#### Esker

##### Hero

I was curious how often you would expect to waste superiority dice using your method, so I did a simulation, where I assumed exactly 20 attack rolls between short rests (itself an optimistic assumption, since if rests happen unevenly in the 20 round day, you'll either waste more dice or be forced to use them more aggressively than when the success rate is 80%). Taking a four number range (it doesn't really matter which four, since the probabilities are uniform, and so this generalizes to any enemy AC as long as you're not too close to the floor or ceiling), and counting how many of the 20 rolls fall in that range, obviously the average result is 1/5, or 4, which is ideal for this strategy. But 41% of the time it's less than 4, in which case you wind up wasting one of your dice. And 20% of the time you waste 2. 6% of the time you waste 3.

So, in the spirit of wildly excessive precision and intellectual masturbation, let's actually calculate the expected number of misses you turn into hits per 20 round short rest using this strategy. Taking the "use a die when the result is within 4" strategy, you can expect each rolled die to have an 81.25% chance of turning a miss into a hit. 59% of the time you use all four and wind up with 3.25 misses converted. 21% of the time you only use 3 and wind up with 2.4375 conversions. 14% of the time, you use two, and net 1.625 conversions. And 5% of the time you use only one, getting 0.8125 conversions.

On average, then, you get about 2.7 extra hits per 20 attacks assuming evenly spaced short rests. If the rests are unevenly spaced, the gain is capped at 3.25 during the long stretches, but will go down during the short stretches. So it may be a little lower than that overall. You may be able to find a less stringent threshold for "near miss" that gives you a better result by shifting the average number of near misses above 4 so that the chances of wasting dice goes down*, but that was my point about rolls not being uniformly distributed. But as I speculated, it doesn't make a huge difference (maybe 1.5 DPR or something; pretty close to the approximation error from assuming the rogue always has advantage).

EDIT: I checked; it turns out you do minisculely better by using your dice when you're within 5 rather than within 4, by like 2 total damage throughout the day. And using then when you're within 6 is only minisculely worse than within 4 (by about the same margin).

So, in the spirit of wildly excessive precision and intellectual masturbation, let's actually calculate the expected number of misses you turn into hits per 20 round short rest using this strategy. Taking the "use a die when the result is within 4" strategy, you can expect each rolled die to have an 81.25% chance of turning a miss into a hit. 59% of the time you use all four and wind up with 3.25 misses converted. 21% of the time you only use 3 and wind up with 2.4375 conversions. 14% of the time, you use two, and net 1.625 conversions. And 5% of the time you use only one, getting 0.8125 conversions.

On average, then, you get about 2.7 extra hits per 20 attacks assuming evenly spaced short rests. If the rests are unevenly spaced, the gain is capped at 3.25 during the long stretches, but will go down during the short stretches. So it may be a little lower than that overall. You may be able to find a less stringent threshold for "near miss" that gives you a better result by shifting the average number of near misses above 4 so that the chances of wasting dice goes down*, but that was my point about rolls not being uniformly distributed. But as I speculated, it doesn't make a huge difference (maybe 1.5 DPR or something; pretty close to the approximation error from assuming the rogue always has advantage).

EDIT: I checked; it turns out you do minisculely better by using your dice when you're within 5 rather than within 4, by like 2 total damage throughout the day. And using then when you're within 6 is only minisculely worse than within 4 (by about the same margin).

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