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AP scaling per second

Varnagas August 28, 2012 User blog:Varnagas

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.
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