Let's do the same for daily powers, where the the daily powers have half-damage on a miss.
Recall for half-damage on a miss: R = 2N/(1+p).
For a daily power, the average damage per hit scales approximately as (after level 10):
level*(average[W])/5 + 7*(level-10)/20.
For the easy case where the daily powers of non-strikers always miss, "R" approaches
R -> 2*ROLE/{p*[(average[W])/5 + 7/20]} = ROLE/{p*[(average[W])/10 + 7/40]}
as the level goes to infinity.
Comparing this to the expression "R" for at-wills, it means that daily powers always missing and producing half-damage, is slightly worse than generic daily powers.
For non-striker daily 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])/5 + 7*(level-10)/20]
So as the level goes to infinity, "R" approaches:
R -> 2*ROLE/{(p+1)*[(average[W])/5 + 7/20]}
For different [W] weapons attacking this 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 = 6.46
average[d10] = 5.5 --> R = 7.36
average[d8] = 4.5 --> R = 8.53
average[d6] = 3.5 --> R = 10.16
average[d4] = 2.5 --> R = 12.55
On average, for a player hypothetically repeatedly spamming a daily 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 a half compared to at-will powers, as the level goes to infinity.
This means a repeatedly "spammed" daily power (with half damage on a miss) attacking a skirmisher (of the same level), is on average damage-wise approximately equal to two at-wills in general. If the daily power always misses and always produces half damage, it is damage-wise approximately equal to one at-will power.
