What is the best batting AND Pitching Average a baseball player can get?

Question:

Answers:

Losing a no hitter in 8? Is it an official no hitter?

The best possible batting average a player can get is a perfect 1.000, meaning he gets a hit every time he comes to bat.
Pitcher have had 1.000 averages, but only two plate appearances.
The lowest possible ERA for a pitcher is 0.00, meaning no earned runs were charged to the pitcher. DOOP pitcher have a tendancy to own a 0.00 ERA, however only pitching an inning or so.

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Question about softball rules - Would this count as an out?

batting is 1.000 avg 162 HR and 486 RBI's (4 per game)

pitching 0.00 ERA 25/0 K/BB and 0.000 BAA

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