League of Legends [v2]

[stargroup100]

To understand why buying AD is better than attack speed early on, here's a quick analysis:


Cost analysis:

Let's call the base AD k and attack speed s. The DPS of a champion through autoattacks is therefore ks. (hue)
Let's call bonus AD and bonus attack speed (%) r.

(k+d)s = k(1+0.01r)s


Small items:
Dagger: 12% attack speed for 400g
Attack speed unit cost = 400g/12% = 33.3 g/%
Long sword: 10 AD for 360g
AD unit cost = 360g/10 AD = 36 g/AD

Caitlyn has 50-101 base AD. Factoring in runes/masteries that brings it to about 65-130.
Her base attack speed is around 0.63-1.1.

Level 1:
(65+d)0.63 = 65(1+0.01r)0.63
d = 0.65r
AD is more efficient.

Level 9ish:
(100+d)0.85 = 100(1+0.01r)0.85
d = r
Both are equal now.

Level 18:
(130+d)1.1 = 130(1+0.01r)1.1
d = 1.3r
Attack speed is more efficient.


For bigger items:
Zeal: 18% attack speed for 1175g (equivalent to 23% after accounting for crit chance)
Attack speed unit cost = 1175g/23% = 51 g/%
Long sword: 45 AD for 1550g
AD unit cost = 360g/10 AD = 34 g/AD

Clearly, since attack speed got less efficient and AD got more efficient, AD is better. Since attack speed bonuses are calculated additively, it is less efficient as bonus attack speed increases.

1 attack speed (0.5 with 100% bonus) + 100% bonus = 1.5 attack speed (0.5 with 200% bonus)
1 attack speed (no bonus) + 100% bonus = 2 attack speed (1 with 100% bonus)

Therefore, the gold cost of attack speed items are not justified until there is enough AD to counter the cost.

Level 9ish with BF sword already:
(145+d)0.85 = 145(1+0.01r)0.85
d = 1.45r
Attack speed is extremely efficient.

Level 9ish with Zeal already:
(100+d)1.08 = 100(1+0.23+0.01r)0.85
d = 0.79r - 3.19
AD is more efficient.


So basically it's almost always better to buy AD first. Almost.


Mechanics analysis:

Back there we only factored in the damage and costs if two champions were to simply autoattack each other. However, most AD champions have AD ratios on their skills, which makes AD even better.

Even if some champions do have skills that scale with attack speed, skills which scale with AD have another advantage: poke. When a champion has something that scales with attack speed, they must autoattack constantly in order to make use of that. When you're chasing opponents, that attack speed won't be put to use, because there is a small delay between autoattacks where the champion stops moving, making it harder to catch up and keep optimal attack speed. AD skills, however, simply need to hit once, and the champion can then reposition as needed. Not only does this work for the skills, but autoattacks as well. Unless there is a significant difference in attack speed and/or movespeed, ranged AD champions typically can trade one autoattack each before backing up.

In the cost analysis above, I factored in crit chance equivalent to its cost and damage increase. However, when trading autoattack for autoattack, early on it is much more likely that you will not crit, which means you lose out on the crit chance you paid for. In the event you do crit, however, dealing extra damage equivalent to one autoattack doesn't mean much. Compare level 9-ish BF sword vs. crit: 2*100 - 145 = 55 extra damage. At 4% lifesteal, you can heal that up with about 10 autos on minions. It's not worth all of the extra benefits you get from buying AD first.

On top of all that, finishing large AD items gives you even more benefit, such as cost efficient damage (BT/IE), harder scaling (IE), lifesteal (BT), armor pen (LW), etc.

And hi19hi19 reminded me of another point I somehow missed:

Originally Posted by hi19hi19

Flat AD first also makes for more reliable last hitting. Never hurts to have.

So that's even more incentive to get more AD first.