There are basically three components to consider: The impact of a stun (both in granting the party advantage and in denying the monster an action), the likelihood of a stun attempt succeeding, and the number of attempts the monk can make. If we can come to an agreement on how to crunch those numbers, I think that's a fair experiment.
I think that's exactly right.
I will add that, in my belief, Stunning Strike plus base DPR accounts for most of a monk's combat contribution, and if they come up short after taking that into account, I will concede the class is underpowered. I can't speak for anybody else, but that would be enough to convince me.
Yep, I think that's the most reasonable way to look at it.
1. DPR increase to the party from attacking with advantage. The stun lasts until the end of the monk's next turn; a monk making 3 attacks would average 1 attack with advantage on the same turn as the stun, plus 3 attacks on their next turn. Then we have the other PCs; shall we say two PCs using Treantmonk's "warlock with hex" baseline damage and a base 60% chance to hit? (I figure the rest of the party is doing stuff that doesn't involve an attack roll and won't benefit.)
Seems reasonable.
2. The monster's DPR is reduced to zero for the round. We'll need a ratio to convert "monster damage prevented" to an equivalent of "PC damage inflicted." I'm okay with just doing this 1-for-1, but open to suggestions if you think that's not a valid ratio.
I'm not sure if converting damage-prevented to damage inflicted is necessarily the best way to go about it... I think it may be cleaner to go in the other direction, and convert DPR to a scale that measures 'incoming damage prevented', or even just 'excess or reduced monster turns compared to everyone doing a baseline thing'.
Then we have the likelihood of a stun attempt succeeding. For this, I'd go with picking a target CR based on the monk's level (e.g., "monk level plus 2"), then finding the average Con save of monsters with that CR and comparing it to the expected save DC for a monk of that level. I expect that a monk will start with 16 Wisdom and invest in Dexterity first, so the monk's save DCs will be (11 + prof bonus) for most of their career.
I think assuming monk level + 2 is if anything harsh on the monk. Most monsters, outside big arc-capping bosses, are below the party's level, IME.
Finally, number of attempts. The DMG guideline* is ~7 encounters per day, ~2 short rests per day, which means the monk has (level x 3) / 7 ki points per encounter. We should assume the monk will use their ki in the most efficient way; i.e., the only time a monk will ever use ki for something other than Stunning Strike is if that something provides more value to the party than SS. For this calculation, this means we can simply assume all ki is spent on Stunning Strike (no Flurry, no spellcasting, etc.).
In other analyses I've assumed 8 combat rounds per short rest, split between two fights, which I think is fairly reasonable. If we're doing a mid-tier 2 analysis, which I think is probably the level to focus on, it seems fair to suppose that the monk has about 1 ki per turn. I agree that it makes sense to assume that they use those on stun attempts.
Taking all this into account, the monk's "augmented DPR" would be:
Base DPR for a regular attack with Martial Arts
+
(chance to stun) x (DPR equivalent value of successful stun) x (stun attempts per encounter) / (rounds per encounter)
How about, as a first approximation, assuming one stun attempt per round? Likely they would actually bunch them up a bit, toward the first round and when facing high value targets, but since the chance of failing after two attempts is less than twice the chance of failing after one attempt, assuming that they are spread out boosts the number for them to approximate the tactical value of using them intelligently.
