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Why champions stop leveling

BUD is base ultimate damage: a record of a recent high hit, used when an ultimate needs a damage number. It is not a level cap.

Steam screenshot of Lost in the Underdark: a level 50 purple worm and Rosie selected at level 175.Steam screenshot of Elturel's Last Stand: Tiamat breathes fire while Minsc is selected at level 460.

The sourced answer

Champion level caps have moved between patches. Item level measures equipment progression and differs from the champion’s level. Duplicate gear raises equipment levels rather than adding another equipped item. Searches about reaching level 2500 with BUD, or about champions who stop leveling, do not come with a formula I can cite. The practical checks are: you are out of gold, the champion is benched, or you are looking at item level and expecting the portrait level to match.

The FAQ is the source for the BUD definition. The gear page is the source for item level. I leave the 2500 threshold blank.

FAQ

What is BUD?

Base ultimate damage, a memory of a recent high hit.

Is item level the same as champion level?

No. Champion level is bought with gold during an adventure; equipment has its own levels, increased by duplicate gear or blacksmithing contracts.

Related

Sources