Minimum is +5 or so to hit that's AC 24.
Unless you're an idiot (12-14 prine ability) or less with an A hat DM this isn't a realistic scenario.
.
That....has...
nothing whatsoever to do with what I was talking about???
In 5.0, Champions get one and only one source of bonus damage: They crit when their attack roll die says 19 (more at high level, but my math was focusing <11). That's it. That's their one bonus. Everything else is non-damage, or is
versatility, not damage. As a result,
on average, the Champion is getting...+[W] once in every 20 attacks that the Battle Master isn't. And this, of course, is assuming the Battle Master
never holds onto bonus dice to add to a crit, since in 5.0 those maneuver dice get doubled just like any other dice involved in the crit.
As a result, for the Champion's bonus damage to kick in,
on average you need to get 20 attack rolls. That's 9 rounds of combat + 1 action surge, once the Champion is 5th level (which doesn't seem like much of a stretch, considering you can't even be a Champion until 3rd level anyway). So, for the Champ to keep up with a BM, they need to get,
on average, a number of bonus crit dice equal to the amount of bonus damage dice the BM gets,
per short rest.
Using the best possible option (Greatsword + GWF style), the math works...exactly as I've shown. You need TONS of rounds of combat to make the Champion be even REMOTELY as good as Battle Master.
And then Paladin is
simply better than that.
There's an exceptionally good reason the Champion was one of the worst-rated subclasses in 5.0, beaten only by the Berseker (which was actively harmful to itself, as opposed to merely being weak) and Beast Master (which was like the Champion, but more actively obvious about it).