Ok, I've been able to replicate the base idea lynn is asserting. I'm posting this to help explain the overall effects.
Simplified conditions (no kicks, 95% acc, 5% DA)
For a given amount of HP remaining, n hits are required on average based on average damage per hit (standard model with cRatio, crits, etc).
For the n hits needed to kill the mob, r rounds are required on average. Same principle as the weaponskill TP model.
Given that, how does the average number of rounds needed vary based on mob HP and player attack?
In general, for varying mob HP, the number of rounds changes in increments roughly matching the average damage per hit (as might be expected). If average damage per hit is 100, about every 100 mob HP (mob HP can vary based on mob type/level/outside sources of damage/etc) will have a different average number of rounds required.
For player attack, there are a number of factors that determine the extent of the scaling (eg: crit rate, level correction, etc). In general, however, changing attack can be considered a 'shift' in perceived mob HP for the purposes of calculating average number of rounds needed. That shift appears to be approximately 5 to 8 HP per 1 point of attack for a few common variances (higher effectiveness with lower crit rates; 8 HP was at 10% crit rate, 5 HP was at 54% crit rate), and drops with higher attack values (got down to 4 HP at near capped attack).
So, for example:
Level Correction: 0.25
Crit rate: 54%
Crit damage: +30%
Base damage + fStr: 79
cRatio of 1.121
Avg damage per hit of 158.403
A mob with 3009 HP will take an average of 9.802 rounds to kill
A mob with 3010 HP will take an average of 10.293 rounds to kill
A mob with 3169 HP will take an average of 10.803 rounds to kill
You'll note that there's a gap of about 159 damage where the average number of rounds remains constant (3010 HP to 3168 HP), which matches the average damage per hit.
Now, add 1 point of attack. Total attack of 481, avg damage per hit of 158.665. The mob now needs 3015 HP for it to take an average of 10.293 rounds to kill, and the HP range of 3010-3014 which used to take 10.293 rounds now takes 9.802 rounds.
5 HP out of 159 is about 3%, so adding 1 attack gives about a 3% chance of dropping about half an attack round on average, and out of 10 rounds has an average fight time reduction of 0.14%. Compare that with the .165% increase in cRatio due to the added attack.
Edit: The value scales with the HP of the mob such that you always get fairly comparable total reduction in average fight time.
For most purposes, mob HP has to be treated as infinitely variable. Other DDs doing damage to the mob (melee or nukers), DOT spells such as Dia, counters/Perfect Counters, level variation (can have a dramatic effect inside Abyssea, though a somewhat more limited impact outside), job variation (eg: different types of Mamool Ja or Dynamis mobs), weaponskills (as we're only looking at the melee side), mobs healing themselves and so on and so forth all mean that we can never expect the target amount of damage done to always stay within a predetermined range. That means there's always a chance for that shift in HP to have an impact in average number of rounds to kill.
Overall: Yes, lynn is correct in that adding 1 attack will often have no impact on average fight length. He is incorrect, however, in asserting that it will *never* have an impact, and that very large changes in attack are necessary in order to manifest any difference in fight length. This is because he was looking at a fixed value for HP rather than considering the variability of it, or the 'jitter' as milich notes.
Higher starting attack and crit rate and more crit damage (as we have in Abyssea) all dampen the value of additional attack, but never negate it entirely (until attack is capped, of course).
It was interesting to look at the value of attack from a different perspective, but I'm going to maintain my current methodology for DPS calculation.
Edited, Dec 6th 2010 11:11am by Kinematics