I guess I need to weigh in on this. Or at least Bill Jenkinson will. He authored the book titled, "The Year Babe Ruth Hit 104 Home Runs." On page 197 of the book, Jenkinson writes:
In this case, Mickey didn't hit the ball nearly 565 feet, but more likely about 510 feet. The fact is that Yankee publicist Red Patterson went in search of the ball as soon as it left the premises and found a ten-year-old boy holding it in a backyard across the street. Patterson did his job too well when he announced that it was 563 feet (2 feet were soon added for the thickness of the outer stadium wall) to the point where the gall was located. The media went crazy, reporting that the ball had flown 565 feet. When I interviewed Patterson thirty years later, he stated in a rather bemused fashion that he had wondered all those years why nobody had ever challenged the reputed distance. He readily acknowledged that he had no idea where the ball actually landed.
The truth is that it was 462 feet to the point where the ball left the stadium. The horsehide was also about fifty feet above ground level and on a rapidly declining trajectory. Plus, the ball actually glanced off an advertising sign as it left the lot. My conclusion, which is backed by computer analysis, is the this drive flew about 510 feet.
He goes on to state that it was still an historic shot, as some of the game's strongest right-handed hitters had plenty of chances at Washington's Griffith Stadium, including Jimmy Foxx and Josh Gibson, who each played close to 150 games there. But only Mantle cleared that 32-row stand of bleachers.
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