Let's examine the case for new encounter powers which produce half-damage on a miss. (These are purportedly being introduced in 4E Essentials). Let's assume the new encounter powers still follow the same damage of the Heinsoo 4E D&D encounter powers, but with the "half-damage on miss" tacked on.
For non-striker encounter powers with half-damage on a miss and a probability p of a hitting a monster of the same level, the average damage per round scales approximately as (after level 10):
0.5(p+1)*[level*(average[W])/7 + 7*(level-10)/20]
So as the level goes to infinity, "R" approaches:
R -> 2*ROLE/{(p+1)*[(average[W])/7 + 7/20]}
For different [W] weapons attacking a skirmisher monster (ROLE=8) with the player having a p=50% of hitting the monster, we have average number of rounds "R" as the level goes to infinity:
average[d12] = 6.5 --> R = 8.34
average[d10] = 5.5 --> R = 9.39
average[d8] = 4.5 --> R = 10.74
average[d6] = 3.5 --> R = 12.55
average[d4] = 2.5 --> R = 15.08
On average, for a player hypothetically repeatedly spamming a new encounter power (with half-damage on a miss) against a skirmisher monster of the same level, the average number of rounds "R" to kill the monster is approximately shorter by 45% compared to at-will powers, as the level goes to infinity.
For completeness, there's at-will powers with half-damage on a miss. (IIRC, there's a few monsters with such an at-will power from the 4E MM2 and/or MM3).
With half-damage on a miss, the at-will with half-damage on a miss reduces the number of rounds R to kill a monster by a factor = p/(1+p) in comparison to ordinary at-will powers. (p is the probability of hitting a monster).
For different p:
p = 100% --> factor = 50%
p = 75% --> factor = 42.6%.
p = 50% --> factor = 33.3%
p = 25% --> factor = 20%
So with a probability 50% of hitting a monster, an at-will power with half-damage on a miss will reduce the number of rounds to kill the monster by 33.3%, in comparison to the same at-will power without the half-damage on a miss part.
