WoG heal modifier: Method to the madness?

[Jeremoot]

At 85 the equation is ((1929 + 2149 / 2) + 0.198 * AP), at level 50 it's ((240 + 266 / 2) + 0.198 * AP) and so on. The equation remains the same other than the first two numbers (1929 and 2149 at 85, and 240 and 266 at 50).

Is there a curve used to determine these two numbers? I can't seem to find one, and it would be really helpful for my purposes.

[Iminmmnni]

A linear interpolation of the form f(x) = ax + b gives:
f(85) = 1929 = a*85 + b (1)
f(50) = 240 = a*50 + b (2)
Solving for a using (1) - (2)
1689 = 35*a
a = 48.257
=> b = 1929 - 85*a = -2412.86

So a linear interpolation of your lower bound is 48.257 * level - 2414.86

Unfortunately, you'll need more than two data points if your interpolation is not linear and I suspect it isn't. Given other equations, it's probably piecewise linear or exponential and you'd need data points for each expansion to work that out (eg 50, 55, 60, 65, 70, 75, 80, 82, 85).

[Jeremoot]

Wowhead has a slider bar that allows you to adjust the equation for every level.

It's certainly not linear. I'm pretty sure it is a piecewise equation, I went and mapped out the lower bound data for (level-9) up until 59, but I'm not smart enough to figure out an equation from it.

f(L) = {
[74+0, L-9 = 0]
[74+2, L-9 = 1] +2
[74+4, L-9 = 2] +2
[74+5, L-9 = 3] +1
[74+6, L-9 = 4] +1
[74+10, L-9 = 5] +4
[74+27, L-9 = 10]
[74+43, L-9 = 15]
[74+57, L-9 = 20]
[74+79, L-9 = 25]
[74+102, L-9 = 30]
[74+130, L-9 = 35]
[74+160, L-9 = 40]
[74+190, L-9 = 45]
[74+568, L-9 = 50]

80-85:

[1809, L-9 = 71]
[1833, L-9 = 72] -> Increase of 24
[1858, L-9 = 73] -> Increase of 25
[1881, L-9 = 74] -> Increase of 23
[1905, L-9 = 75] -> Increase of 24
[1929, L-9 = 76] -> Increase of 24

[Jeremoot]

I suppose I'll suck it up and hardcode 76 else if statements for now.

[theckhd]

I'd think a table or array would be less annoying. For example, make an 85-element array, store the base heal value for each level in that element of the array.

So for example, arrayName(85) would return the 85th element, which is the base heal value for level 85. arrayName(70) would similarly return the 70th element, which is the base heal value for level 70. And so on.

[yappo]

I'd think a table or array would be less annoying. For example, make an 85-element array, store the base heal value for each level in that element of the array.

So for example, arrayName(85) would return the 85th element, which is the base heal value for level 85. arrayName(70) would similarly return the 70th element, which is the base heal value for level 70. And so on.

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

[gibborim]

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

Depends on if the language likes to start at 0 or 1 for array numbering.

[yappo]

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

Depends on if the language likes to start at 0 or 1 for array numbering.

This tank greets antiquity

During the days we kind of didn't have much of an option.

[Jeremoot]

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

In C, declaring an array with size n starts at 0 and ends at n-1, which I believe is what you're referring to. For my purposes I just defined its size indirectly and used L-9 as the index.

Strange that in C an array is the first thing that would come to mind, but now that I'm wading through the uncharted waters of Lua the first thing that comes to mind is to write a series of conditional expressions.

[PsiVen]

1-60, 60-70, 70-80, 80-85 probably all obey well defined formulas, with rounding error. Does wowhead get its numbers from tables in the game files?

[yappo]

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

In C, declaring an array with size n starts at 0 and ends at n-1, which I believe is what you're referring to. For my purposes I just defined its size indirectly and used L-9 as the index.

Strange that in C an array is the first thing that would come to mind, but now that I'm wading through the uncharted waters of Lua the first thing that comes to mind is to write a series of conditional expressions.

Haven't done Lua, but some C-based languages implemented complex conditions for switch case. If you're basically running with number of expac conditions, ie vanilla, TBC, WotLK and Cata, then an 85 position vector is a huge overkill. I guess you could just go with else if, even though a conditional (if supported) switch case followed by a break for each case ought to make it marginally faster. If Lua is compiled, however, then it won't matter at all. Should be implemented as a 85 condition long switch on integer case, due to exclusitivity, by the compilator.

Bah, ok, I'm rambling.

[Jeremoot]

Haven't done Lua, but some C-based languages implemented complex conditions for switch case. If you're basically running with number of expac conditions, ie vanilla, TBC, WotLK and Cata, then an 85 position vector is a huge overkill. I guess you could just go with else if, even though a conditional (if supported) switch case followed by a break for each case ought to make it marginally faster. If Lua is compiled, however, then it won't matter at all. Should be implemented as a 85 condition long switch on integer case, due to exclusitivity, by the compilator.

Bah, ok, I'm rambling.

Lua doesn't actually have a "switch" statement.

1-60, 60-70, 70-80, 80-85 probably all obey well defined formulas, with rounding error. Does wowhead get its numbers from tables in the game files?

I believe so, but I wouldn't know where to look, or if it's obfuscated.

[theckhd]

Gah, vectors changed in programming? I recall level[n] referring to position n+1.

Depends on if the language likes to start at 0 or 1 for array numbering.

What he said. MATLAB starts at 1, and that's the language I tend to think in since I use it more frequently. In any event, the indexing issues wasn't the main point.

1-60, 60-70, 70-80, 80-85 probably all obey well defined formulas, with rounding error. Does wowhead get its numbers from tables in the game files?

I believe so, but I wouldn't know where to look, or if it's obfuscated.

More to the point, it's probably more of a hassle to come up with the formulas than to hardcode an array. Unless someone else has worked the formula out and posted it somewhere, you'll have to manually collect all of those coefficients and then attempt to fit each section. If you're going to manually collect the coefficients anyway, you may as well just put them in an array immediately and reference them that way.

Coding the piecewise formula only saves you memory (instead of 85 integers, you can probably represent the piecewise with 10-15 values or less). But it'll cost you computation time in calculating the value whenever you want it, too. If the size of the array were much bigger, or you had to do this for a few thousand abilities, then the memory savings might be important. But one 85-element integer array takes a pitiful amount of memory, so it's probably the better choice based on performance.

[Jeremoot]

As well as greater performance, it's also "cleaner" code. That's why I made the thread, in hopes that somebody had worked out the formula.

To save trouble for anybody else, this is the resulting array:

Code: Select all

local base =
{
  345,354,363,367.5,372,390,408,420,438,
  451.5,469.5,483,499.5,517.5,531,544.5,562.5,574.5,588,
  601.5,610.5,624,646.5,667.5,690,712.5,735,756,778.5,796.5,
  819,840,867,894,919.5,951,978,1008,1035,1062,1092,1119,1149,
  1176,1203,1233,1260,1287,1312.5,2683.5,2997,3049.5,3244.5,
  3442.5,3651,3867,4089,4323,4561.5,4809,5065.5,5325,5599.5,5878.5,6169.5,
  6465,6775.5,7093.57416,7752,8097,8449.5,8560.5,8676,8785.5,8896.5,9010.5
};


base[0] is level 9, whereas base[76] is level 85. The resulting function is:

Code: Select all

function W39_HPS(AP)
  local L = UnitLevel("player");
  if L < 9 then
    return 0;
  end
 
  local base =
  {
    345,354,363,367.5,372,390,408,420,438,
    451.5,469.5,483,499.5,517.5,531,544.5,562.5,574.5,588,
    601.5,610.5,624,646.5,667.5,690,712.5,735,756,778.5,796.5,
    819,840,867,894,919.5,951,978,1008,1035,1062,1092,1119,1149,
    1176,1203,1233,1260,1287,1312.5,2683.5,2997,3049.5,3244.5,
    3442.5,3651,3867,4089,4323,4561.5,4809,5065.5,5325,5599.5,5878.5,6169.5,
    6465,6775.5,7093.57416,7752,8097,8449.5,8560.5,8676,8785.5,8896.5,9010.5
  };
 
  local m = (0.594 * AP);
  if L >= 10 then -- Vengeance
    -- Base health is level / race dependant, this value is stolen from matlabadin.
    local basehealth = 43285;
    m = m + 0.0594 * (MODEL_STAM + (0.1 * basehealth));
  end
  m = base[L-9] + (m *((RAID_10AP == true) and 1.1 or 1));
  return
  (
    (
      1 +
      (TalentRank(2,16)*0.05) + -- Guarded by the Light
      (TalentRank(2,1)*0.02) +  -- Divinity
      (HasGlyph(54936)*0.1)     -- Glyph of Word of Glory
    )
    *
    (
      1 +
      (
        (TalentRank(3,5)*0.05) +  -- Rule of Law
        (
          (
            RAID_5CRIT == true and
            HasBuff(17007)==0 and
            HasBuff(90309)==0 and
            HasBuff(24604)==0 and
            HasBuff(51701)==0 and
            HasBuff(51470)==0 and
            HasBuff(29801)==0
          ) and 0.05 or 0 -- 5% Crit raid buff
        ) +
        (GetSpellCritChance(2)/100)
      )
    )
    *
    (m / 20) -- WoG is now on a 20 second CD.
  );
end


I left AP as a function parameter, so I could compare the gains from strength / AP.

EDIT: Updated for vengeance correction / 200% crit modifier change.