Wow, ok, this is an amazing response and has taken me some time to address everything.
I appreciate that you consider my equations to have potential accuracy and I agree that there are outstanding inconsistencies between the displayed damage numbers and the effect damage done to an enemies actual health. My equations can only predict how the red text numbers will range from, but they can't account for the odd difference in damage that usually occurs. I've done some tests in the past on gray enemies to record the changes in damage that occur and measure the deviation from what the red text damage displays. Quoting from a previous post of mine:
So, in an environment where a lot of hits are being done, I think that the use of my red text damage equation is still accurate because the health loss deviations balance out to line up with the red text damage. This is why I consider looking at the damage ranges alone to be an accurate representation of damage which can then be merged into understanding OH potential (average damage) and TTK (animation timing and HP)
Furthermore, if we consider two weapons, say two swords, that are different but have identical damage, then both swords using the same attacks on the same enemy will be able to produce the same range of red text damage numbers. Now, these swords will also be producing those weird shifts in damage to the actual health of the enemy compared to what the red text says, but
shouldn't the two swords experience the same shifts in the long term? My answer to that question is yes. Weapons experience these damage deviations, but they don't appear to be so radical that a rusty sword could ever deviate and do a mercer's critical hit amount of damage; they consistently deviate a short distance around what the red text damage is. So, with my equations saying that mercer's and beckett's have identical red text damage (ignoring crits) when using take aim and steel shot, shouldn't my sword example apply and the damage deviations from these guns be the same? Therefore when killing the same enemy over and over, shouldn't they display the same consistency (or rather inconsistency) in their OH potential?
Now, if we can say that because the red text damage range of the two guns is identical, and that therefore the deviations in damage health damage are too, then we can conclude that, on any given enemy, these guns should have equal chance to kill the enemy in one hit or not. So, outside of critical strike these guns should have equal 'consistency' in OH kills. However, taking into account Mercer's critical strike 3 (which I take as a nice even 10% crit chance after 2000 tests), Mercer's should have shots that will do more damage than beckett's on the same enemy, therefore allowing Mercer's to OH more targets. While critical strikes are, as you say, inconsistent, it is the integral aspect of mercer's that makes it more deadly than beckett's and it should not be ignored.
I recognize that your data did not find mercer's to OH more than beckett's and that's why I implore you to kill a consistently leveled enemy more than 50 times for each gun. With only a 10% chance at criticals, this means that on average only 5 enemies (but possibly more or less) would have gotten a critical hit, and even then it's possible for it to be a low crit or be adjusted lower on the enemies actual health resulting in no OH kill. Due to damage variance we likely won't see exactly 10% more OH with mercer's than beckett's, but in a very large sample size I think it will show that beckett's and mercer's tend to be exactly similar except on the occasion that mercer's gets a favorable crit that translates to health damage for a OH when beckett's could not, translating to slightly more OH kills with mercer's.
View attachment 115110
Here's the reference data to my claim of a 10% at critical strike rank 3, which is that third column. The first and second column were similar tests with rank 1 and rank 2 critical strike, respectively. All tests were done with swords on Timothy Dartan.