And, just for complete transparancy, that 2d6+15 (or 22 on average) might be "only" 1d6+15 (since we could be talking, not greatswords, but hand crossbows). Still, that averages out to 18 if we round down.
Okay, so what's the deal with "22 on average" - don't you ever miss? Yes, we do. And so 22 is actually slightly high.
Say our attack bonus is +12, or +7 when using -5/+10. Note: no magic bonuses assumed - this assumes Archery, and is equivalent to a GWM user with a magical +2 greatweapon.
Against AC 15, this means he has a 87% chance of hitting. In other words, there is only a 13% risk of having to use his superiority d10's.
But wait! The risk of actually rolling so low that a d10 doesn't stand a very good chance of turning miss into hit is only... (at this point, let's assume we won't "waste" our superiority dice on rolls of 1, 2 and 3. The probability of rolling 4, 5, 6 or 7 on a d20 with advantage is 10%. The probability of the miss actually becoming a hit is then 70%, 80%, 90%, and 100% respectively, or 85% on average.
So we have the following outcomes:
Rolling 1-3: 2.25%
Rolling 4-7, adding Precision and still missing: 1.5%
Rolling 4-7, adding Precision and turning miss into hit: 8.5%
Rolling 8-20: 87%
Our character has an excellent ~95% chance of delivering his 18 (1d6+15) damage each attack, which means that his average DPR will be 18x5x95%=86.5
Also note that he will have to spend an average of 0.5 superiority dice (10% chance each attack) each such round, so he can keep this up for ten (10) rounds.
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Now let's contrast this to another character that didn't pick GWM (or SS/CE) and didn't pick Precision. This character's party is just as good at fixing advantage for our hero, so that part stays the same.
The best base damage will be 2d6+1d10+7 or 19. (Now I'm generously giving this guy a +2 Greatsword. He's going to need it)
Everything else stays the same, so he still hits on 8+
So we have the following outcomes:
Rolling 1-7: 13%
Rolling 8-20: 87%
His average DPR is 19x5x87%=83
83 is almost equal to 86. What gives?
Now note that this hero spends a superiority die in 87% of all attacks. He spends an average of 4,35 superiority dice per round, burning through all his such dice in less than two rounds.
(Though to be fair: he will gain something more than the superiority damage. He might for instance make the foe prone, thus saving on other advantage-enabling party resources)
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