It's impossible to name the "greatest player" in a single sport. There are different generations in sports, and each generation has different rules, game styles ect. ect. I'm going to just list a few athletes who I think were the best of their generation. And I only feel like doing baseball. Sorry.

Baseball
Honus Wagner, Ty Cobb, Babe Ruth, Tris Speaker Walter Johnson, Cy Young, Christy Matthewson

Joe DiMaggio, Ted Williams, Stan Musial, Bob Feller, Bob Gibson, Willie Mays, Hank Aaron, Mickey Mantle

Josh Gibson, Cool Papa Bell, Satchel Paige, Buck Leonard, Oscar Charleston

Pete Rose, George Brett, Rickey Henderson, Barry Bonds, Roger Clemens, Steve Carlton, Nolan Ryan