The day after slugging his 40th home run of the season — and leaving his pitching duties early because of a cramp in his right middle finger — Shohei Ohtani walked into the Los Angeles Angels clubhouse dressed, as always, in Southern California chic: flip-flops, navy shorts, black T-shirt and a backward black baseball cap.

Whether or not he expected to be here, that’s hard to say.

As the Angels came back to Anaheim for their first homestand after the Aug. 1 trading deadline, they were celebrating a successful trip to Detroit, Toronto and Atlanta that had revived hope in the team’s season. And more important, they returned with the face of the franchise still in tow.

Countless pundits had expected Ohtani, a free agent after this season, to be traded at the deadline, but nobody working at Angel Stadium seemed to think things would play out any other way than they did.

“We have a special player who is having a really unique, special year with a team that’s competitive,” General Manager Perry Minasian said. “And for us not to give ourselves an opportunity to get better and go for it would have been, in my opinion, the wrong decision.”

Minasian added: “He’s somebody that we all love, somebody I love, and I hope he’s here for a long time.”

Whether Ohtani remains an Angel for two more months, or the rest of his career, is a decidedly open question. His free agency is expected to be among the wildest pursuits of a player in baseball history. Rather than bow out, the Angels kept him close while making a number of deadline moves in hopes of adding depth to their top-heavy club.

In adding starter Lucas Giolito, relievers Reynaldo Lopez and Dominic Leone, first baseman-outfielder C.J. Cron and outfielder Randal Grichuk, the injury-decimated Angels, who stood three games back in the A.L. wild-card chase the morning of Aug. 1, believed they had strengthened themselves in their ongoing battle to make the playoffs for the first time since 2014.

The deadline moves also presented a good-faith gesture to Ohtani, whose words from two Septembers ago continue to echo loudly: He likes his team, loves its fans, but, above all, he just wants to win.

Outside the white lines, Ohtani, 29, remains the game’s greatest enigma. He doesn’t say much, and he offers fewer clues regarding his life outside of the game. He takes questions only after he pitches, which is every six days or so. Even then, it is in the tunnel outside the Angels’ clubhouse — one lone man and his interpreter backed up against a concrete wall, blank eyes, short answers, little depth.

Angels officials stand sentry as he speaks, ready to cut off the first part of the interview scrum to transition to the Japanese media portion. Then they remain poised to cut that off as well so Ohtani can escape back into the protective cocoon of the clubhouse and the pureness of the baseball to which he passionately and fully devotes his life.

When he was done talking after Thursday’s heartbreaking 5-3 loss to the Mariners, in which the Angels had been two outs away from victory, Ohtani retreated quietly to the chair in front of his locker, doing what many young people do after work has separated them from their devices for hours: Phone in his left hand, he stared intently at the screen as a large ice bag encased his right elbow. Ippei Mizuhara, his interpreter, sat cross-legged on the carpeted floor next to him as they decompressed from another day in Shohei-land.

That night’s game had produced yet another viral moment in a career full of them. Ohtani left the game as a pitcher after only four innings and 59 pitches because of the cramp but stayed in the game as a designated hitter and blasted an eighth-inning home run with an exit velocity of 107 miles per hour.

“How do you do that?” Mark Gubicza, the Angels radio broadcaster and longtime pitcher, said. “It’s like watching Michael Jordan, Wayne Gretzky and Tiger Woods play baseball, all in one. He’s a freak. A cramp in your right hand and you still hit the ball 107 m.p.h.?”

In the midst of another staggering season, Ohtani was leading the majors in homers (40) through Monday, and was also leading in total bases (282), extra-base hits (66) and on-base plus slugging percentage (1.082). He was tied for the major-league lead in triples (seven).

On the mound, he was leading the majors in lowest opponents’ batting average (.186). A second Most Valuable Player Award seems like a foregone conclusion.

His importance to the Angels is off the charts: He was leading the team, by a wide margin, in plate appearances (501) and innings pitched (124⅔).

“He is mentally as strong as anyone I’ve ever been around,” Manager Phil Nevin said.

By retaining him at the deadline, the Angels clung to what they feel is an important piece of rope tethering the two sides together. Rivals will line up on the free agent market — the universal belief is that the Dodgers are retrenching this summer so they can throw all available resources at Ohtani this winter — but the Angels have every intention of extending what has been a great relationship, even if it has not yet resulted in team success.

Though the frustration of October-less baseball continues, the Angels have done everything they could to build a perfect environment for their unique star. He has been given the creative space to flourish both as a hitter and as a pitcher. He has the freedom to follow his own individualized routines. And the club has shielded him from the news media, ensuring that all of this is possible without much outside interruption.

Had they opted to trade a player who has been building a strong case for himself as the greatest in history, it would have been a humiliating admission of failure. Deciding to keep him while knowing they could lose him for a draft pick this winter is risky as well — especially given that the Angels, in their attempt to reload, traded two of the best prospects in a mediocre farm system: catcher Edgar Quero and the left-handed pitcher Ky Bush. Additionally, the Giolito acquisition helped push the Angels over the $233 million luxury-tax threshold — a first under the owner Arte Moreno.

“What he’s allowed me to do, I don’t take lightly,” Minasian said of working with Moreno. “I’ve said this since Day 1 — I want to be with people who want to win as badly as I do.”

Nobody understands the overall value of Ohtani more than the Angels. Club officials feel his impact daily as they watch the throng of fans entering Angel Stadium. They see it in the lines outside the team store as Ohtani merchandise flies off the shelves, including his jerseys, which are the second most popular in baseball behind Atlanta’s Ronald Acuña Jr. And visible reminders are all around the stadium via advertisements for tires (Yokohama), probiotic beverages (Yakult), imaging products (Konica Minolta) and felines (Churu, “Japan’s No. 1 cat treat”).

By the time Moreno announced this spring that his 124-day exploration of selling the club had finished and that he would maintain ownership, the franchise’s value, according to Forbes magazine, was $2.7 billion, a huge increase from the estimate of $1.8 billion when Ohtani joined the club — and an unfathomable leap from 2003, when Moreno purchased the team for $183 million.

The team is in the Ohtani business, and from ownership to the front office to the dugout, no one wants that to change.

“Honestly, the only time we thought of him leaving was when others brought it up,” Logan O’Hoppe, the team’s injured rookie catcher, said of Ohtani. “We’ve never talked about it internally. And he’s done more than an incredible job of not bringing it into the room. Obviously, everyone knew what was going on, and he makes it clear he is a part of this group. And everyone appreciates it.”

He added: “It’s crazy. You don’t even realize he is who he is because he is so humble and he stays who he is.”

O’Hoppe is one of an M.L.B.-leading 18 players on the Angels’ injured list. The team activated infielder Brandon Drury over the weekend. The returns of O’Hoppe (shoulder), third baseman Anthony Rendon (bruised shin bone) and pitcher Sam Bachman (shoulder) are anticipated in the coming weeks. And outfielder Mike Trout, the team’s other pillar alongside Ohtani, hopes to return soon from a fractured bone in his hand.

“So that was part of it, too,” Minasian said, referring to the team’s optimism at the deadline.

Things have not gone as well since.

The Angels had won 10 of 13 entering August, but after a pair of losses to Atlanta, a four-game sweep by the Mariners and a brutal late inning collapse against San Francisco on Monday, the Angels had fallen to eight games back in the wild-card race. Ohtani had muscle cramps in three games over an eight-game stretch and guessed the culprit was “fatigue.” He had played in 112 of the Angels’ 114 games, and he had been the starting pitcher in 21 of them — this after he had led Team Japan to the gold medal in the World Baseball Classic this spring.

As is his custom, he addressed neither the trading deadline nor his future with the Angels after Thursday’s start. He spoke only of the game he had just played.

“Ideally, I wish I could have gone 100 pitches and saved the bullpen,” he said ruefully.

Still, he had reached base in all four plate appearances, swiped second to put himself in position to score the team’s first run and then smashed another epic homer, cramp or no cramp.

It was all part of the continuing, maddening pattern. The superlative Ohtani plays out of this world, and the flawed Angels remain stuck on the ground. As they hope and wait — and try to get better — his teammates have a front-row seat to a performance that has no true precedent in M.L.B. history.

“While I’m smiling ear to ear and looking left and right, everyone else was like, ‘Yeah, it’s just what he does,’” Giolito, the newcomer, said of watching Ohtani homer with a cramped hand. “I think everyone else is kind of used to it by now.”

He added, “But for me, it’s pretty special to watch and be on this side of it rather than on the other end.”