[Vladimir] - Crimson Pact stacks with itself + wrong life total calculation

When the AP part of the passive is calculated, the Health given by the passive is taken into account. **Repro steps :** 1. Choose Vladimir 2. Get % Health runes (seals + quints), Juggernaut and Archmage masteries (nothing else impacting AP or Health, except Veteran's Scars in order to get Juggernaut). 3. Buy Rabadon 4. For example, at level 18, passive will give 236.32 Health and 12.71 AP, which is wrong (should give 233.15 Health and 7.50 AP) 5. Also, take note that Vladimir full Health is 2439 and full AP is 182. **Maths part :** **Facts we know :** Vladimir base Health at level 18 is 1930. Rabadon gives 120 AP. Veteran's Scars mastery gives 36 flat Health. % Health runes and Juggernaut give 12% bonus Health. Rabadon's passive and Archmage mastery give 36.5% bonus AP (stacks multiplicatively) **Facts seen in game at level 18, with the setup seen in the repro steps before :** Vladimir total Health is 2439. Vladimir total AP is 182. Passive's Health bonus is 236.32. Passive's AP bonus is 12.71. **How the numbers are obtained :** For the passive's Health part, I can't find the right calculation. The closest I can find is this one : ((Base AP + Items) x (1 + % AP bonus) + (Passive's AP part x % AP bonus)) x 1.4 -> ((0 + 120) x (1 + 36.5%) + (12.71 x 36.5%)) x 1.4 = 235.81481 For the passive's AP part : (((Base Health + VS bonus) x % Health bonus) + VS bonus + Passive's Health bonus) x 2.5% -> (((1930 + 36) x 12%) + 36 + 236.32) x 2.5% = 12.706 Here, we can see that the passive's Health part (236.32) is taken into account in the passive's AP bonus calculation (where it shouldn't). We can also see that the bonus Health from the Runes and the Masteries isn't taken into account to calculate the passive's AP bonus. **What it should be :** Passive's Health bonus calculation is OK : ((Base AP + Items) x (1 + % AP bonus) + (Passive's AP part x % AP bonus)) x 1.4 Passive's AP bonus calculation should be : (((Base Health + VS bonus + Passive's Health bonus) x % Health bonus) + VS bonus) x 2.5% Which, in the test case, would be : (((1930 + 36 + 233.15) x 12%) + 36) x 2.5% = 7.49745 (rounded) Note that I wrote 233.15 for the passive's Health bonus, and not 236.32. This is because the calculation needs to be done with the correct passive's AP bonus (because of Archmage and Rabadon's passive). **Steps to calculate the passive's bonuses :** **Algorithm :** Both parts of the passive are calculated based on its rules. Then we apply any percentage bonus (items, runes, masteries) and calculate them again, until the difference between the previous iteration and the new one is smaller than 0.01. Results will be rounded with 2 decimals. **First iteration :** Passive's Health bonus : ((0 + 120) x (1 + 36.5%)) x 1.4 = 229.32 Passive's AP bonus : ((1930 + 36) x 12% + 36) x 2.5% = 6.80 % Health bonus : 229.32 x 12% = 27.52 % AP bonus : 6.80 x 36.5% = 2.48 No test here, there will always be a second iteration (we need two results to check if the difference is smaller than 0.01 for both) **Second iteration :** Passive's Health bonus : ((0 + 120) x (1 + 36.5%) + 2.48) x 1.4 = 232.79 Passive's AP bonus : ((1930 + 36) x 12% + 36 + 27.52) x 2.5% = 7.49 % Health bonus : 232.79 x 12% = 27.94 % AP bonus : 7.49 x 36.5% = 2.73 Test : 232.79 - 229.32 = 3.47 >= 0.01 7.49 - 6.8 = 0.69 >= 0.01 -> continue iterating **Third iteration :** Passive's Health bonus : ((0 + 120) x (1 + 36.5%) + 2.73) x 1.4 = 233.15 Passive's AP bonus : ((1930 + 36) x 12% + 36 + 27.94) x 2.5% = 7.50 % Health bonus : 233.15 x 12% = 27.98 % AP bonus : 7.50 x 36.5% = 2.74 Test : 233.15 - 232.79 = 0.36 >= 0.01 7.50 - 7.49 = 0.01 >= 0.01 -> continue **Fourth iteration :** Passive's Health bonus : ((0 + 120) x (1 + 36.5%) + 2.74) x 1.4 = 233.15 Passive's AP bonus : ((1930 + 36) x 12% + 36 + 27.98) x 2.5% = 7.50 % Health bonus : 233.15 x 12% = 27.98 % AP bonus : 7.50 x 36.5% = 2.74 Test : 233.15 - 233.15 = 0 < 0.01 7.50 - 7.50 = 0 < 0.01 -> end of iteration **In the end, we have :** Passive's bonus Health : 233.15 Passive's bonus AP : 7.50 Where, on live, we had : Passive's bonus Health : 236.32 Passive's bonus AP : 12.71 **Now, onto the totals calculation part :** With the numbers shown in game : Health calculation should be : (Base Health + VS bonus + Passive's bonus Health) x (1 + % Health bonus) -> (1930 + 36 + 236.32) x (1 + 12%) = 2466.5984 But, in game, we can see that Vlad's total Health is 2439. I think it comes from this : (Base Health + VS bonus) x (1 + % Health bonus) + Passive's Health bonus -> (1930 + 36) x (1 + 12%) + 236.32 = 2438.24 (rounded up to 2439 in game I guess ?) Vlad's Health should be : -> (1930 + 36 + 233.15) x (1 + 12%) = 2463.0493 (rounded by myself) AP calculation is done right, only with the wrong passive's AP bonus : (Base AP + Items + Passive's AP bonus) x (1 + % AP bonus) -> (0 + 120 + 12.71) x (1 + 36.5%) = 181.14915 (again, rounded up to 182 ?) With the correct passive's calculation, it would be : -> (0 + 120 + 7.5) x (1 + 36.5%) = 174.034 (rounded by myself) Hence, Vlad's Health and AP totals would be : HP : 2463 (2464 if rounded up) AP : 174 (175 if rounded up) **Edit :** Two other remarks : **First**, I think the passive's text is misleading. It says "Every 40 points of bonus health gives Vladimir 1 ability power and every 1 point of ability power gives Vladimir 1.4 bonus health (does not stack with itself)." It should say (text taken on the LoL wikia) : "Vladimir gains ability power equal to 2.5% of his bonus health and bonus health equal to 140% of his ability power. These bonuses do not stack with themselves." Because, in the first case, the passive would give integer values of AP (1 point every 40 points of bonus health means that if you have 39 bonus health, you get 0 AP). Where, in the second case, the passive is as applied today. **Second thing**, I have a problem with the algorithm applied on live. While studying Vlad's case, I took note of its characteristics' values at different levels. And here they are (all including the setup in Repro steps) : Level 10: HP 1676 (Crimson Pact 235.26) AP 178 (Crimson Pact 10.64) Level 12 : HP 1867 (Crimson Pact 235.39) AP 179 (Crimson Pact 10.9) Level 16 : HP 2248 (Crimson Pact 236.05) AP 181 (Crimson Pact 12.19) Level 17 : HP 2343 (Crimson Pact 236.19) AP 181 (Crimson Pact 12.45) Let's recall the formula I found before, for the AP part of the passive : (((Base Health + VS bonus) x % Health bonus) + VS bonus + Passive's Health bonus) x 2.5% Level 10 : (((1250 + 36) x 12%) + 36 + 235.26) * 2.5% -> 10.6395 (rounded to 10.64 ingame) Level 12 : (((1420 + 36) x 12%) + 36 + 235.39) * 2.5% -> 11.1495 (not 10.9) Level 16 : (((1760 + 36) x 12%) + 36 + 236.05) * 2.5% -> 12.1695 (almost 12.19, but a difference of 0.02) Level 17 : (((1845 + 36) x 12%) + 36 + 236.19) * 2.5% -> 12.4245 (almost 12.45, still a 0.02 difference) Note the huge difference at level 12, where it is much closer at other levels. Can't explain that :/ I must be wrong somewhere (not talking about the health part, as I already think my assumption is wrong there).
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