User:Trang Oul/Utils
Calculating skill params formulae and values per level
This tutorial's goal is to obtain two results:
- a formula for a given skill's property (damage, range, duration and so on)
- values for that property at different levels (1-60, as on skill pages).
1. Obtaining data
First we need to find the formulae. They are stored in data files, in skills.txt and in skillcalc.txt.
They are ordinary TSV files, and while there are specialized tools for modding Diablo 2, plain old MS Excel suffices, with features like freezing headers, filtering or searching.
This part is based on Phrozen Keep.
File: skills.txt
Columns
Formulae
Formulae are stored in the following columns (this list may not be exhaustive):
calcX- general skill formulae - seecalcX descfor descriptionprgcalcX- Assassin finishers; also Shock Web, Blade Furyauralencalc- length of aura/curse/buff/debuff, in framesaurarangecalc- range of aura/curse/buff/debuff; also used by other skillsaurastatcalcX- stats of aura/curse/buff/debuff - seeaurastatXfor stat namepassivecalcX- passive skills - seepassivestatXfor stat namepetmax- max number of petsDmgSymPerCalc- synergy to physical damageEDmgSymPerCalc- synergy to elemental damageELenSymPerCalc- synergy to the duration of elemental damagecltcalcX
Params
ParamX- numeric param used in formula - seeParamX Descriptionfor description- other columns (including, but not limited to
ELen...,EMin...,EMax...) - referenced by formulae below.
Multipliers
hitshift- used to multiply the damage by a power of 2 (2^(hitshift-8); 8 = ×1). See Phrozen Keep guide for details.SrcDamage- used as weapon damage multiplier (for skills such as Multiple Shot), in 1/128 (128 = ×1, 96 = ×3/4 and so on).
Formula details
- hardcoded numbers
- basic math operators and functions: arithmetic,
min,max - conditional operator:
condition ? value_if_true : value_if_false - functions and params as defined in
skillcalc.txt:
lnXY,dmXY- linear and diminishing (rational) functions. We will be the most interested in these formulae.
- All of them use skill level and additional params.
- Currently all those functions are the same per category.
parX- parameter (columnParamX)lvl- soft skill level (i.e. with bonuses)blvl- base skill level (i.e. only hard points); used mostly for synergiesulvl- character level; used by Druid summons only- references to other column or columns - used mostly for progression based on level ranges
- Examples:
edns- "Elemental Damage Min (256ths)"
- Used by Prayer to calculate life regen.
- As per Phrozen Keep:
- EMin: and EMax: Controls the basic minimum and maximum elemental damage dealt by this skill at sLvl 1.
- EMinLev1: to EMinLev5: and EMaxLevDam1: to EMaxLevDam5: Controls the additional elemental damage added to the skills minimum and maximum damage for every additional sLvl.
- LevDam1 is used for sLvls 2-8, LevDam2 for 9-16, LevDam3 for 17-22, LevDam4 for 23-28 and LevDam5 for sLvls above 28.
- So, Prayer starts with 2 (col
EMin) life points at level 1, increasing by 1 per level at levels 2-8 (EMinLev1), again by 1 at levels 9-16 (EMinLev2) and so on, ending by +3 per each level above 28.
edmn- "Elemental Damage"
- Used for Energy Shield's' Damage % Absorption (
min(edmn,95)) - It starts at 20% (
EMin), increased by 5 percentage points per skill (EMinLev1), then by 2 p.p. (EMinLev2), then by 1 p.p. (EMinLev3,EMinLev4,EMinLev5), capped at 95%.
- Notice that although these functions refer to "Elemental Damage" columns, for those skills these columns just hold the values, used for other properties than damage.
edmx- "Elemental Damage Max"
- Used by Dire Wolf's max cold damage (in D2R); cols
EMax....
skill('Skill Name'.fun)- reference to another skill - used for synergies:- Examples:
skill('Golem Mastery'.ln12)-ln12formula calculated using Golem Mastery params.skill('Summon Fenris'.par2)-Param2of Summon Fenris (i.e. Summon Dire Wolf).skill('Summon Fenris'.lvl)- (soft) skill level of Summon Fenris.
stat('stat_name'.fun)- used mostly to make pets inherit character stats- Examples:
stat('item_pierce_ELE_immunity'.accr)- Sunderstat('passive_ELE_pierce'.accr)- Enemy Resistancestat('passive_ELE_mastery'.accr)- Skill Damage
2. Calculation
Examples:
| Skill Name | Column description if present |
Formula | Params (besides lvl) |
Simplified Formula | Values (sample) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Jab | calc1 : Damage % |
ln34 |
Param3=-15, Param4=3 | 3*lvl - 18 |
| ||||||||||||
| Battle Cry | auralencalc |
ln12 |
Param1=300, Param2=75 Since this is duration, we convert it to seconds by dividing by 25 and allowing fractional values. |
12*lvl/5 + 48/5or 2.4*lvl + 9.6 |
| ||||||||||||
| Clay Golem | aurastatcalc1 : item_slow |
dm34 |
Param3=0, Param4=75 | 165*lvl/(2*lvl + 12) |
| ||||||||||||
| Blaze | auralencalc |
dm12 |
Param3=50, Param4=500 Since this is duration, we convert it to seconds by dividing by 25 and allowing fractional values. |
(109*lvl + 60)/(5*lvl + 30) |
| ||||||||||||
| Chain Lightning | calc1 : # of target jump hits |
ln34/par5 |
Param3=26, Param4=1, Param5=5 | lvl/5 + 5 |
| ||||||||||||
| Strafe | aurastatcalc1 : Minimum # of Missiles created |
min(par3 + lvl - 1, par4) |
Param3=0, Param4=75 | Min(10, lvl + 3) |
| ||||||||||||
| Raise Skeleton | petmax |
(lvl < 4) ?lvl:(2+lvl/3) |
(none) | Piecewise((lvl, lvl < 4), (lvl/3 + 2, True)) |
| ||||||||||||
| Prayer | aurastatcalc1 : hitpoints |
edns |
EMin...: 2, 1, 1, 2, 2, 3 | Piecewise((lvl + 1, (lvl <= 8) | (lvl <= 16)), (2*lvl - 15, (lvl <= 22) | (lvl <= 28)), (3*lvl - 43, True)) |
| ||||||||||||
| Energy Shield | aurastatcalc1 : Damage % Absorption |
min(edmn,95) |
EMin...: 20, 5, 2, 1, 1, 1 | Min(95, Piecewise((5*lvl + 15, lvl <= 8), (2*lvl + 39, lvl <= 16), (lvl + 55, True))) |
|
The following Python script can be used to simplify the formula and calculate values per level.
#coding: utf-8
import math
from fractions import Fraction
import sympy
FRAMES_PER_SECOND:int = 25
lvl, par1, par2, par3, par4, par5, par6, par7, par8, base, lev, lev1, lev2, lev3, lev4, lev5 = sympy.symbols('lvl, par1, par2, par3, par4, par5, par6, par7, par8, base, lev, lev1, lev2, lev3, lev4, lev5', integer=True)
# the formulae are the same per category, but for ease of use they are defined with names from skillcalc.txt
ln12: sympy.core.expr.Expr = par1 + (lvl - 1) * par2
ln34: sympy.core.expr.Expr = par3 + (lvl - 1) * par4
ln56: sympy.core.expr.Expr = par5 + (lvl - 1) * par6
ln78: sympy.core.expr.Expr = par7 + (lvl - 1) * par8
# dm12: sympy.core.expr.Expr = sympy.floor(((110 * lvl) * (par2 - par1)) / (100 * (lvl + 6))) + par1 #floor because of the integer division
# dm34: sympy.core.expr.Expr = sympy.floor(((110 * lvl) * (par4 - par3)) / (100 * (lvl + 6))) + par3
# dm56: sympy.core.expr.Expr = sympy.floor(((110 * lvl) * (par6 - par5)) / (100 * (lvl + 6))) + par5
# dm78: sympy.core.expr.Expr = sympy.floor(((110 * lvl) * (par8 - par7)) / (100 * (lvl + 6))) + par7
# A formula different than in skillcalc.txt, but the results match those in the game (credit: Onderduiker).
dm12 = sympy.Min(par1 + sympy.floor((par2 - par1) * sympy.floor((110 * lvl) / (lvl + 6)) / 100), par2)
dm34 = sympy.Min(par3 + sympy.floor((par4 - par3) * sympy.floor((110 * lvl) / (lvl + 6)) / 100), par4)
dm56 = sympy.Min(par5 + sympy.floor((par6 - par5) * sympy.floor((110 * lvl) / (lvl + 6)) / 100), par6)
dm78 = sympy.Min(par7 + sympy.floor((par8 - par7) * sympy.floor((110 * lvl) / (lvl + 6)) / 100), par8)
levelwise1: sympy.core.expr.Expr = sympy.Piecewise(
(base, lvl == 1),
(base + lev * (lvl-1), True)
)
levelwise3: sympy.core.expr.Expr = sympy.Piecewise(
(base, lvl == 1),
(base + lev1 * (lvl-1), lvl <= 8),
(base + lev1 * 7 + lev2 * (lvl-8), lvl <= 16),
(base + lev1 * 7 + lev2 * 8 + lev3 * (lvl-16), True)
)
levelwise5: sympy.core.expr.Expr= sympy.Piecewise(
(base, lvl == 1),
(base + lev1 * (lvl-1), lvl <= 8),
(base + lev1 * 7 + lev2 * (lvl-8), lvl <= 16),
(base + lev1 * 7 + lev2 * 8 + lev3 * (lvl-16), lvl <= 22),
(base + lev1 * 7 + lev2 * 8 + lev3 * 6 + lev4 * (lvl-22), lvl <= 28),
(base + lev1 * 7 + lev2 * 8 + lev3 * 6 + lev4 * 6 + lev5 * (lvl-28), True)
)
def make_formula(formula:str) -> sympy.core.expr.Expr:
FORMULA_PARTS: dict[str, sympy.core.expr.Expr] = {
'lvl' : lvl,
'par1' : par1,
'par2' : par2,
'par3' : par3,
'par4' : par4,
'par5' : par5,
'par6' : par6,
'par7' : par7,
'par8' : par8,
'base' : base,
'lev' : lev,
'lev1' : lev1,
'lev2' : lev2,
'lev3' : lev3,
'lev4' : lev4,
'lev5' : lev5,
'ln12' : ln12,
'ln34' : ln34,
'ln56' : ln56,
'ln78' : ln78,
'dm12' : dm12,
'dm34' : dm34,
'dm56' : dm56,
'dm78' : dm78,
'levelwise3': levelwise3,
'levelwise5': levelwise5,
}
return sympy.sympify(formula, FORMULA_PARTS)
def _levelwise_params(params:tuple[sympy.core.symbol.Symbol], values:str) -> dict[sympy.core.symbol.Symbol, int]:
"""
Builds parameters for levelwise formula from the values directly copied from data file.
The same number of values as params are expected, separated with a tab.
"""
return {params[i]: int(val) for i, val in enumerate(values.split('\t'))}
def levelwise1_params(values:str) -> dict[sympy.core.symbol.Symbol, int]:
"""
Builds parameters for levelwise formula from the values directly copied from data file.
2 values are expected: base, lev, separated with a tab.
Used for columns such as [Range, LevRange] or [ToHit, LevToHit].
"""
return _levelwise_params((base, lev), values)
def levelwise3_params(values:str) -> dict[sympy.core.symbol.Symbol, int]:
"""
Builds parameters for levelwise formula from the values directly copied from data file.
4 values are expected: base, lev1, lev2, lev3, separated with a tab.
Used for columns such as [ELen, ELevLen1, ELevLen2, ELevLen3].
"""
return _levelwise_params((base, lev1, lev2, lev3), values)
def levelwise5_params(values:str) -> dict[sympy.core.symbol.Symbol, int]:
"""
Builds parameters for levelwise formula from the values directly copied from data file.
6 values are expected: base, lev1, lev2, lev3, lev5, lev5, separated with a tab.
Used for columns such as [EMin, MinELev1, MinELev2, MinELev3, MinELev4, MinELev5].
"""
return _levelwise_params((base, lev1, lev2, lev3, lev4, lev5), values)
class Stat:
def __init__(self, desc:str, formula, params:dict|None=None, hitshift:int=8, rational:bool=False, places_int:int=1, places_frac:int=0, pad_sign:bool=False, seconds:bool=False) -> None:
if params is None:
params = {}
self.desc = desc
self.params = params
self.rational = rational
self.places_int = min(places_int, 1)
self.places_frac = places_frac
self.pad_sign = pad_sign
self.formula = self.make_formula(formula, hitshift, seconds)
if isinstance(self.formula, sympy.core.expr.Expr):
print(self.desc)
self.print_expr(seconds)
@classmethod
def make_formula(cls, formula, hitshift:int=8, seconds:bool=False):
if isinstance(formula, (str, int, float, Fraction)):
formula = make_formula(formula)
factor = sympy.Pow(2, hitshift-8)
formula = formula * factor
if seconds:
if isinstance(formula, sympy.core.expr.Expr):
formula = formula / FRAMES_PER_SECOND
return formula
@classmethod
def round(cls, val: sympy.core.numbers.Number) -> str:
if not val.is_integer:
val = float(val)
return str(val)
@classmethod
def do_format(cls, val:sympy.core.numbers.Rational, rational:bool=False, places_int:int=0, places_frac:int=0, pad_sign:bool=False) -> str:
'''
rational - whether to use rational or decimal fractions
places_int - number of places to be padded on the left side of an integer part
places_frac - number of places to be padded on the right side of a decimal part (in case of decimal numbers)
or on the left side of numberator and denominator (in case of rational numbers)
pad_sign - whether to pad the nonnegative numbers to be aligned with negative ones, prepended by a minus sign
'''
def pad_with_text(s:str) -> str:
return f'{{{{0|{s}}}}}' if s else ''
def pad_with_zeroes(places:int) -> str:
return pad_with_text('0' * places)
def pad_int(val: sympy.core.numbers.Integer, places:int, hide_zero:bool=False) -> str:
if not val.is_nonnegative or not val.is_integer:
raise ValueError(f'Number must be a nonnegative integer (got {val})')
places = max(places - len(str(val)), 0)
if hide_zero and val.is_zero:
val = ''
places += 1
return f'{pad_with_zeroes(places)}{val}'
def pad_frac_irrational(val:sympy.core.numbers.Number, places:int) -> str:
if not val.is_nonnegative or val >= 1:
raise ValueError(f'Number must be a nonnegative proper fraction (got {val})')
if val.is_integer:
if not places:
return ''
frac_part = '0' * places
return pad_with_text(f'.{frac_part}')
frac_part = val - int(val)
frac_part = str(float(frac_part))[2:] #without '0.'
places = max(places - len(frac_part), 0)
return f'.{frac_part}{pad_with_zeroes(places)}'
def pad_frac_rational(val:sympy.core.numbers.Number, places:int) -> str:
if not val.is_nonnegative or val >= 1:
raise ValueError('fNumber must be a nonnegative proper fraction (got {val})')
if val.is_integer:
if not places:
return ''
num_part = den_part = '0' * places
frac_part = f'{num_part}/{den_part}'
return f' {pad_with_text(frac_part)}'
frac_part = val - int(val)
num, den = frac_part.as_numer_denom()
return f' {pad_int(num, places)}/{pad_int(den, places)}'
pad_sign = '-' if val.is_negative else '{{0|-}}' if pad_sign else ''
absval = abs(val)
absval_int = sympy.Integer(absval)
absval_frac = absval - absval_int
int_part = pad_int(val=absval_int, places=places_int, hide_zero=rational and val.is_nonzero)
pad_frac = pad_frac_rational if rational else pad_frac_irrational
frac_part = pad_frac(val=absval_frac, places=places_frac)
# return f'{pad_sign} ## {int_part} ## {frac_part}'
return f'{pad_sign}{int_part}{frac_part}'
def calc(self, slvl:int) -> int|float|str:
val = self.formula.subs({lvl: slvl} | self.params)
return self.do_format(val, self.rational, self.places_int, self.places_frac, self.pad_sign)
def print_expr(self, seconds:bool=False) -> None:
expr: sympy.core.expr.Expr = self.formula.subs(self.params)
expr = expr.simplify()
print(expr)
if seconds:
print(expr.evalf())
def build_table(stats, maxlvl:int=60, splitlvl:int=10):
'''
Builds a wiki table of given stats for given level range.
'''
return '\n\n'.join(
f'''{{{{Levels {lvl_group+1}-{lvl_group+splitlvl}}}}}
{'\n'.join(f'|-\n!align=left| {stat.desc}\n| {" || ".join(str(stat.calc(lvl_group+lvl_unit)) for lvl_unit in range(1, splitlvl+1))}' for stat in stats)}
|}}''' for lvl_group in range(0, maxlvl, splitlvl)
)
"""
USAGE
Make a list of stats to be included in the table of values (levels 1-60).
Formulae can be defined in two ways:
1. SymPy: use SymPy expressions - either defined here (fun) or other expressions, using appropriate SymPy functions (for exampe sympy.Min instead of min).
1. Formula as string directly from the data file. Allowed formula parts: lvl, parameters (parX), functions (lnXY and dmXY) and some math functions (min, max). Remove synergies to calculate values without them.
See the examples below. Use only one formula per stat; the repeated stats below are to show how to define formulae.
For level-based values, use "levelwise" formulae, either for 3 or 5 columns.
To convert time values from frames to seconds, set the "seconds" flag.
Simplified formulae are also printed.
For time values formulae with integer and decimal coefficients are printed.
If th
stats: tuple[Stat] = (
Stat(desc='Inner Sight Duration (Seconds)', formula=ln34, params={par3: 300, par4: 150}, seconds=True),
Stat(desc='Inner Sight Duration (Seconds)', formula='ln34', params={par3: 300, par4: 150}, seconds=True),
Stat(desc='Slow Missiles [[Missile]] Speed %', formula= 100-dm12, params={par1: 25, par2: 75}),
Stat(desc='Slow Missiles [[Missile]] Speed %', formula= '100-dm12', params={par1: 25, par2: 75}),
Stat(desc='Impale Durability loss chance %', formula= par6-dm34, params={par3: 0, par4: 30, par6: 50}),
Stat(desc='Impale Durability loss chance %', formula= 'par6-dm34', params={par3: 0, par4: 30, par6: 50}),
Stat(desc='Thunderstorm perdelay', formula= (100-dm56) * par4/100 + par3, params={par3: 25, par4: 100, par5: 0, par6: 100}, seconds=True),
Stat(desc='Thunderstorm perdelay', formula= '(100-dm56) * par4/100 + par3', params={par3: 25, par4: 100, par5: 0, par6: 100}, seconds=True),
Stat(desc='Battle Cry duration (Seconds)', formula= ln12, params={par1: 300, par2: 60}, seconds=True),
Stat(desc='Battle Cry duration (Seconds)', formula='ln12', params={par1: 300, par2: 60}, seconds=True),
Stat(desc='Chain Lightning hits', formula= ln34 / par5, params={par3: 26, par4: 1, par5:5}),
Stat(desc='Chain Lightning hits', formula= 'ln34/par5', params={par3: 26, par4: 1, par5:5}),
Stat(desc='Strafe min hits', formula= sympy.Min(par3 + lvl - 1, par4), params={par3: 4, par4: 10}),
Stat(desc='Strafe min hits', formula= 'min(par3 + lvl - 1, par4)', params={par3: 4, par4: 10}),
Stat(desc='Prayer healing', formula=levelwise5, params={base: 2, lev1: 1, lev2: 1, lev3: 2, lev4: 2, lev5: 3}),
Stat(desc='Prayer healing', formula='levelwise5', params={base: 2, lev1: 1, lev2: 1, lev3: 2, lev4: 2, lev5: 3}),
Stat(desc='Energy shield absorption',
formula=sympy.Min(levelwise5, 95),
params={base: 20, lev1: 5, lev2: 2, lev3: 1, lev4: 1, lev5: 1}
),
Stat(desc='Energy shield absorption',
formula='min(levelwise5, 95)',
params={base: 20, lev1: 5, lev2: 2, lev3: 1, lev4: 1, lev5: 1}
),
Stat(desc='Spirit Wolf coldlength', formula=levelwise3, params={base: 25, lev1: 25, lev2: 25, lev3: 25}, seconds=True),
Stat(desc='Spirit Wolf coldlength', formula='levelwise3', params={base: 25, lev1: 25, lev2: 25, lev3: 25}, seconds=True),
Stat(desc='Chilling Armor cold length', formula=levelwise3, params={base: 100, lev1: 0, lev2: 25, lev3: 25}, seconds=True),
Stat(desc='Chilling Armor cold length', formula='levelwise3', params={base: 100, lev1: 0, lev2: 25, lev3: 25}, seconds=True),
Stat(desc='Clay Golem slow', formula=dm34, params={par3: 0, par4: 75}),
Stat(desc='Clay Golem slow', formula='dm34', params={par3: 0, par4: 75}),
Stat(desc='Blaze length', formula=dm12, params={par1: 50, par2: 500}, seconds=True),
Stat(desc='Blaze length', formula='dm12', params={par1: 50, par2: 500}, seconds=True),
# advanced example: poison damage (Poison Javelin)
# duration first (will be used in subsequent formulae)
Stat(desc='Seconds', formula=levelwise3, params=levelwise3_params('75 5 5 5'), seconds=True),
# total poison damage = poison bit rate (from data file, in 1/256 per frame) * duration (from data file, in frames) / 256 (to converts bits into full points); we round it down to the full point
Stat(desc='Minimum Poison Damage', formula=sympy.floor(levelwise5.subs(levelwise5_params('196 64 128 208 440 640')) * levelwise3.subs(levelwise3_params('75 5 5 5')) / 256)),
# poison DPS = (poison bit rate * duration / 256) / duration * 25 (to calculate per second, not per frame)
# = poison bit rate * 25 / 256; we round it down to the full point
Stat(desc='Minimum Poison Damage/s', formula=sympy.floor(levelwise5.subs(levelwise5_params('196 64 128 208 440 640')) * sympy.Rational(25, 256))),
#similar calculations for maximum damage
)
print(build_table(stats))
stats = (
#build your own table
)
#print(build_table(stats))