Imagine a sports superstar of Lou Gehrig’s magnitude dying in this era, two years removed from his playing days, and then someone making a movie about him or her a year after that.

It is unlikely that the public would learn much new. Today we watch athletes grow up, chronicled endlessly via video, audio and text, allowing us to know them well — or at least believe we do.

Not so in Gehrig’s time, which is part of what for 75 years now has made the film “The Pride of the Yankees” unique. Never before or since has a sports biopic more fully come to be the accepted reality of a star athlete’s life.

Gary Cooper was skinnier than Gehrig, sounded nothing like Gehrig and sure as heck could not replicate the baseball skills of Gehrig, and yet in many ways he is more Gehrig than Gehrig himself in America’s collective memory.

Many people understood that reality from the beginning, as explained in the new book, “The Pride of the Yankees: Lou Gehrig, Gary Cooper, and the Making of a Classic,” by Richard Sandomir. It’s due out June 13.

Paul Gallico, a sportswriter who authored the original version of the screenplay, recognized as much in a letter to Gehrig’s widow, Eleanor, about halfway through filming that is recounted in the book:

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“Lou seems to have become more Gary Cooper than Lou Gehrig but I suppose they had to do that. I think he still comes out a very lovely character.”

That he does, but again, the fans of Gehrig’s time did not have much to go on. He removed himself from the lineup for good four months before the first televised Major League Baseball game.

It’s complicated, in a good way, and Sandomir does a fine job telling the story not only of a classic sports film but a pioneering one in a genre that barely existed before.

One of the most effective means to that end is letters from Eleanor in which she sought input into the script, often for the sake of simple accuracy. She believed, correctly, that fans do not like games and dates messed with.

She did not win many battles, no surprise given that the producing boss, Sam Goldwyn, was more interested in marketing a romance that would appeal to female filmgoers than a film about baseball, of which he was not a fan.

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Perhaps the worst of the sports inaccuracies is Gehrig giving way to Babe Dahlgren on May 2, 1939, in the sixth inning of a game when in fact he pulled himself out earlier that day, ending his streak of 2,130 games played.

The most impactful alteration, though, is in Gehrig’s iconic farewell speech of July 4, 1939.

The movie version differs significantly from the real one, especially in moving its famous line, “Today, I consider myself the luckiest man on the face of the Earth,” to the end, which is not where it was uttered originally.

There is not a reliable, complete transcript of the actual speech, nor full newsreel footage, and some of the next day’s newspapers got it wildly wrong from their longhand notes.

Gehrig does not appear to have thanked journalists in his actual speech, but Cooper does, noting “my friends, the sportswriters.” (It pays to have a sportswriter on screenplay duty!)

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The film softens the caustic relationship between Eleanor and Gehrig’s mother and other less pleasant aspects of the tale, and there are plenty of corny scenes and lines by modern standards. But even after three-quarters of a century, it packs an emotional wallop.

It’s all in the book, including nuggets such as Babe Ruth losing 50 pounds to play himself, Dahlgren negotiating himself right out of the movie with excessive demands and Cooper’s efforts to try to look plausibly like a lefthanded baseball player. In one sequence, it is believed that he was filmed righthanded, then the image was flipped.

Eleanor did not want Ruth in the film at all. According to Gallico’s notes, she told him, “He should not appear in the flesh. Feeling that he would make a further mess of baseball and ruin the beautiful tribute to Lou, who represented the clean side of the sport.”

Eleanor lost that argument, like most of the others, but she need not have worried. The film remains what it always has been: a beautiful tribute to Lou.