This is an analysis of the ranger's "twin strike" power. (We'll ignore the additional complication of hunter's quarry).
We will calculate the average number of rounds "R" it takes to kill a monster (of the same level as the ranger) by being repeatedly twin striked.
We'll assume twin strike is two attacks in one round, where each attack is separately rolled for attack and damage. To make the problem general, we will use the notation:
p1 = to-hit probability of first attack
p1 = to-hit probability of second attack
d1 = damage of first attack
d2 = damage of second attack
The expectation value ED of the twin strike damage in one round is:
ED = p1 p2 (average[d1] + average[d2]) + p1 (1-p2) average[d1] + (1-p1) p2 average [d2] + (1-p1)(1-p2)*0
(EDIT: The first term is when both attacks hit. The second and third terms are when one attack hits and the other misses. The fourth term is when both attacks miss).
Doing the algebra, we get:
ED = p1 average[d1] + p2 average[d2]
(More generally this result can be generalized to any number of attacks. For example, three attacks in one round: ED = p1 average[d1] + p2 average[d2] + p3 average[d3]).
If we assume p1 = p2 = p, and d1 = d2 = d, we have ED = 2p*average[d].
For twin strike, the damage is d = [W] + magic enhancement for each attack.
The magic enhancement scales approximately as level/5, assuming the progression on page 225 of the 4E PHB1.
For the sake of argument, we will look at the case where the weapon damage dice per attack remains [W] for all levels to infinity. (ie. Weapon damage does not change to 2[W] per attack at level 21).
Hence the damage scales approximately as:
average[d] = average[W] + level/5
and ED = 2p*(average[W] + level/5)
Now the average number of rounds "R" to kill a monster by a player of the same level is:
R = [ROLE*(level+1) + CON]/(2p*[average[W]+ level/5])
As the level goes to infinity, R approaches
R -> 5*ROLE/2p = 2.5*ROLE/p.
Recall from the previous post that a similar result for generic at-will powers having weapon dice damage [W] for all levels to infinity was:
R -> N/p -> 20*ROLE/7p = 2.86*ROLE/p.
So even without the stat mod added to the damage to twin strike, the scaling limit for R is slightly better than for generic at-will powers as the level goes to infinity.
If the same analysis is done again for twin-strike, but adding in an egregious assumption where the weapon dice damage per attack increases with level in the form:
level 21 - 30 --> 2[W] per attack
level 31 - 40 --> 3[W] per attack
level 41 - 50 --> 4[W] per attack
etc ...
We will assume the magic enhancement scales approximately as level/5.
Hence the damage per attack scales approximately as:
average[damage] = (level/10)*average[W] + level/5
The expectation value of the damage per round for twin strike with these egregious assumptions is:
ED = 2p*[(level/10)*average[W] + level/5]
Now the average number of rounds "R" to kill a monster by a player of the same level is:
R = [ROLE*(level+1) + CON]/(2p*[(level/10)*(average[W]) + level/5])
As the level goes to infinity, R approaches
R -> ROLE/[2p*( (average[W])/10 + 1/5)].
Plugging in some numbers for a ranger twin striking a skirmisher (ROLE=8), the weapon dice [W] for ranger weapons could be d6, d8 or d10.
average[d6] = 3.5 --> N = 7.27
average[d8] = 4.5 --> N = 6.15
average[d10] = 5.5 --> N = 5.33
(We used R = N/p to get N = average number of hits to kill monster).
In the end twin-strike is also "always fighting orcs" as the level scales to infinity.
