SAN DIEGO — Once the Tampa Bay Rays made the World Series, just squeezing past the Houston Astros on Saturday, something odd happened in a room off the team’s clubhouse at Petco Park: The Rays ran out of ways to explain Randy Arozarena this October.

“I don’t have any words that can describe what he’s done, what he’s meant to us this postseason,” Manager Kevin Cash said of the player who has lifted his team again and again, then again with a two-run shot in Game 7 of the American League Championship Series. Kevin Kiermaier and Mike Zunino just shook their heads and laughed a bit. When it comes to Arozarena — the shooting, slugging star of these playoffs — his coaches, teammates and opposing pitchers are brain-twisted and stumped.

To date, on the doorstep of the World Series, Arozarena has the rookie record with seven postseason homers and counting. His 11 extra-base hits are a franchise record. He was named the ALCS MVP after bullying the Astros with four homers, a double and nine total hits in 28 at-bats. He’ll be the Los Angeles Dodgers’ biggest problem in a lineup that, to reach this title chance, fought inconsistency and had to scrap.

But Arozarena is its constant, and a fitting illustration of these Rays. The St. Louis Cardinals tossed him into a trade this past January. The deal was headlined by José Martínez for a former first-round pick — not the 25-year-old Cuban outfielder with speed and hints of power. Now, though, Arozarena is the reason that swap looms above this month. The Rays landed an unknown player fit to guide them through the wringer.

They just need four more wins.

“Ever since I got traded over, it’s felt like a family,” Arozarena said through a team interpreter. “They welcomed me with open arms. They let me be myself. They let me have the freedom to be out there and be the player I want to be.”

Before this run, while Tampa Bay was building the AL’s best record, Arozarena toiled at the team’s alternate training site in Port Charlotte, Fla. He had been a fringe outfielder with the Cardinals. At first, he had to make the Rays. Then they had a roster spot after sending Martínez — yes, the same José Martínez — to the Chicago Cubs on Aug. 30 near the trade deadline. Arozarena was given a shot.

And when that happened, Misha Dworken had a prediction. Dworken, one of the club’s bullpen catchers, told reliever John Curtiss that recalling Arozarena was the best deadline acquisition in baseball. Curtiss, in truth, knew little about Arozarena. Neither did most of the Rays. He flashed talent in spring training before a four-month break amid the novel coronavirus pandemic. How he got to the majors, let alone how he got to the country, was lost on most of his new teammates.

In 2015, Arozarena defected from Cuba on a small boat bound for Mexico. Cuba was where he grew up, where his family lived, where at age 8 he went from being a soccer player to loving baseball. But he always felt there was better opportunity in America. He wanted to provide more for his mother and siblings after his father died when he was a teenager. He left at age 19, chasing a dream.

“It was very scary,” Arozarena said recently. “It’s something I hope I won’t have to experience anymore. It was about eight hours of risking my life, not knowing exactly what’s going to happen. But I knew if I escaped successfully, I was going to be able to help out my family in the end.”

So Curtiss met Dworken’s bet with skepticism, saying, “Man, that’s a bold claim.” But last week, when the Rays were a win from the World Series, Curtiss admitted that Dworken was right. Arozarena erupted for seven homers in September. Then the playoffs started and he zoned in.

Arozarena notched four hits and a triple in a first-round sweep of the Toronto Blue Jays. He punched the New York Yankees with eight hits and three homers in their AL Division Series. He got even hotter against the Astros, growing his legend, but it wasn’t just the offense. Arozarena has worn borrowed, black-sequenced cowboy boots for good luck. He celebrates like a kid. When the Rays edged the Yankees to advance, Arozarena took down teammate Brett Phillips in a dance contest in front of their dugout. He’s the heartbeat of Tampa Bay’s order and its attention-grabbing frontman.

“You sit here and look at this group of guys, and I always say we don’t have a lot of household names,” Kiermaier said of the small-market team. “But at the same time, people are making a name for themselves right now.”

Put Arozarena at the top of that list. Count the number of fans who now consider him their favorite, then add one to the tally. Earlier this month, as he tore through the AL, Arozarena was asked about Cuban players he admires. He mentioned Astros first baseman Yuli Gurriel. He played the game for a moment.

Yet his real answer came quickly, perhaps revealing how he, of all people, has often bent the playoffs to his will.

“My favorite player is Randy Arozarena,” said Randy Arozarena, allowing himself to grin.