Anyone with 2 Bloodthirsters, a Phantom Dancer, and Berserkers Greaves can solo Baron.
That said, if you want to do it a bit sooner, your best options are high-sustain champs like Warwick and Olaf, who can both solo it with much less lifesteal present in their build.
Sion and Nasus
I've done it with ryze, in a bot game...
Necro'd from 2009....
And lots of champions can solo baron...
Udyr, Yi, Fiora, WW, Elise, jax, Nasus, Noc, Yorick, Xin.
Anyone built with enough sustain and some tankiness can do it.
Especially if you have some free AS in your kit and build a wriggles and blade of the ruined king.
with jax soo easy
With Darius 3 Blood thirsters and 3 phantom dancers...I know not the most effective build but it gets it done
are you trying to solo baron with or without smite? It makes a pretty big difference
Vayne can do it, Ive done it, but u have to be really fed. #TrueDamageFerDayz
any with botrk, an attack speed item, and another lifesteal item.
I personally do it on a game to game basis as jax. I get gunblade, boots of swiftness, rageblade, wriggles, and blade of the ruined king. You can get it all by the 35 minute mark easily.. so...
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