Several managers and pitchers made the Hall of Fame without hitting one single home run in their entire batting career. Don Sutton, for instance, despite coming to the plate 1559 times, never did so.
Amongst non-pitchers, Ray Schalk made the HoF despite hitting a mere 11 homers in his 18-year career.
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I don't know if I have found the HoF outfielder with THE fewest HRs, but here's a start:
Billy Hamilton had a mere 50 home runs in his HoF career.
Hall of Famer Robin Yount who played with the Brewers between 1974-1993.
Hall of Famer Joe DiMaggio won the American League MVP award in 1947. He hit .315 with 20 home runs and 97 RBIs that year.
Dodger with the most home runs over all is Manny Ramírez 554. Hall of Famer Duke Snider has 407 with 389 of those as a Dodger most of any player. Gil Hodges is next at 370 with 361 of those hit as a Dodger.
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Ernie White He hit 144 home runs in mlb history.