#### GMMichael

##### Guide of Modos

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.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.

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.