Third baseman Adrian Beltre, 37, continues to deliver for the Texas Rangers

It’s not only Adrian Beltre’s agility, range and cannon arm, or his ability to hit for average, power and in the clutch and play through pain that impresses Angels closer Huston Street.

It’s the way Beltre does a little dance while pointing to the first-base umpire on a check swing; the way the Texas Rangers third baseman playfully jostles with shortstop Elvis Andrus over the right to catch a pop up, and the way he glares menacingly at anyone who dares to touch his head — a pet peeve of his — during dugout celebrations.

“The game is becoming so much about flair, of having more emotion,” Street said. “But there’s a right and wrong way to do it. Beltre absolutely has swag and flair, but he does it in a way that is respectful to his teammates, the other team and the game.

“You enjoy playing against him because of his energy and that level of respect. When he does get excited and celebrates, you can tell he’s doing it because he helped the team. He rarely does anything to celebrate himself.”

The Angels have had their fill of Beltre for 19 years, and they’ll get another dose of him when they open a three-game series Friday night at Arlington, Texas.

As much as they appreciate Beltre for his sustained excellence, which has put the 37-year-old on a direct path toward the Hall of Fame, they are not always happy to see him. And it’s not only because Beltre has hit more homers (36) and driven in more runs (137) against the Angels than any other team.

“I think I would have 3,000 hits already if it wasn’t for him,” Angels slugger Albert Pujols said. “He probably robs me at least twice in every series.”

Beltre, a standout defender when he came up with the Dodgers as a 19-year-old in 1998, has maintained that high level for two decades.

According to baseball-reference.com, Beltre ranks 13th all-time in defensive wins above replacement for all position players, a list that includes Ozzie Smith, Mark Belanger and Brooks Robinson at Nos. 1-3.

Beltre is among the best in baseball at charging a slow roller, making a barehanded grab and delivering a strong, off-balance throw to first. Street’s personal favorite is Beltre’s backhanded stab of a hard grounder.

“I’m talking about a rope, a missile, a wicked one-hopper,” Street said. “He just sticks his nose in there. You can tell it’s skill because his head is right on the ball. Sometimes guys wave at the ball and come up with it. He doesn’t do a lot of waving.”

If the four-time All-Star and four-time Gold Glove winner gets his glove on a ball, Street said, “the guy is probably out, because of [Beltre’s] arm.

“All he has to do is catch it, because with his arm, his release, his ability to throw from all arm angles, from his butt, his back, his knees, underhand, overhand … he’s always able to finish a play, which is a huge asset.”

Beltre’s bat, which he wields in a way best described as violent, is an even bigger asset and the primary driver of the Beltre-to-Cooperstown conversation.

The native of the Dominican Republic has a career .285 batting average, with 2,790 hits, 416 homers, 566 doubles, 1,347 runs and 1,479 runs batted in.

Only two Hall of Fame third basemen — Mike Schmidt (548) and Eddie Mathews (512) — hit more home runs than Beltre. Only Schmidt and George Brett (both with 1,595) have more RBIs.

With Beltre signing a two-year, $36-million extension through 2018 and showing few signs of slowing down, he could finish with career numbers comparable to Hall of Famer Cal Ripken (.276, 3,184 hits, 431 homers, 1,695 RBIs) and Hall of Fame lock Chipper Jones (.303, 2,726, 468, 1,623).

“I think at the end of the day he’s going to be a first-ballot Hall of Famer,” Pujols said. “The numbers speak for themselves.”

Beltre, who is batting .319 with three homers and 12 RBIs in 19 games this season, will not speak for himself on the topic.

“To be honest,” he said this month, “I don’t have the numbers to get there and I’m not going to stay in this game for an extra year or so just to get some numbers. After I retire, if I get that call, it would be an honor. But it’s not something I think about now.”

What drives Beltre is winning a World Series ring after coming so close in 2011, when the Rangers twice came within one strike of winning the title but lost Games 6 and 7 to the St. Louis Cardinals.

That experience, which included a score-tying Game 5 homer by Beltre that he famously hit while his right knee cork-screwed to the ground, both haunts and drives Beltre, who spurned the Angels before the 2011 season to sign a five-year, $80-million contract with a sixth-year option with the Rangers.

“Being in the World Series, being close enough to win but not winning it yet,” Beltre said, “it’s one of the things that keeps me hungry, motivated, to play every day, every year. I know how hard it is to get there.”

The Rangers won the American League West by going 38-22 over the final two months of 2015 but lost a five-game division series against the Toronto Blue Jays. They’re relying heavily on Beltre, their cleanup batter, to get them back to the playoffs this season.

“He’s the centerpiece of our team, the DNA; he makes everything easier for everybody,” Andrus said. “He loves to put the pressure on his shoulders. He’s had a lot of success over his thousand years in the league. He’s a guy you can rely on, who’s not going to change in good times or bad.”

Or when he’s hurt. Beltre played the second half of last season with a torn ligament in his left thumb and still batted .287 with 18 homers and 83 RBIs.

He hit .318 with 11 homers in the second half, including an Aug. 4 game against the Houston Astros in which he needed only the first five innings to hit for the cycle for the third time in his career.

Beltre suffered a lower-back strain in Game 1 of the division series against the Blue Jays, took a cortisone shot between innings and had an RBI single in his next at-bat before departing. He sat out Games 2 and 3 but returned for Game 4, notching two hits despite his pain and limited mobility.

“As long as he can get on the diamond,” Andrus said, “he will.”

Beltre’s toughness goes back to January 2001, when he experienced complications caused by an emergency appendectomy performed in a small-town Dominican hospital.

“I watched him take ground balls that spring with a colostomy bag and green fluids oozing out of him,” said Scott Boras, Beltre’s agent.

Beltre, then 22, underwent a second procedure that March in which 15 inches of his small intestine were removed. He lost weight and strength but returned in early May and hit .265 with 13 homers and 60 RBIs in 126 games for the Dodgers. He has averaged 146 games in his 17 full seasons.

“Some things you can play with, some things you can’t,” Beltre said. “Somehow, I’ve been able to produce with injuries.”

Beltre takes the game seriously. He does not take himself too seriously. In April 2015, he sent Angels pitcher Garrett Richards an invoice for $300 — “cash only, no checks,” he wrote on the slip — after the right-hander broke three of Beltre’s bats in a game. Richards laughed about it.

“He’s a pretty cool player,” Street said, “and people are drawn to that.”

Young Rangers players gravitate toward Beltre, who provides counsel in English and Spanish and whose leadership extends well beyond the clubhouse.

“He’s a coach on the field,” Rangers Manager Jeff Banister said. “The experience, the calmness, the edge, the competitiveness we talk about as a staff, he carries that onto the field. There aren’t too many situations that come up that he hasn’t already seen or been a part of.”

Boras calls Beltre “a freak” because he is playing a demanding position and hitting well at an advanced age. But those on-field skills are only part of Beltre’s resume.

“If I were to tell a position player coming into the game who you should model your career after in totality,” Boras said, “the answer would be Adrian Beltre.”

mike.digiovanna@latimes.com

Twitter: @MikeDiGiovanna