Combat Mechanics? Attack Speed, Recovery

[Daemonjax]

@kmbogd 

 

Good ideas.  

 

@Akos 

 

I don't think anyone would disagree that flat damage increases benefit faster attacks more than slow attacks. There's just not many sources of flat damage bonuses in this game compared to other RPGs.  The only thing that comes to mind is DR reduction from stilettos (drawback: must use stilettos) and the DR reduction from a talent choice (drawbacks: costs a talent and lowers attack speed).  IMO any penalty on a talent is ridiculous.

 

I plan to wait until after patch 1.03 (there will probably be some code changes they're not going to advertise) before doing a frame by frame analysis with all weapons with both a dex 10 and dex 20 character. Since nothing affects animation frames except dexterity, that should help me to determine what's what.  It's possible there are frames during the attack which are not affected by any attack speed modifiers (aka a global cooldown).

Edited April 3, 2015 by Daemonjax

[hugin7]

Great work, guys.  I was about to spend hours on collecting data via Fraps and you saved me a lot of trouble .

 

I updated the spreadsheet at the following link:

 

https://docs.google.com/spreadsheets/d/1vDm5MOrCK6S95h5u0EzZbGTv_u_rYqjuO0-zupqk0_A/edit#gid=292500223

 

My changes include the following:

 

1.  Fix issue with "Total damage mod" column (M).  Average accuracy mod is a multiplicative modifier for total damage.

2.  Added support for "To Hit Mod," "Damage Reduction Debuff," and Quick Switch weapon cycling - first cycle, as well as subsequent iterations through weapon slots.

3.  See top-left corner for documentation of new features.

 

Note that the Quick Switch calculations still need verification through Fraps.  My conjectures based on rough stopwatch timings seem to be consistent with the derived formulas, but I would be grateful to anyone who gets around to testing with Fraps before me.  Keep in mind that the timing of your weapon switching will introduce variation in this trick's effectiveness.

 

Kudos for Myrten for adding support for DR normal distribution.  For those who played the entire game, does the default setting of average DR of 10 and standard deviation of 5 seem reasonable for PotD difficulty?

 

Please keep the enhancements and fixes rolling.

[AlphaMagnum]

MATH

 

The problem is basically EVERY modifier is percentage-based. Weapon enchants deal a percentage of your final weapon damage. Every skill and ability adds a percentage along with Might.

 

Strictly speaking, my rough calculations suggest that DR penetration and enemy DR are the tipping points. If effective enemy DR (DR Bypass - Enemy DR) = 0, fast dual wield weapons are better. If you have un-bypassed DR remaining, 2H weapons eventually become superior because the flat subtraction represents a smaller loss of their raw damage per hit.

 

The exact value of enemy DR for which this is the case is unclear and would require precise damage calculation.

 

Other details to keep in mind are that independent of attack speed, different classes have "instant-cast" abilities that may attack with one or both equipped weapons. These are not normalized for speed and hence 2H weapons with lots of encounter abilities have an intangible advantage that isn't well-suited to calculation.

[Myrten]

1.  Fix issue with "Total damage mod" column (M).  Average accuracy mod is a multiplicative modifier for total damage.

Actually it's additive and then multiplicative. So if you have 1.5 damage mod on your character and you graze then you multiply your damage by (0.5+0.5) so it's 100% base damage, in case of crits it's (1.5 + 0.5) which is 200% damage.

 

I'll change it so damage mod is expressed as 1.x instead of 0.x to make it more natural.

 

Kudos for Myrten for adding support for DR normal distribution.  For those who played the entire game, does the default setting of average DR of 10 and standard deviation of 5 seem reasonable for PotD difficulty?

I completed entire game and I'd say 10 +-5 DR is what you should you prepare your party for - extremes below\above that range are rare. 10 might seem a bit high, but I've made a party with blunderbusses assuming lower DR values and it was underperforming even with penetrating shot.

Please keep the enhancements and fixes rolling.

It would be nice if someone could collect data for different melee weapons because they got bonuses like +5 accuracy or ignore 5 DR and this could change things a bit - especially 2h vs dual comparison. Edited April 3, 2015 by Myrten

[hugin7]

 

1.  Fix issue with "Total damage mod" column (M).  Average accuracy mod is a multiplicative modifier for total damage.

Actually it's additive and then multiplicative. So if you have 1.5 damage mod on your character and you graze then you multiply your damage by (0.5+0.5) so it's 100% base damage, in case of crits it's (1.5 + 0.5) which is 200% damage.

 

I'll change it so damage mod is expressed as 1.x instead of 0.x to make it more natural.

 

 

Sorry, I see what happened - I noticed the Total damage mod issue when I first opened the spreadsheet and took Avg Accuracy Mod to be the weighted probability to hit, so I used it as a multiplier to total damage.  This is indeed incorrect.  However, the formula I replaced still seems a bit off.  Consider the following example:

 

Miss - 5

Graze - 35

Hit - 50

Crit - 10

 

Avg Acc Modifier = (35 * 0.5 + 50 * 1 + 10 * 1.5)/100 = 0.825

 

Now let's add a damage mod of 0.5:

 

Avg Acc Modifier = (35 * 1 + 50 * 1.5 + 10 * 2)/100 = 1.3

 

My new formula produces 1.24, while the one that was in place before my changes resulted in 1.33, so it appears that both formulas are incorrect.

 

I'm out of time tonight, but I'll check the thread/doc tomorrow and might have time to fix this if it's not taken care of by then.

[hugin7]

 

I completed entire game and I'd say 10 +-5 DR is what you should you prepare your party for - extremes below\above that range are rare. 10 might seem a bit high, but I've made a party with blunderbusses assuming lower DR values and it was underperforming even with penetrating shot.

 

 

Was this on PotD difficulty?  I wonder if game difficulty has a dramatic impact on the range of DR.

[Myrten]

 

I completed entire game and I'd say 10 +-5 DR is what you should you prepare your party for - extremes below\above that range are rare. 10 might seem a bit high, but I've made a party with blunderbusses assuming lower DR values and it was underperforming even with penetrating shot.

 

Was this on PotD difficulty?  I wonder if game difficulty has a dramatic impact on the range of DR.

 

No, on hard, I'm not sure about POTD, but if I were to play it I'd change average DR to at least 12.

[Myrten]

 

 

1.  Fix issue with "Total damage mod" column (M).  Average accuracy mod is a multiplicative modifier for total damage.

Actually it's additive and then multiplicative. So if you have 1.5 damage mod on your character and you graze then you multiply your damage by (0.5+0.5) so it's 100% base damage, in case of crits it's (1.5 + 0.5) which is 200% damage.

 

I'll change it so damage mod is expressed as 1.x instead of 0.x to make it more natural.

 

 

Sorry, I see what happened - I noticed the Total damage mod issue when I first opened the spreadsheet and took Avg Accuracy Mod to be the weighted probability to hit, so I used it as a multiplier to total damage.  This is indeed incorrect.  However, the formula I replaced still seems a bit off.  Consider the following example:

 

Miss - 5

Graze - 35

Hit - 50

Crit - 10

 

Avg Acc Modifier = (35 * 0.5 + 50 * 1 + 10 * 1.5)/100 = 0.825

 

Now let's add a damage mod of 0.5:

 

Avg Acc Modifier = (35 * 1 + 50 * 1.5 + 10 * 2)/100 = 1.3

 

My new formula produces 1.24, while the one that was in place before my changes resulted in 1.33, so it appears that both formulas are incorrect.

 

I'm out of time tonight, but I'll check the thread/doc tomorrow and might have time to fix this if it's not taken care of by then.

 

This is because calculation is more complicated and damage mod would have to be combined into accuracy table for everything to be 100% accurate. That's why it's called AVERAGE accuracy mod We might change it to 100% accurate version though

 

For instance 1.5 damage mod changes following when compared to 1.0 damage mod

Graze damage is multiplied by 2x

Hit damge is is multiplied by 1.5x

Crit damage is multiplied by 1.33x

 

So in this particular case total damage would actually be increased by 1.57 instead of 1.5.

[AlphaMagnum]

My tests indicate the following:

 

1) EVERYTHING is additive, then multiplicative.

 

I tested Might, Reckless Assault modal, Savage Attack modal, "Superb" quality weapons, and Critical Hits.  I have no reason to believe that Sneak Attacks are any different.

 

2) "XX Lash" Weapon Enchantments work a little strangely.

 

Their base damage is calculated as 25% of final damage pre-DR (as defined in point 1 above). 

They ignore DR Bypass but only deal with 25% of the enemy's base DR in the appropriate element.

 

Example:

 

Rogue 10 damage piercing weapon.  20 Might, Reckless Assault, Savage Attack, Superb weapon, and a Crit.  Corrosive Lash enchant. 5 DR Bypass.

Enemy Pierce DR = 20.  Enemy Corrosive DR = 16.

 

Base (Pre-DR) Piercing Damage         = 10 * (100% base + 30% from Might + 20% Reckless Assault + 20% Savage Attack + 45% Superb Weapon + 50% Crit)

= 10 * (265%)

= 26.5 Damage

Base (Pre-DR) Corrosive Damage       = (Base Physical Damage) * 25%

                                                              = (26.5) * 25%

                                                              = 6.63 Damage

Final Piercing Damage = (Base Pierce Damage) - (Enemy Pierce DR - DR Bypass)

                                      = (26.5) - (20 - 5)

                                      = 26.5 - 15

                                      = 11.5 Piercing Damage

Final Corrosive Dmg     = (Base Corrosive Damage) - (Enemy Corrosive DR * 0.25)

                                      = (6.63) - (16 * 0.25)

                                      = 6.63 - 4

                                      = 2.63 = 2.6 Corrosive Damage

Final Damage = 11.5 Piercing + 2.6 Corrosive Damage (combat log will say 14.1 Piercing Damage unless you hover over it to see this breakdown)

 

EDIT - I'm currently fiddling with a spreadsheet that incorporates all of this information.  The only wrinkle is that I'm not fully sure as to how attack animation frames and recovery animation frames are modified to determine attack speed.  If someone could point me to definitive information on this subject, I would be very thankful.

Edited April 3, 2015 by AlphaMagnum

[Myrten]

My tests indicate the following:

 

1) EVERYTHING is additive, then multiplicative.

 

I tested Might, Reckless Assault modal, Savage Attack modal, "Superb" quality weapons, and Critical Hits.  I have no reason to believe that Sneak Attacks are any different.

 

2) "XX Lash" Weapon Enchantments work a little strangely.

 

Their base damage is calculated as 25% of final damage pre-DR (as defined in point 1 above). 

They ignore DR Bypass but only deal with 25% of the enemy's base DR in the appropriate element.

 

Example:

 

Rogue 10 damage piercing weapon.  20 Might, Reckless Assault, Savage Attack, Superb weapon, and a Crit.  Corrosive Lash enchant. 5 DR Bypass.

Enemy Pierce DR = 20.  Enemy Corrosive DR = 16.

 

Base (Pre-DR) Piercing Damage         = 10 * (100% base + 30% from Might + 20% Reckless Assault + 20% Savage Attack + 45% Superb Weapon + 50% Crit)

= 10 * (265%)

= 26.5 Damage

Base (Pre-DR) Corrosive Damage       = (Base Physical Damage) * 25%

                                                              = (26.5) * 25%

                                                              = 6.63 Damage

Final Piercing Damage = (Base Pierce Damage) - (Enemy Pierce DR - DR Bypass)

                                      = (26.5) - (20 - 5)

                                      = 26.5 - 15

                                      = 11.5 Piercing Damage

Final Corrosive Dmg     = (Base Corrosive Damage) - (Enemy Corrosive DR * 0.25)

                                      = (6.63) - (16 * 0.25)

                                      = 6.63 - 4

                                      = 2.63 = 2.6 Corrosive Damage

Final Damage = 11.5 Piercing + 2.6 Corrosive Damage (combat log will say 14.1 Piercing Damage unless you hover over it to see this breakdown)

 

EDIT - I'm currently fiddling with a spreadsheet that incorporates all of this information.  The only wrinkle is that I'm not fully sure as to how attack animation frames and recovery animation frames are modified to determine attack speed.  If someone could point me to definitive information on this subject, I would be very thankful.

 

Thanks for the info on how weapon elemental enchants work.

 

Check our colaborative spreadsheet: https://docs.google.com/spreadsheets/d/1vDm5MOrCK6S95h5u0EzZbGTv_u_rYqjuO0-zupqk0_A/edit#gid=292500223 (but please download it and make changes on your copy unless you want to add\fix something)

 

I'll add your info to the spreadsheet tomorrow, if you got time could you also check how chanter's lvl 3 fire damage chant really work?

[AlphaMagnum]

It also appears as if using Savage Attack is strictly superior to not using Savage Attack, regardless of Accuracy or enemy DR.  Tested at -10, 0, and +10 Accuracy differentials between our Accuracy and enemy Deflection, and at enemy DR = 8 as well as enemy DR = 22.  In all combinations, the 20% damage bonus was worth more DPS than the 5 Accuracy you trade.

[Myrten]

It also appears as if using Savage Attack is strictly superior to not using Savage Attack, regardless of Accuracy or enemy DR.  Tested at -10, 0, and +10 Accuracy differentials between our Accuracy and enemy Deflection, and at enemy DR = 8 as well as enemy DR = 22.  In all combinations, the 20% damage bonus was worth more DPS than the 5 Accuracy you trade.

Savage Attack according to our spreadsheet is like 22-26% more DPS - the lower your accuracy the bigger DPS increase you get from damage modifier bonus.

[Baki]

 

 

 

@Myrten:

 

https://docs.google.com/spreadsheets/d/1MO3U4gv7VPQtfHwPNy_MKPZl_3wJow34QTARLH8ILLI/edit?usp=sharing

I've made some changes to make it more clear and closer to game mechanics :

 

https://docs.google.com/spreadsheets/d/1vDm5MOrCK6S95h5u0EzZbGTv_u_rYqjuO0-zupqk0_A/edit?usp=sharing

 

 

explain the speed mods please.

 

In game increasing speed - for example doubling reload speed is described as "Reload Speed x2", or bonus to ranged speed is "Ranged attack speed x1.25"

 

To make it closer to in-game descriptions I've modified the spreadsheet so that frames are divided by matching speed modifier. It also works great for recovery time - if you take Plate Armor's -50% recovery time just write 0.5 in recovery mod and recovery frames will be doubles as in game.

 

 

please explain this then:

 

Crossbow Speed without modifiers is

Attack: 53

Recovery: 76

Reload: 101

 

Now i used a buffed Chanter.

Dex: 30% -> Attack+Recovery+Reload?

Penetrating Shot: -20% Recovery

Chant: x1.2 Rate of fire, x2 reload Speed

Armor: -50% Recovery

 

Test Results:

Attack: 40

Recovery: 89

Reload: 41

 

i also thought i knew how it worked but i just cannot explain these test results. i've triple checked the frames, the test is accurate.

 

with only 1 modifier it works pretty well. as soon as we get multiple modifiers i cant explain the results.

Edited April 3, 2015 by Baki

[Myrten]

please explain this then:

 

Crossbow Speed without modifiers is

Attack: 53

Recovery: 76

Reload: 101

 

Now i used a buffed Chanter.

Dex: 30% -> Attack+Recovery+Reload?

Penetrating Shot: -20% Recovery

Chant: x1.2 Rate of fire, x2 reload Speed

Armor: -50% Recovery

 

Test Results:

Attack: 40

Recovery: 89

Reload: 41

 

i also thought i knew how it worked but i just cannot explain these test results. i've triple checked the frames, the test is accurate.

 

with only 1 modifier it works pretty well. as soon as we get multiple modifiers i cant explain the results.

I'm afraid we would need to check multiple combinations to have some conclusive results:

 

Can you check the following:

 

Only dex

Only armor

Only reload chant

Only penetrating shot

[Myrten]

Some updates to spreadsheet:

 

https://docs.google.com/spreadsheets/d/1vDm5MOrCK6S95h5u0EzZbGTv_u_rYqjuO0-zupqk0_A/edit#gid=292500223

 

- 20% min damage included (not my work so kudos to the person who did this )

- accuracy and damage mod is now 100% correct

- elemental bonus on weapons is also included

[hugin7]

Some updates to spreadsheet:

 

https://docs.google.com/spreadsheets/d/1vDm5MOrCK6S95h5u0EzZbGTv_u_rYqjuO0-zupqk0_A/edit#gid=292500223

 

- 20% min damage included (not my work so kudos to the person who did this )

- accuracy and damage mod is now 100% correct

- elemental bonus on weapons is also included

 

Sorry, I forgot to mention the minimum damage fix that I added.  Also, thanks for correcting the accuracy table.

Edited April 3, 2015 by hugin7

[Baki]

created a new char to do the tests. female human chanter

 

1st try, base stats, no mods

AT 48

REC 75

REL 98

 

2nd try, base stats, no mods

AT 52

REC 75

REL 98

 

third try, base stats, no mods

AT 53

REC 74

REL 98

 

fourth try, base stats, no mods

AT 52

REC 75

REL 98

 

i don't now why but the attack speeds seem to vary. doesnt make much sense to go any further. i won't do 10+ tests every time to get an average.

Edited April 3, 2015 by Baki

[Myrten]

created a new char to do the tests. female human chanter

 

1st try, base stats, no mods

AT 48

REC 75

REL 98

 

2nd try, base stats, no mods

AT 52

REC 75

REL 98

 

third try, base stats, no mods

AT 53

REC 74

REL 98

 

fourth try, base stats, no mods

AT 52

REC 75

REL 98

 

i don't now why but the attack speeds seem to vary. doesnt make much sense to go any further. i won't do 10+ tests every time to get an average.

This is weird - maybe the way in which you measure it is innacurate. Anyways we don't have to be 100% correct here, +-5 frames error margin is absolutely fine for me.

[Baki]

the only thing i could think of that might cause this is fraps or virtual dub.

[lionspaw]

Assuming the attack speed formulas here are correct, it seems like DW edges out 2 Hander on 0 effective DR targets on an optimized rogue.

 

Take stiletto versus Estoc on a melee rogue. 

 

Stiletto's base average damage is 10, Estoc's base average damage is 17. 

 

rogues have a 2.5 damage multiplier with Deathblow + Reckless Assault + Might bonus self buffed. 

 

so 25 versus 42.5 per hit pre-DR. let's assume DR is perfectly cancels by each weapon here for simplification of calculations, so we effectively get +3 and +5 damage, 28 vs. 47.5.

 

Assume rogue specs into two weapon style and two handed style, the damage becomes 28 vs. 50.55.

 

Now, let's look at attack speed (with two weapon style talent for DW). DW stiletto speed with 20 dex is 20/1.3 + 24/1.5 = 15.3+13.3, round up = 30, and estoc speed with 20 dex is 30/1.3 + 54/1.3 = 23.07 + 41.5, round up = 66

 

stiletto damage over 1000 frames (arbitrary, just pick any relatively large constant time) = 28 * (1000/30) = 933.333

estoc damage over 1000 frames = 765.9

 

When enemy DR is lower than DR penetration, stiletto will win even more because estoc will get less damage per hit effectively.

 

When enemy DR is higher than DR penetration, estoc will close the gap, until you get to a point where enemy DR negates stiletto damage completes, but estoc is still doing meaningful damage per hit.

 

As far as accuracy versus deflection, if your accuracy is higher than their deflection, DR penetration becomes less impactful, and vice versa is true. 

 

This is just my napkin math for trying to optimize my rogue, so there are some assumptions for simplification. Let me know if you guys see any problems. 

Edited April 3, 2015 by lionspaw

[kmbogd]

Could you guys tell me if during your tests dual wielding recovery was performing as expected? I have quite a large deviation from the expected value:

 

2W Fast&Fast: expected 24, observed 19.

2W Fast&Average: expected 24 & 36, observed 19 & 28

2W Average&Average: expected 36, observed 28.

 

For other styles (2H and S&S) I was able to be close to the expect value (as mentioned before around 2 frames below expectation). But for 2W I think the deviation is too high. Could you reproduce the above results?

 

If my results are correct and applying the 1-2 frame error that I observed for other styles, I would say that in 2W mode the recovery for fast weapons is 20 frames and for average/slow weapons the recovery is 30 frames. Thus recovery animation length is the same as attack animation length, which might be a bug or feature .

Edited April 3, 2015 by kmbogd

[Myrten]

Assuming the attack speed formulas here are correct, it seems like DW edges out 2 Hander on 0 effective DR targets on an optimized rogue.

 

Take stiletto versus Estoc on a melee rogue. 

 

Stiletto's base average damage is 10, Estoc's base average damage is 17. 

 

rogues have a 2.5 damage multiplier with Deathblow + Reckless Assault + Might bonus self buffed. 

 

so 25 versus 42.5 per hit pre-DR. let's assume DR is perfectly cancels by each weapon here for simplification of calculations, so we effectively get +3 and +5 damage, 28 vs. 47.5.

 

Assume rogue specs into two weapon style and two handed style, the damage becomes 28 vs. 50.55.

 

Now, let's look at attack speed (with two weapon style talent for DW). DW stiletto speed with 20 dex is 20/1.3 + 24/1.5 = 15.3+13.3, round up = 30, and estoc speed with 20 dex is 30/1.3 + 54/1.3 = 23.07 + 41.5, round up = 66

 

stiletto damage over 1000 frames (arbitrary, just pick any relatively large constant time) = 28 * (1000/30) = 933.333

estoc damage over 1000 frames = 765.9

 

When enemy DR is lower than DR penetration, stiletto will win even more because estoc will get less damage per hit effectively.

 

When enemy DR is higher than DR penetration, estoc will close the gap, until you get to a point where enemy DR negates stiletto damage completes, but estoc is still doing meaningful damage per hit.

 

As far as accuracy versus deflection, if your accuracy is higher than their deflection, DR penetration becomes less impactful, and vice versa is true. 

 

This is just my napkin math for trying to optimize my rogue, so there are some assumptions for simplification. Let me know if you guys see any problems.

I see one basic problem - enemies almost never have 0 effective DR and it's the hard fighs you want to optimize for - not the easy ones. You should calculate it again for like 5-8 effective DR.

[ErlKing]

I made post about Penetrating shot, but hardly anyone saw it, so:

 

 

Penetrating Shot talent work for spells.

Tested:


Cipher:

Affected (DR reduced by 5):

1) Mind Blades

2) Mind Lance



Not affected (ones that do not target enemy)

1) Soul shock

2) Antipathetic Field

3) Ectopsychic Echo

4) Amplified Thrust



Wizard



Affected (DR reduced by 5):

1) Thrust of Tattered Veils

2) Necrotic Lance

3) Crackling Bolt

4) Minoletta's Minor Missiles

5) Minoletta's Bounding Missiles

6) Minoletta's Concussive Missiles

7) Rolling Flame



Not affected

1) Fan of Flames

2) Ghost Blades

3) Kalakoth's Sunless Grasp





So... it seems Penetrating Shot talent affect powers/spells that

- single target (also ones that jump from enemy to enemy)

- straight line aoe



Which makes Penetrating Shot talent interesting choice for casters.





ps:

Also Vulnerable Attack talent affect Wizard's touch spells:

1) Kalakoth's Sunless Grasp

2) Jolting Touch



pps:

I havnt tested Druid, and Cleric dont have direct damaging spells (one that line aoe seems not working)

 

ppps:

 

Could anyone frapstest how Pen Shot affect casting time?

[lionspaw]

Myrten:

 

that's true. I pointed out that as DR gets higher, 2 handed starts to close the gap. but I didn't try to calculate a breaking point. In my example, the break point is around 9 effective DR, which is actually 12 total DR because Stiletto has 3 DR penetration, and Estoc has 5 DR penetration.  

 

but also my calculation didn't include enchants and other potential damage multiplier like priest buffs. The effect of increasing the damage multiplier further (enchants are damage multipliers in this game, not flat increases) is that it will make enemy DR less impactful. So with enchants, the break even DR for Estoc would be higher.

 

Also, keep in mind that you can reduce enemy DR with the Chanter spell, and also with talents like Vulnerable Attack. So I think it's possible to keep enemy DR below the break even point in most cases for stiletto users. 

[Baki]

Base

AT 48-53

REC 74-75

REL  98

 

Only Chant (Rec x1.2, REL x2)

AT 49

REC 60 = Base x (1-0.2) <-works             Base / (1+0.2) <- does not work!

REL 51 = Base x (1-0.5) 

 

Only Armor (Rec 50%)

AT 48  

Rec 112 = Base x (1+0.5)

Rel 97

 

Only Dex (AT, REC, REL 24%)

AT 41  <- can't explain

REC 60 <- can't explain

REL 78 <- can't explain

 

Only Pen Shot (Rec -20%)

AT 48

REC 90 = Base x (1+0.2)

REL 97

 

ALL

AT 41  <- can't explain

REC 91  <- can't explain

REL 41 <- can't explain (Base/1.5/0.76=37)