How important is batting order? As the Phillies experiment with their lineup, let’s look at the numbers.

Never mind that the Phillies scored the fifth-most runs in baseball last season. They went Arctic cold in the playoffs for a second consecutive year, so fans grabbed their pitchforks, dialed up sports-talk radio, and screamed for changes.

Internally, the cooler heads in the front office mulled possible moves.

But only so much could be done to a lineup that features five players who will make at least $20 million this year. Early in the offseason, then, Rob Thomson said the quiet part aloud: Improvements would need to come from within, and the manager didn’t rule out anything, including alterations to the batting order.

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“The lineup construction, we’re going to go through that and try and figure out a better way to score runs on a consistent basis a little bit more,” Thomson said after the Phillies were booted from the divisional round by the Mets. “Is there a different way? Is it best to have Kyle [Schwarber] in the leadoff spot? I don’t know.”

And with that, a well-worn Phillies debate was resuscitated.

Every armchair manager’s favorite pastime within the national pastime is to grab a pencil and paper and scratch out the ideal batting order. Just think of the acres of newspaper space and hours of airtime since 2022 that were spent on these questions: Is Schwarber the best leadoff option? … Doesn’t a slow-footed home-run hitter belong in a middle-of-the-order, run-producing spot? … If not Schwarber atop the order, then who?

For three seasons, Thomson mostly stuck with Schwarber — and for good reason. Hardly a prototypical leadoff man, the barrel-chested slugger set a single-season major league record with 15 leadoff homers last year. The Phillies also are 219-161 — a 93-win pace over a full season (not including a 20-14 mark in the playoffs) — with Schwarber in the leadoff spot.

This spring, though, Thomson is experimenting. Trea Turner was slated to lead off, with Schwarber in the No. 2 spot, on Monday against Pirates sensation Paul Skenes, but the game got rained out. Two days later, Turner led off and Schwarber batted second against the Rays.

Maybe it’s a hint about the opening day lineup March 27 in Washington.

But here’s the thing: It probably won’t matter.

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Old-school managers have long contended that shuffling the batting order like a deck of cards is overrated in the pursuit of improving an offense. Many data-driven analysts agree. Move one hitter up and another down, shift this hitter there and that one here, and the difference in run-scoring output is negligible over 162 games, according to various projection models.

“If you swap, let’s say, the No. 2 and No. 3 hitter, any reasonable swap like that, you’re going to get two or three runs [per season],” said Tom Tango, a statistical analyst who has consulted for several teams and written extensively on the subject. “That’s basically what we’re always talking about. A couple of runs here, a couple of runs there, that’s really what the impact is.

“At the same time, if you can make [the lineup] better, you may as well do it. But the [public] discussion should probably be proportionate to its impact. And while you are correct to try to squeeze those two or three or five extra runs by doing multiple swaps, the discourse on it is not proportional to that.”

Go figure, then, that the leadoff question is among the hotter topics from a quiet Phillies camp.

In 2006, Tango wrote The Book: Playing the Percentages in Baseball and devoted a chapter to assembling the optimal lineup.

Among other things, Tango challenged conventional thinking that the fastest player must lead off, the No. 2 hitter should be adept at moving a runner, even if it means giving away an out, and the team’s best hitter should bat third followed by its most powerful slugger in the cleanup spot.

Tango wrote that a manager should put his best hitters near the top of the order to maximize their plate appearances. More specifically, he asserted that the three best hitters should bat first, second, and fourth, with walks and on-base percentage as a priority for the top two spots, a strategy that generally is accepted in modern baseball.

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But Tango also conceded that players are human, with preferences for certain positions. When he consulted for the Mariners two decades ago, he believed Ichiro Suzuki would be “the ideal No. 2 hitter.” But Tango said he also learned that leading off is a prestigious lineup spot in Japan. If the Mariners tried to move Ichiro to the No. 2 spot, he might have viewed it as a demotion.

In the Phillies’ case, Bryce Harper’s on-base skills align with the profile of a contemporary No. 2 hitter. He hasn’t balked at batting second or fourth (he doesn’t like leading off), but self-identifies with one particular spot in the order.

“Obviously I’m a three-hole hitter,” said Harper, who has the numbers to back the claim, notably a .942 career OPS in the No. 3 spot compared with .783 in the two-hole.

Besides, based on research by Tango and others, it’s unlikely that the boost from moving any player up one spot in the order would outweigh the benefit of keeping him where he feels most comfortable.

In his book, Tango tested an optimal lineup with the pitcher batting ninth (remember when National League pitchers batted?), and the team was projected to score 4.605 runs per game. With the pitcher in the cleanup spot and the cleanup hitter batting ninth — “The worst thing you could possibly do,” Tango said — the same team was projected to score 4.504 runs per game.

Over 162 games, it translated to 16 runs.

The point: “It basically level-sets the idea as to how much impact could all this have,” Tango said.

Like every team, the Phillies have proprietary projection models. Surely, their analytics team has run the numbers on swapping Schwarber and Turner.

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By using Baseball Musings’ lineup analyzer tool, we can hazard a guess at the Phillies’ findings. Based on Steamer’s preseason projections for weighted on-base average and slugging percentage, here are the run-scoring outputs for the same version of a Phillies lineup with Schwarber and Turner flip-flopped:

“Out of all the things to spend a lot of time on, that’s not the one to do it,” Tango said of the leadoff debate. “More important than stuff like that is looking at who you put into the lineup. You look at the platoon advantage. Is a team actually putting in the right guys to take advantage of the platoon matchups? That matters a whole heck of a lot more.”

If anything, the sequencing of hitters matters more than each individual spot.

Turner, for instance, is among the fastest players in the sport and a two-time league leader in steals. But he’s less likely to run when he reaches base directly in front of Harper because vacating first base may precipitate an intentional walk.

“At times in the last few years, even when I played in Washington and L.A., there were times where I could steal a base, but I’ve got to stay there to let those guys hit,” Turner said. “That’s part of the game. I’m not going to act like I could steal 70-80 bases or anything like that, but there’s a handful of times where the opportunity’s there for a stolen base specifically, but it’s not always the right play, I guess.”

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Maybe Turner will feel more compelled to run if Schwarber is batting behind him. But Tango suggested in his book that the best way to leverage a player’s speed is to bat him in front of a hitter who is unlikely to drive him in from first base. That won’t happen with Turner unless the Phillies move him down in the order in front of, say, Stott.

Thomson also prefers to alternate left- and right-handed hitters. If Turner leads off, the only way to separate lefty-swinging Schwarber and Harper is to bat them second and fourth, likely with Bohm in between.

Harper seems open to the idea. He batted cleanup throughout most of the 2022 postseason, including Game 5 of the NL Championship Series, when he hit his famous Bedlam at the Bank two-run homer to clinch the pennant. But a cleanup hitter doesn’t come to the plate as often as a No. 3 hitter and isn’t guaranteed to do so in the first inning.

“If I wasn’t hitting in the four-hole, I probably wouldn’t have the moment,” Harper said. “If I was hitting three-hole, I’m leading off that inning instead of J.T. Anything can happen in the game. If I’m just in the lineup, I’m cool.”

There’s also an argument that the Phillies’ optimal batting order would begin with Schwarber against right-handed pitchers and Turner, a right-handed hitter, against lefties. But even if Thomson goes that route, he isn’t inclined to shuffle the top of the order.

“I think the top four or five guys are going to be pretty consistent,” he said.

The bottom of the lineup could be more fluid, especially if the Phillies platoon Kepler or, more likely, Marsh with a righty-hitting outfielder. But Johan Rojas had a .526 OPS against lefties last season compared with Marsh’s .552 mark.

Whatever happens, this much is clear: Other factors, including how at-bats are allocated among the outfielders to get the best possible platoon advantage, will prove to be more important than the order in which the three best hitters on the team bat.