User blog:Varnagas/AP scaling per second

''So I've not been able to normally play LoL for a while now, got some spare time and so happens, I thought about how to better determine AP scaling on champions. Summing up green numbers in main page sometimes gives wrong, misleading impressions.''

''So, can I make up better system to better determine how well AP champions scale with AP? In this blog I'll try to do my best to make such statistic.''

Main idea is to determine how effective AP stat is to do damage based on time scale. As with widely used statistic Damage Per Second, I ought to use same time scale - AP per second.

How to determine such statistics in a way, most accurate through out the champions and their skill-sets? One other stat in the game multiplies effectiveness of the AP - cooldown reduction. To provide a big picture for users two instances of the stat should be calculated: In such manner one can see how effective CDR stat is on that champion too. Or in the case that two numbers are too much, average value of above could be used, giving statistics at 20% cooldown reduction. However in this way insight about effectiveness of CDR is lost and top-bottom values remains hidden behind that average value. I'd rather provide both values to give most informative content. In case champion has in-build CDR stat like, these values shall be ignored and AP/s calculated as if no CDR present.
 * AP scaling per second with 0% CDR
 * AP scaling per second with 40% CDR

AP/s stat for the whole champion is but a sum of its separate abilities AP/s. So every single ability must be determined AP/s first. When all abilities are calculated and values are added together, champions AP/s is determined. Values before CDR and after it shall be calculated separately.

To determine single ability's AP/s, one shall use ability's:
 * AP scaling
 * Greatest rank cooldown (with 0% CDR and with 40% CDR)
 * In case of area of effect abilities, greatest possible spell succession ratio on a single target
 * In case of different spell damage against champions and monsters, AP scaling on champions should be used for calculation.

Example of the AP/s statistic's calculation of :
 * Cooldown at rank 5: 5 seconds (3 seconds with CDR)
 * AP ratio: while greatest possible AP scaling is achieved when fires hit 3 separate targets (1.2 AP), scaling of all fires hitting one target shall be used to get better single target bursting power value, so in this case we use 0.8 AP scaling.
 * 0% CDR: 0.8AP / 5s = 0.16 AP/s
 * 40% CDR: 0.8AP / 3s = 0.266 AP/s

Let's calculate AP/s for remaining abilities and then determine her AP/s value:


 * Cooldowns at rank 5: 7s - 4.2s
 * AP scaling: 0.66
 * 0% CDR: 0.66 / 7 = 0.094 AP/s
 * 40% CDR: 0.66 / 4.2 = 0.157 AP/s
 * 40% CDR: 0.66 / 4.2 = 0.157 AP/s


 * Cooldowns at rank 5: 12s - 7.2s
 * AP scaling: 0.35
 * 0% CDR: 0.35 / 12 = 0.029 AP/s
 * 40% CDR: 0.35 / 7.2 = 0.048 AP/s
 * 40% CDR: 0.35 / 7.2 = 0.048 AP/s


 * Cooldowns at rank 5: 80s - 48s
 * AP scaling: 1.05
 * 0% CDR: 1.05 / 80 = 0.013 AP/s
 * 40% CDR: 1.05 / 48 = 0.022 AP/s
 * 40% CDR: 1.05 / 48 = 0.022 AP/s


 * Total AP/s before CDR:
 * 0.296
 * Total AP/s with 40% CDR:
 * 0.493

First conclusion:

CDR statistic in case of provides 66% AP/s increase, so for now CDR stat is effective on her as the percentage AP/s increase is higher than 40% CDR. Also, AP/s value of the ultimate kinda misleads total value as ultimate abilities tend to have longer cooldowns, even when AP scalings are high. More calculation examples are needed to understand better.

AP/s calculation on damage over time, like poisons and channeled abilities, is different. Variables to consider when calculating such abilities:


 * If ability has potency to be kept for extended periods of time uninterrupted or even indefinitely, in calculation it has no real cooldown and should be held as raw damage per second (AP scale divided by 1). Examples of such abilities:


 * Ability takes time to apply full effect. If such ability lasts longer than its cooldown (reduced or not), in calculations its full effect duration is held as cooldown, since lower cooldown does not increase AP impact to damage output any further. Examples:

Done some more calculations for many more champions:

AP/s google docs spreadsheet for champions - not editable - champion selecting is at the bottom of the page

Orange cells means that number are derived indirectly to make approximate impact value. Reasons for those cells to be orange:


 * AP ratio on percentage HP scaling is calculated with 2000 health and AP influenced damage is held as AP ratio.


 * AP dependence auto-attacks. In such cases cooldown is calculated as as number of auto-attacks needed to deal AP scale, multiplied by attack speed. For current calculations I use standard attack speed of 1 attack per second. Naturally, cooldown reduction do not affect such abilities in 40% CDR calculations.


 * AP scaling on on-hit damage and consequent attacks multiply AP impact while effect holds. Auto attacks number is picked by most likely (or average) amount of attacks to be inflicted in time of the effect.


 * Some cooldowns are marked orange too, as they have different impact on AP effectiveness than their cooldown. Value is derived approximately.


 * For other reasons varying mostly on ability mechanic. Some abilities have few of those cases in one place.