To get the average number of rounds to kill a monster (including the attacks which missed) by a player of the same level as the monster, it turns out it is related to "N". Let's call this average number of rounds to kill a monster, as "R".
We won't include stuff like critical hits, attacks with half-damage on a miss, and other stuff which I haven't thought of yet. With that being said, it turns out the average number of rounds "R" to kill a monster for a player with probability p of hitting the monster, is:
R = N/p
To get this result, this is from the geometric probability distribution. A geometric probability distribution model includes the hits and misses when a player attacks a monster.
More generally, "R" is the ratio:
(hit points of monster)/(expectation value of damage per round).
Let's call
H = hit points of monster
ED = expected value of damage per round.
So R = H/ED.
Let's assume a player has a probability p of hitting a monster.
For an at-will power with weapon damage dice [W] at lower levels, the expectation value of the damage for one round is:
p*average[W + stat mod + magic enhancement] + (1-p)*0
which is simply: ED = p*average[W + stat mod + magic enhancement]
For a hypothetical at-will which does half damage on a miss, the expectation value of the damage for one round is:
p*average[W + stat mod + magic enhancement] + 0.5*(1-p)*average[W + stat mod + magic enhancement]
which is simply: ED = 0.5 (1+p)*average[W + stat mod + magic enhancement].
If every at-will power had "half damage on a miss", then "R" would be:
R = 2N/(1+p)
If one includes critical hits to an at-will power with weapon damage dice [W] at lower levels, the expectation value of the damage for one round is:
ED = (p-0.05)*average[W + stat mod + magic enhancement] + (0.05)*(maximum[W + stat mod + magic enhancement] + average[criticalextra]).
("criticalextra" is the extra damage dice from magic weapons on a critical).
As one can see, incorporating "half-damage on a miss" or "critical hits", can make the equations look a lot messier. They don't fit into a nice form like R = N/p.
