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D&D 5E (Fun) - Gravity Proves Standard Human has 9 HP

Stalker0

Legend
Disclaimer: This topic is completely silly and for fun. Lets keep it light, I know how serious some people like to take this stuff. Also, for my 4d6 statistics, I ran 4 million random number simulations to get the numbers. So the % should be very close, certainly close enough for this, but they are not statistically perfect.

Its the eternal question. Sure PCs get big hitpoints and levels and XYZ, but how about your normal, stock human. How many hitpoints do they really have? Its the eternal question, and through the power of physics, it can finally be settled, once and for all!

So lets start with a fun fact: A human that falls from a height of 48 feet (4 stories) has a 50% chance to die. Yes its really that high, apparently we humans are more durable than you might think. Now doesn't mean your not heinously injured, but you can survive a very high fall a decent amount of the time.

5e teaches us that falling deals 1d6 damage per 10 feet, or 4d6 damage. Some of you may want to round up to 50 feet or 5d6....but this is dnd damn it, and we round down!

Now in 5e, there are two ways that a fall could kill us:
  • Deals damage = double our hitpoints = instant death
  • Deals damage above hitpoints -> die by death saves
We are going to assume that the person has full hp when they make the fall, and that they do not receive any assistance or further damage afterward, aka they are at the whims of the death saves if they fall unconscious.

So our second fun fact: An unconscious 5e character has a 57.6% chance to survive without assistance. If nothing else in this post interests you, enjoy that statistic. That includes rolling 20s and nat 1, its the whole show, and took me some effort to calculate!

So now we crunch the numbers. What hitpoint number gives us the appropriate life and death numbers to get us our 50% survive rate?

The answer: 9 hp.

At 9 hp:
% Live Straight up (aka take 9 or less damage on 4d6): 9.75%
% Die Straight up (aka take 18 or more damage on 4d6): 15.90%
% Fall Unconscious (10-17 damage): 74.35%
  • Unconscious but Stable: .7435 * .576 = .428 = 42.8%
  • Unconscious and bleed out: .7435 * .424 = .315 = 31.5%
Total % Live Chance: %Live + %Unconscious but Stable = 52.6%
Total % Death Chance: %Death + %Unconscious and Bleed out = 47.4%

That is the closest to the 50% number we can get. At 8 hp, the death chance is way too high (59.4%).


So I expect everyone to take this number as gospel and now go update all of your adventures so that all normal humans have 9 hp. The math has spoken! :)
 
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Horwath

Hero
And in D&D5E the normal human who survives that fall will be perfectly fine after an 8 hour nap.
HPs are abstraction :p

you either fell on your head, dying almost instantly or you landed on your feet on a grass field that has a decline and went into a perfect roll to absorb falling energy.

in D&D those are only 2 options.
 



HPs are abstraction :p

you either fell on your head, dying almost instantly or you landed on your feet on a grass field that has a decline and went into a perfect roll to absorb falling energy.

in D&D those are only 2 options.
This is hysterical but also really makes me feel we need a simple, preferably WotC-approved (so 6E, likely) system which applies injuries when someone recovers from being at 0 HP (if they don't recover, who cares!), much like Pillars of Eternity has. I kind of wonder if someone has some nice house-rules or a 3PP on the subject. Ideally you'd want them to reflect whatever caused you to hit 0 HP (i.e. non-lethal damage, no injury, falling, roll on a chart for anything from bruising to broken bones - I mean, you did recover, probably via magic, so we don't need to go too far, fire damage, burns of some kind, etc. etc. but the list should be short).
 

el-remmen

Moderator Emeritus
That was a fun calculation.

In my games people either have a name and a stat block - they can tussle. Or they have a name and no stat block, you can basically knock out or kill them at will if you have a stat block and a weapon (or time).

As for injuries, I use a modified Lingering Wounds option. Adventurers and the link roll on the table if they survive after having failed two death saves. Normal folk roll any time they hit 0 hps but live.
 


This is hysterical but also really makes me feel we need a simple, preferably WotC-approved (so 6E, likely) system which applies injuries when someone recovers from being at 0 HP (if they don't recover, who cares!), much like Pillars of Eternity has. I kind of wonder if someone has some nice house-rules or a 3PP on the subject. Ideally you'd want them to reflect whatever caused you to hit 0 HP (i.e. non-lethal damage, no injury, falling, roll on a chart for anything from bruising to broken bones - I mean, you did recover, probably via magic, so we don't need to go too far, fire damage, burns of some kind, etc. etc. but the list should be short).
You mean like the Lingering Injuries option that WotC present in the DMG?
 

Stalker0

Legend
Shouldn't this be "take 8 or less damage" since at 9 damage you are unconscious?
Oh!!!! You are 100% right, there's some old 3.5 logic creeping in, in my head I had thought 0 was up but staggered. So I redid the numbers, and actually this works out even better. We are almost at a perfect 50/50 now with 9 hp.
 


DeviousQuail

Explorer
Oh!!!! You are 100% right, there's some old 3.5 logic creeping in, in my head I had thought 0 was up but staggered. So I redid the numbers, and actually this works out even better. We are almost at a perfect 50/50 now with 9 hp.
The updated numbers. Also 9HP is now canon in my games.

% Live Straight up (aka take 8 or less damage on 4d6): 5.4%
% Die Straight up (aka take 18 or more damage on 4d6): 15.9%
% Fall Unconscious (9-17 damage): 78.7%
  • Unconscious but Stable: .787* .576 = .453 = 45.3%
  • Unconscious and bleed out: .787* .424 = .334 = 33.4%
Total % Live Chance: %Live + %Unconscious but Stable = 50.7%
Total % Death Chance: %Death + %Unconscious and Bleed out = 49.3%
 

ECMO3

Villager
So I expect everyone to take this number as gospel and now go update all of your adventures so that all normal humans have 9 hp. The math has spoken! :)
Ah but this is not ALL humans but the AVERAGE human has 9hp. So we have a mean of 9 and we need to apply a statistical distribution around this number.

To do this properly and create the proper distribution, I will need to match the standard deviation to the propensity for people to die at 30ft and 50ft respectively. Can you calculate these numbers for me so I can get an upper and lower datapoint?

Thanks. I will wait for your answer ........ j/k :p
 

NotAYakk

Legend
Also, that 48' median is actually 30% of the way to 5d6 from 4d6. We can replace the 4d6 with a normal curve of damage; average 14, variance of 35/12*4. If we want 4.3d6 we get 15.05 average and 12.54 variance, or 3.54 standard deviation. Call this random variable Fall.

We then find distribution of human HP, with the goal that P(dead) is 50%

P(instant gib) = P(Fall >= HP*2).
P(KO) = P(Fall >= HP)
P(OK) = P(Fall < HP)

P(DEAD) = P(instant gib) + P(KO)*.576
P(LIVE) = P(OK) + P(KO)*.424

Now we need a distribution for HP. We can start with Con being 3d6 flat out. Then we have to model HD; as medium creatures, humans have d8 HD. Humans probably have a distribution of HD; some are 1HD some are 2HD and some are 3HD. Naturally you roll each HD, taking the average is for losers.

For the sake of simplicity, I'll assume there is no correlation between Con and HD.

Average of 3d6 is 10.5 and Var is 105/12. Your modifier is (Con-10.5)/2, rounded; variance is linear, so this means your modifier has an average of 0 and a variance of 4.38, or SD of 2.09. Taking 3d6 as a normal variable is not that far off, and I'm lazy.

A 1 HD human has a uniform 1 to 8 HP plus the modifier. Using the normal distribution here is going to be error prone, so we won't.
A 2 HD human has a triangular 2 to 16 HP plus twice the modifier.
A 3 HD human has a decently bell-curved shaped 3 to 24 HP plus 3 times the modifier.

At a max of +4 con modifier, the min HP is 1 and the max HP is 36 in this model. For each HP from 1 to 36 calculating the z-score of Fall for HP and 2HP is easy (subtract average, divide by SD), and from z-score to probability is a simple table lookup (and spreadsheets have it as a built in function). So a map from HP to survival chance should be a relatively simple spreadsheet table, or maybe even formula.

Then for each of 1 to 3 HD, we can work out the distribution of HP each HD total gives us. I think we end up with a degree of freedom; so we'll say that X% of humans have 1 HD, (1-X%)*X% have 2 HD, and (1-X%)(1-X%) have 3HD to kill that degree of freedom.

Then solving for X such that survival chance hits 50% at 4.3d6 of falling damage gives us the average HP of humans. Well, at least a 2nd approximation.
 

You mean like the Lingering Injuries option that WotC present in the DMG?
Yeah like it but vastly better-implemented and more about injuries (which might go away naturally in a few weeks or w/e) than solely focused body-part-loss and permanent stuff. That's a messy and half-baked rule which isn't at all balanced and isn't really thought-through or integrated into the rules in a serious way, and relies extremely heavily on using a 7th-level spell to fix things, which is obviously not viable gameplay-wise. It's basically just the sort of thing we'd come up with here in an afternoon, but someone wrote it in a rulebook and didn't actually think about it as hard as we would.

(lol re-reading that table I'd forgotten how terminally bad and dumb it is, like the festering wound, where if some idiot heals you for 1 with a Goodberry it instantly cures, but if it's a medicine check, you need to do succeed 10 times (checking once a day) to cure it - that's stuff most OSR games would roll their eyes at!)
 


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