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

[OptionalRule]

I posted up a bit of a nerdy and complex breakdown of why die average numbers are what they are, since this seems to be a point of confusion that comes up now and again.

The confusion seems to get more mixed when people apply it to rules or in generating player hit points vs monster hit points.

On Die Averages and Hit Points in 5e

 

[el-remmen]

This just reminds that while I often simply choose the monsters' hit points from within the range depending on how tough I want them to be to kill, when I choose "average" I always give them max hps for the first die (assuming they have more than one) and average for the rest because what is good for the PC is good for the monster.

 

[commandercrud]

There's confusion on this?

 

[NotAYakk]

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).

 

[Charlaquin]

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).

Oh my god, I can’t believe I never thought of this before! It’s always bugged the crap out of me that the fixed value rounds up from the average for rolling, making it the clear better choice. But this totally fixes that problem! And it removes the feel-bad moment of deciding to roll HP and getting a 1. I’m totally adopting this.

 

[Cadence]

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).

I like that reroll 1 a lot. Thanks for the idea!

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Would it be better to call it a prediction interval and not confidence interval (you aren't making an interval for estimating a parameter from a sample, you're giving the 95% range where an individual observation from doing the experiment is likely to be).

The upper interval is off by 1 (9*5+12=57).

 

[NotAYakk]

Oh my god, I can’t believe I never thought of this before! It’s always bugged the crap out of me that the fixed value rounds up from the average for rolling, making it the clear better choice. Bur this totally fixes that problem! And it removes the feel-bad moment of deciding to roll HP and getting a 1. I’m totally adopting this.

I played with a DM who did this, and I was like "wait a second, that fixes the average". I blame 4e's Brutal1 weapon mechanics for it being obvious.

...

An interesting variation is to remove con-to-HP, and instead have it give rerolls.

 

[Charlaquin]

I posted up a bit of a nerdy and complex breakdown of why die average numbers are what they are, since this seems to be a point of confusion that comes up now and again.

The confusion seems to get more mixed when people apply it to rules or in generating player hit points vs monster hit points.

On Die Averages and Hit Points in 5e

Umm… Ironically, you’ve made an error in your attempt to clear up confusion. Rolling player HP is the only case where 5e rounds up on the average for each die. In both mister HP and the average damage value given for mister attacks, they take the true average, multiply that by the number of dice, and round the final result down to the nearest whole number. A bugbear, for example, has 5d8 hit dice and +1 con, for an average of 27 hp (5.5 * 5 = 27.5, which rounds down to 27). If they rounded up the average on each die, they would have 35 hp (7 * 5 = 35).

 

[OptionalRule]

There's confusion on this?

I run into it a lot in conversation. It's on several levels. The most basic is why is the 'average' what it is, then there's understandable confusion on generation of average PC hit points vs Monster Hit points.

 

[OptionalRule]

Umm… Ironically, you’ve made an error in your attempt to clear up confusion. Rolling player HP is the only case where 5e rounds up on the average for each die. In both mister HP and the average damage value given for mister attacks, they take the true average, multiply that by the number of dice, and round the final result down to the nearest whole number. A bugbear, for example, has 5d8 hit dice and +1 con, for an average of 27 hp (5.5 * 5 = 27.5, which rounds down to 27). If they rounded up the average on each die, they would have 35 hp (7 * 5 = 35).

Hmm, making a mistake isn't new to me but I don't see it from what you described here. I mention in the post that there aren't any 0.5 increments on a die and they roll up for players. The to examples I give have those values (bugbear at 27 hp).