Aggressor and double attack merits

After meriting on greater colibri for a bit, I was wondering whether I would be "better off" had I merited double attack to level 5 instead of Aggressor recast. (Unsynchronized Berserk and Aggressor timers would be really annoying though.) This May 2007 discussion comparing Aggressor and double attack merits shows, despite the muddled presentation, a situation where fully merited double attack is more effective than fully merited Aggressor recast, since Aggressor supposedly provides an accuracy bonus of 25, which corresponds to only a 12.5% hit rate increase (on average). However, we might be interested in the magnitude of difference between the two Group 1 schemes, which is more difficult to quantify.

One approach is to calculate the average number of attack rounds to reach 100 TP for both 5 DA/0 Aggressor and 0 DA/5 Aggressor. (The number of attack rounds is independent of specific damage values.) Of course, the relative effectiveness of Aggressor is higher when your hit rate is lower, as is usually the case when targeting anything more difficult than greater colibri. Then it might be useful to compare max DA and max Aggressor for lower levels of a baseline hit rate.

Ultimately we want to know what the differences in long-run "damage over time" are, but first we can look at the average number of attack rounds, as that is an indirect measure of time. (Assume number of seconds per attack round is constant.) Unfortunately, an analytic expression of the average number of attack rounds to reach 100 TP is too annoying to derive primarily because the number of attack rounds needed to reach 100 TP depends on the TP return of the previous weapon skill, which is almost never zero for a multi-hit weapon skill with a decent hit rate. The number of hits to 100, given initial TP, seems basically to follow a Poisson process, but I'd rather not worry about cumbersome calculations. Therefore, I resorted to simulation to generate the following approximate values based on my warrior setup (varying the Group 1 merit configurations, obviously), given baseline hit rate and the use of a 3-hit weapon skill (Raging Rush or King's Justice):

Average number of attack rounds given baseline hit rate

       5/0   2/4   0/5
0.2   20.19 19.81 19.87
0.3   14.60 14.52 14.61
0.4   11.40 11.39 11.47
0.5    9.31  9.33  9.41
0.6    7.83  7.86  7.95
0.7    6.73  6.78  6.84
0.75   6.29  6.33  6.39
0.8    5.88  5.93  5.99
0.825  5.71  5.74  5.81

Here, the first column corresponds to baseline hit rate (before the Aggressor bonus), and the next three columns correspond to different Group 1 merit configurations:

"5/0": 5 double attack, 0 Aggressor
"2/4": 2 double attack, 4 Aggressor (mine)
"0/5": 0 double attack, 5 Aggressor

Then, we can obtain values representing "damage over time" in terms of hits per round, given the baseline (or nominal) hit rate:

Average number of hits per round given baseline hit rate

       5/0   2/4   0/5
0.2   0.336 0.341 0.340
0.3   0.458 0.460 0.456
0.4   0.580 0.579 0.573
0.5   0.702 0.698 0.691
0.6   0.819 0.818 0.811
0.7   0.946 0.935 0.925
0.75  1.006 0.996 0.983
0.8   1.069 1.054 1.041
0.825 1.097 1.085 1.071

The max DA configuration is already about even with max Aggressor at 30% baseline hit rate, and it really starts to pull away as the baseline hit rate increases (especially after the point where Aggressor does not provide the full accuracy bonus, past 82.5% hit rate), so to me there is scant justification for 5/5 Aggressor. This makes sense as fully merited Aggressor provides an average 1.5% hit rate increase over non-merited Aggressor, which pales in comparison to the increase in "damage over time" that can be conferred by 5 double attack in the presence of high levels of accuracy. This analysis doesn't account for multi-hit weapons such as Ridill and Joyeuse, but the relative differences between 5/0 and 0/5 should still favor 5 DA merits even though the gap may close. And of course, this post doesn't account for actual damage per hit, but DA and hit rate are "independent" of damage per hit anyway (hits/time × damage/hit = damage/time!) and it's not that much of a reach to estimate real "damage over time" by factoring in an average damage per hit.

I found it helpful to plot attack rounds vs. hit rate to illustrate that the average number of attack rounds to 100 TP levels off as hit rate increases:



Obviously the rate of change in the number of attack rounds to 100 TP is decreasing in magnitude (but is still negative) with hit rate. But the number of attack rounds is not a direct measure of damage over time. Damage over time is a ratio of, yes, damage over time. The number of attack rounds is a proxy for time, and is not a ratio.

The number of hits, given the number of attack rounds, on the other hand, is a measure of damage, so dividing the number of hits by the number of attack rounds gives a quantity that can stand in for "damage over time," as plotted below vs. nominal hit rate:



Of course, there is no reason to plot such a thing because intuitively the rate of change of hits/round must be constant (we're plotting hit rate vs. hit rate!), especially if you believe that 2 points of accuracy always corresponds to 1% hit rate between 20% hit rate and 95% hit rate. If you do, it's complete nonsense to speak of damage over time showing "diminishing returns" to hit rate. Hit rate leveling off with accuracy in some logistic fashion is another story though.