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[Texasmotiv]

~WARNING! POST CONTAINS MATH!~

 

 

Hello BSN,

 

I recently Went and did some theorycrafting to get an idea on how willpower affects your damage. I set out with an open mind and was actually surprised at what I found. I took a look at Longshot. Mainly because it had a large reliable multiplier.

 

 

 

LONGSHOT:

 

I made these calculations with these constants and suppositions:

Lvl3 archer using the Bow of the Dragon with the following spec http://da-skills.net...0,000,00000,000

 

No rings, not flanking, no rune, no grip. Target had 20 armor. I calculated both greater than and less than 15m (so with bonus and without bonus). Crit and non crit damage.

 

At 10 willpower (base) You have +41% Attack from the Bow and you get +3 dexterity from the First Blood passive you unlock to get longshot. This calculation is including the damage bonus from the passive, so we are assuming the targets are at above 80% health.

 

We see that at 10 willpower you will get the following averages:

 

         

If we increase the willpower to 30 (20 mage promotions) the numbers grow slightly:

 

               

 

You will notice, that this is a rather small bump. Only 30.4 damage from 0-20 promotions. This is the equivalent of putting on the Purple attack % ring. This nets on average a 30 damage increase on non crits and 43 damage increase on your critical hits. We extrapolate this out and see that it is incredibly linear:

 

 

Looking at this graphically we can see that each point of willpower equals 1.52 damage to longshot non crit and 2.1736 damage for crits.

 

Looking at various willpower milestones:

 

                                               

 

 

At the magic defense softcap (170 willpower/80% magic defense) you will see your longshot crits only hitting for 347.776 more damage than when you had NO mage promotions at all.

 

 

LONGSHOT UPDATE:

I went ahead and made my calculation sheet more dynamic and started messing with the values a little.

 

I made some tweaks to the outfitting of the bow and found some interesting interactions.

 

I equipped a superb rune to the bow (+25 base damage) and saw that the damage per point upped significantly. This is a more realistic scenario than no rune or grip at all. I also decided to test with adding a Thick Longbow Grip created (using 18 craggy skins for +%54 critical damage bonus). Here are how they affected the 'damage-per-willpower' values:

 

                             

This shows that as your base damage increases this increases the value of your willpower (likewise your Attack% from other items). It seems that in terms of long shot damage you are not getting such a large increase form the Attack % alone but there is a larger more noticeable difference to your damage when this is increased alongside crit damage as they multiply eachother. That is to say that increasing your willpower (and attack%) also will increase the value of critical damage, flanking bonus, and ability rings as it will multiply them. Whereas the the "damage bonus" you get from your skill tree and from the ability descriptions is added to Attack% and therefore only works in a linear fashion.

 

As you can see when you start adding in stats that can be multiplied by Attack% the difference is more noticeable. A difference of 557.904 on longshot crits >15m as contrasted from the previous figure of 347.776

 

                                           

And If we inspect the graph carefully you can see that the line for the equipped bow is ever so slightly is angled a little more up than the non equipped bow. In real damage, for Longshot you get a more significant increase in damage by equipping your bow than getting 160 mage promotions. In fact to equal the damage increase that you get from adding enhancements to your bow you would need 259 willpower (that's 4980 levels).

 

 

 

Since Longshot has such a low Ability damage multiplier (200%- denoted by 'weapon damage' in the tool tip) Willpower has little effect on it. If we look at the damage without the range bonus we can see that even though willpower is more effective than it was at range, it still is a little underwhelming.

 

It ends up taking 62 willpower for to equal the damage boost you get from equipping the bow with a superb rune. However, I suspect that willpower will prove to increase more dramatically when inspecting an ability with a higher weapon damage %. I will begin looking at Fade Cloak next.

 

 

TO BE CONTINUED...

[Texasmotiv]

FADE CLOAK:

 

We looked at Longshot which is an ability that has a Large static attack multiplier. Because of the way that damage is calculated, this is added to the attack% that you get from gear instead of multiplying it. We saw that since the majority of the damage was being upped by the multiplier on the back end that adding more attack% to this with willpower was a drop in the bucket and had an underwhelming effect on the final damage. Let's see what happens if we look at an ability with a large 'Weapon damage' multiplier and no 'damage bonus'. I am testing Decloaking Blast on a lvl4 keeper. I chose the keeper because the passive that you pick up before Fade Cloak on the keeper grants constitution and will not affect the attack%. We are assuming that there is no armor due to the fact that Spirit damage will ignore enemy armor.

 

As before, no other rings or accessories and for the comparison we added numbers for a base damage Staff of the Dragon and Staff of the Dragon equipped with the Superb Spirit rune (+25 base spirit damage).

 

 

If you are noticing anything about this graph, you probably notice that these lines are quite a bit more steep. This is due to the fact that since you are now loading all the damage to the front of the calculation and not just adding the damage bonuses to your Attack%, you are seeing the damage increase at a higher rate per willpower:

 

                         

 

This illustrates that abilities with a high weapon damage % will scale better with willpower than those with a low 'weapon damage%' and high 'bonus damage%'. This is due to the multiplicative nature of the damage formula and how attack% is calculated.

 

We can see that differences in base damage compared to certain willpower milestones are much more dramatic with Fade Cloak than they were for longshot.

 

                                                 

 

CONCLUSION:

 

To sum up my findings:

 

1) Damage from willpower (and attack%) scales in a linear fashion if it is the only variable.

2) Attack% scales positively with Critical Damage bonus, Base Damage, and Flanking Damage (Can extrapolate to Armor penetration for physical attacks and magic resistance for magic attacks) as they operate multiplicatively with Attack%.

3) Spells that rely on 'bonus damage' will scale less favorably with willpower than ones that have a high 'weapon damage' multiplier.

4) Graphs are cool.

 

Thank you for your attention and feel free to discuss and ask any questions you have with my conclusions. Please feel free to notify me if there are any gaps or errors.

 

Thanks!

[jvaz]

Higher attack equals higher damage period. It affects basic attacks too

[Wavebend]

Long Shot doesn't work well with attack %, but nice graphing skills!

[Texasmotiv]

I plan on repeating the testing, while changing some variables. Also repeating the same with different spells. I will also when I get time try messing with crit damage variables to see if the weight per point changes. More to come!

[Texasmotiv]

Higher attack equals higher damage period. It affects basic attacks too

Exactly but my aim is to quantify exactly how much willpower will contribute to your overall damage. Just from this it seems you might get more bang for your buck from cunning and + crit damage. But that's yet to be seen.

[Wavebend]

Exactly but my aim is to quantify exactly how much willpower will contribute to your overall damage. Just from this it seems you might get more bang for your buck from cunning and + crit damage. But that's yet to be seen.

 

^^ this.

[Pork]

Willpower best functions for magic defense. The attack increase is a bonus. For straight DPS, cunning is the best way to go hands down.

[Drasca]

Willpower best functions for magic defense. The attack increase is a bonus. For straight DPS, cunning is the best way to go hands down.

 

Only once you have enough critical damage bonus gear, AND the primary damage abilities you use require use of 'bonus damage' that adds to the attack power rather than multiplies with it, instead of pure weapon damage abilities.

 

i.e. Long shot or Power Chord (both with bonus damage that does not scale with attack power) vs Bolt (no bonus damage, pure weapon damage scaling with attack power)

 

 

Exactly but my aim is to quantify exactly how much willpower will contribute to your overall damage. Just from this it seems you might get more bang for your buck from cunning and + crit damage. But that's yet to be seen.

 

 I love charts. Nice job.

 

That said, I can calculate what it is with and without other bonuses. Notice  how 10% attack power translates to about 1% actual increase in damage before crits. After crits and other bonuses, the gap can increase a bit... but realistically the damage increase is not signifigant when the majority of damage is from other bonuses that do not scale from attack power.

 

I've done similar tests and it is pretty much a waste to put on attack power rings when it comes to long shot or power chord if you have other options. Other abilities that do scale directly with attack power (bolt for example) fair better.

 

This is also why promotions aren't end all be-all, even though they are definitely an increase in power, they aren't magically insta-gib everything overnight.

[SpaceV3gan]

1.52 damage per Willpower point on an ability which is known not to benefit much from Attack is very substantial in my book. Not game breaking by any means, but certainly substantial.
I would like to see the effect of Willpower being tested on abilities which possibly benefit more, such as Chain Lightning, Spirit Blade, Walking Bomb, Fade Cloak, Wrath of Heaven, among others. Not entirely sure to what extent they may benefit, but I've noticed a significant damage boost on those after I decided to go Willpower heavy.

[Drasca]

1.52 damage per Willpower point

 

An additional 2 damage (rounded up) against a 4k hp target is significant to you? I prefer my significant figures to be within the same order of magnitude as what I'm dealing with.

[Shadohz]

Why not just port all this data to a calculation sheet? You can pull the weapons data from the EQ doc and JRandall built a sheet that contains all the abilities with their damage stats. You can import all that information, run some formulas and build charts around those.

[yarpenthemad21]

1.52 damage per Willpower point on an ability which is known not to benefit much from Attack is very substantial in my book. Not game breaking by any means, but certainly substantial.
I would like to see the effect of Willpower being tested on abilities which possibly benefit more, such as Chain Lightning, Spirit Blade, Walking Bomb, Fade Cloak, Wrath of Heaven, among others. Not entirely sure to what extent they may benefit, but I've noticed a significant damage boost on those after I decided to go Willpower heavy.

You can get the feeling of it just from tables presented alone, but you should look at longshot < 15 m (so if I understand calculations it's just longshot without bonus damage from distance => so just normal ability with some ability %)

Base 10 willpower has 474
And if I read table correctly on 170 willpower we have 717
so 80% attack in that case, for normal ability, dragon bow (or other weapon with similar amount of attack bonus)gave around 51% more damage.
Because dragon staff has pretty much similar +attack as dragon bow, skills like CL, FC, Walking bomb etc should work in similar way.

[Beerfish]

[Texasmotiv]

Why not just port all this data to a calculation sheet? You can pull the weapons data from the EQ doc and JRandall built a sheet that contains all the abilities with their damage stats. You can import all that information, run some formulas and build charts around those.

 

If you have these sheets handy, please send links to me. If not I can do some searching to find them. I am at work but when I get a lull I can do some more maths.

 

I could try to link these sheets but I'm not a hero with excel like some. I just know enough excel to do some data collection and some simple algebra. Other than that making it a working presentable document that I would feel confident sharing would not be something I think would be doable for me.

[Texasmotiv]

Updated OP with more in-depth analysis of long shot. I am currently looking at fade cloak and will have this updated soon.

[Spin-Orbit]

Nice work, thanks for your efforts.

Something like the fade cloak will be nice since it will be base damage multiplier. This is important in terms of discussions about which weapons to carry and etc. Especially for characters that has much special ability damage based on the weapon base damage such as the Katari's charge, Fade step/cloak etc.

[Texasmotiv]

Updated the reserved post with my complete findings from fade cloak and my conclusions from the data.

[Denrok1]

An additional 2 damage (rounded up) against a 4k hp target is significant to you? I prefer my significant figures to be within the same order of magnitude as what I'm dealing with.

 

Is it safe to say willpower is the least important stat then Drasca? Besides needing it for magic defense. I have lots of cunning but very little willpower.

[Shadohz]

If you have these sheets handy, please send links to me. If not I can do some searching to find them. I am at work but when I get a lull I can do some more maths.

 

I could try to link these sheets but I'm not a hero with excel like some. I just know enough excel to do some data collection and some simple algebra. Other than that making it a working presentable document that I would feel confident sharing would not be something I think would be doable for me.

http://forum.bioware...t#entry18281063

Use Google Docs and use the Import Data feature to pull the names and weapon damage from EQ doc and JRandall's abilities docs onto separate sheets. I have plenty of formulas and some formula examples in JRandall's posts that you can use to extrapoloate how to make your own 3rd presentation sheet from our data. You'd just have to plug your formula(s) and the cell ranges. You probably can use Excel as well but I won't swear to it. GDocs also has the sheet(s) available online so that's one less problem you'd have to worry about. If you need help then drop a reply or PM I may be able to help.

[Angelus_de_Mortiel]

If you need help then drop a reply or PM I may be able to help.

 

I am loving the actual sheer productiveness of this... Kudos to Texasmotiv for acquiring hard data and thanks to Shadohz for being helpful!

[Rolenka]

~WARNING! POST CONTAINS MATH!~

 

[K_A_Rnage]

So from what I've learned here my Katari's Mighty Blow will be directly increased by willpower promotions but the upgrade will only be a flat 300% weapon damage increase.
So let's say my weapon dmg is 300, I will do 900 with MB + 900 with upgrade.
If I then added 20 willpower for 10% att I would do 990 + 900.
Could you confirm if I'm on the right path?
Quality post OP

[Texasmotiv]

So from what I've learned here my Katari's Mighty Blow will be directly increased by willpower promotions but the upgrade will only be a flat 300% weapon damage increase.
So let's say my weapon dmg is 300, I will do 900 with MB + 900 with upgrade.
If I then added 20 willpower for 10% att I would do 990 + 900.
Could you confirm if I'm on the right path?
Quality post OP

On an enemy that is knocked down, It would be calculated this way:

Base Damage: 300
Ability Damage: 2 (for %200)
Damage Bonus: 2 (for %200 from the base ability) + 3 (From the upgrade) = 5
Attack %: minimum from 'clear a path' to get mighty blow: .015 (%1.5 from +3 str)
Enemy Armor: 50

So the formula would be:

Damage = ( 300 - 50 ) * 2 * ( 1 + 0.015 + 5 )
Damage = 3007.5

If you were to add 20 willpower you would change it to this:

Damage = ( 300 - 50 ) * 2 * ( 1 + 0.115 + 5 )
Damage = 3057.5 (50 extra damage)

 

Edit: Jaywee1 pointed out that I had .15 for clear the path when it should have been .015. I corrected the math above for the appropriate value.

Second Edit: Jaywee1 also noticed that on my edit I added .20 for 20 willpower when I should have added .10. Corrected the formula above.

[Denrok1]

On an enemy that is knocked down, It would be calculated this way:

Base Damage: 300
Ability Damage: 2 (for %200)
Damage Bonus: 2 (for %200 from the base ability) + 3 (From the upgrade) = 5
Attack %: minimum from 'clear a path' to get mighty blow: .015 (%1.5 from +3 str)
Enemy Armor: 50

So the formula would be:

Damage = ( 300 - 50 ) * 2 * ( 1 + 0.015 + 5 )
Damage = 3007.5

If you were to add 20 willpower you would change it to this:

Damage = ( 300 - 50 ) * 2 * ( 1 + 0.215 + 5 )
Damage = 3107.5 (100 extra damage)

Edit: Jaywee pointed out that I had .15 for clear the path when it should have been .015. I corrected the math above for the appropriate value.

 

20 promotions / +10 % attack power equals an additional 3.58% damage. Boooo. Willpower stinks.