Dodge used to be a stat in the game and Jax’s entire champion revolved around it. His current E lets him dodge all attacks for a period of time. His old E activated whenever he dodged, so he got a LOT of stuns off. Sivir’s old passive was to gain dodge chance while moving (it didn’t make her more viable she’s always been a mess).
Plated Steelcaps used to be Ninja Tabi which used to give dodge chance. Yi building these meant there was just very little chance of hitting him even when he wasn’t in Q.
It was also very common to take a single dodge rune, like a single crit rune, with the old system. The crit rune used to be for level 1 fights being coinflipped by a 1% lucky crit. 1% dodge was useful all game tho and you’d randomly miss an auto attack because of it.
There was also only one (1) item to counter dodging — Sword of the Divine. It gave a passive attack speed boost and an active that gave a timed duration where your autos couldn’t be dodged. It was a meme item because it lost the passive while on cd so it was a dead item slot, worse than current GA on cd. It was reworked after dodge to be an active of 3 autos w/ 100% attack speed guaranteed crits, but still lost the passive on cd. I think Vayne used it quite well for an assassin playstyle but was still a meme item.