City Of Heroes/Enhancements/Math

Types of Enhancements
There are five known types of enhancements in City of Heroes: Training Enhancements (TO), Dual Origin Enhancements (DO), Single Origin Enhancements (SO), Trial Reward Enhancements (TR), and Hamidon Enhancements (HO).

Enhancements are broken down into two categories. Range, cone range, defense and damage resist enhancements use the lower of the two numbers in the following table; all other enhancements use the higher number.

Effect of Level
The level of the enhancement does not directly affect the benefit that enhancement. However, the level of the enhancement relative to the level of the hero does. Enhancements at a higher level than the hero provide a 5% bonus per level difference; those at a lower level have a 10% reduction per level difference. To calculate the value of an enhancement, take its base strength (e.g., 33% for a single-origin damage enhancement), and multiply it by the level modifier (one of .7, .8, .9, 1, 1.05, 1.1, and 1.15).

To calculate the effect of multiple enhancements for a single power, calculate the modifying factor as follows: $$Modifying Factor = 1 + \sum Base Enhancement Strength * Level Modifier$$

For instance, if a level 32 hero has three single-origin damage enhancements (levels 31, 32 and 35) and one dual-origin damage enhancement (level 33) in one attack, the modifying factor will be: $$1 + .3333*.9 + .3333*1 + .3333*1.15 + .1666*1.05 = 2.19$$

To see how this affects the power, either multiply or divide the power's basic "value" by the modifying factor (depending on whether the "value" is being increased or decreased). For instance, the above-mentioned hero will be doing 2.19 times as much damage with that attack. Or, if those were endurance reduction enhancements instead, that attack would use $$1/2.19 = 46%$$ of the base endurance.

Note that accuracy enhancements are affected by level difference, but are additive to your base to-hit instead of being multiplied.