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

[GMMichael]

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.

That's a lot of work on an argument based on the premise that hitting someone with a planet only uses a d6 (d6s) for damage.

I like my standard human to have 10 HP, each representing 10% of a standard human's survivability.

Show me math that says a standard human doesn't have 100% health.

 

[NotAYakk]

Planets use class based damage. Earth is class M, so rolls d6s.

 

[Sword of Spirit]

Cool!

However, since the same rules if physics that declare that 4d6 falling damage also declare that the average human has 4 hit points, you've in fact demonstrated something else. You have demonstrated that average humans in D&D are more subject to death by immediate trauma than real humans. Of course, once they get a few adventurer levels under their belt they gain action hero and then superhero levels of durability.

I think just acknowledging a discrepancy with real world humans is a better way integrating the math than rewriting the Monster Manual to make it fit.

 

[S'mon]

I like to give a lot of my 1 hd Commoners 6-8 hp, with 4 more as a minimum. 4 feels too world-of-cardboard especially when baseline mooks get 2hd & 9-11 hp.

 

[John R Davis]

I think that's a good number. A full on blow from a longsword or centre strike from a longbow arrow puts you down ( so a 6 or 7 rolled on the dice plus a stat mod)

 

[Sword of Spirit]

I like to give a lot of my 1 hd Commoners 6-8 hp, with 4 more as a minimum. 4 feels too world-of-cardboard especially when baseline mooks get 2hd & 9-11 hp.

Those are baseline mook warriors. Hence my comment about rewriting the MM if you want to raise commoner hit points.

 

[S'mon]

Those are baseline mook warriors. Hence my comment about rewriting the MM if you want to raise commoner hit points.

Is a Cultist really a 'Warrior'?

I typically give a barmaid around 4 hp, a farmer around 6 hp, a miner 8 hp. A miner or smith may well be stronger than a Guard, the main difference IMO will be weapon proficiency.

 

[Blue]

Besides everything else, I have to say that I love all of you for putting such rigorous evaluation into it. My peeps!

 

[rmcoen]

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!

Lol, I did that research too, read the Trauma Report with the analysis of the 48' fall - except the trauma report said that fall is 100% lethal, not 50% - but I worked from "commoners have 5.5hp", instead of "falls do 1d6 dmg". I ended up with "falls do 1d10 damage, summation. DEX/Acrobatics (know how to fall) or CON/Acrobatics (superhero landing) for DC 5+half the height fallen = half damage". 40' fall kills average human most of the time; sometimes you roll low on 10d10 (still 100% unconscious, but survive with death saves), and rarely they make their save (nat 20, maybe a little DM homebrew, some dex, some training). one-in-a-million, you roll min on damage and they Nat20 that landing, and walk away from the fall with 1HP left. Mr. (or Ms.) average human.