Does rerolling all Hit Dice at each level make any statistical difference?

[Yora]

I am very certain that it was always intended that you roll one additional Hit Dice every time you level up, but you regularly find people mentioning the alternative interpretation that you instead roll all your Hit Dice and the new result is your new hit points. Then there's also the further addition that you only use the newly rolled number if it is higher than your old one, so that you can't end up with less hp after gaining a level.

Now I am wondering if this actually makes any difference, one way or another for the average in either direction? Does it affect how much hp characters have on average at all?

 

[squeen]

No. The only bias would be from the "only keep if higher" mod.

That said, I'd still never do it (re-roll all).

 

[Two orcs]

Rerolling each level (allowing hp to go down on a lower roll) means your hp over time is going to be closer to average (especially if you reroll after 9th level when new HD stop being added). If you only roll the new HD, the earlier rolls puts you permanently below or above average. Example:
You roll 8 for your first HD. At 9th level your average hp will be 8+(4,5*8) = 44
You roll 1 for your first HD. At 9th level your average hp till be 1+(4,5*8) = 37

If you reroll but only keep the new roll if higher you'll skew close to somewhere above average, as a high fluke roll might put you above average for several levels (I use this method in my campaign, it feels good if someone who's been a weak combatant for several levels suddenly get a huge boost, like they found their stride + it means early luck doesn't mean permanent statistical advantage).

I use the opposite method for drained HD, reroll your now lower HD and only keep it if lower.

 

[WrongOnTheInternet]

If you wanted to play around with hit point rolling, Hackmaster has a rule of dubious origin for you.

 

[Johann]

I've been doing re-rolls for many years. Else, a bad roll can permanently cripple a character.

For my upcoming campaign, I'll switch from "reroll all, improve at least one point" to "reroll all, take what you get even if it's lower". I don't like inflated hit points. That said, players can send their PCs to mountain retreat or on vacation etc. for a year to get another reroll. Gotta play another PC in the meantime, though.

Finally, I replace 1d6 with 1d4+1 (and 1d8 with 1d4+2 etc.). Average is the same, but it's less swingy, so there's no need for further shehanigans (max. at first level, at least half the maximum etc. etc. etc.).

 

[The1True]

We just reroll 1's. and 2's as well for fighter/barbarian types.