Impact of mage champion point rebalances

Asayre

As is well known, the PTS has introduced significant changes to the mage champion point system notably

• Capped impact of increasing CP on maximum stat at 20% (On Live, maximum increase is 19.88)
• Spell Erosion no longer has any impact (it is assumed that this will work correctly soon) (Fixed according to PTS v3.0.2)
• Introduction of Master-at-Arms
• Front loading of passives
• Damage done and Champion Point bonus are now additive instead of multiplicative. This implies that stacking Damage Done is less effective now but stacking Damage Taken (on the enemy) is more effective.
• Flooring of all bonuses to the nearest integer

These changes, when considered in isolation, suggest a 3.7% increase in average damage done at the CP cap (630) and a substantial reduction in the difference between players who optimise their champion point distribution and those who do not. Damage gain as a function of number of champion points remains practically linear. The developers stated that the goal of these changes was to “improve the balance and diversity of Champion Point picks while also raising the power floor so that those with Champion Points will be more effective”. The former goal appears to be achieved as a more even spread is more effective on the PTS than on Live. However, the latter goal does not appear to be fulfilled.

These conclusions were made by considering three champion point distribution schemes based on the Live and PTS game mechanics. These champion point distributions are

• Optimised
  On Live, the following equation is optimised via gradient descent
  
  On PTS, the following equation is optimised via genetic algorithm
  
  where
  
  where
  DD = Direct Damage ratio
  DoT = Damage over Time ratio
  DDDoT = Ratio of skills that are both Direct Damage and Damage over Time
  S = Staff ratio
  EE = Elemental Expert
  MaA = Master-at-Arms
  T = Thaumathurge
  SE = Staff Expert
  Done = Damage Done
• Even
  Champion points are evenly distributed across Elemental Expert, Elfborn, Spell Erosion, Staff Expert, Thaumathurge and Master-at-Arms.
• Irrelevant
  Champion points are placed in stars that have no effect on damage but still placed to increase maximum magicka

The figure below demonstrates the performance of these three champion point distribution with Live mechanics. A player with 180 champion points who reaches the 630 champion points can expect a DPS gain of 4% due to gain in maximum magicka. Players who optimise their champion point distribution (from an even distribution) can expect a DPS increase of about 13%. However, players going from 180 CP to 630 CP can expect a DPS increase of 27% with an optimised champion point distribution or 20% with an even champion point distribution. Both the optimised and even champion point spread show a very linear relationship between number of champion points and ability metric.



Since the maximum magicka multiplier due to CP is capped at 20% on the PTS, a CP180 player going to CP630 will notice a DPS gain of 1.26% from the increase to their maximum magicka. The increased front loading in the champion point system causes an even champion point spread strategy to be substantially better than on Live thus optimisation is not as important. An optimised champion point distribution will yield a 4% DPS increased when compared to an even spread strategy. Contrary, to the developers claim, both the optimised and even champion point spread have a strong linear relationship. It is noted that the coefficient for the optimised distribution is practically identical which leads me to conclude that the power gap between high and low champion point players remain comparable. The flooring of all bonuses to the nearest integer has caused jump points in the ability metric for the even spread strategy.



Edit:

Jump points apply to most percentage based stars except for those that apply a cost reduction. List of current jump points


CP optimisation links
http://solinur.de/AsayreCP/CPOptimisation.html
https://woeler.eu/cp/

Partial list of which skills are classified as what
https://docs.google.com/spreadsheets/d/18LptRy_AfGVehOyIioJJ6PQD98HB0lCOO_GWOcs7Tr4/edit

ArtOfShred

Appreciate you spending the time to do the backing math on this.

I was concerned right away that the large performance disparity between lower and higher CP would remain about the same. I have a feeling they basically countered themselves when they added an additional node that increases/decreases all direct damage. Despite the diminishing returns theres too many effective nodes to spread your damage around.

DPShiro

@Asayre
Very insightful and interesting as always! Please continue doing this awesome work for the community

GilGalad

Quick question concerning the comparison of the different CP scaling on live vs. PTS:

How does the DPS increase by CP on live compare to the DPS increase on the PTS?

The more front loaded CP should give a lot more value out of the spend CP, on the other hand they nerfed some major DPS sources like elemental expert and mighty.
Making the CP dmg boni additive with other sources of dmg increase is a significant nerf.

Asayre

Based on the linear regression, I would say that DPS increase for optimised CP distribution on Live is ~0.2% per Mage CP (Ability Metric = 214*Mage CP + 111668) and similar to the DPS increase on PTS ~0.2% per Mage CP (Ability Metric = 215*Mage CP + 112212). For an even CP distribution it is about 0.15 on Live and a bit lower than 0.2 on PTS. So the power gap between high and low CP players should increase a bit (unchanged for optimised CP distributions but less optimised CP distributions get increased).

The front loaded CPs make it such that an even CP distribution is much more effective on the PTS than on Live. Making CP bonuses additive with damage done additive bonus does decrease top end DPS more but it is does depend on which class is considered as well.

PS4_ZeColmeia

All hail @Asayre

Good to see ya friend! Thanks as always for your community support.

lunalitetempler

I don't even understand.

Nolic1

So not to say this is not good work but the fact its really broken down and I have not used calculus in a long while. But this is with what kind of optimized cp spread and what quality of weapon legendary?

Again not to look down on but after reviewing this more it seems the dev's want to make the CP attribute cap at CP 300 an easier goal them it is now so players at CP 300 and CP 600 are not as far apart as before. And that makes sense the other changes with the Direct Damage and having to put into ether Physical Weapons or Staff expert depending on your DPS is whats going to separate the gap in DPS cause of more point distribution making lower CP players not as well off in DPS as max CP. This is what will make getting to CP cap a mush more rewarding thing when you think about it.

But no matter like the work great math by the way and did you test these factors on both live and PTS?

Feanor

@Asayre

Gear traits have not been touched. I guess the disparity between running divines/sharpened and lesser traits makes even more of an impact henceforth than anything else. Thanks for your great posts.

dpencil1

@Asayre Can you use some example numbers for the optimal distribution equation?

And will you be updating your online calculator?

Asayre

@dpencil1 It's a bit hard to give example numbers because there were so many optimisations. But here is an example output for a particular testing scenario (not related to this post)


I am the process of thinking about what to do with the online calculator. The online CP calculator was my first web project and to be honest it's really bad. It's not striking and it doesn't work on small screen sizes. So I'm thinking if it's better for someone else to do it instead.

@Nolic1, this was done with legendary sharpened and the optimised CP distribution was varied for each case and was solved using the fitness function provided. What I'm saying is the gap between players of equal CP with an optimised CP distribution and those without (even CP spread) will be smaller but the power gap between low (180 CP) and high (630 CP) players will remain roughly the same (or a bit larger) than on Live. The results are based on knowledge of mechanics on both Live and PTS.

Ghettokid

Doesn't affect me cause I'm orc.

dpencil1

@Asayre Thanks for the reply. I wonder, if you're not going to update the website calculator if you'd make your calc program you used available for download. Really though, I was asking if you could do an example with concrete numbers using the formulas in the OP. I would like to do the math as well, but it's tough for me without seeing an example of the formula in action. For example, I'm not really sure what the "damage done" portion is, or at what point in the formula I would be able to determine how many points belong in a particular star. Also, if there are jump points to consider, whether that is taken into account or how to correct for that.

smhzdmr

@Asayre

Hey dude,

Have a nice day and thanks for this awesome work of yours im waiting for more *hyped*

I need to ask you this. What is that ''Done'' Buff.

Do we get it from CP or like combat prayer exct.

Masel

Double phone post.

Masel

A thing I experimented with a lot is the spell erosion/piercing stars. I have been using non sharpened weapons with spinner on live for alt chars because I didn't want to move gear all the time and it was very close to the old BiS setups. Now with 50 Points in one of the Penetration cps you get 5160*0.75=3860. This is very close to spinner and in raids with all Buffs applied you get to 19128 Spell Penetration without using any sharpened weapons, which is still 928 too much. So the question is: does this frontloaded cp star allow for non-sharpened weapons to be viable?

In raids you will still most likely invest to unlock the exploiter passive, so 75 points in thaumaturge. Leaves 135 points: 50 in spell erosion, 25 in Elfborn, 50 in elemental expert, 10 in staff expert? Or take out a few from elemental expert and 0 in staff expert and put them in master at arms?

On magblades with higher critical rating it might be better to put more into elfborn and take them out of ele expert or Master at arms.

For stamina builds this could enable to use a lot more builds. So with sharpened weapons you can put into piercing and drop twice-fanged serpent or use twice-fanged serpent and use non-sharpened weapons without losing too much damage.

Any thoughts on this?

Malamar1229

So basically....

clocksstoppe

lunalitetempler wrote: »

I don't even understand.

The power gap will still be huge between high and low cp players because frontloading allows high cp players to just use many more frontloaded passives.

Dagoth_Rac

I think they need to add front-loading of power to stats and resources, too. Like 4000 spell damage should not have 100% more impact on your abilities as 2000 spell damage. And having 45,000 magicka should not have 50% more impact on your abilities than having 30,000 magicka. And so on for a whole bunch of stats. That would go a lot further to "Lower the Ceiling/Raise the Floor" than blanket nerfs to sustain and skills and sets, which tend to hurt average player a lot more than the elite/optimized/min-max players.

It is the linearity of power in so many aspects of this game that makes min/max builds so much better than average builds. I don't want a return to soft caps. I have been here since PC early access. The soft caps made you hit a pretty stiff wall and while they did lead to people spreading out stats, most everyone just spread out stats in same way. Nowadays everyone puts all attribute points in magicka. In soft cap days, everyone put all attribute points into health. There were lots of problems with the pre-CP system. People are looking back at it with rose-colored glasses. Or they played the sticks-and-skirts magicka DK meta that dominated in the early days and miss being totally OP.

It was like soft caps sent you off a cliff after a certain point. Current design is nearly linear ascent. Some happy medium, with more smoothly diminishing returns in all aspects of player power, CP and stats, would be more effective balance than the constant (and largely ineffective) blanket nerfs to everything to combat this highly linear power trajectory.

Asayre

@dpencil

I've made a webpage for it but there are a few improvements I still want to do. With regards to a concrete example, perhaps this spreadsheet by @decay might explain it better? If not, let me know and I'll see if I can explain it better. Damage Done is stuff in game that says something along the lines of increases your damage done such as Minor Berserk (from Combat Prayer) or racial passives (High Elf > Elemental Talent). It is not to be confused for Damage Taken like the nearest enemy of Puncturing Sweeps taking 140% extra damage or the health scaling of Radiant Oppression. It's a rather troublesome variable to work out properly and I don't have any ideas on how to get a good estimate of it.

dpencil1

@Asayre
Thanks! That's exactly what I needed. Looks like my optimal build is gonna be 50 Ele Expert, 35 Elfborn, 35 Erosion, 15 MaA, 75 Thau.

It would be interesting to be able to see at what point the Exploiter passive no longer becomes worth putting 75 points into Thau.

Izaki

Sooooo do Elfborn and Precise Strikes still suffer from Jump Points?

STEVIL

Dagoth_Rac wrote: »

I think they need to add front-loading of power to stats and resources, too. Like 4000 spell damage should not have 100% more impact on your abilities as 2000 spell damage. And having 45,000 magicka should not have 50% more impact on your abilities than having 30,000 magicka. And so on for a whole bunch of stats. That would go a lot further to "Lower the Ceiling/Raise the Floor" than blanket nerfs to sustain and skills and sets, which tend to hurt average player a lot more than the elite/optimized/min-max players.

It is the linearity of power in so many aspects of this game that makes min/max builds so much better than average builds. I don't want a return to soft caps. I have been here since PC early access. The soft caps made you hit a pretty stiff wall and while they did lead to people spreading out stats, most everyone just spread out stats in same way. Nowadays everyone puts all attribute points in magicka. In soft cap days, everyone put all attribute points into health. There were lots of problems with the pre-CP system. People are looking back at it with rose-colored glasses. Or they played the sticks-and-skirts magicka DK meta that dominated in the early days and miss being totally OP.

It was like soft caps sent you off a cliff after a certain point. Current design is nearly linear ascent. Some happy medium, with more smoothly diminishing returns in all aspects of player power, CP and stats, would be more effective balance than the constant (and largely ineffective) blanket nerfs to everything to combat this highly linear power trajectory.

i agree. this combined with the sustains coming up, would also do a lot for rejuvenating hybrid builds.

Bladerunner1

Dagoth_Rac wrote: »

I think they need to add front-loading of power to stats and resources, too. Like 4000 spell damage should not have 100% more impact on your abilities as 2000 spell damage. And having 45,000 magicka should not have 50% more impact on your abilities than having 30,000 magicka.

Stats like spell and weapon damage are kinda front loaded. Each increment of extra damage stat provides less and less percentage to the total damage. It's more of a flat increase, like gaining 1000 more magic could increase the damage of a skill by 100 whether you have 10,000 magicka or 35,000 magicka.

Zarrakon

Dagoth_Rac wrote: »

I think they need to add front-loading of power to stats and resources, too. Like 4000 spell damage should not have 100% more impact on your abilities as 2000 spell damage. And having 45,000 magicka should not have 50% more impact on your abilities than having 30,000 magicka. And so on for a whole bunch of stats. That would go a lot further to "Lower the Ceiling/Raise the Floor" than blanket nerfs to sustain and skills and sets, which tend to hurt average player a lot more than the elite/optimized/min-max players.

It is the linearity of power in so many aspects of this game that makes min/max builds so much better than average builds. I don't want a return to soft caps. I have been here since PC early access. The soft caps made you hit a pretty stiff wall and while they did lead to people spreading out stats, most everyone just spread out stats in same way. Nowadays everyone puts all attribute points in magicka. In soft cap days, everyone put all attribute points into health. There were lots of problems with the pre-CP system. People are looking back at it with rose-colored glasses. Or they played the sticks-and-skirts magicka DK meta that dominated in the early days and miss being totally OP.

It was like soft caps sent you off a cliff after a certain point. Current design is nearly linear ascent. Some happy medium, with more smoothly diminishing returns in all aspects of player power, CP and stats, would be more effective balance than the constant (and largely ineffective) blanket nerfs to everything to combat this highly linear power trajectory.

Linear scaling with no cap means much more build diversity, and it is not really leading to any problems in the game currently. Removing this would mean much less meaningful choices between damage and tankiness, and damage and sustain (and on Live, these choices are not meaningful as it is).

You don't make a very clear point in your post; what exactly is your problem with linear scaling? What is happening in the game right now or on the PTS that is a problem caused by this? As far as I can tell, your argument is:

- 50% more stats should not mean a 50% greater increase in base damage.
- People who wear 2 sets with +spell damage do proportionately more damage per spell than people who wear 1 set with +spell damage and another set with no relevant bonuses to their damage output.
- Linear ascent is bad. Old soft caps are bad. Something in between, just not a 'highly linear power trajectory'.

If you think that sustain nerfs hurt the average player a lot, then it seems like you really just want that to be reverted. If you want everyone to be roughly as powerful as everyone else no matter what they wear (which I think is really what you're going for here), just say so outright.

Haroeris

Excellent work as always, @Asayre! Quick question: are you using your staff ratio for both LA/HA (for use with staff expert) as well as destro staff abilities? I'm curious how the spell erosion might optimize using the extra pen from destro passive vs not. Thanks!

Asayre

@dpencil, you can figure out how much off-balance uptime you need for it to be worth putting 75 points into Thaumathurge in this way

1. Fill in all the fields, I'll use the default values on the page. Click calculate and note the 'Function value'. It is 1.59771.
2. Set the minimum CP limit for Thaumathurge to 75. Click calculate and note the 'Function value'. It is 1.55133.
3. Increase the damage done to say 3% (off-balance uptime of ~30%) and just select any field in the Suggested Distribution and press Enter and the function value will recalculate and you'll get 1.58803
4. Increase the damage done to 4% and recalculate the function value (by selecting any field in the Suggested Distribution and pressing Enter) and you'll get 1.60027

So this is saying that, in this scenario, if you have an off-balance uptime of ~40% it is worth putting 75 points into Thaumathurge.

@IzakiBrotherSs, now pretty much everything has jump points! It's more fun that way. Here's an example for the 25% stars like Elfborn, Master-at-Arms, Thaumathurge etc. The blue dots are the in-game tooltip values and the orange dots are the actual increase


@Hoeris, no I'm not accounting for Penetrating Magic. I guess I could but then I would need an additional field for the percentage of damage from Destruction Staff abilities (and staff LA/HA). I suppose a bad solution would be to put limits on the maximum points in Spell Erosion. It kind of achieves what you want but in a really horrible way.

@Masel92, It's a tough question and I'll probably need to think about it more. I think in the situation you describe Precise will be better. If you visit the webpage and add Major Breach, Minor Breach, Infused Crusher, Alkosh and just calculate assuming your stats will be close to the default values you get a function value of 1.83263. If we remove Sharpened and add 7% critical chance for using Precise we get a function value of 1.86566. I could do the same thing but add Spinner (put 4000 into Penetration > Other) and with Sharpened I'll get a function value of 1.83263 (same as before because we were already over penetrating) and with Precise I'll get a function value of 1.90023 so showing that in these ideal debuff situations is better. But then again in ideal debuff situations at the moment Precise is already better. I suppose the threshold on a scale of ideal raid buffs and no buffs will be lowered for when Precise becomes better than Sharpened.

Rinmaethodain

Great post as always

Rinmaethodain

Asayre wrote: »

(...)

@IzakiBrotherSs, now pretty much everything has jump points! It's more fun that way. Here's an example for the 25% stars like Elfborn, Master-at-Arms, Thaumathurge etc. The blue dots are the in-game tooltip values and the orange dots are the actual increase


(...)

@Asayre do defensive CP like Hardy, Elemental Defender, Thick Skinned, Shadow Ward also have jump points? Do literally every CP have jump points now?

Haroeris

Ah, ok. Probably minor for most rotations, but wasn't sure with respect to force pulse spammable and blockade.

That's hilarious about the jump points though -- I had (incorrectly) assumed that having 4 sig figs would fix the problem, not propagate it. Are there jump points for Ele Exp (15%) and Staff Exp (35%) now too?

Asayre

There are jump points for every 15%, 25% and 35% star so yes to Elemental Expert, Staff Expert, Hardy, Elemental Defender, Shadow Ward and Thick Skinned. It seems only the 5280 stars do not have jump points (i.e. Piercing, Spell Erosion etc.)