Hi I'm Ryan8Ross, and I'm a Silver 1 player who mains jungle. THIS IS NOT A GUIDE. I will not tell you how to play lucian in this guide, nor will I claim I am a good lucian player, or that this is the best build to use. However, this IS the maximum damage you can do with The Culling (as of 3.10) WITHOUT THE INCLUSION OF RUNES. More to the point, it answers the question, AS vs AD.

Note: If you think you have found a build that can do more damage, feel free to PM me, and I will update the guide.

Note: I have not included Mejai's Soulstealer or Sword of the Occult in any calculations, as they are not viable items in any league of legends game, in my opinion

ACTIVE: Lucian starts firing shots in the target direction for 3 seconds, each shot dealing physical damage to the first enemy it hits. The amount of shots fired scales with his attack speed. The Culling is considered a channeled ability and it can be interrupted, but Lucian can move freely (including movement abilities) without interrupting it himself.
Reactivate The Culling to cancel the ability early.

The Culling deals quadruple damage to minions but not monsters.

We are only interested in the damage, which at level 18, is calculated by

(60 base damage + 25% bonus ad +10% ability power) x (17 + (bonus AS x 0.149))
which is simply: (damage per shot) x (amount of shots)

Blade of the Ruined King while this provides some nice stats for The Culling, giving bonus attack speed and attack damage, the passive is not utilised when using The Culling, and the stats make it a a more mediocre version of the Zephyr

Sword of the Divine The culling uses the attack speed of lucian when it is used to decide how many shots are fired, Riot realised very early that if The Culling took advantage of SotD's unique active, you could reach max attack speed with just 1 or 2 items and it would be way too strong, so they made it explicit that this would not work when using SotD

Muramana Same as before, Riot have made it expliticly clear that each shot will not benefit from the muramana toggle, or it would almost double the damage you can do

Infinity Edge Since the shots cannot crit, an infinity edge would not give you as much damage as Bloodthirster and therefore is just a worse option

The full AD build includes

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This is the maximum bonus AD you can achieve while retaining the armour penetration from the BC and LW, and without a fully stacked Sword of the Occult which WILL give 110 AD, but I'm ignoring it for practicality.

This build gives 490 bonus AD, which translates to 122.5 bonus damage per shot.

Overall damage = (60+122.5) x 17 = 3102

Advantages of build: Lifesteal for basic attacks, otherwise, none.

Lucian has 0.996 AS at level 18, and to reach the maximum attack speed, he needs 251% attack speed to be at the maximum.

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In this build, you have the maximum attack speed which will give you 34 shots, and 115 bonus AD, which translates to 29 extra damage per shot

Overall damage = (60+29) x 34 = 3026

Advantages of build: Black cleaver stacks applied as quickly as is possible, 10%MS & 10%cdr from Zephyr

Note: before his release, the attack speed cap did not cap the amount of shots that could be fired when using The Culling, however this was corrected before release, and 34 IS definitely the maximum

The Zephyr provides the stats that seem ideal for The Culling (escpecially the movespeed and cooldown bonuses) so I thought I'd look at a build made up of just Zephyr's

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Bonus AS = 200%, Bonus AD = 190

Overall damage = (60+47.5) x 30 = 3225

Advantages of build: Black cleaver stacks applied quickly, 40% (max) cdr, 40% movespeed (very useful when trying to kite or chase down enemies)

They heavily nerfed the AP ratio upon release, because 40% scaling meant 11000 damage was achievable with a full build. With 10% scaling, it has now become impossible to produce a significant amount of damage without sacrificing the pentration needed for the physical damage dealt by The Culling

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I know this isn't the best AP build possible, but it's just a generic AS/AP build (while maintaining the AD pen) I will test to show it isn't as effective.

Bonus AS = 100%, Ability Power = 486; translates to 47 extra damage per shot
Bonus AD = 90; translates to 23 extra damage per shot

Overall damage = (60+70) x 24 =3120

Advantages of build: 40% (max) cdr

After calculating the damage dealt by the ultimate, with builds focused on attack speed, attack damage, the Zephyr, and ability power, it is clear that the Zephyr build will do the most overall damage, whilst applying black cleaver stacks in exactly 0.5s, providing you hit every shot. It is also a very good build in terms of utility, as it provides 40%cdr, meaning you can fire The Culling every 30seconds, and 40% movespeed which -without runes or masteries- will give you a very respectable 462 movespeed, for making sure you land every shot.