A Mathematical look at Flurry vs. Power Attack vs. Critical Strike

#1spweaselPosted 2/9/2013 5:18:04 PM
*Assume Mainhand stats for Double-Bladed Lightsabers.
*For 2-Lightsabers, M (Mainhand) and O (Offhand) will be used to preface any stat.
*Stats are after all bonuses from Crystals/Buffs, but without any Feat bonuses/penalties.
*Assume Master Speed is active.
*Assume no Nextor/Opila.
*These formulas only apply to Master-Rank Feats.

Let Hit = 21 + Your Attack Bonus - Enemy Defense
Let AWD (Average Weapon Damage) = (Weapon Min Damage + Weapon Max Damage)/2

.....................

If Higher Hand's Hit < 20:

Double-Bladed Lightsaber:
Flurry > Critical Strike if Hit > 11
Flurry > Power Attack if AWD > 40 - 420/(Hit + 7)

2-Lightsabers:
Critical Strike > Flurry if OAWD > 2/3 * MAWD
Critical Strike > Power Attack if (3*MAWD*MHit + OAWD*OHit) > 11*(10*(MHit + OHit/3) - (3*MAWD + OAWD + 40))

.....................

If Lower Hand's Hit >= 23:

Double-Bladed Lightsaber:
Flurry > Critical Strike. Period.
Flurry > Power Attack if AWD > 40

2-Lightsabers:
Critical Strike > Flurry if OAWD > MAWD/2
Critical Strike > Power Attack if (3*MAWD + OAWD)/4 > 35

......................

Yes, there is a gap of about 5 Hit between the 2 groups. At those Hit values, different Feats start hitting the Crit Cap at different times, making the whole thing more complicated than what is worth figuring out mathematically.

Note that due to the minimum Hit rate and how Critical Hits work, these formulas don't hold true for extremely low hit rates, either.
#2spweasel(Topic Creator)Posted 2/9/2013 5:18:26 PM
Analysis:

Power Attack is the clear winner when Crit Capped, since hitting 40 Average damage is unlikely for most players (anti-droid builds can pull it off under ideal conditions). The drawback is that you fall below the Hit Cap sooner and lose damage faster than the other Feats due to that nasty Hit penalty. If you aren't afraid of the Hit penalty (which is often moot by the end-game anyways if you stack Strength), Power Attack is the strongest choice numerically. Soldier/Guardians will benefit the most from it due to their great Base Attack Bonus.

Critical Strike has the highest multiplier and the highest Hit rate, but suffers the inherent faults of 2-Lightsaber builds (lower damage, Crystal limitations). Being able to exploit Opila helps with the lower damage somewhat, but Opila's lower Attack Bonus partly counteracts a major advantage of using Critical Strike in the first place. There are also considerations such as the Stun (+4 Hit, automatic Sneak Attack on subsequent hits) and the ability to use an off-hand utility Saber. Former Scoundrels should definitely use Critical Strike, but any player with questionable Attack can also benefit from it.

Flurry is the middle-of-the-road option. The Hit penalty doesn't hurt as much as Power Attack's and you can use Double-Bladed sabers effectively, but you also have less potential than the other two Feats. The biggest advantage is probably that it is generally the strongest attack to use against the high-defense, crit-immune final boss. It also has the benefit of being somewhat less random than the other choices due to the extra damage roll.

Whether Flurry or Critical Hit is stronger really depends on the specific builds you are comparing. The smaller the difference in damage, the better Critical Strike fares.

Early Game:

Flurry gains a lot of power when Master Speed isn't around, though Power Attack will generally still be stronger if you can get all the hits to land. You need to be careful, though, since either option can absolutely kill your Hit very early on if you are Dual-Wielding. Critical Strike lets you abuse the two Opila you get, which are a lot of damage compared to other non-MotF/HotG Crystals.

Personally, I'd just stick with whatever your class starts with. If nothing else, it makes the three starting classes feel a little more unique.

NPCs (Replace Melee Feats with Ranged Feats as necessary):

Since none of the NPCs like to cast Knight/Master Speed and tend to have questionable Attack Bonuses, Flurry will generally be the preferred Feat all else being equal. It's never completely equal, though.

HK-47 and Juhani have fairly respectable Attack rates but a very limited number of Feats to work with, making their starting Power Attack preferable. Bastila and Mission get few Feats and start with Flurry/Critical Strike, so they will also stick with what they have by necessity more than choice. Canderous, Carth, and Zaalbar can go either Power Attack or Flurry, but save a Feat by going with Power Attack.

Jolee... I'm not sure if I would bother giving him an attack Feat. He'll probably be sticking with a single Lightsaber due to starting with Improved Dueling and having almost no Feats, so I like to finish Dueling off and then take either Implant or Toughness to give him some more survivability.
#3sigma_1932Posted 2/10/2013 6:47:29 PM
[This message was deleted at the request of the original poster]
#4sigma_1932Posted 2/10/2013 7:06:36 PM
First off, you can simplify everything by taking the to-hit value out of the equation because it means jack squat in this game past the very early sections due to low enemy AC's. After you switch to Jedi and get a few levels under your belt, connecting on attacks is pretty much a given even with default AB values.

If you take the to-hit value out of the mix, then critical hits can basically be broken down to a 5% increase to average damage for Double-bladed sabers (or 10% for 2 singles) for Flurry and Power attack, and a 20% (w/ a double) or 40% (w/ 2 singles) increase for Critical Strike (for which you're better off using Opila + a damage crystal, such as Upari, over Nextor's "keen" effect).

That said, I've worked the math out on all three of these at the maximum possible levels on a number of occasions and, even at the extreme top end of the possible damage/swing scale (i.e. all focus is put on increasing raw damage over everything else), the result, IIRC, was that all three modes fall within a 5-10 point range of each other (which would then scale down to a smaller window the more you reduce raw damage ouput).

Even then, for all practical applications, they all reach a point around the midpoint of the game where adding more damage output does nothing but increase margin of overkill... especially given the conditions you presented at the start.

In the end, I mostly agree with your overall conclusion-- they're all pretty much the same in practice.

The only thing I'll add is that Flurry has a distinct advantage in that you only need the first rank to get the full effect (the extra swing is gained on the first rank and doesn't increase-- subsequent ranks just reduce to-hit penalty, which, as I said, can be ignored), where all three ranks of PA and CS are needed to get their full effects (i.e. the damage bonus and threat range multiplier increases with every rank). Even that, though, only opens up two feat slots... or one if you start as Scoundrel/Soldier and just take the first rank of Flurry instead of adding two ranks of their "free" combat mode.
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Forgive him father, for he knows not what ticket he purchases...
Yeah I do... see? Zombies! =^.^=
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Forgive him father, for he knows not what ticket he purchases...
Yeah I do... see? Zombies! =^.^=
#5spweasel(Topic Creator)Posted 2/10/2013 8:21:26 PM
sigma_1932 posted...
First off, you can simplify everything by taking the to-hit value out of the equation because it means jack squat in this game past the very early sections due to low enemy AC's. After you switch to Jedi and get a few levels under your belt, connecting on attacks is pretty much a given even with default AB values.

I don't entirely agree. While this is true for many enemies throughout the game, there are exceptions. The turrets near the final boss, for example, have a respectable 35 defense, while Desert Wraids (who I did quite a bit of my testing against) hit about 26 defense.

If you aren't stacking Strength and/or AB Crystals, it's entirely possible you won't be Hit Capped for them, especially if you are using only Rank 1 Flurry. Just looking at your companions will show how low an unfocused build's AB can get.

Of course, if you aren't focusing on Strength, you aren't really min/maxing to begin with, but hey - it never hurts to look at the math.