Jack99
Adventurer
Another issue which comes into play, is the probability of hitting the monster and how many rounds it takes to finally kill a monster. In general, a harder to hit monster can significantly drag on an encounter to more and more rounds.
Here's a model of this which is exactly solvable mathematically. The assumptions are:
- a target starts off with H "hit points"
- an attacker has probability p of hitting the target
- the attacker attacks the same target each round
- each time the attacker hits the target, 1 "hit point" of damage is done on the target
For this model, the average number of rounds (denoted A) it takes to kill the monster is A = H/p, with variance H(1-p)/(p^2).
Looking at this formula A = H/p, an attacker with a 50% probability (ie. p=0.50, or a roll of 11 or higher on a d20) of hitting a target monster with 2 "hit points" (ie. H=2), it takes on average around A = 2/0.50 = 4 rounds to kill the target monster. For an attacker with a 25% probability (ie. p=0.25, or a roll of 16 or over on a d20) of hitting the target monster with 2 "hit points", it takes on average around A = 2/0.25 = 8 rounds to kill the target monster.
The "hit points" of the above model can be thought of as "health units". Using my first elaboration of Jack99's example in a previous post, a monster's 3d8+9 damage roll has an average numerical damage of 22 hit points of damage, which can thought of as 1 "health unit" damage. For a target paladin/fighter/barbarian with 175 hit points, this can be thought of as the target having around 8 "health units". If a monster attacking a paladin target has a 25% chance of hitting the paladin, it would take an average of A = 8/0.25 = 32 rounds to kill the paladin. For a monster attacking the paladin with a 50% chance of hitting the paladin, it would take an average of A = 8/0.5 = 16 rounds to kill the paladin.
For my second elaboration of Jack99's example, the monster having a 3d8+31 damage roll has an average numerical damage of 44 hit points, which can be thought of as 1 "health unit" damage. For a target paladin/fighter/barbarian with 175 hit points, this can be thought of as the target having around 4 "health units". If a monster attacking a fighter target has a 25% chance of hitting the fighter, it would take an average of A = 4/0.25 = 16 rounds to kill the fighter. For a monster attacking the fighter with a 50% chance of hitting the fighter, it would take an average of A = 4/0.5 = 8 rounds to kill the fighter.
I am not quite sure of what point you are making. If you are saying that increasing the to hit of a monster equals increasing it's average damage, well duh, yes. It is however not the best of handling things. Mostly because it becomes quite boring if players are always hit by the monsters. At least IME and all that jazz.
Anyway, will run all monsters with the +100% damage -50% hit points model next time we play (thursday) - I have a decent mix of standard, elites and a solo, so plenty of variation to test how well it works out. Will report back, should anyone care.