Yakk
2007-09-30, 12:39 PM
I'm poking around with "goal-based mechanics" -- build mechanics for a D&D homebrew based around the goal of how I want a D&D game to play, rather than based on existing balance and/or making up numbers.
So first I need some goals... Damage rate, HP and Accuracy end up determining how many "rounds" a given combat takes. So let's tweak the numbers so that we can get results we want.
Stuff in ()s is my opinions.
How long should combat between "equals" last in a D&D type game (how many rounds)? (aim for 6ish)
How long should each round last? Ie, how many rolls and decisions to resolve a round?
How often should you hit? (about half of the time)
How many HP should a fighter/tank-type have, roughly? (5+(5+ConBonus)*level and assume a con of approx 14+level/2. L1:12 L5:45 L10:95 L15:155 L20:245)
...
So that works out to a total damage per combat round of:
L1: 4
L5: 13
L10: 32
L15: 52
L20: 82
with a 50% accuracy rate. A lower accuracy rate will boost total damage per round (ie, 3 "perfect hit rounds" take out an opponent, which takes 6 rounds)
The damage per hit at L 1 seems too low. Let's revamp L 1 fighter HP to be:
5 average roll + Con Bonus + Base Con
giving us a boost in HP at L 1.
HP: (using same stats)
L1: 21 HP--7 damage per full-hit round
L5: 56 HP--19 damage per full-hit round
L10: 109 HP--36 damage per full-hit round
L15: 171 HP--57 damage per full-hit round
L20: 264 HP--88 damage per full-hit round
Math crunch:
HP =~ L*(C/2) + C
C =~ 14+(L/2)
D =~ HP/3
HP =~ L*(7+L/4) + 14+L/2
HP =~ L^2/4 + 7.5*L + 14
D =~ HP/3
[-7.5 +/- sqrt(56.25 - 14)]*2
=~ -15 +/- 13
=~ -2 or -28
HP =~ 1/4 * (L+2)(L+28)
Note that the rate of con gain (1 every 2 levels, including magic items etc) effects this equation.
For the attack side, let's use a sneak attacking rogue as our baseline.
A 1d6 damage weapon, with +1d6/2 levels of damage, and +1/2*level other bonuses (strength, enchantment, etc).
That's 3.5 + 2.25*(Level+1) damage per hit, or:
Actual--Goal--Goal as Percent of Actual
L1: 8--7--87.5%
L5: 17--19--112%
L10: 28.25--36--127%
L15: 39.5--57--144%
L20: 50.75--88--173%
This assumes a 50% hit rate and a single attack per combat round.
And we are well under our goal.
If you add in tricks (like TWF or even full-attacks), the rogue ends up doing well more than 100% of our target damage.
Now the game is to play with the HP curve and the Damage curve so that they move in sync nicely, and the mechanics that bring about those curves are nice.
...
The damage curve per full-round "should" thus look like:
HP =~ 1/12 * (L+2)(L+28)
=~ L^2/12 +2.5*L +4+2/3
=~ L^2/12 + 2.5*L + 5
Solving for when the L^2/12 equals half of the rest of the term:
L^2/12 = .5*(5+2.5*L)
L^2 = 30+15*L
L^2 -15L-30 = 0
L = [15+/-sqrt(225+120)]/2
L = [15+-/18.6]/2
L =~ 16.8
That's a pretty slow term. Which means I might want to go back and tweak the HP curve so we can have a steeper damage curve without having combat over in a blink at high levels between two evenly matched combatants.
More to follow. Anyone else interested in this kind of theorycraft?
So first I need some goals... Damage rate, HP and Accuracy end up determining how many "rounds" a given combat takes. So let's tweak the numbers so that we can get results we want.
Stuff in ()s is my opinions.
How long should combat between "equals" last in a D&D type game (how many rounds)? (aim for 6ish)
How long should each round last? Ie, how many rolls and decisions to resolve a round?
How often should you hit? (about half of the time)
How many HP should a fighter/tank-type have, roughly? (5+(5+ConBonus)*level and assume a con of approx 14+level/2. L1:12 L5:45 L10:95 L15:155 L20:245)
...
So that works out to a total damage per combat round of:
L1: 4
L5: 13
L10: 32
L15: 52
L20: 82
with a 50% accuracy rate. A lower accuracy rate will boost total damage per round (ie, 3 "perfect hit rounds" take out an opponent, which takes 6 rounds)
The damage per hit at L 1 seems too low. Let's revamp L 1 fighter HP to be:
5 average roll + Con Bonus + Base Con
giving us a boost in HP at L 1.
HP: (using same stats)
L1: 21 HP--7 damage per full-hit round
L5: 56 HP--19 damage per full-hit round
L10: 109 HP--36 damage per full-hit round
L15: 171 HP--57 damage per full-hit round
L20: 264 HP--88 damage per full-hit round
Math crunch:
HP =~ L*(C/2) + C
C =~ 14+(L/2)
D =~ HP/3
HP =~ L*(7+L/4) + 14+L/2
HP =~ L^2/4 + 7.5*L + 14
D =~ HP/3
[-7.5 +/- sqrt(56.25 - 14)]*2
=~ -15 +/- 13
=~ -2 or -28
HP =~ 1/4 * (L+2)(L+28)
Note that the rate of con gain (1 every 2 levels, including magic items etc) effects this equation.
For the attack side, let's use a sneak attacking rogue as our baseline.
A 1d6 damage weapon, with +1d6/2 levels of damage, and +1/2*level other bonuses (strength, enchantment, etc).
That's 3.5 + 2.25*(Level+1) damage per hit, or:
Actual--Goal--Goal as Percent of Actual
L1: 8--7--87.5%
L5: 17--19--112%
L10: 28.25--36--127%
L15: 39.5--57--144%
L20: 50.75--88--173%
This assumes a 50% hit rate and a single attack per combat round.
And we are well under our goal.
If you add in tricks (like TWF or even full-attacks), the rogue ends up doing well more than 100% of our target damage.
Now the game is to play with the HP curve and the Damage curve so that they move in sync nicely, and the mechanics that bring about those curves are nice.
...
The damage curve per full-round "should" thus look like:
HP =~ 1/12 * (L+2)(L+28)
=~ L^2/12 +2.5*L +4+2/3
=~ L^2/12 + 2.5*L + 5
Solving for when the L^2/12 equals half of the rest of the term:
L^2/12 = .5*(5+2.5*L)
L^2 = 30+15*L
L^2 -15L-30 = 0
L = [15+/-sqrt(225+120)]/2
L = [15+-/18.6]/2
L =~ 16.8
That's a pretty slow term. Which means I might want to go back and tweak the HP curve so we can have a steeper damage curve without having combat over in a blink at high levels between two evenly matched combatants.
More to follow. Anyone else interested in this kind of theorycraft?