Thursday 11 April 2013

Updated Death and Dismemberment Table

After a bit of playtesting, I realized that there are two problems with my Death & Dismemberment Table:
  • The Horrific Demise happens too much
  • The rolls 1-3 happen too rarely

Model to Validate the Problem

I suspected that there was a statistical reason for this, but I wasn't sure.  Here's a proof that is approximate, but shows clearly that there is a problem.  Note that I'm choosing assumptions that make this into a simple discreet problem:
  1. Assume that when a character first drops to 0 or fewer HP then they usually end up in the 0HP to -9HP range
  2. Assume that there is an equal chance of that number being 0HP,-1HP, -2HP,...-9HP(really it's probably weighted a bit towards the 0-end of the spectrum)
  3. So for each potential number of HP, what are the chances of getting each entry in the table?
First let's calculate the chance of each roll value, given a specific number of HP:
  • 0HP
    • 1-10: 10% chance
  • -1HP
    • 1: 0% chance
    • 2-9: 10% chance
    • 10+: 20% chance
  • -2HP
    • 1-2: 0% chance
    • 3-9: 10% chance
    • 10+: 30% chance
  • ...
  • -9HP
    • 10+: 100%
So given these assumptions, what is the total chance of each entry occurring for a given roll(add up the percentages above and divide by 10)?

  • 1 Now You've Made Him Mad: 1%
  • 2 That'll Leave a Scar: 2%
  • 3 A Stunning Blow: 3%
  • 4-5 Hit an Artery: 9%
  • 6-7 Maiming Locational: 13%
  • 8 Death Defying Stand: 8%
  • 9 Killed Instantly: 9%
  • 10+ Horrific Demise: 55%

The Solution

OK, so this model validates my intuitive claims that there are a lot of Horrific Demises and very few low rolls.  It also shows that limb loss, which I wanted for my pirate game, is pretty rare.  So now that we know we have a problem, how can we re-balance the table to get a more even spread?  I would suggest that we spread out the rolls more such that all entries in the table have two numbers.  Now let's recalculate the chances for each entry in the table as we did above:

  • 0HP
    • 1-10: 10% chance
  • -1HP
    • 2-11: 10% chance
  • -2HP
    • 3-12: 10% chance
  • ...
  • -9HP
    • 10-14: 10% chance
    • 15+: 50% chance

  • 1-2 Now You've Made Him Mad: 3%
  • 3-4 That'll Leave a Scar: 7%
  • 5-6 A Stunning Blow: 11%
  • 7-8 Hit an Artery: 15%
  • 9-10 Maiming Locational: 19%
  • 11-12 Death Defying Stand: 17%
  • 13-14 Killed Instantly: 13%
  • 10+ Horrific Demise: 15%

That's more the sort of distribution I was looking for.  So, for reference, here is the updated table:

Updated Death & Dismemberment Table

Upon taking damage which leaves a character with 0 or fewer HP, roll a d10 + the number of negative hitpoints the character has.

1-2 Now You've Made Him Mad: +1 to victim's strength bonus for remainder of fight
3-4 That'll Leave a Scar: gains or loses 1d3 CHR
5-6 A Stunning Blow: character is not killed, but falls unconscious for 1d10 rounds
7-8 Hit an Artery: Unconscious. Lose 1 HP per rounds until bandaged. If reaches -10 is dead
9-10 Maiming Locational Hit(see sub-table)
11-12 Death Defying Stand: lose 1HP per round, cannot be bandaged. When reaches -10 is dead.
13-14 Killed Instantly
15+ Horrific Demise: It's going to take a Resurrection spell to bring them back.

Maiming Locational Hit Sub-Table

For these, weapon type matters(heavy gun, slashing, piercing, small firearm, bludgeoning). Roll area of the body and then see the details below.

1 Right Leg
2 Left Leg
3-4 Right Arm
5-6 Left Arm
7-8 Torso
9-10 Head

Arms & Legs Details

  • heavy gun/slashing- severs the limb for -1d6STR and for legs an additional -1d6DEX. Also see Hit an Artery.
  • piercing/small firearm- lames the limb(due to nerve and other tissue damage). -1d3STR and for legs an additional -1d3DEX.  Also see Hit an Artery.
  • bludgeoning- breaks the limb.  -1d3STR and for legs an additional -1d3DEX until break is set and heals.

Torso Details

  • heavy gun- see Horrific Demise
  • other weapons- see Hit an Artery

Head Details

  • slashing- lose nose or ear(-1d3 CHR)
  • piercing- lose eye(-1 to hit with missile weapons)
  • small firearm- see Killed Instantly
  • heavy gun- see Horrific Demise
  • bludgeoning- see A Stunning Blow

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