Of course the character is going to take a penalty. It's just not the one you are thinking off. Because the opportunity cost of the feat is +2 ASI, that means that STR/DEX mod is one less. So every single attack they make, regardless if they are engaging the feat or not, is at -1/-1.
So if the baseline is +2 ASI, then compared to that the feat either gives:
-1 to hit / -1 to damage (when not using it)
OR
-6 to hit / +9 to damage (when using it)
So either you are strictly inferior with -1/-1, or you're getting about +1.5 damage potential for every point of to hit you are losing, but that lost to hit means that you are also gabling the base damage.
Let's try a few examples. I'll start 50/50 and go up and down.
Baseline: Greatssword (2d6 avg 7) +5 (str, magic, whatever) = 12 avg damage
GWF: Greatsword but -2 STR = 11 avg damage.
Good analysis, but there are a few problems with it I see. To ground this analysis into a specific example, lets take a 5th level fighter w/18 STR and a +1 greatsword - so he has +8 to hit and does 15 avg damage, twice per round. His avg opponent would be a CR 5-7 boss (AC 15, hp 150) or a few CR 3-4 guys (AC 13-14, hp 100).
So first, lets dispel the idea of overkill mattering since hp are plenty big enough for it to rarely matter, and just say the feat is not good at really low levels.
Now consider that his avg chance of hitting is going to be 75% normally w/o GWM or STR bonus, throughout levels +/- a bit. Damage at this level would be 15 as above.
Now lets look at your specific examples:
If baseline has a 50% chance to hit, that's 6 expected damage per attack (50% * 12)
GWF not using it has a 45% for 11 damage = 4.95
GWF using it has a 20% for 21 damage = 4.2 damage
Okay, even chance to hit definitely favors not taking the feat.
Almost never gonna happen that L5 guy faces AC18. But if it does, here is the revised stats based on 15 dmg.:
Baseline has a 35% for 15 = 5.25
GWF not in use = 30% for 14 = 4.2
GWF in use is 5% for 24 = 1.2
So if facing such a high AC, he can turn the feat off and does 20% less damage than if he had taken STR buff instead.
Let's try +3 AC harder to hit.
Baseline has a 35% for 12 = 4.2
GWF not in use = 30% for 11 = 3.3
GWF in use is 5% for 21 = 1.05
As expected, anything harder makes the feat even worse.
Never gonna happen that L5 guy faces AC21.
Let's go -3 AC easier to hit.
Baseline has a 65% for 12 = 7.8
GWF not using it has 60% * 11 = 6.6
GWF in use has 35% * 21 = 7.35
Hmm, GWF is pulling close, but it's still better not to have taken the feat. But at least if you had taken the feat it's finally better to use it then ignore it.
Revised to baseline 15 dmg:
Baseline has a 65% for 15 = 9.75
GWF not using it has 60% * 14 = 8.4
GWF in use has 35% * 24 = 8.4
So against the few AC 16 guys he faces, our L5 guy is at a 10% disadvantage by taking GWM.
Let's go up another to -6 to AC, make it REALLY easy to hit.
Baseline has 80% for 12 = 9.6
GWF not using 75% for 11 = 8.25
GWF using it 50% for 21 = 10.5
Woo, GWF is finally better!
And so here we finally have a more common scenario for our L5 hero - against AC13, here is the stats revised for 15 baseline dmg.:
Baseline has 80% for 15 = 12
GWF not using 75% for 14 = 10.5
GWF using it 50% for 25 = 12.5
Here he does 5% more damage on average w/GWM as opposed to STR buff. Not exactly game breaking.
I think my revised data above (based on baseline 75% chance to hit and 15 dmg) shows that GWM is on par the STR buff. BUT - while GWM in combat is arguably equal to +2 STR in combat effect, the STR buff adds Athletics checks and STR saves - at least until it maxes out, and that makes +2 STR "better" imo. Even after STR maxes out, GWM is not a HUGE advantage - so I am revising my opinion and I think GWM is not imbalanced for combat. I think it is a cool and balanced option.
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