[Champion] Diana - Page 5

assuming level 12, Diana has 81 damage, which is the amount that sheen will add to her auto attack. Lets say Caitlyn is who you're diving. Her Armour (assuming she is also level 12, although she is probably lower) will be 51.5 base + 13 from runes (flat armour yellows) totaling 64.5. Her magic resist will be 30 + 12 from runes (flat MR) totaling 42. The gold difference between Sheen and Lichbane is 1740, so you can realisticly have a Needlessly Large Rod and sheen, where you would otherwise have Lichbane. NLR is 80AP, 2 Doran's is another 30, and sheen offers you 25AP and 200 mana. With NLR + Sheen, you have 25 more AP, but 50 less mana and 5% less movement speed.

Runes: Assuming flat AP quints, MPen reds (This favours lichbane the most)
Masteries: Assuming blast (+18AP at 18), Arcane knowledge (8% pen), mental force (+6AP) and archmage (+5% AP)

total: AP: ((4.95*3) + 12 + 6) * 1.05 = 34.5

Assuming max Q and 2 ranks in R at level 12, and that you just Q -> R auto:

Sheen + NLR:
Sheen adds 81 * (100 / (100 + 64.5)) = 49.2
AP difference adds ((25 * 1.05) * (0.7+0.6)) * (100 / (100 + ((30*0.92) - 7.8))) = 28.5
Total: 49.2 + 28.5 = 77.7 additional damage from items.

Lichbane:
total AP * 1.25 + 50:
((34.5 + ((30 + 80)*1.05))*0.75 + 50) * (100 / (100 + ((30*0.92) - 7.8))) = 135.6
Total: 135.6 additional damage from lichbane.

If we look at Diana's full combo:
Q W R R Passive her ratio goes to (0.6 + 0.7 + 0.6 + 0.6 + 0.6) = 3.1

Recalculating the AP difference for Sheen + NLR:
((25 * 1.05) * 3.1) * (100 / (100 + ((30*0.92) - 7.8))) = 67.9
Total: 67.9 + 49.2 = 117.1


The second major part to this problem is the deathcap timing. From a NLR, a deathcap costs an additional 1700g. So, a player going Lichbane -> Deathcap can realistically be at Lichbane + NLR where a sheen -> Deathcap player will have this complete. At this stage:

Lichbane:
total AP * 1.25 + 50:
((34.5 + ((30 + 80 + 80)*1.05))*0.75 + 50) * (100 / (100 + ((30*0.92) - 7.8))) = 188.23
Total: 188.23 additional damage from lichbane.

Sheen + deathcap:
total: additional AP * spell ratios + sheen damage:
Deathcap AP - Lich AP * ratios * MR:
(((32.85 + 30 + 25 + 120)*1.35)- (34.5 + ((30 + 80 + 80)*1.05))) * 3.7 * (100 / (100 + ((30*0.92) - 7.8))) = 120.6
Sheen damage:
81 * (100 / (100 + 64.5)) = 49.2
Total: 120.6 + 49.2 = 169.8

Conclusion: When you first get a lichbane, the proc does significantly more damage than if you were going sheen -> deathcap. When you first hit your deathcap, someone who is going lichbane -> deathcap will still be doing more damage than the person who rushed deathcap after a sheen and if you proc lichbane more than once in a fight you start to jump way ahead. Also ahead if you can't land all hits of your shield or your passive, as this would reduce the AP ratio of the deathcap diana further.