Do you roll/allow rolling HPs in your game? If so are you a 'hard line' "You decided to roll so your stuck with that 1" or do you have a way to mitigate bad rolls?
What options I've seen are:
Player and DM roll, DM rolls behind a screen, and player can decide to take either roll. Of course the player cant see the DMs roll before deciding.
Re roll 1's.
If you roll lower then half take half.
How do you go about it.
1st level full hp
Every level after 1st: Roll. A roll of 1 can be rerolled once but then the roll stands.
No problems so far.
I prefer this over a normalized fixed HP increase, it can lead to some PCs being slightly over or under the average, but at least e.g. not every fighter with same CON has the same HP on a given level.
Think of it like that: If you take the average, then I have to ask you why you do not use the average damage output of mobs also? I bet you do not use them except evtly. in mass combat. Am I correct?