AP scaling per second
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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.
First draft
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:
- AP scaling per second with 0% CDR
- AP scaling per second with 40% CDR
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 Zyra, these values shall be ignored and AP/s calculated as if no CDR present.
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.
Variables and computation
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.
- AP value shall be divided by base ability cooldown to determine base ability AP/s.
- AP value shall be divided by base ability cooldown multiplied by max CDR (0.6 modifier) to determine cooldown reduced ability AP/s.
- All base AP/s values to be summed up to determine champions base AP/s.
- All CDR AP/s values to be summed up to determine champions CDR AP/s.
- CDR AP/s value of the champion shall be divided by the base AP/s value of that champion to determine percentage increase of one's AP/s by applying cooldown reduction. Higher than 40% effectiveness shows good CDR effectiveness on that champion's AP/s ratio, lower value, however, means that building CDR may be less effective than building AP in the matter or damage output.
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:
Example of AP/s calculation
AP/s statistic's calculation of Fox-Fire:
- 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 = 0.267 AP/s
Let's calculate AP/s for remaining Ahri's abilities and then determine her AP/s value:
- Orb of Deception
- 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
- Charm
- 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 = 0.049 AP/s
- Spirit Rush
- Cooldowns at rank 3: 80s - 48s
- AP scaling: 1.05
- 0% CDR: 1.05 / 80 = 0.013 AP/s
- 40% CDR: 1.05 / 48 = 0.022 AP/s
- Total AP/s before CDR:
- 0.297
- Total AP/s with 40% CDR:
- 0.494
Conclusion:
CDR statistic in case of Ahri provides 66% AP/s increase, so CDR stat is effective AP/s increase on her as percentage increase value is higher than 40%. 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. This difference represents a little greater Ahri's ability to deal burst damage than to do sustained damage.
AP/s table of Champions
Reason listing of indirectly derived (therefore debatable) AP scaling values |
Champion has a way to reset cooldown on a damaging ability that scales with AP. |
Champion has a damaging ability with AP and percentage enemy's health scaling. |
Champion with attack speed dependant damaging AP ability. |
Champion with ability that has no AP scaling, but it has an indirect impact in dealing damage through AP. |
Champion has no ability that use AP as damage increase. |
Champion has perfectly straight AP ratios and cooldowns, therefore AP/s ratio is definite. |
Champion | total AP ratio | base AP/s | CDR AP/s | % effect. |
---|---|---|---|---|
Ahri | 2.86 | 0.297 | 0.494 | 66.67 |
Akali | 1.6 | 0.333 | 0.556 | 66.67 |
Alistar | 1.3 | 0.142 | 0.236 | 66.67 |
Amumu | 2.2 | 0.378 | 0.497 | 31.40 |
Anivia | 2.25 | 0.575 | 0.792 | 37.68 |
Annie | 2.95 | 0.292 | 0.487 | 66.67 |
Ashe | 1 | 0.013 | 0.021 | 66.67 |
Blitzcrank | 1.2 | 0.143 | 0.238 | 29.24 |
Brand | 3.45 | 0.272 | 0.453 | 66.67 |
Caitlyn | 1.4 | 0.155 | 0.258 | 66.67 |
Cassiopeia | 3.3 | 1.522 | 2.259 | 48.42 |
Cho'Gath | 2.7 | 0.477 | 0.594 | 24.71 |
Corki | 1.84 | 0.214 | 0.356 | 66.67 |
Darius | 0 | 0 | 0 | 0 |
Diana | 2.5 | 0.477 | 0.661 | 38.40 |
Dr. Mundo | 0.2 | 0.2 | 0.2 | 0.00 |
Draven | 0 | 0 | 0 | 0 |
Evelynn | 1.85 | 0.416 | 0.694 | 66.67 |
Ezreal | 2.65 | 0.254 | 0.480 | 89.04 |
Fiddlesticks | 5.85 | 0.515 | 0.683 | 32.69 |
Fiora | 1 | 0.167 | 0.278 | 66.67 |
Fizz | 3.05 | 0.278 | 0.434 | 56.18 |
Galio | 1.94 | 0.134 | 0.223 | 66.67 |
Gangplank | 0.6 | 0.005 | 0.009 | 66.67 |
Garen | 0 | 0 | 0 | 0 |
Gragas | 2.4 | 0.217 | 0.361 | 66.67 |
Graves | 0.6 | 0.038 | 0.063 | 66.67 |
Hecarim | 2 | 0.069 | 0.115 | 66.67 |
Heimerdinger | 1.35 | 0.372 | 0.453 | 21.82 |
Irelia | 2.5 | 0.103 | 0.171 | 66.67 |
Janna | 1.35 | 0.075 | 0.125 | 66.67 |
Jarvan IV | 0.8 | 0.062 | 0.103 | 66.67 |
Jax | 1.9 | 0.533 | 0.889 | 66.67 |
Jayce | 1 | 0.1 | 0.167 | 66.67 |
Karma | 2.1 | 0.250 | 0.417 | 66.67 |
Karthus | 1.45 | 0.854 | 1.256 | 47.15 |
Kassadin | 2.5 | 0.414 | 0.691 | 66.67 |
Katarina | 3.15 | 0.508 | 0.881 | 73.22 |
Kayle | 3 | 0.250 | 0.417 | 66.67 |
Kennen | 3.1 | 0.389 | 0.649 | 66.67 |
Kog'Maw | 2.7 | 0.280 | 0.466 | 66.67 |
LeBlanc | 3.9 | 0.368 | 0.614 | 66.67 |
Lee Sin | 0 | 0 | 0 | 0 |
Leona | 1.9 | 0.129 | 0.215 | 66.67 |
Lulu | 1.1 | 0.131 | 0.219 | 66.67 |
Lux | 2.05 | 0.142 | 0.237 | 66.67 |
Malphite | 1.8 | 0.114 | 0.189 | 66.67 |
Malzahar | 3.9 | 0.291 | 0.485 | 66.67 |
Maokai | 2.7 | 0.237 | 0.394 | 66.67 |
Master Yi | 1 | 0.2 | 0.333 | 66.67 |
Miss Fortune | 2.6 | 0.082 | 0.136 | 66.67 |
Mordekaiser | 3.26 | 0.374 | 0.623 | 66.67 |
Morgana | 3.3 | 0.196 | 0.326 | 66.67 |
Nasus | 4.2 | 0.125 | 0.208 | 66.67 |
Nautilus | 3.35 | 0.229 | 0.382 | 66.67 |
Nidalee | 2.425 | 0.452 | 0.753 | 66.67 |
Nocturne | 1 | 0.091 | 0.152 | 66.67 |
Nunu | 3.5 | 0.194 | 0.324 | 66.67 |
Olaf | 0 | 0 | 0 | 0 |
Orianna | 2.35 | 0.436 | 0.626 | 43.71 |
Pantheon | 2 | 0.119 | 0.199 | 66.67 |
Poppy | 1.4 | 0.250 | 0.417 | 66.67 |
Rammus | 3.4 | 0.123 | 0.206 | 66.67 |
Renekton | 1.5 | 0.013 | 0.021 | 66.67 |
Rengar | 1 | 0.125 | 0.208 | 66.67 |
Riven | 0 | 0 | 0 | 0 |
Rumble | 3.61 | 0.258 | 0.431 | 66.67 |
Ryze | 2.575 | 0.299 | 0.608 | 103.49 |
Sejuani | 2.45 | 0.165 | 0.275 | 66.67 |
Shaco | 3.8 | 0.263 | 0.438 | 66.67 |
Shen | 1.1 | 0.213 | 0.354 | 66.67 |
Shyvana | 1.48 | 0.105 | 0.170 | 61.74 |
Singed | 1.3 | 0.4 | 0.467 | 16.67 |
Sion | 1.8 | 0.188 | 0.290 | 54.55 |
Sivir | 0.9 | 0.1 | 0.167 | 66.67 |
Skarner | 2.1 | 0.247 | 0.520 | 110.282 |
Sona | 1.5 | 0.108 | 0.180 | 66.67 |
Soraka | 1.15 | 0.235 | 0.392 | 66.67 |
Swain | 3.12 | 0.555 | 0.765 | 37.84 |
Syndra | 2.975 | 0.303 | 0.504 | 66.67 |
Talon | 0 | 0 | 0 | 0 |
Taric | 2.1 | 0.152 | 0.253 | 66.67 |
Teemo | 2.4 | 0.748 | 0.890 | 19.11 |
Tristana | 3.3 | 0.202 | 0.336 | 66.67 |
Trundle | 1.2 | 0.020 | 0.033 | 66.67 |
Tryndamere | 1 | 0.2 | 0.333 | 66.67 |
Twisted Fate | 1.45 | 0.275 | 0.407 | 47.88 |
Twitch | 1.2 | 0.15 | 0.25 | 66.67 |
Udyr | 1.5 | 0.25 | 0.3 | 20.00 |
Urgot | 0 | 0 | 0 | 0 |
Varus | 1.65 | 0.35 | 0.417 | 19.05 |
Vayne | 0 | 0 | 0 | 0 |
Veigar | 2.8 | 0.263 | 0.439 | 66.67 |
Viktor | 3.86 | 0.25 | 0.417 | 66.67 |
Vladimir | 1.96 | 0.271 | 0.451 | 66.67 |
Volibear | 2.1 | 0.073 | 0.122 | 66.67 |
Warwick | 1 | 0.167 | 0.278 | 66.67 |
Wukong | 0.6 | 0.06 | 0.1 | 66.67 |
Xerath | 3.2 | 0.230 | 0.383 | 66.67 |
Xin Zhao | 0.6 | 0.067 | 0.111 | 66.67 |
Yorick | 1 | 0.083 | 0.139 | 66.67 |
Ziggs | 3.75 | 0.329 | 0.564 | 71.09 |
Zilean | 1.8 | 0.240 | 0.4 | 66.67 |
Zyra | 3.8 | 0.452 | 0.753 | 66.67 |
Tons of background calculations
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.