Does Lifesteal Proc off Crit Damage?
I would like to know if Lifesteal benefits from Critical Strike Damage Totals as well as Regular Attack Damage Totals?
I am working on a Rune build and I wanted to know if it would be beneficial to stack Critical Strike Damage Percentage at all... and part of my reasoning for doing so would rely on being able to gain health (via lifesteal) through large Critical Strike damage bonuses. 
Lifesteal works based on how much damage you deal. Crits increase this damage, so you will leech back more health from crits. Thornmail, on the other hand, calculates reflect damage before mitigation, so it's possible to lose life even with lots of lifesteal if the opponent has too much armor.
Crit on runes is bad. Optimal statsforgold gives an equation whose solution says that 0% crit is optimal at around 120 AD and 100% crit is optimal at around 240 AD (before IE is calculated in), so getting any crit before the ~120 AD benchmark is nonoptimal use of gold. The standard ADC page uses AD Marks and Quints for much better last hitting whose gold will far outweigh the slight difference from the endgame dominance of crit runes. 
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Also, crit chance becomes the most valuable stat later and also increases in value the more crit you have, up to 100 obviously. You usually will only have about 55  63 with standard carries. Late game, 14% crit chance is Huge dps increase compared to the 15 AD, and getting more crit becomes increasingly harder the higher you have. 
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I'm focusing on the math. Let's say that an ADC starts with 55 AD and would normally get +15 AD from Runes or +14% crit from runes for the sake of some math with masteries giving +3 AD and +4% crit.
The ADC with 58 AD and 18% crit will be dealing an average of 69.5 damage per strike after crit normalization. The ADC with 73 AD and 4% crit will be dealing 76.2 damage per strike after crit normalization. The pure AD ADC will be dealing, on average, 6.7 more damage per strike. In addition, 73 AD gives a much larger margin for error in last hitting than 58 AD does, and many abilities that are leveled early on ADC's scale based on AD meaning that the burst is also higher with pure AD. I'd rather get more gold and more consistent harass instead of hoping for a lucky crit string to give me an undeserved kill. The gold gained from extra last hits on an AD page is more consistent and therefore more dependable. Other factors in determining optimal stats would be to consider how much AD/level the champ gains and at what amount of AD the equation normalizes to determine when Crit will start dealing more damage than AD; items will also decrease the level required assuming they're ADbased like DBlades or a BF Sword. Despite the scaling potential, LoL is mostly a snowball game, so getting an early advantage will help you to earn more gold faster than the enemies (map and objective control gives you more income based on farmable jungle and ganking potential), and the early advantage lost by dying without proccing one crit will force you to lose out on enough farm throughout the course of the game that you'll be missing an item that could have provided those stats had you chosen a different rune page. 
If you want Crit, only build 1 crit rune. Extra AD with a 1% Crit Chance is better than 10% Crit, but no AD.

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If I crit you for 210% damage with about 60 ad, its gonna take your single extra ad 66 attacks to make up for it and honestly, someone will have died long before that happens. A difference in 1 AD can't determine a lane the way 1% crit can. The 1 AD makes a difference when someone escapes with less than ~7 hp left (1 hp for each aa it would take to kill them) . Example: say you are in a straight up aa duel with someone. You have 60 ad to start. They have X amount of health to start. If they have 421427 health, the 1 ad would make the difference of one attack. If they have 428480 health, though, that 1 ad doesn't make a difference at all. It is very likely that the 1 AD doesn't make a difference. At certain AD/enemy armor combinations, the single AD wont even make a difference at all because you wil be doing the same damage per auto attack (from what I understand, something that calculates to say, 44.7 damage rounds up while 45.3 rounds down (numbers you could easily end up with when you have a difference of 1 ad)). Taking into account the fact that AD might not even have a chance to make a difference because of armor AND the low percent chance that the extra damage will reduce the amount of attacks you need to do to begin with, I would guess that the amount of auto attacks saved by one crit rune vs one ad rune is fairly equal. Because of this, the question for me becomes whether or not you want the 1 AD for spell scaling (which some ad carries dont have anyway) or for shock effect (enemy being frightened because a crit and spell at level 1 just took half their health. I personally choose the shock effect. 
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I took the most efficient items of each stat (BF Sword, Recurve Bow, Cloak of Agility), calculated their stat to gold ratio, plugged in the formula for raw damage (no ARP), and made a chart showing the most efficient purchase with each iteration of stats. The starting point was 50 AD, 0.6 AS, and 0% Crit assuming a 100% Crit modifier. I solved for the general case so that I didn't have to spend too much time on it and then memorized the key points of the results. You're welcome to do the math yourself; I personally wrote my own program to iterate the formula for me, and I can't find the program right now.
And even though a good case was presented for the 1% crit, I still prefer the law of averages. In most fights, if I get off about 78 autos, that still only gives me a ~78% chance of getting ONE crit; I'd have to fight about 12 times for that one crit to happen (assuming a sufficient sample size), and that means I'm technically less powerful for 11/12 fights in addition to having a smaller margin for error on last hits and lower ability damage. I do remember playing as Trynd once and getting 4 crits in a row pre6 to nearly instantly kill someone. In the over 2500 games I've played, that's only happened one time where I got such an undeserved kill that should have simply been harass. EDIT: Now that I think about it, that crit string happened before Riot made Crit Chance more consistent. At the time, you could potentially get 4 crits in a row with only ~10% crit; today, it more or less functions as an addition that procs when it hits the threshhold. For example, if you have 22% crit, then you won't crit on attack 1 (0+22%), attack 2 (22+22%), attack 3 (44+22%), or attack 4 (66+22%), but you will crit on the fifth attack (88+22%  100%), and the process repeats. With this in mind, and with more testing, it may be possible to manipulate the timing of the crit making your point valid. However, I'm not about to begin testing this. 
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