Wednesday, August 25, 2010

Scaling of 4E encounter powers.

Let's examine the scaling behavior of the encounter and daily powers, in the unrealistic scenario where they can be repeatedly spammed every round. We will calculate the average number of rounds "R" to kill a monster by a player of the same level.

Recall that a non-striker repeatedly using at-will powers against a monster of the same level, "R" approaches the limit

R = N/p -> N -> ROLE/{p*[(average[W])/10 + 7/20]}

as the level goes to infinity.

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 --> N = 8, R = 16
average[d10] = 5.5 --> N = 8.89, R = 17.78
average[d8] = 4.5 --> N = 10, R = 20
average[d6] = 3.5 --> N = 11.43, R = 22.86
average[d4] = 2.5 --> N = 13.33, R = 26.66


For non-striker encounter powers, the average damage per hit scales approximately as (after level 10):

level*(average[W])/7 + 7*(level-10)/20.

So for non-striker encounter powers, the average damage per round scales approximately as (after level 10):

p*[level*(average[W])/7 + 7*(level-10)/20].

So as the level goes to infinity, "R" approaches:

R -> N/p = ROLE/{p*[(average[W])/7 + 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 = 12.51
average[d10] = 5.5 --> R = 14.01
average[d8] = 4.5 --> R = 16.12
average[d6] = 3.5 --> R = 18.82
average[d4] = 2.5 --> R = 22.63

On average, for a player hypothetically repeatedly spamming an encounter power against a skirmisher monster of the same level, the average number of rounds "R" to kill the monster is shorter by approximately 4 rounds (compared to at-will powers) as the level goes to infinity. (For a 50% probability of hitting the monster, this would mean that it takes approximately 2 less hits to kill the skirmisher monster).

More generally, a hypothetical spammed encounter power takes approximately 15% to 20% less rounds to kill a monster (of the same level).