Logan grew up in Endicott, New York, and attended Union-Endicott High School, where he was a five-sport star.

His father John Sr., was from Tsaritsyn, now Volgograd, and his mother, Helen Senko, was born in Croatia, but also lived in the borderland of Poland.

While Logan was playing for the minor league Milwaukee Brewers on June 25, 1951, Kansas City Blues catcher Clint Courtney hit him in the face with an elbow while sliding hard into second base, knocking Logan's front two teeth out.

[4][5] Logan had one of his best seasons in 1955, playing in all 154 games, batting .297, leading the league with 37 doubles, and finishing 11th in Most Valuable Player voting.

He was involved in the founding of the Milwaukee Braves Historical Association, and he often visited Miller Park for Brewers games.