D&D 5E On Die Averages and Hit Points in 5e

[Lakesidefantasy]

For the "roll vs fixed value", if you aren't worried about cheating, simply let PCs reroll 1s on their HD.

1d8 reroll1s has an average of 5, identical to the "take the average" choice. And it lets people who want to have fun rolling HD not be worse off, on average.

At level 10, 9d8 drop 1 has an average of 45 and a Variance of 48/12*9=36, thus a SD of 6 and a 95% CI of 33 to 58. So a constitution 14 cleric using "pick take average" has 73 HP, while the cleric who rolls has 61 to 86 95% of the time (and has an identical average).

Does this work out the same way for d6, d10, and d12?

 

[Shiroiken]

I personally hate fact that this is the only "round up" in 5E. Personally I'd rather it be round down, making rolling a worthwhile risk. You could take the 0.5 HP loss or risk rolling low, with a chance of getting better.

 

[Charlaquin]

Does this work out the same way for d6, d10, and d12?

Yep!

d4: (2+3+4)/3=3
d6: (2+3+4+5+6)/5=4
d8: (2+3+4+5+6+7+8)/7=5
d10: (2+3+4+5+6+7+8+9+10)/9=6
d12: (2+3+4+5+6+7+8+9+10+11+12)/11=7

 

[Charlaquin]

I personally hate fact that this is the only "round up" in 5E. Personally I'd rather it be round down, making rolling a worthwhile risk. You could take the 0.5 HP loss or risk rolling low, with a chance of getting better.

I agree. Fortunately the reroll 1s house rule totally fixes the problem for me, since it makes the average the same as rounding up.

 

[OptionalRule]

It makes a pretty small difference on each attack, sure. The reason you’d take it is because you’re planning to use two-handed melee weapons (so you won’t benefit from archery, dueling, two-weapon fighting, or protection) and you want an offense fighting style (so defense won’t be satisfying.) The benefit, while small, also compounds the more attacks you make, so it works best with Polearm Master and Sentinel.

It’s definitely the weakest fighting style (well… maybe second weakest after protection), but since it’s the only one that boosts the damage of two-handed weapon users, which is an extremely strong build, it still has its niche.

I don't know I agree with any comment that it makes any measurable difference at all. Putting the numbers out the makes just a few points difference at most and even then really only on crits. Protection grants at least some measurable benefit to someone (even if it's not you). GWF doesn't pretty much nothing.

 

[OptionalRule]

Yep!

d4: (2+3+4)/3=3
d6: (2+3+4+5+6)/5=4
d8: (2+3+4+5+6+7+8)/7=5
d10: (2+3+4+5+6+7+8+9+10)/9=6
d12: (2+3+4+5+6+7+8+9+10+11+12)/11=7

I don't get this.

The difference when rerolling ones is so insignificant as to have no impact on individual characters. The only thing it really does it lower the floor. Every number you're listing here is the average on the die type rolled normally (without rerolling).

Specifically, the average HP results for a 20th level character using normal rolls or the reroll 1s house rule is EXACTLY the same. That's kind of the point of this post. People are making rules around this misconceptions. (I've done it too). I use a house rule like this and mention it in my post, I keep it because it actually does other things for me as a bit of DM slight of hand rather than the numbers having any actual meaning.

I hope you take that in the good spirit it's meant. It's the misconception I'm trying to address. Perhaps It's mine though and I'm not understanding what you're saying?

 

[Umbran]

True, but you’re still more likely to get a lower result than the fixed value when you roll than you are to get a higher result.

Correct. Entirely irrelevant to the point, but correct.

 

[Charlaquin]

I don't get this.

The difference when rerolling ones is so insignificant as to have no impact on individual characters. The only thing it really does it lower the floor. Every number you're listing here is the average on the die type rolled normally (without rerolling).

No it isn’t. If you roll normally without rerolling 1s you get:

d4: (1+2+3+4)/4=2.5
d6: (1+2+3+4+5+6)/6=3.5
d8: (1+2+3+4+5+6+7+8)/8=4.5
d10: (1+2+3+4+5+6+7+8+9+10)/10=5.5
d12: (1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5

Specifically, the average HP results for a 20th level character using normal rolls or the reroll 1s house rule is EXACTLY the same.

Not true. If you roll every time and don’t re-roll 1s, a 20th level character with, say, a d8 hit die, has an average of 90 hp. If you do reroll 1s, that character has an average of 100 hp. The same average as a character who takes the average-rounded-up value of 5 hp every time. That’s the point of the house rule. To eliminate the slight advantage of choosing to take the rounded-up average instead of rolling.

 

[Charlaquin]

I don't know I agree with any comment that it makes any measurable difference at all. Putting the numbers out the makes just a few points difference at most and even then really only on crits.

Your own article demonstrated that it makes around a 0.3 point difference per hit. Now multiply 0.3 by the number of hits a fighter makes over the course of their career. That’s not nothing. It’s less than dueling or two weapon fighting give you, but you can’t use those with a two handed weapon.

Protection grants at least some measurable benefit to someone (even if it's not you). GWF doesn't pretty much nothing.

Of course, you can’t use protection with a 2-handed weapon. Also, the benefit GWF gives may be small, but it isn’t nothing.

 

[OptionalRule]

Your own article demonstrated that it makes around a 0.3 point difference per hit. Now multiply 0.3 by the number of hits a fighter makes over the course of their career. That’s not nothing. It’s less than dueling or two weapon fighting give you, but you can’t use those with a two handed weapon.

Of course, you can’t use protection with a 2-handed weapon. Also, the benefit GWF gives may be small, but it isn’t nothing.

Aggregating total damage over a career isn't a thing. It means nothing. Damage only matters against individual opponents, any any overflow is waisted. The numbers for GWF mean they make absolutely no difference in a fight.

True that they get no benefit from protection with two handed weapons but they can at least switch to a shield and get some bonus. GWF gives no measurable benefit in an individual fight.