League of Legends: Attack Damage vs Armour Penetration Runes

Robb's been talking a bit while we've been playing League of Legends about how armour penetration runes are 'bad' now and attack damage carry characters should be running all attack damage runes instead. I've been using attack damage quints and armour penetration reds for an awfully long time but I do have attack damage reds (I got them to use on Yorick who did a fair amount of magical damage that scaled off of the attack damage stat). Should I be switching my ADC rune page around?

First, note that from masteries you get 5 flat armour penetration, 3 attack damage, and .67 attack damage per level. Base stats for someone like Caitlyn are going to have no armour penetration and 50 attack damage. Most people buy a 10 ad item to start (doran's blade or long sword). So at level 1 we're looking at attacking with 63.67 attack damage and 5 armour penetration. The enemy is likely to have something like 30 armour. (Caitlyn starts with 16.5 armour and could have 12.69 from yellow runes.)

I made a little spreadsheet to calculate the damage done with an autoattack and a Q activation for each of the 40 possible combinations of reds/quints between AD and ArP. Autoattack damage at level 1 is maximized for Caitlyn by running entirely AD runes. Her Q damage is maximized by running entirely ArP reds and AD quints. The difference between best and worst combination is 3.0 damage on autoattack and 1.2 on Q.

Level 1 isn't the only useful spot. What about level 6? At this point you probably haven't gone back to buy yet, so you're just gaining the 3 AD per level while your Q gets 80 more base damage. You also get an ult. Your enemy gains 3.5 ac per level. In this configuration her autoattack remains optimized with entirely AD runes. Her Q changes and lines up with her ult, however, and are both optimized with entirely ArP runes. The damage differences swing here as well. The autoattack is now only up 2.1 damage, the Q is up 8.4 damage and the ult gains 23.0 damage.

How about level 11? By this point you probably have some attack speed (which only helps to change your attack mix by tossing in more autoattacks, it doesn't change the absolute power of any ability) and maybe, say, a bloodthirster. At this point the numbers swing entirely in one direction. All abilities are made better by stacking entirely ArP runes. Autoattack is now up 6.9, Q is up 23.7, and ult is up 54.4.

Ok, well, maybe we need to get some armor pen from somewhere else to make up that gap. Lets make the next item we buy a last whisper. Level up to 14 and add that on to our build and what happens? Nope. No go. It's still all ArP runes and the difference just keeps widening. I can give the enemy 100 bonus armour, and take away the last whisper penetration. ArP is still better. Caitlyn even has pretty good ratios on her abilities, with a 1.2 on Q and 2.0 on ult. It doesn't seem to matter. At the very beginning of the game you might want attack damage, but later in the game there's no contest. You want to have armour penetration.

Based on how Robb was talking I was expecting to come out of this with a need to build a good page with all attack damage on it. Now, I think I need to buy some armour penetration quints.

But wait! Caitlyn is probably the best champion for armour penetration since all of her abilities that scale on attack damage also do physical damage. What about someone like Ezreal or Corki? Ezreal's ult does magic damage, so armour penetration won't help it at all!

Well, at level 1 EZ wants all AD runes for his autoattack just like Caitlyn, but actually wants all ArP runes for his Q. His Q has a higher flat bonus and a smaller AD ratio and I guess those are good enough. At level 6 both of those remain true, and his ult obviously wants straight AD reds. At 11 with the bloodthirster he wants straight ArP for both his autoattack and his Q, and he more than makes up the difference from his ult with a single Q. At level 14 with the last whisper it's all ArP again, and this time a single auto-attack makes up for the difference on his ult and his Q has almost triple the gains of his ult.

Looking at this closer it seems that while Caitlyn may be awesome for ArP since she does all physical damage she's also awesome for AD because her ratios are so good. Corki actually only scales with AP when he does magical damage except his ult which only has a .2 AD ratio so I can't imagine it's actually different for him either. It's entirely possible he wants hybrid penetration instead of ArP, but he definitely doesn't want AD into the late game.

I guess if you're trying to get a kill at level 1 with a very aggressive support or a gank then maybe stacking AD makes sense. And maybe if you can't last hit well enough the extra 2.8 damage is relevant. I can see sticking with AD on some of my top laners who do try to snowball early. But for an ADC who really wants to come into power in the late game it feels like all ArP is the way to go.