Jay Bruce’s tenure with the Mets has been defined by turbulence.

At the trade deadline, he was dealt to New York, a destination that later was revealed to be far from the top of his list. After more than a decade in the Reds’ organization, Bruce found himself in a new city and has bounced from hotel to hotel since his arrival, five in all.

Then Bruce stopped hitting, and his bat was the reason the Mets had coveted him in the first place. The familiar chants of his name — Bruuuuuce! — morphed into unmistakable boos.

Bruce, 29, became the anti-Yoenis Cespedes, the slugger who arrived under similar circumstances a year earlier and thrived under the spotlight to lift the Mets to the pennant.

But just when he appeared to be a lost cause, Bruce has roared to life, and he could play a key role as the Mets enter the final series of the year with a chance to win a furious three-team race.

The Mets have a magic number of two to clinch not only a wild card but the first wild card. That means that if they take two of three from the Phillies, they will host the wild-card game even if the Giants and Cardinals both win out.

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The Mets could clinch as early as Friday. If they beat the Phillies and the Cardinals lose to the Pirates, the Mets are in the playoffs. If the Mets win and the Giants (who will play the Dodgers) and Cardinals both lose Friday, they will clinch the first wild card.

Bruce will try to do his part. “At the end of the day, results are what the game is about,” said Bruce, who has homered in each of the Mets’ last two games. “It feels good to help the team.”

Since joining the Mets, Bruce’s average had tumbled to .174, ultimately prompting a temporary benching. But on Saturday, Bruce came off the bench and slammed a pinch-hit homer, triggering his hot streak.

In his last five games, Bruce is 7-for-16 (.438) with three homers and five RBIs. Even his outs have been loud.

“He’s locked in,” manager Terry Collins said. “He’s laying off pitches. It couldn’t have come at a better time.”

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No different from most hitters mired in a slump, Bruce has been working on minor adjustments that Collins believes have made a big impact.

“He’s starting to get his extension out in front of the plate,” Collins said. “He’s not letting the ball get too deep on him. He’s getting out front and he’s staying through the baseball a little longer. I think he’s made a lot of adjustments. He says he doesn’t notice them but I think he has because I see a different swing.”

Bruce insists he has merely stuck with his process, which he has learned through the years is “the only thing you can really count on.”

“All year, you work and you work and you work,” Bruce said. “You know you have a routine and you prepare, you keep preparing. You expect success at some point. I think that’s the biggest thing: to see a little bit of what you expect.”

Whatever the explanation, the turnaround has been stark. According to talent evaluators, pitchers boldly challenged Bruce, banking on him being late. When he began cheating on those fastballs, he left himself more vulnerable to off-speed pitches. But he has since shown signs of escaping that cycle.

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“I feel a little more on time,” Bruce said. “I think a lot of times when you are missing balls, you may be a little late or a little out front or you kind of get in between. I’ve been taking quality swings on quality pitches and not missing them. But the preparation’s the same.”

The results, however, have been different, and one explanation might be the most simple. Throughout his career, Bruce has been a streaky player, and his extended downturn may have just been another extreme example of that tendency.

Although the results are different, one longtime talent evaluator said he has spotted nothing significantly different about his swing. “Not sure it’s a big difference — same guy,” the scout said. “He was just struggling for a while.”

The Mets hold a $13-million option on Bruce for next season. For now, the sense around the organization is that it will be picked up, even if that doesn’t necessarily mean that Bruce will be back next season.

After picking up the option, the Mets easily could shop Bruce. One rival NL executive believes the market could be healthy given that Bruce’s $13-million salary next season still would be below the one-year qualifying offer for departing free agents.

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“At that price,” the executive said, “teams would line up.”

But for Bruce, those matters can wait for another day. For now, he’s too focused on making all of the upheaval of this season worthwhile.

“Since the day that I got here, that’s all that I wanted to do,” Bruce said. “I didn’t want to be anyone that I wasn’t. I just wanted to come here and play good baseball and be a professional and contribute to the team. Lately, I’ve been able to do that more and that’s very, very important. It’s the only thing that’s important to me.”