The Real Effects of Base Attack Speed Nerfs

Introduction

The second preseason balance patch recently went through, and it made a ton of changes to both champions and items. There was a lot of talk about the patch, from Rengar and Diana fans were bubbling about how their champions were playable again to Eve players were mourning the lost damage on their favorite AP assassin. 

However, I didn't see anyone talk about Ezreal. His change seemed small - just an adjustment of his base attack speed from 0.665 to 0.625 - so I understand why it wasn't the talk of the century. But is a base attack speed change actually insignificant? Just how much does fiddling with that stat change his power? Considering that he's one of the most popular champions in the League right now, I figured I'd do a very quick write up on what the 0.04 drop in base attack speed does to the Prodigal Explorer.

Attack Speed Changes Ripple

Why would I even think that a base attack speed reduction is a big deal? Part of my concern comes from how attack speed stacks. When you purchase an item that gives +20% AS (like Berserker's Greaves), it does not increase the attacks-per-second value you see on your character sheet by 20%; instead, it increases your attacks-per-second by an additional 20% of your base attack speed. This applies to any source of bonus attack speed, ranging from masteries to runes to items to the attack speed gains granted for leveling up. All of these bonuses are multiplied by your base attack speed and then added to your attacks-per-second.

attacks-per-second = ASbase * (1 + (level - 1) * AS/level + ASbonuses)

When Ezreal's base attack speed was reduced by 0.04, it did not mean that he has 0.04 fewer attacks-per-second for the whole game. It means that every single source of bonus attack speed is made worse because all bonus attack speed is multiplied by base AS. Ezreal now gets less benefit from AS runes, AS masteries, and AS items than any other AD carry (he's tied for the lowest base attack speed with Graves, every other carry beats them). This has a direct effect on his sustained autoattack damage and is only accentuated in lategame at full item build. The equation for your "stand there like an idiot and only right click" damage includes attack damage (AD), attacks-per-second (APS), critical strike damage (CD), and critical strike chance (CS).

AAdps = AD * APS * (1 + (CD - 1) * CS)

So when attacks-per-second is reduced by a fixed percentage (because base attack speed is nerfed) it reduces your overall autoattack damage by the same percentage. Using the Ezreal numbers pre- and post-patch, we see that his sustained autoattacks hurt 6% less than previously. While this percentage stays fixed, the value of that percentage will increase over the course of the game; 6% of puny autoattacks compared to 6% of beefy crit autoattacks. 

(0.625-0.665)/0.665 = -6.015%

Summary: Ezreal now does 6% less sustained autoattack damage than before, at any point in the game and with any item build.

What DPS Changes Mean in Real Stats

It's easy to see 6% and think that it's superficial but the truth is that it's far from negligible. That's six percent of actual damage output; not six percent of attack speed lost. 

In more understandable numbers, it's the same as if any of the other terms in the sustained autoattack damage equation were reduced by 6%. For a reasonably typical build of Berserker's Greaves, Bloodthirster, Statikk Shiv, Iceborn Gauntlets, and Last Whisper (I really don't care if another build is better, this is just an example), that 6% decrease in dps is as if...

• Berserker's Greaves only gave 3.7% attack speed instead of 20%, or
• Each stack of Rising Spell Force only gave 6.7% attack speed instead of 10%, or
• Bloodthirster only gave 83.71 attack damage instead of 100, a loss of 16.29. or
• Statikk Shiv only gave 13% critical strike instead of 20%, a loss of 7%. 

Only the Berserker's Greaves and Rising Spell Force analogies are perfectly appropriate (since these are AS comparisons, the other two stats affect the strength of his abilities too), but overall you can see that a mere 0.04 change to a base stat ripples into a quite sizable damage reduction. Imagine the outrage if they cut his passive by a third instead... 

Summary: Ezreal's base attack speed reduction loses him 16.3% of bonus attack speed in lategame, close to the amount that Berserker's Greaves gives him. 

Why Nerf Base Attack Speed?

Clearly Riot believed that Ezreal did too much damage, but why did they choose base attack speed specifically as the stat to reduce? Why not adjust one of the other autoattack stats? 

Modifying his attack damage values (either base AD or AD/lvl) have far reaching consequences. It hurts his ability to last hit, lowers the damage on his Mystic Shot and Trueshot Barrage, and makes sporadic autoattack harass in bot lane be less punishing. These are also extremely unpopular nerfs, since the last hitting is really noticeable in game. Changing the base value consolidates most of the pain into the early levels before it's overwhelmed by your AD items, while changing the AD per level slowly accumulates the disadvantage into a weaker lategame but roughly equivalent early/mid. 

My personal theory is that Riot is okay with Ezreal becoming a Q spamming on-hit applier who's a real terror with Iceborn Gauntlets, but are looking to adjust just his autoattack strength. Attack speed is literally the only stat they can fiddle with that doesn't impact his skills whatsoever and only touches his autoattacks, and the choice of base attack speed rather than attack speed per level hint that they wanted a flat power adjustment across all game phases rather than concentrated at the end game.  Attack speed nerfs also have the bonus of being mostly silent. Few people notice and few people complain.

Conclusion

Ezreal will still be a popular and strong AD carry. Everything that people find appealing about his kit is unchanged, and his abilities are just as strong as ever. However, the "small" change to base attack speed hurts his autoattack damage by 6% at any point in the game, which is roughly equivalent to entering every teamfight without Berserker's Greaves.