Official Stat Formula

[Math Fish]

Fair Warning: This is a very technical post. If you hate math ... I would recommend walking the other way. You have been warned.

I have been very hesitant to release this for a few months now for several reasons. The two big ones were:

• I felt I needed permission from the Otters to release it since I derived it from the Python code. I have gotten that permission from Sarah Otter. Thank you Sarah!
• I was very concerned that this might drive a wedge between the so-called "elite" and casual groups of players. I am simply going to trust that the number of people on the true elitist side of the scale is too small to be important in the long term and that the community as a whole will endure them.

Since I have resolved both of these issues in some fashion, I will now give you all the current (as of this post) formula for the effect of any and all stats:
Version 1: Full Complicated Version

​

Version 2: Simplified Version

​

In both versions of this formula you may notice that there are 3 variables:

1. STAT is the number of points you put into a stat like Mastery, Armor, Savagery, Voidstrike, Shielding ... anything but Vitality.
2. LEVEL is simply your character's level. You will need to multiply your stats by 1.0718 each level to maintain the same effect as you level (or a 7.18% increase).
3. MAX is the highest possible value a stat can have. This works with stat-breakers from raids as well. You may use a value of 1 to get a decimal (part of a whole), a value of 100 to get a percentage, or whatever value the maximum actually is. All three have their uses. Just know that the maximum value is what is being used in the code.

This gives the exact (as exact as a computer can be anyway hehe) value of your stats. Any value you see in your character sheet will be a truncated version of this. This final value will not necessarily be what you see on the right side of your character screen. It only shows what you get from your stats.

---

So, what can you do with this information? Here is a short list I have made up:

• Determine how much of an effect a change in stats will have before gnogging that rune.
• Determine how much of an effect your stats have on your DPS.
• Compare stats to see which ones are better suited for your build. With some assumptions you can actually compare every stat in the game to one another. This is a tool I would like to develop in the distant future, but I just don't have the drive to do so.
• Perfect that stat calculator that was using approximations before.

I look forward to seeing what you all will do with this new information in the future. If you have any questions, feel free to post them and I will do my best to answer. Also, Damon or Sean, if I messed up somewhere, please correct me. lol

 

[Clonkie]

I don’t get the some variables, u mean stat value or the percentage value? So inserting STAT as actual value and mAX as a percentage? There is no maximum value for variable STAT, with that being said, how is diminishing returns accounted for?

 

[Giruv]

So inserting STAT as actual value and mAX as a percentage?

That sounds correct, the max value not necessarily a percentage, depending the stat you want to check for example savagery than Max is 20%, but if you're checking blasting for level 95 then the Max is 29k

There is no maximum value for variable STAT, with that being said, how is diminishing returns accounted for?

The possible value for 1.67^C will hover around 0 and 1 so it will never go above the Max. The stat also inputted as part of power function of negative which make the higher the stats it will become closer and closer to 0 but never become negative, which is where the diminishing return come from. So the maximum value you'll get is from

(1-1.67^C)*Max
is
(1-0)*Max = Max

Hope I explain that clearly

 

[Giruv]

I tried to use the equation, but it seems there still some rare small error(under 1%), especially at lower stats. I heard the game have weird way of rounding things any idea on that?

 

[Math Fish]

I don’t get the some variables, u mean stat value or the percentage value? So inserting STAT as actual value and mAX as a percentage? There is no maximum value for variable STAT, with that being said, how is diminishing returns accounted for?

Ah, yes, I should clarify that. I'll use mastery as an example:

​

• STAT is the left-side value - the same number you see on your armor/weapon/runes/etc. In the pic it is the 30.2k. The exact value is 30187 - gotten from highlighting the 30.2k itself.
• MAX is the highest right-side value - the percentage that comes out. In the pic it is the 30% you see in the pop up.

​

You can enter it into the formula as a percent (30), as a decimal (0.3), or do the calculations later and use a generic value (1 or 100 - both give the percentage of the max in different forms).

In my case, you should be able to plug 30187 in for STAT, 95 in for LEVEL, and 30 in for MAX and get 23.74833. Here is a crude way to do this in Excel and a comparison to my stat value in game:

​

If I decide to use Steady and Dread Bolts to increase my mastery, here's what happens:

​

They increase my mastery STAT by 9274 with the result of increasing my mastery by 2.390296%.

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As for diminishing returns, that is accounted for here by the exponential part of the function: As STAT approaches infinity, the exponent part of the formula approaches 0, which causes the entire thing to approach MAX. Here is what the graph for mastery looks like at level 95:

​

 

[Math Fish]

I tried to use the equation, but it seems there still some rare small error(under 1%), especially at lower stats. I heard the game have weird way of rounding things any idea on that?
View attachment 9171
View attachment 9172

For this one I don't know. There are three things I can think of and all of them are bugs:

1. Something to do with roundoff error in calculations. I find this one extremely unlikely as values are stored with an accuracy more than high enough to avoid any significant error.
2. A bug that I am not aware of in the code that does something other than this simple (by coding standards) calculation.
3. Perhaps ... the maximum value isn't precisely 40%? I know that at least one other stat off the top of my head has a very strange 23.1% max value. If this is the case we would have to get confirmation from a dev: I have no way to find out myself. The highest value that would give the actual result displayed (with truncation) is about 39.87 ...

​

View attachment 9170
View attachment 9173

With this one I believe it is because values that are displayed are truncated rather than rounded off. I don't have access to anything that can confirm this or any other strangeness that may be occurring with certain stats.

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EDIT: I merged this to avoid the triple post:

That sounds correct, the max value not necessarily a percentage, depending the stat you want to check for example savagery than Max is 20%, but if you're checking blasting for level 95 then the Max is 29k

In case you want an exact value, the maximum blasting is 5 times the standard damage/healing value, or 40 * 1.0718 ^ LEVEL

 

[Jalandra]

Fair Warning: This is a very technical post. If you hate math ... I would recommend walking the other way. You have been warned.

I have been very hesitant to release this for a few months now for several reasons. The two big ones were:

• I felt I needed permission from the Otters to release it since I derived it from the Python code. I have gotten that permission from Sarah Otter. Thank you Sarah!
• I was very concerned that this might drive a wedge between the so-called "elite" and casual groups of players. I am simply going to trust that the number of people on the true elitist side of the scale is too small to be important in the long term and that the community as a whole will endure them.

Since I have resolved both of these issues in some fashion, I will now give you all the current (as of this post) formula for the effect of any and all stats:
Version 1: Full Complicated Version

View attachment 9159​

Version 2: Simplified Version

View attachment 9160​

In both versions of this formula you may notice that there are 3 variables:

1. STAT is the number of points you put into a stat like Mastery, Armor, Savagery, Voidstrike, Shielding ... anything but Vitality.
2. LEVEL is simply your character's level. You will need to multiply your stats by 1.0718 each level to maintain the same effect as you level (or a 7.18% increase).
3. MAX is the highest possible value a stat can have. This works with stat-breakers from raids as well. You may use a value of 1 to get a decimal (part of a whole), a value of 100 to get a percentage, or whatever value the maximum actually is. All three have their uses. Just know that the maximum value is what is being used in the code.

This gives the exact (as exact as a computer can be anyway hehe) value of your stats. Any value you see in your character sheet will be a truncated version of this. This final value will not necessarily be what you see on the right side of your character screen. It only shows what you get from your stats.

---

So, what can you do with this information? Here is a short list I have made up:

• Determine how much of an effect a change in stats will have before gnogging that rune.
• Determine how much of an effect your stats have on your DPS.
• Compare stats to see which ones are better suited for your build. With some assumptions you can actually compare every stat in the game to one another. This is a tool I would like to develop in the distant future, but I just don't have the drive to do so.
• Perfect that stat calculator that was using approximations before.

I look forward to seeing what you all will do with this new information in the future. If you have any questions, feel free to post them and I will do my best to answer. Also, Damon or Sean, if I messed up somewhere, please correct me. lol

Is this formula still valid or has there been a change?

 

[Massakari]

This is kind of driving off topic a bit but I've read in a few places that Savagery is 20% for max value. That being said, is there no actual way to know this in-game besides being told so? Because mine is at 23% , and if I'd not been told so, I wouldn't know.
Basically, my extra 3% is just extra that I could/should be replacing for a different stat?

 

[Jalandra]

This is kind of driving off topic a bit but I've read in a few places that Savagery is 20% for max value. That being said, is there no actual way to know this in-game besides being told so? Because mine is at 23% , and if I'd not been told so, I wouldn't know.
Basically, my extra 3% is just extra that I could/should be replacing for a different stat?

I've heard this before and have several chars above 20%. If it works the same way as armour does then it should not display more than the 20% maximum.

 

[Antavious]

Some things can put it over most likely the origin buff you picked, the 20% is the most you can get from stats alone (savagery) another cool thing that can put it over the top is raid relics

 

[Massakari]

So you're saying if it is over the cap (20%) then, that's not an error or anything, it's simply something else thats pushing it past the cap? Because my armor goes over 50% occassionally too, so that makes sense. Gonna figure out what is making it go over. Thanks

 

[Massakari]

Ohh, Origin. After reading that again, I realized what you meant. That's the one then because that is indeed the innate buff that I chose! (Seemed like the obvious choice outside of crafting/gathering ones.)

 

[Antavious]

In the case of armour maybe a friendly warrior nearby is using rally? The zombie eye from the EZ can take you way over cap think I got closer to 80% with that one

 

[Math Fish]

As far as being over max is concerned, the formula does not account for base stats or stuff like relics. For Savagery you start with 2% crit chance. Then the realm bonus adds a bit more (forget off hand how much). Just take away those values and you should have your crit rate from Savagery.

And @Jalandra the formula is still valid for all stats. The catch is that the max values aren't knowable in game. You can use this link to see a stat calculator with the max values already in there: Stat Calculator using exact formula - Google Sheets.

 

[Jalandra]

As far as being over max is concerned, the formula does not account for base stats or stuff like relics. For Savagery you start with 2% crit chance. Then the realm bonus adds a bit more (forget off hand how much). Just take away those values and you should have your crit rate from Savagery.

And @Jalandra the formula is still valid for all stats. The catch is that the max values aren't knowable in game. You can use this link to see a stat calculator with the max values already in there: Stat Calculator using exact formula - Google Sheets.

Thank you!

 

[Egelin]

So you're saying if it is over the cap (20%) then, that's not an error or anything, it's simply something else thats pushing it past the cap? Because my armor goes over 50% occassionally too, so that makes sense. Gonna figure out what is making it go over. Thanks

There is a premium ring that also gives +5% flat physical protection. This might also be the reason for seeing 50% physical protection. No kind of buff to armor will actually let you get 50% physical protection directly from armor because there is a huge exponential increase in required base stat for reaching anywhere near the cap. This is true for any stat in the game.
There are few stats that start with default values even before we consider realm bonuses and these are all exempt from diminishing returns or stat caps. Critical damage has 50% default value, critical chance has 2%, mana regen has 4/s.