Heroes of Might and Magic IV Duel Tournament: "Honor and Blood"

Maybe give them an artifact with neutral alignment at the start?

Actually, that's not a bad idea. With their meat, they could definitely become leaders, or at least become competitive.

As for the combat effectiveness of the barbarians, I'm not convinced. :)
They were only effective against other weak factions like Nature. Chaos, Life, and Order can easily defeat them, if you don't make mistakes, of course. And Undead, with proper magic, would also defeat them.

The statistics aren't entirely conclusive because the number of restarts isn't specified.
I'm willing to bet that Nature and Barbarians would be leading by a large margin. :)

Added after 10 minutes

What if you gave Nature and Undead a stack (or half a stack) of level 4 units, and gave the Barbarians an additional stack of level 1 units (or something similar)?

Nature is only weak because of its randomness. If the monsters are placed without much variation, Nature is actually quite good. In this case, the enhancement would be an obvious overkill.
Ideally, you should exclude portal monsters. It's theoretically possible to implement this with scripts... but it would be tedious. :)

As an alternative, increasing the number of choices for Nature could help. Instead of 3 lines of monsters, make it, say, 5. :)