Unit Cost Equation

[The_Tauren13]

50 morale is symbolic, but I think 30 morale is real...

As for your equation, while it may be perfect for all units already in the game, it doesnt do much for modding, which is what I was interested in; I ran the Size 1, 5 HP, 3 Prot, 10 Mor, 5 MR, 2 Enc, 5 Str, 11 Att, 10 Def unit Im including in my mod through your equations and he came out costing -133 from your combined euation, and 20 from the unit only one. So, it isnt really a global equation that can be applied to any unit a modder might come up with, which is what I was hoping to eventually get. Not that Im claiming any equation can fully encompass this complicated game I just want to make a stab at it...



Now, I have a couple questions: Can the same 'diminishing returns' idea be applied to attack and defence? That is, is the difference between 10 and 13 attack greater than between 20 and 23? How much attack or defense skill would be required to double the effectiveness of a 'normal' unit (that is, 10 HP, 0 Prot, 10 Att, 10 Def, etc.)? Is defense really worth more than attack? For some reason I have gotten that into my head, but then, Im a n00b at Dominions...

In my initial equation, should the magic resistance be pulled out of the square root? Should it be wieghted more? Does low magic resistance make an otherwise powerful unit worthless?

new equation: (thanks Saber Cherry )
sqrt( ( ( HP * ( 10 + Prot ) * Def * MR ) / 1000 ) * ( ( Str * Att ) / 10 ) ) * ( ( 3 + Move ) / 5 ) * ( ( 40 + AP ) / 50 ) * ( 9 / ( 6 + Enc ) ) * f( Mor )
f( x ) = 0.5 + ( ( 0.75 ) ^ ( 10 - x ) ) / 2 | x < 10
f( x ) = 2 - ( ( 0.75 ) ^ ( x - 10 ) ) | x >= 10


Heres another (crazy) idea:
sqrt( HP * ( 10 + Prot ) * f( Def ) * f( Str ) * f( Att ) ) * ( ( 3 + Move ) / 5 ) * ( ( 40 + AP ) / 50 ) * ( 9 / ( 6 + Enc ) ) * f( Mor ) * f( MR )
f( x ) = -sqrt( 10 - x ) / 3 + 1 | x < 10
f( x ) = sqrt( x - 10 ) / 3 + 1 | x >= 10

This is assuming that morale, magic resistance, attack, strength, and defense all follow the same cost distribution...
Attatched is a graph of this f(x).

[sushiboat]

How did I do it? Many statistics programs exist that can do a multiple
regression in a few seconds. The tricky part is recognizing problems and
interpreting the output.

What use is it to a modder? Use it as you will. It is an imperfect description of
the way that the unit stats are related to unit costs in the original game.

Below are some new formulae. I added some stats, and I removed stats post
hoc that didn't make a significant unique contribution. Something I might do
in the future is separate mages from non-mages.

Non-commander (adjusted R-squared = .81)

Cost = -51.7 + (11.2 * Size) + (3.1 * HP) + (.9 * Prot) + (5.9 * Morale) +
(4.5 * MagicRes) + (-1.6 * Encumb) + (-8.6 * Str) + (-1.8 * Prec) +
(.5 * TacMove)

Commander (adjusted R-squared = .82)

Cost = -269.6 + (1.6 * HP) + (-1.7 * Prot) + (8.9 * Morale) +
(12.4 * MagicRes) + (3.6 * Def) + (2.2 * TacMove) + (.6 * Ldr_Norm) +
(1.5 * Ldr_Undead) + (3.3 * Ldr_Magic)



Edit: OK, here are separate formulae for non-mage and mage commanders.

Non-mage Commander (adjusted R-squared = .77)

Cost = -125.6 + (9.2 * Size) + (1.4 * Prot) + (10.9 * Morale) +
(7.6 * MagicRes) + (-6.6 * Encumb) + (-3.5 * Str) + (-2.0 * Def) +
(2.3 * TacMove)

Mage Commander (adjusted R-squared = .79)

Cost = -233.0 + (7.7 * Morale) + (16.0 * MagicRes) + (4.1 * Str) +
(-10.7 * Att) + (11.5 * Def) + (-5.7 * Prec) + (.9 * Ldr_Norm) +
(1.1 * Ldr_Undead) + (3.5 * Ldr_Magic)