4.0 Character Sheet Equations

[dipstik]

did you try base_time/(1+alacrity)?

[KeyboardNinja]

did you try base_time/(1+alacrity)?

 

This.

 

The way I think about it is that alacrity doesn't reduce your cast times, it increases your cast time reduction. Subtle semantic difference, but this is how (for example) a zero-alacrity Combat sentinel will see a 2.3 second Blade Dance channel under Zen, rather than the 2 second channel you would expect.

[JediUmbra]

Damage Reduction = ArmorRating / ( ArmorRating + 240 * 65 + 800 ) * 100

looks like dummy now has 40% (10875 armor rating)

 

Plugging in 10875 gives me 0.39872. Solving for 0.4 gets me 10933.5. Which value did you derive, and which is the source value? Or is my arithmetic wrong?

 

EDIT:

Nevermind, I read some of the responses in the thread which cleared it up for me.

Edited November 2, 2015 by JediUmbra

[mathieuportal]

This.

 

The way I think about it is that alacrity doesn't reduce your cast times, it increases your cast time reduction. Subtle semantic difference, but this is how (for example) a zero-alacrity Combat sentinel will see a 2.3 second Blade Dance channel under Zen, rather than the 2 second channel you would expect.

 

Hmm... You must confuse one third (33%) and 30% (the amount of alacrity given during Zen). With the basetime/ (1+alacrity) formula, as a combat sentinel you should expect 2.3 s Blade Dance channel, not 2 s.

--> 3/(1 +0.3) =2.3

It seems correct to me

 

And even with 1.33, you can't expect 2 s... The only way is to think 30 % alacrity means a channel time reduction by one third, which is obviously not the case.

Edited November 2, 2015 by mathieuportal

[KeyboardNinja]

Hmm... You must confuse one third (33%) and 30% (the amount of alacrity given during Zen). With the basetime/ (1+alacrity) formula, as a combat sentinel you should expect 2.3 s Blade Dance channel, not 2 s.

--> 3/(1 +0.3) =2.3

It seems correct to me

 

It is correct. Most people think that alacrity works in the following way though:

 

3*(1-0.3) = 2.1

 

I rounded to 2 seconds, but the point is that it's distinct from the 2.3 that is seen in game. 1/(1+alac) is the correct scalar, even though (1 - alac) is slightly more intuitive (and would result in a more powerful effect).

[fuji_hiro]

equations no longer hold for levels 20 through 65. there are weird changes from 50 to 65.

 

Standard Health / Base Damage Value at 65 = 4465

Base HP at 65 = 12775

Base healing value for level 65 = 27510.

 

Defense Chance = 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( DefenseRating / 65 / 1.2 ) )

Shield Chance = 50 * ( 1 - ( 1 - ( 0.01 / 0.5 ) )^( ( ShieldRating / 65 ) / 0.78 ) )

Absorb Percentage = 50 * ( 1 - ( 1 - ( 0.01 / 0.5 ) )^( ( AbsorptionRating / 65 ) / 0.65 ) )

 

Damage Reduction = ArmorRating / ( ArmorRating + 240 * 65 + 800 ) * 100

looks like dummy now has 40% (10875 armor rating)

 

Max Health = BaseHealth + Endurance * 10.5

 

Critical Chance (from crit rating) = 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( CritRating / max(level,20) ) / 0.8 ) )

Critical Chance (Mastery) = 20 * ( 1 - ( 1 - ( 0.01 / 0.2 ) )^( ( Mastery / max(level,20) ) / 5.5 ) )

Surge Percentage = 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( CritRating / max(level,20) ) / 0.8 ) )

 

Alacrity Percentage = 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AlacrityRating / 65 ) / 1.25 ) ) )

Accuracy Percentage = 30 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( AccuracyRating / 65 ) / 1 ) )

 

Bonus Damage (Mastery) = (Mastery) * 0.2

Bonus Damage (from force/tech power) = (Force or Tech Power) * 0.23

Bonus Damage (from power) = Power * 0.23

Critical Hit Damage = [Normal Hit] * ( 1 + [surge Percentage] * max(1 , [Critical Chance] ) )

 

Bonus Healing (Mastery) = (Mastery) * 0.14

Bonus Healing (from force/tech power) = (Force or Tech Power) * 0.17

Bonus Healing (from power) = Power * 0.17

 

not sure if these are right:

PvP Damage Boost = 60 * ( 1 - ( 1 - ( 0.01 / 0.6 ) )^( ( Expertise / 65 ) / 0.5605 ) )

PvP Damage Reduction = 60 * ( 1 - ( 1 - ( 0.01 / 0.6 ) )^( ( Expertise / 65 ) / 0.5605 ) )

PvP Healing Boost = 35 * ( 1 - ( 1 - ( 0.01 / 0.35 ) )^( ( Expertise / 65 ) / 1.6816 ) )

 

 

Hello!

 

Thanks for sharing those équations. But i've got little questions about.

I must change " max(level,20)" by the level of my character, in my case i'm LVL65 so i must change it by 65?

I've got some problem to graph those équations, I don't have the same result as http://imgur.com/hv5sWX9 (from a post of MusicRider, is there any Latex plug-in to write it correctly?

 

Thanks for reading, it's only a year i play this game and now i want to understand a little bit more about it

[TankAviator]

This.

 

The way I think about it is that alacrity doesn't reduce your cast times, it increases your cast time reduction. Subtle semantic difference, but this is how (for example) a zero-alacrity Combat sentinel will see a 2.3 second Blade Dance channel under Zen, rather than the 2 second channel you would expect.

 

I don't think of alacrity as affecting my abilities cast, channel, and cooldown time. I think of those in terms of how many GCDs they take to occur (the number of GCDs remain constant). However the GCD can be sped up so that it *looks* like the abilities are going faster.

 

For example, the previous user posted they have a 10.5% alacrity, and an ability with a 1.5s cast and 15s cooldown. This translates to 1 GCD channel and 10 GCDs to cooldown. That is assuming 0% alacrity and a GCD of 1.5s. Now if we look at those values in terms of GCDs @ 10.5%...

 

GCD = 1.357s (1.5/1.105)

Cast time = 1 GCD (1.357s) (1.5/1.105)

Cooldown = 10 GCDs (13.57s) (15/1.105)

 

Keep in mind these numbers do get rounded for display purposes.

 

I have found its easier to think this way about alacrity. Instead of having to figure out how fast each one recovers/casts/etc just realize they still take the same amount of GCDs to cooldown, its just that the GCD is running a little hotter than normal.

[TankAviator]

The point of diminishing returns, in the strictest sense, is as soon as you have more than 0 rating. There is no point at which DR "kicks in". It's ALWAYS diminishing. That's one of the fundamental properties of gearing in SWTOR.

 

If by "point of diminishing return" you mean, "point at which it isn't worth stacking any more", that's a very complicated question, and not one that has a single answer. There is no point at which you get zero value out of more of a rating (except for expertise and accuracy, which are weird). Seriously. You could have every single tertiary slot on your gear be critical rating, and adding more crit would still increase your DPS/HPS.

 

What is a more useful question is where it becomes more valuable to put points into a different stat. In general, the answer to that is "always and forever, stack pretty evenly" because of the fact that diminishing returns start at rating = 1. The more nuanced answer to that question is, "look at Bant's post".

 

tl;dr: There is no line that can be drawn to indicate a "point of diminishing returns", because there is no "point".

 

There is a line that can be drawn to indicate a point of diminishing return. Diminishing return means that you get less out of something than you put in. To figure this out, plot the value rating (i.e. crit) vs value percentage (crit chance). If you plot a tangential line anywhere along the graph (the derivitive) you will find that there is a single point where that line has a slope of 1. Anything up to that point increases faster than what you put in, after it increases slower than what you put in. So the ideal soft cap would be where this line has a slope of 1 (i.e. f(x) = 1).

 

So to solve the DR problem for any rating just take the derivative of the equation and solve for f(x) = 1.

[TankAviator]

Hello!

 

Thanks for sharing those équations. But i've got little questions about.

I must change " max(level,20)" by the level of my character, in my case i'm LVL65 so i must change it by 65?

I've got some problem to graph those équations, I don't have the same result as http://imgur.com/hv5sWX9 (from a post of MusicRider, is there any Latex plug-in to write it correctly?

 

Thanks for reading, it's only a year i play this game and now i want to understand a little bit more about it

 

The max(level, 20) is really only there so that all toons up to 20 will use the same base numbers. For example max(1, 20) would return 20, whereas max(65, 20) returns 65. For your case you could replace all of the max(level, 20) parts of the equation with 65. Keep in mind that if you ever want to figure things out for lower level toons you will have to make sure you use the right numbers there.

[KeyboardNinja]

There is a line that can be drawn to indicate a point of diminishing return. Diminishing return means that you get less out of something than you put in. To figure this out, plot the value rating (i.e. crit) vs value percentage (crit chance). If you plot a tangential line anywhere along the graph (the derivitive) you will find that there is a single point where that line has a slope of 1. Anything up to that point increases faster than what you put in, after it increases slower than what you put in. So the ideal soft cap would be where this line has a slope of 1 (i.e. f(x) = 1).

 

So to solve the DR problem for any rating just take the derivative of the equation and solve for f(x) = 1.

 

In := Solve[D[Critical[x], x] == 1 && x >= 0, {x}]
Out := {}

 

Huh. It's almost as if… there is no "point of diminishing return". There is no point at which the tangent has a slope of 1.

 

Also, your units are wonky, because 1 point of rating isn't really comparable to one point of "percentage crit", nor is there any way for you to do that conversion. So even though it's humorous to point out that the concept as you have defined it still lacks a valid solution, it doesn't change the fact that your definition of the "point of diminishing returns" is probably not the right one.

 

I like the way you put it though. Specifically, it's where "you get less out of something than you put in". The problem is determining the value of what you put in. Crit and alacrity trade off against each other, so it is reasonable to try to define the value of a point of rating put into crit in terms of what you could have gotten from that point had you put it into alacrity (and vice versa). Thus, the point of diminishing returns for alacrity is the point at which you get more DPS value out of increasing crit than increasing alacrity.

 

The problem with this definition is it is dependent on amount of alacrity rating you already have (or more generally, the competing stat)! Increase the amount of alacrity you have, and the amount of crit you need to stack to reach a point where alacrity is more valuable goes up (in fact, it goes up exponentially). The inverse is also true.

 

Because of the general form of percentage as a function of rating, there is never going to be a definitive point along the curve where the equation balances out. Increasing the amount of alacrity rating increases the value of critical rating, and vice versa, and they increase their value directly in proportion to the value diminishment they suffer with respect to one another.

 

In short, there is no point of diminishing returns, because you cannot define in any fixed way the value of one point of "rating", and the value of one point of either alacrity or critical rating shifts depending on how much you already have.

 

---

 

As a sidebar, based on how you describe your thought process, I believe you are intuitively grasping at the concept of a "half value" as a way of defining the hypothetical point of diminishing returns. The half value can be easily defined as the rating increase (or derivative) is half of what it is when you have 0 rating. This can be solved in a somewhat roundabout way:

 

f[x_] := Critical[x]

Solve[f'[x]/f'[0] == 0.5, {x}]

 

Or a more direct way:

 

Solve[Critical[x] == 0.15, {x}]

 

Critical ranges from 0 to 30%, and thus the half value is found, appropriately enough, at the 15% mark.

 

In general, I think half values are a pretty reasonable way to look at the rate of return for a given stat, which is equivalent to examining how fast a stat rating "falls off" as you get progressive higher gear levels. It's clearly not a "point of diminishing return", since we can and do optimally stat beyond the half values for given stat ratings (as an example, in the 2.0 era, surge had a half value of less than 150). However, it does give some numerical grounding for the graphical intuition you stated.

Edited December 16, 2015 by KeyboardNinja

[TankAviator]

In := Solve[D[Critical[x], x] == 1 && x >= 0, {x}]
Out := {}

 

Huh. It's almost as if… there is no "point of diminishing return". There is no point at which the tangent has a slope of 1.

 

Also, your units are wonky, because 1 point of rating isn't really comparable to one point of "percentage crit", nor is there any way for you to do that conversion. So even though it's humorous to point out that the concept as you have defined it still lacks a valid solution, it doesn't change the fact that your definition of the "point of diminishing returns" is probably not the right one.

 

I like the way you put it though. Specifically, it's where "you get less out of something than you put in". The problem is determining the value of what you put in. Crit and alacrity trade off against each other, so it is reasonable to try to define the value of a point of rating put into crit in terms of what you could have gotten from that point had you put it into alacrity (and vice versa). Thus, the point of diminishing returns for alacrity is the point at which you get more DPS value out of increasing crit than increasing alacrity.

 

The problem with this definition is it is dependent on amount of alacrity rating you already have (or more generally, the competing stat)! Increase the amount of alacrity you have, and the amount of crit you need to stack to reach a point where alacrity is more valuable goes up (in fact, it goes up exponentially). The inverse is also true.

 

Because of the general form of percentage as a function of rating, there is never going to be a definitive point along the curve where the equation balances out. Increasing the amount of alacrity rating increases the value of critical rating, and vice versa, and they increase their value directly in proportion to the value diminishment they suffer with respect to one another.

 

In short, there is no point of diminishing returns, because you cannot define in any fixed way the value of one point of "rating", and the value of one point of either alacrity or critical rating shifts depending on how much you already have.

 

---

 

As a sidebar, based on how you describe your thought process, I believe you are intuitively grasping at the concept of a "half value" as a way of defining the hypothetical point of diminishing returns. The half value can be easily defined as the rating increase (or derivative) is half of what it is when you have 0 rating. This can be solved in a somewhat roundabout way:

 

f[x_] := Critical[x]

Solve[f'[x]/f'[0] == 0.5, {x}]

 

Or a more direct way:

 

Solve[Critical[x] == 0.15, {x}]

 

Critical ranges from 0 to 30%, and thus the half value is found, appropriately enough, at the 15% mark.

 

In general, I think half values are a pretty reasonable way to look at the rate of return for a given stat, which is equivalent to examining how fast a stat rating "falls off" as you get progressive higher gear levels. It's clearly not a "point of diminishing return", since we can and do optimally stat beyond the half values for given stat ratings (as an example, in the 2.0 era, surge had a half value of less than 150). However, it does give some numerical grounding for the graphical intuition you stated.

 

Yup, looks like you are right, the slope starts below 1. I didn't sit down and actually analyze the formula before writing that. I still think there is some way of framing the question to be able to find a deterministic answer tho, but there may not be. I played around with a few derivatives and couldn't figure out how to define "you get more out than you put in". I'm going to keep playing with this to see if I can't figure out something.

[KeyboardNinja]

Yup, looks like you are right, the slope starts below 1. I didn't sit down and actually analyze the formula before writing that. I still think there is some way of framing the question to be able to find a deterministic answer tho, but there may not be. I played around with a few derivatives and couldn't figure out how to define "you get more out than you put in". I'm going to keep playing with this to see if I can't figure out something.

 

I would be interested to see what you come up with. Half values are basically the best I've ever been able to do. Star Wars's stat scaling system is beautiful, but it doesn't make for a very straightforward answer when beginners ask "how much of X should I stack?"

[Ryuku-sama]

I don't think of alacrity as affecting my abilities cast, channel, and cooldown time. I think of those in terms of how many GCDs they take to occur (the number of GCDs remain constant). However the GCD can be sped up so that it *looks* like the abilities are going faster.

 

For example, the previous user posted they have a 10.5% alacrity, and an ability with a 1.5s cast and 15s cooldown. This translates to 1 GCD channel and 10 GCDs to cooldown. That is assuming 0% alacrity and a GCD of 1.5s. Now if we look at those values in terms of GCDs @ 10.5%...

 

GCD = 1.357s (1.5/1.105)

Cast time = 1 GCD (1.357s) (1.5/1.105)

Cooldown = 10 GCDs (13.57s) (15/1.105)

 

Keep in mind these numbers do get rounded for display purposes.

 

I have found its easier to think this way about alacrity. Instead of having to figure out how fast each one recovers/casts/etc just realize they still take the same amount of GCDs to cooldown, its just that the GCD is running a little hotter than normal.

 

You're actually right. But your method is slightly flawed when talking about spec with rotationnal alacrity variations. Carnage, Marksman, Merc and Sorc comes to mind. Lets take MM because it is the easiest to see.

 

Sniper Volley has a 45s CD. Lets assume our MM Sniper has 0 alacrity for ease of play. Marksman also raise alacrity by 10% for 15s. During the lasts 30s we have 30 GCD/1.5s = 20 GCD. But what about the first 15s? The GCD lasts 1.36s. So we have 15/1.36 = 11.02 GCD. So, our 45s is equal to 31 GCDs instead of 30. This is the first flaw. The CD of every ability used before Sniper Volley (including Sniper Volley) is still using 1.5s GCD while everything used under Sniper Volley is using 1.36s GCD. You can't just uses them both together when you calculate a rotation. You must convert them all to the same unit : seconds. A second problem is even more weird. Sniper Volley lasts 11.02 10% alacrity GCDs. Considering Penetrating Rounds channels for 1.33 GCDs (which is rather hard to calculate with your method) and you use it twice under Sniper Volley, you end up with 0.35 GCD lefts before Sniper Volley ends. Your next GCD or channels would have a duration and a CD of 10% alacrity GCDs. A cast would have a GCD of 10% alacrity GCDs and a CD of 0% alacrity GCDs. It may seems confused, but that is why you can actually calculate duration in GCD for a few specs.

[masterceil]

Awesome thread, first of all!

 

These numbers still good in 4.4? Also, is there a way to tell how many points you're getting in Mastery and Endurance from Datacrons? I could go through and add everything up (not that I have them all yet - mostly missing impside because I don't play there that often), but that seems tedious af and I'm kinda hopin' I can just look at a number somewhere...

[dipstik]

the equations are still good. to find out how many points you are getting from datacrons you can take off all your gear and subtract out the base amounts, which i think are in the hover-over information.

[masterceil]

the equations are still good. to find out how many points you are getting from datacrons you can take off all your gear and subtract out the base amounts, which i think are in the hover-over information.

 

Thanks for the response, very helpful!

 

Could you also tell me about inherent bonuses in gear? For example, I seem to get +41 to my "Skills/buffs" in Health just from putting on my 216 augmented setpiece headgear, +43 from my 220 setpiece hands, etc. Naked, I get +199 from "Skills/buffs"; with all my (average rating 217.2) gear on, I get 703 (comes to an average of +36 per piece, but I don't have time to get all the numbers before maintenance - I'll try to update this post before or after work tonight with more detail).

[DarkLordKarmac]

Great Work by the way.

 

Any ideas on how these will change come 5.0?

[mwissie]

Great Work by the way.

 

Any ideas on how these will change come 5.0?

 

replacing 65 with 70 in the formulas seems to be all the change there is, I've checked it with tanking stats

[masterceil]

replacing 65 with 70 in the formulas seems to be all the change there is, I've checked it with tanking stats

 

I've checked it with all the stats, s/65/70/ is indeed all that's needed there. Also, base HP value is 23,750 at Lv70.

 

What are the new base damage/healing values at Lv70? Also, is there an up-to-date list of the coefficients for each ability?

 

Edit: Google answered most of my previous questions, but not the above ones yet...

Edited January 20, 2017 by masterceil