Stat Calculations and Diminishing Returns

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Stat Calculations and Diminishing Returns

Postby Click » Thu Apr 18, 2013 1:17 am

*****Big thanks to Fizz_Eric for providing me with Resistance and Dodge data! :)

Notes:

*MOST OF THIS APPLIES TO LEVEL 30 ONLY. If you are below level 30 you aren't too strongly affected by diminishing returns anyway so stack your favorite stat as you please, but too much of a good thing isn't gonna get you too far either.
*In general the game likes to ROUND DOWN and TRUNCATE. So 12.6788634031243% is 12.67% in game.

---------------------------------

Might and Stat Growth

Might = All base stats except defense without guild favors if you have no enchants. Add 0.5% Might for every level of enchant on gear.


Base Melee/Magic:
Justicar: +20 Melee and + 10 Magic per level
Shadow Walker: +15 Melee and +15 Magic per level
War Mage: +10 Melee and +20 Magic per level

The maximum amount that a stat can be trained with Hero tokens is +1200 (the cost per upgrade caps out at 500).

To calculate how much a gem will increase your stat, there is a simple multiplication formula:

Stat increase = 2 * GTier * ETier * Loc

GTier: Tier of the gem you are equipping.
ETier: Tier of the equipment to hold the gem.
Loc: Location multiplier = 4 if Chest/Amulet/Ring/2H Weapon, 3 if Head/Legs, 2 if Gauntlets/Cloak/Feet/1H/OH

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Dual Wielding
When Dual Wielding, 75% of Melee Damage from Stats is added to the Main Hand and 25% of Melee Damage from Stats is added to the Offhand. If your Offhand is a Shield then you do not get that 25%.

100% Weapon Damage =
Weapon Damage (shown on weapon) + Melee Damage (on the stat page).

Magic Damage works the same way.

Bj_Knows wrote:The quoted formula is incorrect. The correct formula is:

100% Weapon Damage =
Main Hand Weapon Damage ( shown on weapon) + Offhand Weapon Damage ( shown on offhand weapon) + [ Bonus Damage ( shown on Stat page) * Weapon Speed ( shown on weapon ) ] + Appropriate Enchants

Bonus Damage is Melee Bonus Damage for Melee Attacks. Bonus Damage is Magic Bonus Damage for Magic Attacks.
https://www.venan.com/boh_forum/viewtopic.php?p=22045#p22045


-----

Melee Rating Conversion Formula

Melee/Magic soft cap = 1920?

If Above Soft Cap:
Damage = (Rating÷12.53)+614.78 **

**This is +/- 1 for me. Not totally accurate. I think there is a sin function here since the growth is pretty linear but not perfectly so. Whatever the case, I don't see myself getting any closer to the true formula with my limited data set.

If Below Soft Cap:
Damage = Rating÷2.5

----

Dodge/Crit Rating Conversion Formula

Crit% =
[(45*Crit)÷(1395.6+Crit)]+5

Dodge is the same formula.

----

Crit Power Rating Conversion Formula

Crit Power% =
[(50*CritPow)÷(1395.43+CritPow)]+150

----

Haste Rating Conversion Formula

Haste% =
[50*Haste]÷[999.5+Haste]

This also means that at very high haste values, you can take off several hundred rating and still have unchanged execution times on all or most of your abilities. I believe the game rounds to the nearest hundredth when it shaves seconds off of execution time.

----

Physical/Magic Resistance Conversion Formula

Resistance% =
[50*Resist]÷[5582+Resist]

This abruptly stops working at around 3000 rating and the returns diminish more.
Last edited by Click on Thu Jun 27, 2013 1:23 am, edited 30 times in total.
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Re: Stat Calculations and Diminishing Returns

Postby EricM » Thu Apr 18, 2013 2:05 am

I don't know why no one's done this before. All your formulas fit my stats. Really useful as a prediction tool for SWers.
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Re: Stat Calculations and Diminishing Returns

Postby Click » Thu Apr 18, 2013 2:38 am

Notes on Haste:

I find this stat to be very interesting. While in most games, Haste is a percentage of speed increase. In other words, you go X% FASTER. In BoH Haste is a percentage of the delay time of an ability that is removed. In other words, your ability takes X% less time to complete.

This could very well be why Haste is such a strong stat. While going 50% faster only makes you take 66% of the time to complete actions, reducing the ability execution time by 50% makes it take 50% of the time. This makes it stronger per percentage than in other games.

This also means that while it suffers from diminishing returns, the diminishing returns don't feel as harsh, simply because the more haste % you have, the more haste % is worth:

-If you are at 0% and you get 1% you have reduced your activation time by 1%. (A 1s swing becomes .99s)
-If you are at 50% and you get another 1% you have reduced your activation time by 2%. (A .5s swing becomes .49s)

Meanwhile Crit scales in the opposite direction.

-If you are at 5% crit and gain 1%, you increased your effective damage per action by .01 x (Crit Power) x Base DMG
-If you are 40% crit and gain 1%, you increased your effective damage per action by .01 x (Crit Power) x Base DMG, which is now less significant in proportion to your current damage potential since you are doing more damage than in the first scenario.

Haste also diminishes slower than crit as well.

On the other hand, Haste can mess with your rotation as some abilities cooldowns are reduced by haste while others are not. DoT ticks don't seem affected by haste, making DoTs less desirable over time as you accumulate more haste as well. And while haste may make you faster you, it won't do anything for your actual damage per execution. You can only tickle an enemy so long before you find yourself out of potions and out of luck!
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Re: Stat Calculations and Diminishing Returns

Postby Bbbb » Thu Apr 18, 2013 10:38 am

I'm all for more of this analysis. I do want to say that I think your crit and haste formula disagree with my understanding of the conclusions Mith came up with but he hasn't published his numbers AFAIK. Hopefully, he will weigh in.

In the meantime, I believe a couple of his conclusions were:

1. Token points shift the start of the curve and are not on the curve itself.
2. There is a change in the crit and haste curves - somewhere around 2000 points.
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Re: Stat Calculations and Diminishing Returns

Postby Click » Thu Apr 18, 2013 11:32 am

Bbbb wrote:I'm all for more of this analysis. I do want to say that I think your crit and haste formula disagree with my understanding of the conclusions Mith came up with but he hasn't published his numbers AFAIK. Hopefully, he will weigh in.

In the meantime, I believe a couple of his conclusions were:

1. Token points shift the start of the curve and are not on the curve itself.
2. There is a change in the crit and haste curves - somewhere around 2000 points.


Thank you. I'll have to look into that later and update once I can find more specifics.

The first point is that hero training are not subject to diminishing returns then?
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Re: Stat Calculations and Diminishing Returns

Postby Possessed_Mithrid » Sat Apr 20, 2013 12:52 am

Crap...I owe it to Bbbb to post some of my studies as he helped me collect data back in the day. Here is a sample of it. The stat curves, not knowing the real formulas, are blackbox modeled best as piecewise logarithmic, as far as I can tell. Also the method by which individual stats are affected by "Hero token stat" points and "Gem stat" points varies based on the stat itself.

I am attaching two plots, one is for Haste and one is for Crit. Both are for Lvl30 WM. SW stats are sometimes different sometimes the same as a WM, Justi I have yet to fully model).
For Haste, Hero Stat Points are treated the same as Gem points in value. You can see that because the Base Haste Curves perfectly overlap for a Hero Stat Haste at 544 or one at the max 1200.

Note on Crit however that its changed, per Bbbb's comment.
The curve has shifted based on the Hero Stat value, meaning that crit Hero stat value has a dominant affect on base Crit % compared to straight Gem points. You can see that the same point investment does not give the same base Crit % if your Crit Hero Stat is 600 versus 1200 maxed.

Each of the other stats as well have slightly interesting, sometimes unique characteristics...a lot more than I want to discuss right now.

Something to note is that somewhere near the point of investing a full 9 T5 gems in a stat, the diminishing returns suffer an inflection point...or in other words, it simply gets much worse. This inflection point is why I refer to the curves as piecewise logarithmic. Prior to the "9Gem point" as I call it, the logarithm I use to model the diminishing returns is not too bad...but it shifts and becomes much worse, requiring a second logarithm model.

Note: I do not believe Venan uses Logs in their formulas..I believe it is a polynomial, but without knowing all the specific terms in the polynomial...I can more easily model to within a +/-0.05% accuracy the stat % per point investment with piecewise logarithms.

-Mith

PS: Incidentally I have reams of data modeling every aspect of the game, I owe a lot of thanks to Bbbb, Shekka, Razor Drach, Fero, Romeo and all the rest of my peeps in Kingdom and Spoons for great discussions and shared data.
Attachments
BoH BaseCrit Plots.png
Crit % Plots for Point Investment
BoH BaseCrit Plots.png (21.5 KiB) Viewed 17774 times
BoH BaseHaste Plots.png
Haste % Plots for Point Investment
BoH BaseHaste Plots.png (18.41 KiB) Viewed 17774 times
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Re: Stat Calculations and Diminishing Returns

Postby Click » Sat Apr 20, 2013 1:31 am

That's an interesting shift. Thanks for sharing that.

So the crit formula I put up there does not result in accurate percentages for people with high HT investment in crit? I don't have very much so I can't quite test that out myself.

As for the 9Gem point, that's with +1200 in HT? So about ~6000? With the Haste formula I have , at 6000 Haste, investing another 1000 points would net you only .14% haste. I figured the curve couldn't get any worse than that but I guess I was wrong.
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Re: Stat Calculations and Diminishing Returns

Postby Possessed_Mithrid » Sat Apr 20, 2013 1:55 am

Here is another way of looking at it. I have this plot that shows you the value in % of each investment point at different levels of total investment.

I could also plot it as a differential but I like this curve, its telling.

Note again this is for a WM (In a week I will have a full complement of 18 Haste T5 Gems to plot the true MAX WM Haste value...I'm still short a few (I only have 13 right now) T5 Haste Gems...I had to get rid of some inventory I was using for a different study to make room for them.
Attachments
BoH BaseHastePerPoint Plots.png
BoH BaseHastePerPoint Plots.png (17.78 KiB) Viewed 17761 times
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Re: Stat Calculations and Diminishing Returns

Postby john12345 » Sun Apr 21, 2013 1:34 am

Mithrid wrote:Crap...I owe it to Bbbb to post some of my studies as he helped me collect data back in the day. Here is a sample of it. The stat curves, not knowing the real formulas, are blackbox modeled best as piecewise logarithmic, as far as I can tell. Also the method by which individual stats are affected by "Hero token stat" points and "Gem stat" points varies based on the stat itself.

I am attaching two plots, one is for Haste and one is for Crit. Both are for Lvl30 WM. SW stats are sometimes different sometimes the same as a WM, Justi I have yet to fully model).
For Haste, Hero Stat Points are treated the same as Gem points in value. You can see that because the Base Haste Curves perfectly overlap for a Hero Stat Haste at 544 or one at the max 1200.

Note on Crit however that its changed, per Bbbb's comment.
The curve has shifted based on the Hero Stat value, meaning that crit Hero stat value has a dominant affect on base Crit % compared to straight Gem points. You can see that the same point investment does not give the same base Crit % if your Crit Hero Stat is 600 versus 1200 maxed.

Each of the other stats as well have slightly interesting, sometimes unique characteristics...a lot more than I want to discuss right now.

Something to note is that somewhere near the point of investing a full 9 T5 gems in a stat, the diminishing returns suffer an inflection point...or in other words, it simply gets much worse. This inflection point is why I refer to the curves as piecewise logarithmic. Prior to the "9Gem point" as I call it, the logarithm I use to model the diminishing returns is not too bad...but it shifts and becomes much worse, requiring a second logarithm model.

Note: I do not believe Venan uses Logs in their formulas..I believe it is a polynomial, but without knowing all the specific terms in the polynomial...I can more easily model to within a +/-0.05% accuracy the stat % per point investment with piecewise logarithms.

-Mith

PS: Incidentally I have reams of data modeling every aspect of the game, I owe a lot of thanks to Bbbb, Shekka, Razor Drach, Fero, Romeo and all the rest of my peeps in Kingdom and Spoons for great discussions and shared data.

didn't really see special points on graph:)
but just to keep it simple, whats general purpose gem setup recommended to avoid worst diminished return for 2h wm for example? 8 crit 8 haste 11 magic?
for onslaught I assume ppl wouldnt bother about diminished return and just dump all 18 to haste:)
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Re: Stat Calculations and Diminishing Returns

Postby japster » Sun Apr 21, 2013 2:15 am

This is good information but there's something even more complex at play, which is your weapon choice + your choice of skills.

While we may know how the efficiency of haste works with each stat point (from gem or HT) with the current information, the interaction between haste and the actual cast time of each skill will differ. Due to the way Venan calculates skill cast time with weapon speed and haste, each skill with a different weapon will have different "breakpoints" before we see a meaningful 0.01s decrease.

Thus it isn't just a simple issue of achieving X% haste with the most efficient amount of stat points, for example Y. We also need to consider whether X% would give a sufficient haste improvement that results in a meaningful 0.01s reduction of skill A. Y amount of stats may give us X%, which is statistically efficient and reduce skill A by 0.01s, but it may reduce skill B by 0.03s instead. Similarly, in another hypothetical example, maybe Y+384 will give us X%+0.16% increase in haste, but skill A may remain unchanged in cast time while skill B sees a 0.01s decrease.

This is why when we improve our haste stat, not all our skills necessarily become faster, but only some. Whether or not we see meaningful reduction depends on the base cast rate of the skill as well as the choice of weapon used.

Thus what's "efficient" also really depends on what skills you are trying to prioritize to reach certain breakpoints.
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