyons 4.12 3.82 0.30 89
Miguel Socolovich 5.39 3.88 1.51 90
Samuel Tuivailala 4.92 3.92 1.00 92
John Brebbia 5.29 4.08 1.21 95
Kevin Siegrist 4.56 4.21 0.35 98

Fangraphs doesn’t project FIP-, but I created an estimated one based on taking the percent difference between current FIP and projected FIP, and applied that to each pitcher’s current FIP-. Actually finding projected FIP- is probably more complicated than that even for players like these that are staying on the same team, but this should get us close enough.

This table is sortable, so you can play it around with it a bit. Trevor is expected to regress by nearly a run, but whatever, even if he does that’s still great. Literally every other reliever is expected to do better than they have so far. Even if Oh stays the highest leveraged reliever, as well as Cecil in third, each part of the Cardinals bullpen should exceed the expected performance for their leverage rank.

According to the projections, the Cardinals’ pen will probably be fine. Better than fine really, as they project for the 5th best bullpen going forward. At the same time, trading for relievers in-season is expensive. I found relievers to be more than twice as expensive per win than position players and starting pitchers, and Dave Cameron found that in-season wins are twice as valuable as in the off-season.

Those two things together means a very good reliever like David Robertson would probably require trading one of the Cardinals’ best prospects - such as Luke Weaver - or perhaps two lower ranked prospects of their top 9 prospects featured on my aggregate prospect list. When I made that realization last week, I recommended simply promoting Luke Weaver from Triple-A to the bullpen. He’d project as the second-best option in the pen. Between that and betting on improvements from the rest, and the pen could be a strength rather than a weakness moving forward. I continue to think that’s the best course of action.

Let’s get back to the premise though. The Cardinals need four strong relievers to cover their higher than average leverage situations. Rosenthal definitely counts as one of those. Oh and Cecil haven’t looked like it so far, but they both still project to be above average late-inning arms. Maybe you can’t bet on both bouncing back, but I feel pretty confident that at least one will. Matt Bowman continues to look perfectly acceptable as a fourth best option, and would probably be fine as a third best option.

They could use one more strong option though. Maybe Oh and Cecil bounce-back. Hey, that’s what the projections think will happen anyway. The Cards have time before the deadline to see if that happens. But in the meantime they don’t have games to spare; they need to seize every victory within grasp just to put themselves in a position where buying makes sense. This wasn’t supposed to be about Weaver, but that’s another point of promoting him to the bullpen. He’d almost certainly be one of the team’s four best relievers. Even without it though, the Cardinals should have a better than average top four relievers going forward.