Usually the storyline of the first Red Sox encounter with the Angels each season — this year it starts Tuesday in Anaheim — centers around breathing air in the same ZIP code as the generational talent Mike Trout.

This year, Trout has a teammate who could be on his way to occupying a seldom occupied segment of the rarefied airspace where baseball’s most prized talents ply their trade.

The Angels’ gain of Shohei Ohtani is very much the Red Sox’ loss. They wanted to sign the two-way phenom. They wanted to sign him badly.

The 25-minute video presentation the team presented to Ohtani last winter featured, in both Japanese and English, a red-carpet introduction to everything historic and special about becoming a Boston Red Sox. Babe Ruth, who was the game’s last great two-way player with the Red Sox a hundred years ago, figured prominently. The Red Sox also showcased how their current infrastructure would support Ohtani’s desire to follow in the Bambino’s large two-way footprints.

Alex Cora made a pitch. Dave Dombrowski’s team-building experience was lauded. Ownership had their say. The historic support the Red Sox have offered to Asian players was highlighted.

It wasn’t the virtual reality show one club prepared, nor was it the notebook another mailed in. It was a heartfelt, high-production attempt to lock up a player the Red Sox fully believed could become not only one of their aces, but also another impact hitter.

“Collectively, we agreed that this was a player that deserved that opportunity. We saw a guy we could put into our rotation Day 1 and that, by the end of the season, would make his way up into one of our aces,” said Allard Baird, senior vice president of personnel and the club’s main scout on Ohtani for the last six years. “Then from a hitting standpoint, we felt, ‘Hey, we’ll bring him into camp, we’re going to give him opportunities to give him at-bats’ and then go from there. We felt very comfortable with him coming in and growing into that ace status as a pitcher. From an offensive standpoint, we felt that we liked the bat a lot but we felt it still needed some time to grow into an impact bat.”

Baird first saw Ohtani in 2012, when new Red Sox GM Ben Cherington asked him to watch a video of the then high school senior. Between then and 2017, Baird made 11 trips to Japan and saw Ohtani more times than he can remember.

Baird’s first take on Ohtani never left him. Baird knew, even watching Ohtani as a high schooler, he was watching a baseball talent unlike most he had ever seen.

“It was very, very impressive — physically he looked like a young (Mark) Gubicza,” said Baird of that first 2012 video. “It’s ironic that Gubicza is working for the Angels now (as a color TV analyst), but he had that type of body and he’s kind of grown into that type of body — tall, lanky but very athletic. When you think of a tall, lanky young kid, you always say ‘He’s going to grow into his body, those limbs have to connect a little bit better.’ It’s a natural progression when you look at a young kid’s body.

“This kid was different. He was well-connected. He had really good body awareness and had a really good feel athletically, which for his age stood out when you watched him do those types of things athletically, whether it be running, fielding a bunt, swinging a bat.”

Once Ohtani began playing in Japan’s Nippon Professional Baseball league for the Hokkaido Nippon-Ham Fighters, Baird saw him become a “rock star,” but an unfazed rock star. Ohtani began to lift weights, and continued to get improve as both a pitcher and a hitter.

More importantly, he developed a mental toughness that translated into a drive to always both hit and pitch in his career. That spurred him to come to the major leagues a couple years before for short money. He’s making $545,000 this year, plus a $2.3 million signing bonus, when he could have waited until after the 2019 season and gotten a true free-agent contract well north of $100 million.

That desire and the double dose of talent only elevated Ohtani higher in the eyes of the Red Sox. They embraced the idea of him being a two-way player. They had prepared a plan for each facet, one they had ready to go regardless of how the rest of the offseason played out.

“The other thing we felt strongly about is that he hasn’t thrown that many innings, especially last season because he had an ankle injury, and we were going to have to somehow work a break within the season because you didn’t expect this guy to come in and throw 175, 180 innings,” said Baird. “It was not only a short-term, difference-making sign, but it was also a long-term investment. That had to be worked in. Alex was involved in those discussions. Some of that was where he was at the beginning of the season, but we knew that at some point we were going to have to take some sort of break where we weren’t taxing him from a major jump from last year in terms of pitches and innings.”

If there was a consensus on which part of Ohtani’s game was weakest, it was offense, but the club believed his bat would eventually come around. Even though finding the perfect position sounded like a bit of a jigsaw puzzle the club had not yet cut into pieces, they were going to juggle what they had to in order to satisfy and protect Ohtani.

“We were going to be creative in terms of trying to get him at-bats, whether in the DH spot or maybe even at that time moving him around — it depended on what else we were doing over the course of the offseason, that was going to play into that,” said Baird. “But we were confident if he was ready to hit that we would find a way to get at-bats for him. We were going to work it out over the offseason based on players we either did or didn’t acquire.”

Ohtani faced skepticism in Japan about his desire to pitch and hit, and it was no different here. It took a couple of phenomenal starts, big home runs and clutch hitting the first couple of weeks of the season for him to create believers.

The Red Sox did not need convincing.

“That focus and determination has never changed,” said Baird. “Add in all that amount of money (he passed up), it’s hard to doubt the guy or say he’s got ulterior motives, like ‘It’s his walk year, he really posted up.’ You can’t say that with this kid. He’s a special athlete.”

And he’s also Angels property for a long, long time.

No spoiler alert necessary: The Red Sox never got the chance to even sit down with Ohtani. His agents decided he’d be better off with a team that spends spring training in Arizona versus Florida.

“I wish we were in a position where we could have tackled that challenge,” said Dombrowski. “We liked him a great deal, we thought very highly of him. . . . I thought he was a legitimate two-way player.”

It took 100 years for a two-way player of Ohtani’s caliber to play in the big leagues. Is it going to take another 100 for the next one?

Dombrowski has been working in a front office the last 40 years. One would think he or others would have stumbled across a talent once or twice who could be given that chance, but it was never that simple.

“I’ve never had anybody to point where they would be anywhere near the two-way threat that (Ohtani) is,” said Dombrowski. “I think it’s really, really difficult to do. I don’t think you eliminate players. Having been through this process for a long time, rarely do you have people who are considered a top prospect offensively and pitching wise. Sometimes people say ‘Well, if he fails with this, you can try this with him,’ but rarely do they say, ‘Hey, this guy is so good, he’s going to be able to do both of them right off the bat.’ So, I don’t even think you can per se ‘pursue’ them because they’re just not out there.”

In high school, even occasionally in college, the best athletes will pitch and play another position. They may even play another sport as well. But to excel in both hitting and pitching at the same time? The odds sound like they truly are 1-in-100.

“It’s just so difficult,” said Dombrowski. “You’re focusing on two different crafts, really, and there are very few players who are that gifted to do it. It does happen. I know guys in the big leagues, when they play and they don’t hit, then they can be a pitcher, and vice versa. It’s hard to do that.

“I don’t think they’re easy to find by any means.”

Baird has been on the West Coast, paying attention to Ohtani — as well as Trout and the 23 other Angels — plus Oakland, where the Red Sox will play after Anaheim.

Thanks to a rainout Sunday against the Royals, he will get the start Tuesday night against the Red Sox. Baird saw Ohtani shut down the A’s with 12 strikeouts in seven innings last week.

He saw the same pitcher he saw in Japan.

“This speaks volumes to him in the course of a game. I’ve seen him where he’s 92, 93, 94 (mph) and gets into seventh inning, here comes a 100, here comes another 100,” said Baird. “Well, that’s nice to see from a fan’s standpoint, but that’s very, very hard to do in the course of a major-league game. He did it the other day. All of a sudden, out of the clear blue in the sixth inning, here comes a couple 100’s.

“He’s a unique talent.”

Ohtani has been raking, too. He posted a .346 batting average, .414 on-base percentage, .769 slugging percentage, three home runs, a triple and 11 RBI in his first seven games. He won’t keep up that pace, but Baird said it will be up to opposing pitchers to execute the right game plan before Ohtani adjusts like he already did in a spring training where he looked overmatched at the plate.

“Offensively, he’s had success out over the plate and I would expect teams now to try and pound him in,” said Baird. “When they do that, he’s a smart enough player where all of a sudden he may start looking in. He’s a guy who’s going to make adjustments.

“It’s a hard game. He’s trying to play it on both sides of the ball at the highest level with all eyes on him. They were sold out (in Anaheim) the other day. It’s not like ‘This is a young kid who’s coming up, he’s going to get a few at-bats, he’s going to pitch, we think he’s a really good prospect.’ People are paying to watch this guy. He’s performing and they’re coming out to see him, which even adds to it all.”

The Red Sox are coming out to see Ohtani as well.

They wish they were introducing him to the Angels, but unlike Ohtani, they can’t have it both ways.