Jeremy Hellickson spotted his manager stepping out of the Washington Nationals dugout and knew his fate. He was at the mercy of the numbers on Dave Martinez’s worksheet, and the numbers told Martinez it was time to take out his starting pitcher. Even in a scoreless game with two outs in the sixth inning. Even when that pitcher had thrown just 61 pitches and faced two over the minimum. Martinez was not sparing feelings.

For the second time in five days, Martinez took the proactive route in pulling Hellickson instead of risking a possibly disastrous third voyage through the opposing team’s lineup. This time, in a game Martinez managed as if it were October, it worked in a 3-1 win over the Pittsburgh Pirates.

This time, Sammy Solis came in to get the sixth inning’s third out and the Nationals scored the game’s first three runs in the bottom of the frame on homers by Trea Turner and Ryan Zimmerman. This time, Sean Doolittle converted his first five-out save in nearly three years and the Nationals (16-16) emerged with a four-game sweep of the Pirates (17-15) and a season-best five-game winning streak to reach .500.

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“After the game, I gave him a big hug,” Martinez said of Hellickson. “I said, ‘Keep us in the game. That’s all I ask, keep us in the game, and we’ll be fine.’ ”

Thursday was Hellickson’s first start since he was removed earlier than he would have liked in an extra-inning loss to the Arizona Diamondbacks on Saturday. He was pulled with one out in the sixth inning of a 2-2 game despite having thrown just 57 pitches. He said he didn’t talk to Martinez or pitching coach Derek Lilliquist about it at any point between starts because he knew what they would say. Martinez’s decision-making was predicated on one fact: Hellickson, like most pitchers, isn’t very effective going through a lineup the third time. And his case is starker than most.

Entering Thursday, Hellickson had limited batters to a .677 on-base-plus-slugging percentage the first time through the order in his career. That number climbed to .730 the second time and to .839 the third time. The data this year, though in a tiny three-start sample size, was even more drastic. Hellickson held batters to a .491 OPS his first time through entering Thursday as a National. The number climbed to a still very good .696 the second time before exploding to a 1.911 the third time. In eight plate appearances facing a batter for the third time, the hitters were a combined 4 for 7 with a walk, two doubles and a home run.

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Data obviously isn’t the only factor in the equation. Right-left matchups, pitch count, personal histories, the pitcher’s position in the order and signs of fatigue are all variables a manager must balance. But clubs have increasingly avoided letting starting pitchers — especially those below the top tier — attempt to navigate a lineup three times in recent seasons because of the data.

The Nationals’ approach with Hellickson is why they slotted him in the rotation behind Max Scherzer and Stephen Strasburg. Theoretically, the Nationals bullpen is at its freshest the day after the two all-star right-handers pitch, which would provide Martinez more arms to serve as the bridge to the 27th out when, in most cases, a starter encounters batters a third time between the fifth and sixth innings.

Sure enough, Hellickson plowed through five innings again Thursday. He turned a double play with a runner stealing and saved himself from a line-drive comebacker. He masterfully mixed and matched, nibbling the corners with a 90-mph fastball and coaxing whiffs with a 78-mph curveball. It was inexplicably dominant.

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“He doesn’t make many mistakes,” Zimmerman said. “Even when he does, you’re almost surprised and have to foul it off, or you miss it. He’s a professional, is the best way to explain it.”

Martinez’s hook was quick anyway. Hellickson had recorded the sixth inning’s first two outs on just five pitches before he surrendered a single up the middle to Adam Frazier — the first batter he faced for the third time. On cue, Martinez emerged to take the ball, which Hellickson flipped in the air in frustration as Martinez walked over. Martinez then gave it to Solis, who induced a long flyout from Gregory Polanco to end the inning.

“I would’ve liked a chance to get out of that,” Hellickson said. “But he thought that was best right there. . . . But we won the game. That’s all that matters.”

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The Nationals bullpen was given a lead when, fittingly, Pirates starter Trevor Williams stumbled his third time through Washington’s lineup. First, Turner laced a line-drive, two-run home run, his first homer since March 31. Zimmerman added some padding with a solo shot to left-center field. The three-run lead activated the Nationals’ bullpen troika of Brandon Kintzler, Ryan Madson and Sean Doolittle.

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After Kintzler worked a scoreless seventh, Madson was summoned for the eighth and labored. The 37-year-old hasn’t been the same since pitching three consecutive days in mid-April, and he departed with one out and the bases loaded after Howie Kendrick booted a tailor-made, inning-ending double play ball. That led to Martinez’s second October-like move: bringing in Doolittle to attempt to complete his first five-out save since September 2015.

“They’ve called down several times this year to see if I felt like I was available to go more than one inning, just in case something happened in the eighth,” Doolittle said. “So they’ve put that on my radar enough that I’ve started my routine a little bit earlier.”

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Thrust into the fire, the left-hander allowed one run to score on a fielder’s choice before escaping. He then tossed a perfect ninth inning to seal the four-game sweep and needed 17 pitches to make his manager look good again.

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