So an assassin can start off with a long sword and three potions but a support cant?

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Why do they need 3 potion sustain?

Why do the assassins need 3 potion sustain?

Well supports have items that help them sustain, as well as an adc and there're just generally less fights/trades going on in the bot lane.

That's just...... how it works.

and like i said, most supports have some kind of way to mitigate damage whether it be a heal or a shield. the amount of sustain that potions give is rather high and paired with an adc that scales well, they can just heal through or block whatever damage they would take anyway. This is mainly to allow poke to be a more relevant strategy because the amount of sustain that we have in the bot lane is already really good. Its the same treatment that they gave to teleport. People are abusing the sustain in order to brush though weak laning to have stronger mid and late games while most poke champions fall out of favor because of it. Also the supports like Brand and Zyra are aggressive high risk high reward champions that you take because you want to get kills. You shouldn't be rewarded with a free potion just because other champs have more sustain than you. Same applies to Tank supports, except instead of damage they provide peel and/or cc to keep the adc alive and secure kills.