While mathematically correct, this only holds true if they are exactly as productive from say 12 pm to 2 am after a long day as they are from 5 am to 7 am after

While mathematically correct, this only holds true if they are exactly as productive from say 12 pm to 2 am after a long day as they are from 5 am to 7 am after just waking up. Possible? Yes. Likely? No.