Elemental resist calculation
It's the AOS damage/resist engine, it will split a single damage value into 5 different types and will use all 5 resists against each one. This will fully use DAM[Physical/Fire/Cold/Poison/Energy] and RES[Physical/Fire/Cold/Poison/Energy] by default.

Example:
A single 40 damage can be splitted into 70% physical + 30% cold (DAMPHYSICAL=70 + DAMCOLD=30), so the damage will be 28 physical + 12 cold and this will need physical resist and cold resist to resist this damage.
If the defender has physical resist 40% (RESPHYSICAL=40) and cold resist 30% (RESCOLD=30), the calculation will be like this

1) split the damage:
40 damage = 28 physical + 12 cold

2) apply each resistance:
28 physical damage - 40% physical resist = 16,8
12 cold damage - 30% cold resist = 8,4

final damage = 16,8 + 8,4 = 25

PS: To save hundreds of script lines, sphere will automatically set the DAMPHYSICAL value if it's not set. Eg: if an npc have no DAM* set, sphere will automatically use DAMPHYSICAL=100. And if only DAMPOISON=30 is set, it will use DAMPHYSICAL=70

AR resist calculation:
It's the old pre-AOS combat engine. It uses only 1 damage type and 1 resist (AR).

Sphere always used a wrong AR formula, where the AR is always a random value between 0~AR (example: if you have 50 AR, you will resist a random 0~50 damage).
Now the AR calculation is fixed and it uses the correct AR formula:

max resist = AR * rand(7, 35) / 100
min resist = max / 2

total resist = rand( min, (max-min)+1 )
final damage = total damage - total resist

PS: if for some reason someone still want use the old (wrong) formula, it can be done by scripts too. Just add this simple event on all players/npcs: