Kevin Cash's progressive bullpen usage

Something odd happened last night: Steve Geltz earned his first career save by pitching the ninth inning with the Rays leading the Red Sox 7-5, becoming the fourth Rays reliever to notch one, and continuing the trend of every Rays victory this season being capped by a save.

Geltz has done well for the short-handed Rays so far in 2015, with a 3.00 ERA, although he has walked a few too many batters for comfort (five in nine innings). Still, he did not receive the save opportunity purely because of his own merit. He was simply the best option left.

Brad Boxberger, the Rays best reliever (2.65 ERA Steamer projection), had pitched a scoreless seventh inning. Kevin Jepsen, the Rays second-best reliever (3.25 ERA Steamer projection), had pitched a scoreless eighth inning. That left Geltz and his 3.96 ERA projection as the clear choice against the top of the Red Sox lineup.

Has Kevin Cash lost his mind? Should you run to pick up Geltz in your roto league?

No and no.

The save statistic attaches undue importance to the final inning. It is well-intentioned, but it's only a rough heuristic for something that we can calculate much more precisely. There is nothing special about the final three outs of a game except for their finality, and thankfully Kevin Cash agrees.

When a pitcher gets out 27 with his team ahead, the win expectancy jumps from wherever it is to 100%. If he gives up the go-ahead run in the bottom of the ninth, it jumps from wherever it may be to 0%. That means that single events in the ninth inning of close games can create very wide swings in win expectancy.

This concept is called the "leverage" of a situation, and because the ninth inning often includes very high leverage situations, it's a good idea for managers to have a good pitcher ready for them. But the ninth inning isn't the only time that high-leverage situations can occur.

Everyone who's been watching baseball for awhile intuitively knows this. Taking a situation from last night's game as an example, the highest-leverage at bat came in the sixth inning with no outs and the Rays down 3-5.

Four straight singles and a bases-loaded walk against starter Joe Kelly had brought the Rays back into the game. And with Kevin Kiermaier up to bat, a single would almost certainly tie it while anything more would put the Rays ahead. At the same time, if the Red Sox could have escaped the inning unscathed, they'd have greater than an 80% chance to win the game (roughly calculated from the tool available here). The "leverage," per FanGraphs, was a score of 4.28, which means that moment was over four times more important than the average at bat in a game.

John Farrell knew it was important. He brought on his lefty, Craig Breslow, to face Kiermaier. That's a fine move, because Breslow absolutely destroys opposing lefties. My regressed platoon split projections pegged the matchup with an expected (and very low) .247 wOBA.

But Kevin Cash also knew it was an important moment, so he brought in a righty off the bench, Brandon Guyer, to pinch hit. That raised the projection to a still-below-average-but-much-better .301 wOBA. Guyer came through with a line drive into center, tying up the game.

Now, you might be wondering what would have happened if Farrell had opted to use his best reliever, Koji Uehara. After all, saves in the ninth inning almost never read a 4.28 leverage unless the closer blows the game. Luckily for the Rays we'll never know, but here's the projections:

Kevin Cash knows that the ninth inning isn't the only time to use his best pitcher.

And he proved that he understands the concept and isn't afraid to deviate from the norm by how he managed his own bullpen last night.

Let's return to the Rays and Steven Geltz.

Breslow and Edward Mujica got out of the sixth inning without further damage, and the game was tied 5-5. Starter Nathan Karns was at 108 pitches and was set to face David Ortiz, Hanley Ramirez, and Mike Napoli. The leverage index of that moment was 1.52, meaning about 50% more important than average, but given the quality of the hitters due up, it was an even more dangerous spot. That's why Kevin Cash pulled out his biggest gun and sent in Brad Boxberger to face the heart of the order.

There's more at work here than the single inning, though. Let's think about what could happen in the seventh inning (both the top and the bottom). I don't have the leverage calculator scaled identically to how FanGraphs does, so the numbers are different, but it will work for napkin math. By this scaling, when Boxy entered, the leverage index was 1.4.

• If no one scores, the leverage for the top of the eighth would jump up to 1.7.
• If the Red Sox score one run, the leverage would fall to 0.8.
• If the Red Sox score two runs, the leverage would drop to 0.4 (and more runs means lower leverage going forward).
• If the Rays score one run, the leverage would rise to 1.9.
• If the Rays score two runs, the leverage would fall to 1.2 (and more runs would mean lower leverage).

Kevin Cash, of course, chose Jepsen (the better pitcher) for the eighth inning. That meant that if Jepsen did his job and kept the runs off the board, it would make the decision into a tossup, with both relievers exerting the same influence on the game. If Jepsen failed, it would put more pressure on Geltz. But if the Rays did anything, it would actually turn the ninth-inning into a less-important-than-average spot.

Conclusion

Tonight Cash's strategy worked. The leverages from FanGraphs for his three relievers matched their abilities with Boxberger getting the most important spot at 1.52 and  Jepsen and Geltz clocking in at 1.33 and 1.35 respectively. It won't always work out like that, because the Rays won't always score two runs in the bottom of the seventh inning, but Cash showed that he was willing to think about the overall game situation and the range of possibilities rather than being a slave to a single limited statistic.

The Rays have a manager who's not afraid to use his brain.