Phillies need another arm at the trade deadline. Just look at last October.

A quick math problem for you:

Last postseason, the Phillies’ bullpen logged 44⅓ innings in 13 games. Their top four relievers at the time — José Alvarado, Craig Kimbrel, Jeff Hoffman, Matt Strahm — combined for 26⅓ of those innings. Which means there were 18 innings left over, all of them pitched by a reliever who was outside of the top four.

Question: Who pitches those innings this year?

OK, so it isn’t really a math problem. More like game theory. Or philosophy. Or natural disaster preparedness. Except, the disaster will be entirely man-made if the Phillies do not answer the question before the trade deadline on July 30 at 6 p.m. Philadelphia time.

We’re not talking about luxuries here. Adding another arm is a necessity. Failing to do so would be the single biggest mistake Dave Dombrowski can make at the deadline, short of trading Aidan Miller for a giant glass jug of wooder. The bullpen is priority No. 1. Everyone thinks they need a right-handed bat, until Gregory Soto comes trotting into a playoff game to protect at three-run lead.

It happened last year. Game 4 of the National League Championship Series. Phillies up, 5-2. Before Orion Kerkering walked a man home. Before Kimbrel allowed a two-run home run. Before Alvarado allowed a go-ahead RBI single.

Soto was the one who started things off in the seventh with a one-out walk and a one-out single. Kerkering followed with a couple of two-out walks, the second of which forced a run home, putting the Diamondbacks in position to tie it in the eighth on Alex Thomas’ two-run blast.

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That seventh inning is what Dombrowski should be thinking about. Who pitches it this time around?

Right now, there is no good answer. Look at how the current bullpen sets up. The Phillies have four of the best high-leverage relievers in the majors in Alvarado, Hoffman, Kerkering, and Strahm. But do they have anybody else you would trust to get three pivotal outs with a postseason series on the line?

Soto has been quite good for two months now. Since May 23, he has a 1.08 ERA with 24 strikeouts and nine walks in 16⅔ innings. But he has also allowed five of 11 inherited runners to score during that stretch, in addition to allowing close to a baserunner-and-a-half per inning. Maybe something has clicked. If so, great. But remember, we’re looking to kill 18 innings here.

After Soto, Seranthony Domínguez would likely be the next man up. We’ve spent much of the last two years searching for game-log glimmers that show him returning to his 2022 form. Between May 3 and July 12, he had a 1.21 ERA with 26 strikeouts, eight walks, and one home run in 22⅓ innings. That stretch ended loudly, with a four-spot against the A’s the day before the All-Star break. The command simply isn’t there. And it hasn’t been for a while.

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Even if Soto and Domínguez are both who they’ve been when they’ve been at their best this season, they are still relievers you’d much rather have on a short leash in any postseason outing. What Phils manager Rob Thomson needs is another guy he can turn to in moments of necessity.

Five is the minimum. That’s essentially how many he needed last postseason. Five Phillies relievers finished October with an average leverage index of at least 1.24, which means the stakes they faced were 24% higher than baseline. This year, Hoffman is Kimbrel. Alvarado is Alvarado. Kerkering is Hoffman. And Strahm is some combination of Strahm and Domínguez, who combined for 10⅔ innings as the fourth and fifth men last October.

Five is the bare minimum. Six is the ideal. Last October, Thomson made 22 pitching changes in a situation with an average leverage index of at least 1.24. Those appearances were distributed among seven pitchers:

Alvarado: 5

Kimbrel: 4

Hoffman: 4

Domínguez: 3

Strahm: 2

Soto: 2

Kerkering: 2

Thomson has more faith in Kerkering this season. Probably Strahm, too. Cristopher Sánchez will presumably pitch more than 2⅓ innings this time around. The Phillies are clearly in better shape than they were.

The goal is to bulletproof the thing, to hope for the best but prepare for the likeliest reality. There are few greater postseason weapons in the world than a bullpen that goes five or six deep with shutdown arms. It takes pressure off your starting pitchers. It allows your offense the occasional scuffle. It makes opposing hitters look over their shoulders — or straight out beyond the center-field wall.

We’ll throw plenty of names at you in the coming days. There is never a shortage of options this time of year. Rangers closer Kirby Yates is at or near the top of my list, with the right (presumptive) combination of affordability, availability, experience, and production. The Athletics’ Mason Miller is a flamethrower but could require a significant investment. The available inventory will depend a lot on what happens in the standings next week and a half.

On the Phillies’ end, there should be no doubt what they need.