It’s very simple. (3+3+3+4+5+6)/6=4 and 4*2=8, so the expected damage per attack on a greatsword with Great Weapon Fighting is 8. Compared to the 7 without Great Weapon Fighting. So, +1 expected damage, compared to the +2 you get from Dueling or the +[Dex mod] or +[Str mod] from Two Weapon Fighting. Obviously, Great Weapon Fighting is the worst of these options by a wide margin.
That said, you're applying GWF to arguably the best damage dice for weapons (2d6), so while the
absolute benefit is less on average, you are on the net still doing more damage than you would if you went for the other choices. No one-handed weapon does more than 1d8+MOD damage when wielded in one hand, so getting +2 is very nearly the same as going from 1d8 to 1d12, because the static damage bonus doesn't carry forward into crits (whereas GWF
does apply to crits), trading lower maximum for higher minimum damage. But 1d12 is merely comparable to plain 2d6, and 1d8+2 (average 6.5) is still worse than 2d{3,3,3,4,5,6} (average 8) by 1.5 points. The bigger issue with Dueling is that it allows you to carry a shield
and get +2 damage, meaning it acts like a
Of course, I still think GWF should do something about it being pretty clearly the worst choice of the set, but I'm not sure what that should
be without accidentally making it the best of the set. Perhaps have it increase crit range with one chosen compatible weapon type, which you can then swap out whenever you gain a new level?
Assuming a +5 modifier and 60% hit rate, which contains the percentage points of critting inside it, here's some number cruching.
Duelist: 0.55(1d8+7)+0.05(2d8+7) = 0.55(11.5)+0.05(16) = 7.125 expected damage per attack (eDPA)
Current GWF: 0.55(2d{3,3,3,4,5,6}+5)+0.05(4d{3,3,3,4,5,6}+5) = 0.55(13)+0.05(21) = 8.2 eDPA
"Revised" GWF: 0.5(13)+0.1(21) = 8.6 eDPA
Relatively modest increase, but now at least
closer to that of Dueling, and more importantly having its own distinctive benefit (playing real nice with crit-fishing builds). Diegetically, you're throwing your all into these attacks (whether it's actually a "great weapon" or just a versatile one). This might still be the weakest fighting style option, but it would have a place, especially since Advantage isn't
that hard to get on attacks at higher levels, and characters often get at least two attacks per Attack. With Advantage, my "Revised" GWF becomes 0.65(13)+0.19(12) = 12.44 eDPA, while Duelist only increases from 7.125 to 0.7425(9.5)+0.0975(14) = 8.41875.
Again, not saying this makes it GOOD, just that this would work as a simple, ready-made "fix" for it being smaller in absolute terms than the comparable options for weapons with smaller dice.