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Any discussion about players too handsome for the game should start and end with the man who, in his day, was George Clooney of the diamond: Steve Garvey.
He was a good player, no doubt. But I suspect he was often credited as being better than he was based solely on his looks. He looked like the quintessential ball player.
Go look at a team photo from the mid-70's Dodgers and tell me who on that team was the best, purely on appearance. Cey? Baker? Yeager? Lopes? Nope. Garvey.