Hello Tormyr. Apologies in advance for what I am about to do, which is to rip apart your analysis and all the hours I'm sure you spent on it. I don't have anything personal against you, but I need to show certain posters how this is exactly the kind of imprecise analysis that leads to the wrong conclusions.
Again, I wish I could commend you on your work, Tormyr, I really do.
Now then, my biggest complaint is that you - like every analyst I've seen before you - insist on average damage. Average damage simply isn't what makes the feat stick out like a sore thumb. Your ability too boost your damage when it really matters is much more important.
In other words: insisting it's about average DPR actively obscures the feat benefits. That you aren't always stupidly powerful compared to non-feat martials should not be used as an argument against the fact you *can* and *will be* stupidly powerful when you decide you need to. I'm sure this wasn't a conscious decision on your part, so I'm going to ask you to consider what every minmax analyst should consider: how about calculating some nova damage?
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Another thing I'm sure you weren't intentionally suggesting is that the feat is only good at AC 13 even at high levels. Because that's what you chose for your analysis, which might mislead people to think the feat is alright because we don't need to care about you slaughtering AC 13 mooks at high level.
So I need to tell you that you can slaughter AC 18 critters at high level, you just need to powergame the feat a bit. Which leads me to my next point.
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Also much like every other previous analysis, you don't really go all the way, and so your analysis can't show how devastating the +10 part of the feat really is.
If you have advantage, please notice that most misses will be just one or a few points short of a hit (since the probability curve is no longer flat). This means using a bonus die to "top up" your rolled attack is very likely to turn a miss into a hit.
Since nova damage is much more relevant to game balancing, please recrunch your numbers assuming the first half a dozen misses in a fight are given, say, a +1d8 bonus die unless your initial d20 roll is a 2 or a 3 perhaps (despite advantage, mind you) where the "gap" up to a hit might be too large.
What this should do to your numbers isn't mainly to increase the DPR but to allow the player to use the feat against higher ACs.
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Even after all the analysis, you stll end up with nothing but a guess: Your guess is that guess is that a fighter would see an average bonus of 7 DPR at level 1 and 30 DPR at level 20.
My in-game actual experience is that at low level, the DPR isn't the most egregious thing about the feat, since you have few ways to downplay the -5. Instead, the problem there is your ability to dish out over 20 damage in a single hit. At higher levels, a fighter WILL SEE an average bonus of 40 DPR already at level 12-14 or so. What the numbers are at level 20, I can't say. And that's against far higher ACs than 13.
Meaning that these numbers feel close to what you will actually see in practical play, if we focus on the last number, the DPR:
Fighter: Level 1 - 88% to hit, 9.1 DPR; Level 20 - 99.8% to hit, 49.3 DPR
GWM Fighter: Level 1 - 64% to hit, 21.6 DPR; Level 20 - 91% to hit, 101.4 DPR
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I also need to call you out on your thoroughly unscientific comparison to rolling a crit on an Arrow of Slaying? My response is simply: so what?
More generally, the complaint is contrasting two martials, one with the feat and one with some other available game feature.
NOT with banishment wizards. The fact that other people can do stuff too is utterly irrelevant to the complaint that there are no other ways to compete for DPR if you are a martial with a comrade using GWM.
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Then, for the real whammy.
Now redo the numbers but for Sharpshooter instead of GWM. No longer will there be any misses due to not reaching a new foe. The Cleave part can be turned into an assured extra hit (through Crossbow Expert). And the Archery fighting style gives you a gift you certainly didn't need; increasing your AC threshold by 2.