Crits do variable damage, so correctly speaking it's the likelihood of the crit * the likelihood of the needed damage. And BS is efficient on healing resources.
But really, the only way to resolve this is in the scenario. What level? What are reasonable foes? Set up a Champion.
Not sure what "efficient on healing resources..." means.
Haven't had near enough time to run full simulations but some initial observations:
The BS's survivability in this scenario is even higher than I expected, though it is very swingy. With bladesong the AC (even only using studded leather, because of the high stats) will be 21;
if the BS casts haste that goes up to 23;
if the BS is willing to devote his reaction for shield when necessary then his AC is effectively 27 for the encounter (he has more than enough spell slots to use shield as necessary).
This means his survivability against the hill giants (assuming he's the one drawing all the attacks AKA tanking) is effectively 4 rounds. (math is pretty simple: HGs do 39.6 per melee round each assuming 5% crits and hitting all the time, with the BS's AC this means their combined DPR against him is down to 7.92, I'm going with the BS having 32 HPs) .
The Barbarian's survivability in the same circumstances is 3 rounds (assuming barb with 16 AC, 77 HPs and raging).
The champion's is 2.2 rounds, even assuming plate, shield AND defense style (AC 21 and 71 HPs which means the champ had a very high Stat available for CON and that he pumped it at 4th or 6th, so actually 2.2 is likely high). Note, an eldritch knight could do much better here because they could PUMP AC to 25 when needed (same method as the BS)
On the surface, the BS is the clear winner, but there are some confounds.
The big one is that the BS's high survivability is based on not getting hit. If he does get hit, it only takes 2 average hits to drop him. A crit is almost certain to drop him. To the Hill Giants it's literally like trying to swat a fly and IF they hit, there's a splat.
The Barbarian is getting hit a lot (65% if the time) so his time staying up is much less swingy.
The Champion is also getting hit a lot (40% of the time) so not a huge amount of swinginess here either.
The second confound (as far as tanking anyway), the BS is so hard to hit that the HGs, even with their limited INT, will realize after the first or seconf round, (assuming they didn't get lucky and splat the BS) that they should target the rest of the party Instead. This is much less likely with the barbarian or the champion because, on them, their blows are having a visible effect.
So initial analysis, the BS will do well for himself barring bad luck, but I still maintain the barb is a better tank because they will draw fire MUCH better.
Edit: another takeaway, if your the DM and you allow both the BS and the feat luck prepare to have a lot of frustrated bad guys!
Thoughts? Anyone still care?
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