If you move the toilet seat to your preferred position and then leave it that way, the outcome is that girls will have to adjust the seat 49.5% of the time, while boys only have to do so 45% of the time.
Thus, always put the seat down, boys! BECAUSE MATH!
My estimates about how many girls and boys pee standing up / sitting down are estimates, but under 1% for girls standing (dot your i's, girls!) and around 10% for boys sitting (young kids, elderly, hungover, too sleepy too stand) seems sane. Of course, boys have to move the toilet seat even less if they sit down more often.
(I accidentally swapped actions girls take on the up/down, but the percentage outcomes are the same, so chillax.)