CARLSBAD, Calif. — As autumn extended from leaves changing to leaves falling, Perry Minasian, the general manager of the Los Angeles Angels, was besieged with questions from his children. Why, the kids wanted to know, are our grandparents visiting Uncle Zack and Uncle Calvin but not us?

The answer was easy. The Minasians are a baseball family. Zack is the pro scouting director for the San Francisco Giants, and the Giants won the National League West and were playing the Los Angeles Dodgers in a division series. Calvin is the director of clubhouse and equipment for the Atlanta Braves, and his 2021 ride went all the way to the World Series title. So the brothers’ parents, Zack and Barbara, spent October and early November crisscrossing the country cheering for two of their four sons. (Another brother, Rudy, 42, has his own law firm in Chicago.)

Perry, the third baseball son, chuckled as he recounted this while standing on the back veranda of the hotel where M.L.B.’s general managers meetings were held this week. He and his family were left out of Grandpa and Grandma’s itinerary because the Angels, as usual, were left out of the postseason.

Now, as Minasian, 40, plans for his second year of running the Angels’ baseball operations, there remain more questions than answers, some far more pointed than others, starting with this: Is the organization that fumbled away much of Mike Trout’s prime going to do the same with Shohei Ohtani?

“I’m worried about the organization, putting the organization in the best place to succeed,” Minasian said. “I wake up thinking about it and I go to bed thinking about it. That’s No. 1. It’s not about Mike Trout. It’s not about Shohei Ohtani. I may be the first person to tell you that. It’s about the team. The collective group and achieving something together. That’s what I spend my energy on.”

Ohtani is widely expected to win the American League Most Valuable Player Award next week. If he does, it would give the Angels four M.V.P.s in the past eight years, as Trout won in 2014, 2016 and 2019.

In those eight seasons, the Angels have won zero playoff games, made just one postseason appearance and, in the other seven years, finished a combined 131 games out of first place.

Trout turned 30 in August during a frustrating season in which a calf tear limited him to 36 games, a career low. Ohtani, after battling injuries during his first three seasons with the Angels, finally was healthy in 2021 and produced one of the most remarkable seasons in baseball history, starring both as a hitter and as a pitcher.

But he also seemed to put the organization on notice after the Angels finished fourth in a five-team A.L. West, just as it had in each of his first three seasons. After the home finale he said, via his translator: “I really like the team. I love the fans. I love the atmosphere of the team. But, more than that, I want to win. That’s the biggest thing for me. I’ll leave it at that.”

The comments immediately brought out the speculators: Is Ohtani angling for a trade? Is he threatening to leave via free agency when he becomes eligible after the 2023 season?

Minasian and Nez Balelo, Ohtani’s agent, each emphasized in Carlsbad that the answer to the first question is no, that Ohtani is happy playing in Anaheim. (“Extremely happy,” Balelo said.) The answer to the second question is unknowable this far in advance simply because there is so much time and so much could happen. And that starts with Minasian this winter as he works toward fixing a team that now has had six consecutive losing seasons.

Minasian and Ohtani have spoken multiple times since Ohtani made those comments.

“We’ve had conversations about all kinds of things,” Minasian said. “He’s an impressive guy on and off the field. One thing he has an eye for is talent. I call him and ask him about players. Absolutely. He’s got a good idea about what plays and what doesn’t.”

Minasian did not reveal which potential free agents or trade targets he may have discussed with Ohtani, but it is no secret what the Angels need: pitching. Their rotation ranked 22nd in the majors this summer with a 4.78 E.R.A. and 29th in each of the two previous seasons (5.52 during the 60-game season of 2020 and 5.64 in 2019).

Free agency probably will be an easier route for the Angels than trades given that they do not appear to be deep in prospects. Baseball America ranked the Angels’ farm system 25th in the majors in its 2021 midseason rankings.

There are just-past-their-prime potential Hall of Famers on the free agent market this winter like Max Scherzer, Justin Verlander and Clayton Kershaw. There are pitchers who lived up to their potential this year and are in discussion for the Cy Young Awards (Robbie Ray and Kevin Gausman) and others who are still working toward it (Marcus Stroman, Carlos Rodon, Jon Gray). Ohtani’s Japanese countryman Yusei Kikuchi is a free agent. Top potential trade targets for those seeking starting pitching might be Sonny Gray and Luis Castillo (Cincinnati), and Sean Manaea, Frankie Montas and Chris Bassitt (Oakland).

“There’s a certain type of personality we’re looking for on the mound to fit with what we currently have to kind of set the tone,” Minasian said, noting that one desired quality is aggressiveness and that “it is not just about taking the ball and throwing 100 pitches. We want players that make other guys better around them.”

In addition to collecting 46 homers and 100 R.B.I. at the plate while stealing 26 bases in 2021, Ohtani was also the Angels’ best starter, going 9-2 with a 3.18 E.R.A. and 156 strikeouts over 130 and a third innings pitched over 23 starts.

“I feel pretty confident that I could repeat what I did this year,” Ohtani said at the World Series last month in Houston while receiving the Commissioner’s Historic Achievement Award. “I just need to get out there and play every day and leave the numbers, put up good numbers, and I think I’ll be able to at least have a similar season as this year.”

“Amen,” Minasian said, smiling broadly, when those comments were relayed. “Let’s see it.”

Ohtani right now is back home in Japan, Balelo said, his off-season workouts already underway. Neither the agent nor the general manager would comment on whether they had engaged in talks regarding a contract extension. Ohtani is scheduled to make $5.5 million in 2022, the second year of a two-year, $8.5 million deal, after which he would be eligible for arbitration for a year ahead of free agency.

Both Minasian and Balelo agree that, above all, Ohtani wants to win. He already has proved he is about more than just money by choosing to move from Japan to M.L.B. in the winter of 2017-18 just as new posting rules went into effect. He left millions on the table by not waiting two more years, until he turned 25, to come to the United States.

The Angels have not been disappointed, especially when Ohtani, 27, is healthy.

“As good as he is on the field, the off-the-field stuff is what really impresses me,” Minasian said. “His interaction with teammates, his ability to make adjustments. His dedication to his craft.”

Now, the burden is on Minasian to put Ohtani in position to win.

“I know a lot was made about his comments,” Minasian said. “I think if you ask everyone else in the clubhouse, I don’t know any major league player who doesn’t want to win. If you do, show me one and let me talk to him. I’d be surprised. I was not surprised by what he said.”

Time will tell whether it was the frustration of a losing season talking, or a veiled ultimatum. With sweeping views of the resort golf course and gently rolling hills as a backdrop as he talked in Carlsbad, Minasian said his siblings teased him all fall about being the only brother who wasn’t participating in the postseason. With a productive winter, he could both end that razzing and make Ohtani happy, the priorities, perhaps, not necessarily falling in that order.

James Wagner contributed reporting.