I think you misunderstand. Imagine I wanted to see which arm is better for throwing a ball: right or left. I choose 1000 subjects and ask 500 of them to throw

I think you misunderstand. Imagine I wanted to see which arm is better for throwing a ball: right or left. I choose 1000 subjects and ask 500 of them to throw lefty and 500 to throw righty. Do you see the issue with this experimental method?