D&D 5E Player Hit Points

[ezo]

It's going to give a slight edge over normal rolling. Say you roll 2d8. That's a nice triangular distribution, easy to calculate. Now say you roll 1d8 and call it x. Then your roll 2d8, but the minimum result is x + 1. That minimum result is going to push your result up a bit. As it turns out, it pushes the average roll up by 0.41015625.

Calculating it exactly for all of the possibilities would be a pain. So I programmed some simulations. Compared to a rounded up average, the WWN method is down about 3.7 hit points over 20 levels (assuming rolling for first level). On the other hand, the standard D&D method is 10 hit points behind the rounded up average over 20 levels. One difference is that standard D&D rolling is going to be 10 hit points behind regardless of the size of the hit die (the previous results in this paragraph are based on a d8 hit die). For the WWN method how much is lost compared to rounded up average depends on the size of the hit die. For example, a d10 hit die only loses about 2.3 hit points over 20 levels compared to rounded up average.

I got slightly different values for d8:

at level 20 (max at level 1): rolling 93.5
rolling to beat prior hp: 96.3 (beats rolling by almost 3 hp)
taking avg round up: 103 (beats rolling to beat prior by 6.7 hp)

So, at level 20 it seems to run between rolling from 2nd level on, to taking the rounded-up average after 1st level.

BUT, from levels 1 - 10 (the most often played), it is actually worse than just rolling!!!
At level 10: rolling 48.5
rolling to beat prior hp: 48.3 (LOSES by 0.2 hp).

It is worse at lower levels, but never a huge issue. In tier 1, you average 2 hp lower, and in tier 2 you average just 1 hp lower.

 

[cbwjm]

For a similar result, you could borrow a trick from Pathfinder 2e and have racial hit points (granted once at character creation, about a hit die's worth.) This give you some wiggle room to buff or nerf certain races, or just add a little flair to them.

I did originally consider that at the time (based on starfinder which does the same thing with race hp) but ultimately decided on just a doubling of class hp. I don't know if it would really matter much in the long run, but making the small races +6 hp, humans +8, and dwarves and half-orcs +10 made me wonder if I should change some other race abilities around for a bit more balance so players don't feel like they're missing out playing a gnome fighter and starting out with less base hp compared to a human fighter.

 

[ezo]

Does anyone have the statistics chops to work out how using the WWN method of "reroll hp each level, only keeping the roll if the result is higher than current" affects character HP over the levels, compared to using average?

Here you go.

The WWN method is worse overall from levels 1-10 compared to rolling at each level, but this is due solely the fact that you start with max hp at level 1. If you modify the WWN method to include the max at level 1, it is better overall that rolling at each level. Either way, it is always inferior to RAW using the rounded-up average after level 1.

 

[jayoungr]

I let the players choose. What I don't allow is "roll and then take the average if it's lower than average"--which my players have asked about.

 

[ichabod]

I got slightly different values for d8:

at level 20 (max at level 1): rolling 93.5
rolling to beat prior hp: 96.3 (beats rolling by almost 3 hp)
taking avg round up: 103 (beats rolling to beat prior by 6.7 hp)

Yeah, I was not giving max at first level to either one. If you give max at first level to both, it should have results similar to mine, as your later post shows.

 

[James Gasik]

I'm not a big maths guy, so I'll need someone to weigh in on this (it seems legit to me, but I could be wrong). I was talking to my roommate, and he said that the bigger your Hit Die, the worse off you were rolling.

Get a 1 on your d6? Darn, you lost 3 hit points. Get a 1 on your d12? Yikes.

 

[ezo]

he said that the bigger your Hit Die, the worse off you were rolling.

Rolling compared to what?

Get a 1 on your d6? Darn, you lost 3 hit points. Get a 1 on your d12? Yikes.

And you could just as likely roll a 6 on the d6 and a 12 on the d12 as rolling 1 on either die. The size of the HD doesn't matter.

Ultimately, if you're talking about rolling compared to RAW average (rounded-up), rolling costs you 1/2 a hp every level on average, so you should take the average rounded-up instead of rolling.

Frankly, I always thought that was a mistake by WotC. They should have made it average rounded-down. That way if you played it safe and didn't roll, the penalty was you'd end up with slightly fewer hit points on average compared to rolling.

 

[James Gasik]

Rolling compared to what?

Just taking the flat hit points in 5e.

 

[jmartkdr2]

One thing about rolling for ability scores: there's a very big difference between rolling in order and roll-and-arrange. The latter is the default for 5e and really does just randomize starting character power. I've not seen that be a problem, but it certainly can be and the only up side to the method is pcs are generally a bit stronger out the gate (which can be achieved with higher point buy or better arrays)

It's worth noting that in my experience with this, direct comparison of character power is unusual (because pc end up with different roles) and system mastery is a much bigger factor than how well you rolled.

Roll-in-order could push players to play something unexpected, or at least would if more different arrays were viable. As i stands everyone who's best ability is intelligence is going to play a wizard or an artificer, and the rest of their choices don't really care about ability scores.

 

[ezo]

Just taking the flat hit points in 5e.

edited my post to reflect that.