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About 60 feet. Baseball is played on a " Diamond " right? The dimensions of the baseball Diamond are 90 feet along all four sides. A throw directly across the diamond from 3rd base to 1st base is 127 feet 3 3/8 inches. If the shortstop was positioned exactly midway between 3rd base and 2nd base and 15 feet off the base line toward left field, the throw would be approx. 114 feet.

Q: How far of a throw is it from shortstop to first base?

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about 50 feet

That depends on where the 1st baseman fields the ball. If the 1st baseman can field the ball, throw to second, and have enough time to get safely back to the base to catch the return throw, then (s)he will cover. If not, then it is the responsibility of the pitcher.

On a frozen rope from third to first base is 127 feet 3 and 3/8 inches.

127 feet

it's 63.72 ft

The main issue is that first base is on the right side, so you can't apply the same shift to a righty as you would to a lefty. A real dramatic shift on a left handed hitter like Ryan Howard has the third baseman playing at about the shortstop position, the shortstop playing closer to the second baseman's usual position, the second baseman playing in right field, the right fielder playing in very deep right field, and the first baseman guarding the line. You can't do the same for a righty. On a right handed pure pull hitter, the third baseman may guard the line, the shortstop will move towards third, and the second baseman will be behind the bag. But the first baseman must be close enough to first to handle a throw. And the shortstop can't play in left field, because he'd be too far away from first base to throw the guy out. So you can't shift a righty nearly as dramatically as you can shift a lefty.

The throw from first to third is 127' 3-3/8 inches.

That would depends on where they field the ball. Howeverthe distance from the 3rd base bag and the 1st base bag is just under 85 feet.

The distance from home plate to first base is 90 feet and the distance from first base to second base is also 90 feet making a right angle; you can calculate how far the catcher needs to throw to 2nd base from home by Pythagorean theorem. Answer is 127.3 feet

By "out of play" I presume you mean in the dugout or into the stands, in which case, the batter gets 2nd base If the ball stays in play, the batter could get as far as they can advance. Little League Rule 7.05 g 'states two bases when, with no spectators on the playing field, a thrown ball goes into the stands, or into a bench, etc.' The two bases are awarded from the runner's position at the time of the throw. If the runner is running towards first base and the ball is thrown into the stands, he is awarded 2 bases (1st and 2nd) If the runner has safely reached 1st base and the shortstop throws to first because the runner rounded too far and the ball goes into the stands, it is still 2 bases, but in this case it is 2nd and 3rd as the runner already occupied first at the time of the throw.

The back of the free throw line is 19 feet from the inside of the base line. - The inside of the base line is 5 feet 3 inches from the center of the goal. - The center of the goal is 13 feet 9 inches from the back of the free throw line. This makes the back of the free throw line 19 feet from the inside of the base line.

When hit by right hand-ers (the majority of batters) it means the ball was pulled that direction and is going much faster. So the 3rd baseman must have fast reflexes. Also the 3rd baseman then has to make the throw to 1st base. This is a far throw and the 3rd baseman must have a strong accurate arm.