Softcaps discussion

[Gorlough]

As this discussion came up a few days ago, and there are constantly people assuring they know about them, I wanted to share my thoughts on softcaps in SWTOR and how we might be able to track them down.

Thoughts about Softcaps:

First we have to define, what is meant by the term Softcap.
A Softcap is a theoretical border, that upon reaching it is rewarding optimal performance for a given task by reaching a certain value.
If you decrease that value or increase it, the performance starts to become suboptimal.

As an example you can use two calculated values, where one value is giving diminishing returns, whereas the other value follows a linear progression and both add to one result.
The Softcap in this case would refer to the first value and is reached at the point, where the linear increase cuts the DR-curve.
If you would further increase the DR-value instead of the linear value, the resulting value would be lower than the results when you instead increase the linear value.

So far, this is easy. But we’re talking about a environment here, where at least three values determine the results, in most cases even more.

For example:
Damage is based on stats, on random elements, on skills and on hardcoded modifiers.

To determine the optimal (outgoing) damage we have to rule out the random elements first.
This can be achieved by doing an educated guess, of how the randomness is calculated.
There are two models, we might take into consideration: a Gaussian distribution and a linear distribution.
From a programming point of view, there’s only one that makes sense and that is the linear distribution.
Linear distribution means, each value in a given range will statistically appear the same amount over a large scale than any other value in that range.
Using this assumption, we can statistically rule out the random element of – let’s say critical hits – if we use the probability of its occurance.
On the other hand, if we’re talking about a damage range, we can safely assume that over a large scale, the damage values are an average of the minimum and maximum damage possible.

After ruling out any random elements, we can proceed and take a look on skills. Those can be seen as a constant (you’re only able to have one spec).
Hardcoded modifiers are a constant as well.

Those constants are never the less important for the calculation and may vary from skill to skill, which brings me to the point of making educated guesses on what percentages those skills take in a damage rotation.

These are the things you have to remind, when going over to the Softcap calculation.
Only if you have done these basic preparations, you can fill in the values for stats (aka equipment).

To determine, what’s the best stat set to use, you need to take also into consideration, what’s even possible. This can be done, if you take the highest value for a given enhancement, mod, armoring, augment and hilt/barrel (check the databases and/or rakata/battlemaster vendors) and add them up to the extremes.

The results should show quite different values at this point.
If you start swapping the used values you’ll notice a change in the results. You could do some work and iterate for the best result. But you could also approach this mathematically.
Basically you have to calculate the sum for every set of constants (skills/ability used) in their estimated distribution.
The stat values vary in these calculations in an interval from 0 to the max value possible.

Code:

The formula for this is basically:

f(result) = benefit(stat1) + benefit(stat2) + benefit(stat3)…

What we are searching is:

f'(result)

And from here it gets ugly, as each benefit itself is a function within a certain interval of a given stat, which again is determined by the other stats.
If anybody wanna do the fancy math there – go ahead

Technically it is possible to determine Softcaps in a mathematical manner, but personally I like spreadsheets, iterating and gut feeling better.

[Kaedis]

The sticky point for me is that when most people say "softcap", they mean a universal one. Example, "For Sorcerers, stack surge until the softcap at 90% crit multiplier, then stack Power". This literally cannot be done for SWTOR due to the DR scaling and inter-relation of the stats.

Another often-cited portion of the definition of "softcap" is a breakpoint where a stat suddenly (or at least rapidly) becomes less useful than it was or applies to less of your abilities than it used to. A good example is the 40% crit threshold for Frost mages in WoW, where the 40% was the necessary threshold to reach 100% crit with Shatter. Thereafter, only non-Shatter casts would benefit, and thus crit lost a large portion of its value. Other examples include special hit cap for dual-wield classes like Enhancement Shaman, or Expertise caps for tanks. SWTOR doesn't really have any analogous situations.

This means that soft-cap, for SWTOR, really just means "the point where another stat is more valuable". This is fluid, and thus not a true "cap". For example, the rough napkin-math theory I was doing for Sorc healers on the official forms showed that Power, Alacrity, Surge, and Crit would be within 2% value (for raw healing output) if all 3 of the following were true:

Alacrity = 150 + Power/10
Crit = 150 + Power/10
Surge = 225 + Power/20

I also ran a more complicated version that set all of the stats equal to Willpower in value. All of these equations are fluid and dependent on other stats (the Surge equation is actually technically Surge = 150 + Crit/2), meaning that aren't really "softcaps", they are instead stat weights.

Ideally, according to the MMO community's definition, "Softcap" is mostly independent of other stats, just based on skills, class, and ability information and distribution. They also tend to be something like "stack this stat to X, then keep it there", while in TOR X would be fluid and they'd need to change it with every gear upgrade. Since the SWTOR "softcaps" would be highly volatile based on the character's current stats, it's better to stop referring to them as "Softcaps", since that has a particular definition to the MMO community, and instead use terms such as "stat weights". Stat weights, in point in fact, is actually what you were explaining in the OP, not the traditional definition of "softcap".

[CaseyTheRetard]

I'm beginning to think that use of the term "softcap" on these fora should be a bannable offense. Every time a non-theorycrafter sees the term "softcap," it reinforces the belief that there are static caps that they should be trying to achieve with their stats: "How much crit should I go for?", "Is Surge useless over XX%?". By allowing the term to proliferate, we are doing the gaming community a disservice.

[Kaedis]

(01-21-2012 05:02 AM)CaseyTheRetard Wrote:  I'm beginning to think that use of the term "softcap" on these fora should be a bannable offense. Every time a non-theorycrafter sees the term "softcap," it reinforces the belief that there are static caps that they should be trying to achieve with their stats: "How much crit should I go for?", "Is Surge useless over XX%?". By allowing the term to proliferate, we are doing the gaming community a disservice.

Precisely the point I was trying (probably excessively verbosely) to make.

[Neokarasu]

I agree that I think this would be a futile exercise. I know players like to be spoonfed simplified versions of theorycraft but the way rating conversion works in this game makes a generalized weighting system inaccurate. That is to say, the value of each rating is different on a case-by-case basis. All we can figure out is relative effectiveness of each stats. Since each stat is relative to the other, there is no true "cap" because increasing one stat decreases the effectiveness of the subsequent gain for that stat while also increasing the effectiveness of the other stats.

So while that might sound like a "cap", it's really not since when you stop increasing that stat and start increasing the other ones, that will subsequently increase the value of the former stat once again. Unless one stat is absurdly ahead of the other ones, the relative value of all stats will be around the same.

[Fraser]

So, determining stat relationships, who wants to start solving that, what 4 or 5 order DE? not me, I've already proven that my math is way past its best before date.

[Kaedis]

Honestly, Fraser, while there may in fact be an exact solvable equation for the stat weights, I think it's well beyond the scope of a useful endeavor. Approximations (very good ones) from a well-written sim are rather easier to handle.

Quote:the relative value of all stats will be around the same.

This is what I've been aiming for, actually. I've been attempting to come up with single-variable constraint equations for the various stats to indicate equal-benefit curves. For example, I showed out on the official forums that for a Corruption Sorc who has around 1500 Willpower and 1200 Force Power, all 4 second stats have within 2% value of each other for raw healing output if all 3 of the following are true:

Crit = 150 + Power/10
Alacrity = 150 + Power/10
Surge = 150 + Crit/2 = 225 + Power/20

Valid for the approximate range 0-1000 Power (Power in this does not include Force Power).

These type of equations give a good at-a-glance stat weight approximation that may fulfill the needs of the less math-oriented that just want an easy stat weight table, while maintaining the integrity of the theorycrafting and the validity of the results. Once we have a bit larger knowledge base on each spec's scaling equations, we could probably even build a web-based calc for each class. Put in your stats, out it spits stat weights.

[Gorlough]

I guess you have a point on not using the term 'Softcap' for what we're talking here about.
Therefore I redefine the term 'Softcap' to 'StatOptimal'. Problem solved

[LagunaD]

(01-21-2012 08:11 AM)Fraser Wrote:  So, determining stat relationships, who wants to start solving that, what 4 or 5 order DE? not me, I've already proven that my math is way past its best before date.

It's hardly that bad. Given the relative frequency at which each ability is used (and this doesn't need to be perfect, just a reasonable estimate), a spreadsheet can solve the problem numerically in a couple seconds.

[Kaedis]

Quote:It's hardly that bad. Given the relative frequency at which each ability is used (and this doesn't need to be perfect, just a reasonable estimate), a spreadsheet can solve the problem numerically in a couple seconds.

Problem is, the stats themselves can affect that relative frequency (and it would need to be exact if we are trying to make an exact equation). For example, high crit for a Sorcerer 13/28 build means higher incidence of Lightning Barrage, meaning more Force Lightning usage relative to other abilities (which then slightly decreases force efficiency, reducing the number of Chain Lightnings, which then increases Force Lightnings even more).