Yes, there used to not be any set distance at all No, the distance between bases has not changed since Major League Baseball began in 1876. The distance between home plate and the pitchers mound changed several times before it settled at 60'6" in 1893.
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The distance is measured from the back of home plate to the hill. Hope that helps Answer More accurately, the distance is measured from where the first and third base lines meet (the apex of the plate) to the front edge of the pitcher's plate.
Different distances were experimented with in order to find the optimal distance. The current distance has been proven to be perfect for giving pitchers and hitters no unfair advantage over eachother.
If you drew a line from home plate to first base, first base to second base, second base to third base, and third base to home plate, you would have a square. This is because the distance between those bases is the same (90 feet). A square turned on its side is a diamond.
For Little League (7 - 12 year olds), the distance is 60 feet.