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Mangini and many other coaches on the pro and college levels believe the handshake is necessary _ in great part for the reasons Dungy cites. The ceremony never is comfortable for the loser, but it’s a whole lot less comfortable for, say, the team just beaten in the Stanley Cup playoffs that then lines up, player by player and coach by coach, for a long line of handshakes with the victorious opponent.

“I think there’s a lot of truth to that, the elements of sportsmanship are why maintaining the handshake is important,” said Mangini, now an analyst for ESPN. “We ask our kids to congratulate the other team and I think that is a good policy. It’s easy to be disappointed with a loss and the ability to show sportsmanship is difficult; it’s really easy to be gracious when you win, the talent is to be gracious when you incredibly disappointed.”

Mangini sees another element to what happened at Ford Field. Coaches constantly preach to players about showing self-control and not to display their frustration, especially when it can lead to game-changing penalties. When something happens like the confrontation between Harbaugh and Schwartz, it makes it harder for coaches to insist on such discipline when they violate their own instructions.

Texas Longhorns coach Mack Brown isn’t so sure the handshake is a tradition worth keeping.

“I don’t think it should be a requirement for two (coaches) that don’t have respect for each other or like each other,” Brown said. “Players usually handle it much better than the coaches.”

Indeed, players from both teams often form prayer circles following a game, and their greetings to each other seem more genuine.

Some 49ers not only had no problem with the postgame hubbub, they were inspired by it.

“It was something you don’t see every game,” 49ers left tackle Joe Staley said. “As for how that kind of went down, as a player I was pumped up about it. His whole demeanor kind of rubs off (on) the players. We get to see firsthand how competitive he is and how much emotion he shows.”

So did the rest of the nation at the end of a signature win. It was not pretty on either side.

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AP Sports Writers Janie McCauley in San Francisco, Teresa M. Walker in Nashville and Dave Skretta in Kansas City contributed to this story.

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Barry Wilner can be reached at http://twitter.com/wilner88