A perfect game. The pitcher retires 27 batters in order; no one reaches base. There have been only 23 in Major League Baseball since 1876, making it one of sports’ rarest accomplishments.

Ten years ago this week, Armando Galarraga, a Detroit Tigers pitcher who began the season in the minors in Toledo, Ohio, was on the verge of a perfect game when he retired the first 26 batters. The final batter hit a ground ball that resulted in a close play at first base.

The umpire, Jim Joyce, called the batter safe — perfect game over. But television replays clearly showed the runner was out. Galarraga was denied baseball immortality because the umpire made a mistake.

That’s when baseball showed what a remarkable game it can be. Not the game of steroids, massive egos and overpaid whiners but the game of grace, sportsmanship and humanity. Joyce who umpired for 30 years in the majors, including All-Star Games and World Series, acknowledged his mistake immediately after the game.

“I just cost that kid a perfect game,” Joyce said to reporters. “I thought he beat the throw. I was convinced he beat the throw, until I saw the replay. … Biggest call of my career and I kicked it.”

With tears in his eyes, Joyce went to the Tigers’ clubhouse and apologized personally to Galarraga.

Doug Harvey, one of the game’s greatest umpires and one of only 10 to be inducted into the Hall of Fame, explained Joyce’s pain.

“I would imagine the noise of the crowd was so great, in view of the circumstances, that the umpire had trouble hearing the ball hit the glove. Do you think there is any way in the world that Jim Joyce would have wanted to miss that play? My heart goes out to him, because I know what he must be going through at this time.”

A member of Harvey’s umpiring crew once made a mistake on a crucial call and acknowledged it after the game. Harvey said, “That’s what it means to be an umpire. You have to be honest even when it hurts.”

Considering what it cost Galarraga, he showed uncommon dignity as well. He said of Joyce, “He feels really bad, probably worse than me. I give a lot of credit to that guy, to say he’s sorry. I gave him a hug. His body English said more than the words. Nobody’s perfect. Everybody’s human.”

Jim Leyland, Galarraga’s manager, was understandably livid when he charged out of the dugout to argue the call. He came back to berate Joyce again after the final out. But when he cooled off after the game, Leyland, a superb manager, reconsidered.

“The players are human, the umpires are human, the managers are human,” Leyland said. In this case, they all behaved admirably.

You know who didn’t? Omniscient sportswriters, know-it-all bloggers and carping sportscasters, most of whom are not as good at what they do as Joyce is at what he did. “I don’t feel sorry for Joyce,” brayed one writer, betraying a common sentiment.

“The Tigers’ fans have been cheated out of the greatest pitching experience in Tiger history,” complained their announcers, ignoring the fact fans actually did see a game they will always remember and proving announcers can actually be bigger whiners than players.

Instant replay has minimized the possibility an umpire’s error like that will ever happen again (minimized, not eliminated). But at the same time it has removed some of that aforementioned human element, one of baseball’s unique aspects as a sport.

Doug Harvey said, “Look, you have to prepare yourself to do your job, and then you do it to the best of your ability. That’s the way the game should be played.”

The historical canon of baseball is unparalleled among professional sports. What happened decades, or even a century ago, has contemporary relevance. Before Jim Joyce ever managed a game in the majors, long before Armando Galarraga was even born, a veteran umpire named Ron Luciano prophesized their fate.

Luciano, who tragically committed suicide after retiring, said in a 1975 interview, “Some umpires tend to pull into a shell and build a fence around themselves. I’d rather get it out. It’s like admitting when I made a mistake. There’s no way I can keep it in. It helps me relax to admit I was wrong. People only remember the one mistake, but who the hell is right all the time?

“I’ve never met the perfect man and I know I’m going to miss one now and then. You pray it doesn’t happen at the big moment. The umpire who makes a bad call to blow a no-hitter is going to cry himself to sleep for the next 30 nights.”

The sportscasters, bloggers and sportswriters probably had no such problems sleeping.

The day after the game Jim Leyland arranged for Armando Galarraga, who was technically off-duty, to meet Jim Joyce at home plate and present the lineup cards for that day’s game. Joyce gave Galarraga a pat on the back caught by the television cameras. Leyland, Galarraga and Joyce are all retired now, but they all continue to speak warmly of what could have been an ugly moment a decade ago.

It remains one of baseball’s greatest moments and should be shown to Little Leaguers and amateur players everywhere.