Even if you believe Nathan's more than six wins better than a Triple-A scrub, that number overstates the actual effect on the Twins bullpen. Why? Because the scrub won't directly replace Nathan. He'll be replaced by one of the better relievers already on the team, and everyone else will move up one rung. This is known as bullpen chaining. And it matters because, in general, the innings pitched by a closer are more important than those pitched by a setup man, which in turn are more important than those pitched by relievers lower on the ladder. By leveraging their bullpens to allow runs when they matter less and prevent runs when it matters more, teams can win more games without giving up fewer runs.
Thanks to Tom Tango, FanGraphs provides a statistic that measures the importance of every situation, called leverage index (LI for short). Here's what you need to know:
The average situation (think of the starting pitcher's role) has an LI of 1.
Closers appear in situations with an LI of about 2, meaning runs allowed by closers are typically twice as harmful as the average run.
Setup men will see LIs in the 1.3 to 1.5 range.
What can we do with leverage index? Well, combined with bullpen chaining, we can compare the Twins' bullpen with and without Nathan. First, here's a simplified view of what the Twins bullpen would have looked like with Nathan:
Twins Bullpen, With Nathan
Joe Nathan is not only projected to pitch better, but he’s projected to take the mound when giving up a run is most costly, as measured by the leverage index (LI).
Note: RAR is runs above replacement, which compares a pitcher's ERA to the replacement level ERA for relievers (about 4.75), converts that to runs saved based on the number of innings pitched, and then multiplies by leverage index to account for the importance of the runs saved.
That's a good-but-not-great bullpen, and is definitely carried by Nathan's superstar talent. Now here's the situation if I remove his innings, bump everyone else's leverage index up a bit, and hand the least important innings to the scrub:
Twins Bullpen, Sans Nathan
Without Nathan, the Twins' bullpen is anemic and is projected to have an ERA about one-third of a run higher.
Yikes. That bullpen will only strike fear into the hearts of Giants hitters. Quantitatively, the Nathan-less group is expected to allow 26 additional leveraged runs, or about 2.6 wins worth.
More important to my main point, notice that Nathan's RAR total from the first table implies a value of 33 runs compared to a replacement closer. That 33 number would hold if the scrub took over the closer's role, but because of bullpen chaining, the loss of Nathan is mitigated by three-quarters of a win. That might not sound like much, but the Twins' bullpen is set up to feel the loss of its closer more than most bullpens. If Nathan were a less dominant reliever or if there were a backup option who could post an ERA in the low 3.00s, losing Nathan might only have cost around two wins. Six wins? No way.
Epilogue: I'm not married to the IP and ERA numbers in the table (they're roughly adapted from the CHONE projection system), so feel free to mess around with your own bullpen setups below. Here are some tips:
Change the green cells, but don't touch the orange cells -- they're calculations.
The average bullpen throws around 490 innings, but that's not set in stone
The average LI for the whole bullpen should be around 1
Good LI's to use: closer = 1.8, setup = 1.4, a few around 1 and the rest at 0.7 or less
RAR is runs above replacement, which is (4.75 - ERA) * IP/9 * LI [4.75 is the approximate ERA of a replacement level scrub reliever]
LI is leverage index, the average importance of the situations a pitcher faces. One is average. More at fangraphs.com.
Feel free to distribute and modify the spreadsheet. Please keep all credits intact and don't sell it. Much thanks to Tom Tango and the insidethebook.com/ee community for their help understanding bullpen chaining. For more on bullpen chaining, go here.
Sky Kalkman writes for Beyond the Box Score.