User:GrauGeist/scratchpad

Damage Efficiency
The objective of doing damage with a spell or weapon is to do the maximum amount of damage each turn. The damage that can be done is limited by amount of AP available during each turn. Therefore, when choosing among spells and weapons, it is useful to consider how much damage would be done for each AP spent.

This can be simplified to consider 2 cases: Basic Damage applies whenever the Critical Hit rate is worse than 1/2, while Critical Damage applies only when the Critical Hit Rate is 1/2.
 * Basic Damage
 * Critical Damage

Basic Damage calcuations
For Basic Damage, the Critical Hit rates do not apply, as they are generally rare enough (1/10 or worse) that they do not have significant impact on the average efficiency. Similarly, Critical Failure rates are not considered as they are generally rare as well (typically 1/40 or so). For the purposes of these calculations, Critical Hits are assumed to balance Critical Failures so that both may be ignored.

Further adjustment may only be needed for those items or spells that have very high Critical Failure Rates (1/5 or worse). For those items or spells that have very high Critial Hit rates (1/5 or better), please refer to the Critical Damage calculations.

Standard Basic Damage (SBD)
Standard Basic Damage is the average amount of damage caused by the spell on a regular, non-critical hit:
 * SBD = minBD/2 + maxBD/2

where:
 * minBD = minimum basic damage
 * maxBD = maximum basic damage

Basic Damage Efficiency (BDE)
Basic Damage Efficiency is equal to SBD divided by the AP used:
 * BDE = SBD / AP

where:
 * SBD is defined above
 * AP is the AP used

Standard Critical Damage (SCD)
Standard Critical Damage is the average amount of damage caused by the spell on a critical hit:
 * SCD = minCD/2 + maxCD/2

where:
 * minCD = minimum critical damage
 * maxCD = maximum critical damage

Critical Damage Efficiency (CDE)
Critical Damage Efficiency is equal to the average of SBD and SCD divided by the AP used:
 * CDE = (SBD/2 + SCD/2) / AP

where:
 * SBD is defined above
 * SCD is defined above
 * AP is the AP used

Actual Damage
To calculate ABD from SBD, simply apply the apprpriate class and element damage bonuses. As these are constant for a particular set of equipment, they can be ignored for purposes of direct comparision of similar spells.

Thus, one only needs to compare BDE or CDE of two spells or items to determine which spell is likely to give better results.