Cost Reduction Changes and Issues (Long + Maths)

Ezareth · February 2015

I've spent hours of time testing and researching the various forms of Magick cost reduction available in both live and PTS.

On live, calculating the cost of a spell is a relatively simple calculation. You take the base cost of a spell (which is calculated using your character level) and subtract from it any cost reduction jewelry enchants you have. From this adjusted base number you reduce it further by the total sum of the spell cost reduction percentages you currently receive. These can include, Breton Racial, Class Passives, Light Armor Passive, and various set bonuses (Seducer, Archmage, Wyrm's Rainment etc.), as well as procs like Crystal Fragments(-50%) and even penalties like the Bolt Escape(+50%) Penalty. The math is exact and the benefit of using a particular set or enchant is quite clear.

1.5 Cost Formula = (x-y)*z
where x = Base cost, y = Sum of your Reduction Enchants, and z = Sum of your Reduction percentages.

Enter 1.6

I've been able to create a formula that fits the model within a couple of magicka points but it isn't exact like my understanding of this on live. I've determined that each spell now has percentage of its cost that can't be reduced by spell cost reduction percentages. This percentage of cost works out to roughly 12.3% of the base cost of the spell.

This means that *all* cost reduction set bonus, passives, racials and procs were nerfed by roughly 1/8th.

I think this is pretty absurd as if I spend skill points or craft a set of gear to make my spells cheaper the reduction percentage I receive should match the percentage displayed on the tooltip.

The new calculation is now as follows:
((x*.877)*(100-z))+x*.123)*(100-w)) - (y*((100-(z*.877)))) where x = Base cost, y is the sum of your Reduction Enchants, z is the Sum of your Reduction percentages, y is the Sum of your Reduction Enchants, and w is the champion point reduction percentage.

Jewelry enchant reductions are also pretty hosed. A VR14 magicka reduction neck provides 198 spell cost reduction (the tooltip says 200) yet the same enchant on a ring provides 212 spell cost reduction. Using all 3 enchants nets you 623 cost reduction to base before factoring non-champion cost reduction percentages.

So what can the person who doesn't love figuring out formulas take away from this?

Spell cost reduction percentage bonuses were slightly nerfed
Spell cost reduction enchants were slightly buffed
Champion points spell reduction bonuses are calculated separately from percentage bonuses and because the effect isn't additive, it isn't as powerful as a percentage bonus
Spell Cost reduction on the neck slot is far weaker than on the ring slots

Things I'd like someone to test if they have the time or the gear necessary to do so:

Do the stamina cost reduction equivalents use these same formulas or is it still the simple formula used on live?

Are only spell cost reduction enchants less effective on the neck slot or is this present in all enchants?

XEVENEX · February 2015

Nice work man. I gave up on stuff like this because the game seems to be pretty jacked up in general right now. Many abilities that used to proc frags now wont, out of combat regen is now lower than in combat regen, people are hitting for like 4 million damage, you cant craft anything higher than rank 9, combat is completely different, horses get stuck on ants, all the while theyre nerfing *** like they even know wtf needs nerfed. They have no idea. They know one thing though... They've got a month to fugure it out before lol tamriel unlimited hits the shelves.

Rizcarn · February 2015

Deleted

Helluin · February 2015

I tested this during last week, maybe it can help you or provide some info.

Ezareth · February 2015

Rizcarn wrote: »

((x/1.w%)-y)-((x-y).z%) works right
Example:
base cast
x=1211
Breton 1%
z=1%
jewelry3 items 163 each
y=489
Champ reduction 1%
w=1%
((1211/1.01)-489)-((1211-489).01)
((1199.0099)-489)-((722).01)
(710)-(7.22)
702.78
on Pts READS 703

Champion Reduction reduces by un-modded Cost(1211) while everything else does by modded Magicka(722).

Only thing not working right is the amount that jewelry reduces.
VR 1 gold rune says 179 each but at V1 each gives 145 each and at VR14 163 each.

@Rizcarn‌ That formula isn't correct.

It is easy to model something at the lowest cost reductions but the flaws become much more apparent at higher reduction percentages. You can't trust the tooltips of the Jewelry cost reduction enchants for one. That stumped me for awhile. You have to calculate the exact cost reduction you're getting by checking the spell cost tooltip while you have zero cost reduction passives (Champion point reduction isn't affected by magick cost reduction enchants.

My formula works perfectly for every number possible that you plug in. As I said I spent hours to determine exactly how all aspects of reduction behave.

It is possible to get 92% reduction to Crystal fragments yet even with 623 magicka cost reduction enchants (The V14 max) and 15.8 Champion point reduction (100 points) the cost is still 464. This is why I think they made a portion of spells unable to be reduced, in order to insure that it isn't possible to get magicka return upon costs, or to have nearly free casts.

Using my formula (my original post simplified the percentages and I transposed an error in the magick reduction):
((x*.877)*(100-z))+x*.123)*(100-w)) - (y*((100-(z*.877))))
X=3591 (Base Cost)
Z= 100-92% = 8%(Magick cost reduction percent)
W=100-15.8%=84.2%(The champion point reduction)
Y=623 (Magick reduction enchant total)

(3591*.877)*(100-92))+(3591*.123)*(100-15.8))-(623*((100-(92*.877))))
((3149.307*.08)+(441.693))*(.842)-(623*(100-80.684)
(251.94+441.693)*.842 - (623*(.19316))
(693.633*.842 -(120.33868))
584.038986-120.33868
463.66132

Actual PTS cost = 464.

There are times when my formula will be 1 magicka point off but that is due to rounding issues since we don't know the *true* numbers being used, only the numbers they are being rounded to.

If you want to try my formula in excel or a spreadsheet program use this:
=Sum(((P83*0.877*((100-P86)/100))+(P83*0.123))*((100-P87)/100))-(P88*(100-(P86*0.877))/100)

P83 = Base Cost
P86 = Spell Reduction percentage displayed as a whole number (92 in this case)
P87= Champion Point Reduction displayed as a whole number (15.8 in this case)
P88 = Magick Cost reduction enchant total

The behaviors I've mapped are extremely confusing and some of them don't make sense. For instance on live your spell reduction enchants are reduced by your spell cost reduction percentages which makes sense otherwise your low cost spells would be free. The new formula however *reduces* this reduction by 12.3% which actually makes cost reduction a bit more powerful than they would be otherwise, especially at high spell cost reduction percentages. Maybe they did this to offset the unreducible percentage but the math behind everything is very confusing to someone who is just expecting to receive a certain benefit based upon a tooltip.

Helluin wrote: »

I tested this during last week, maybe it can help you or provide some info.

The real issue with cost reduction is just the tooltips displayed are not what you receive. Once you know exactly how much you're receiving by enchant they are predictable.

Soulac · February 2015

This formula is the closest i got and it works perfectly fine with my build planer.
Tested with many different parts of Light Armor, Medium Armor, Equip Reduction, Glyphs etc.

((BaseCost - ChampionPercentage) - Flatreduction) - (otherPercentages x 0,877)

example:
BaseCost - 2400
ChampionPercentage - 10% (Magickacost reduction)
Flatreduction - one Glyph with 200 reduction
otherPercentages - full light Armor -> 21%

((2400 - 10%) - 200) - (21% * 87,7%)

Well there´re smaller difference like 5-10 cost but they´re based on the roundings in my calculations or better said my program.
86.66667% might be not completly right as well, i´ll test your formula!

Already made a thread about it.
http://forums.elderscrollsonline.com/discussion/151159/new-cost-and-stat-calculations-change-to-reduction-passives#latest

Implemented your formula into my program, but it´s as correct as my formula above.

Ezareth · February 2015

Soulac wrote: »

This formula is the closest i got and it works perfectly fine with my build planer.
Tested with many different parts of Light Armor, Medium Armor, Equip Reduction, Glyphs etc.

((BaseCost - ChampionPercentage) - Flatreduction) - (otherPercentages x 0,866667)

example:
BaseCost - 2400
ChampionPercentage - 10% (Magickacost reduction)
Flatreduction - one Glyph with 200 reduction
otherPercentages - full light Armor -> 21%

((2400 - 10%) - 200) - (21% * 86,6667%)

Already made a thread about it.
http://forums.elderscrollsonline.com/discussion/151159/new-cost-and-stat-calculations-change-to-reduction-passives#latest

@Soulac‌

I'm not getting accurate numbers with that formula and it becomes far less accurate at extremes. I'm glad someone else collaborated the new factor introduced to the calculation (although the number is closer to .877 than .866667. Your formula separates champion point reduction from the enchant cost reduction but the enchant cost reduction is calculated before the spell cost reduction not independent from it.

Using the Crystal fragment example I provided your formula would allow me to be -463 cost when I'm actually positive 464.

I plotted and tested over 60 different combinations of spell cost reduction, champion point reduction and magicka cost reductions and my formula works perfectly (within 1 point of rounding error) on every combination for 5 different spells.

Soulac · February 2015

@ezareth_ESO‌
You probably used my formula wrong.

Base 3591
Flat 623
Champion 15,8
Other 92

New 463,7041455

It´s the SAME, except that my formula is smaller.
According to your result above, mine is actually a bit closer to the the cost on pts.

((3591 x (1-15,8/100)) - 623) x ((92 / 100 * 87,7%))
Changed the percentage a bit based on new calculations.
(86.66667% is close too.)

Ezareth · February 2015

You're not writing your formula correctly then but I see now that it is the simplification of mine that I was hoping someone would come up with.

The only difference now is that the "factor" is close to .877 not .8777 which is too high.

Your (or Our I could say) formula in excel format is:
=sum((X*((100-Y)/100))-Z)*(1-(W/100)*0.877)

This is a reduced form of
Sum(((X*0.877*((100-Y)/100))+(X*0.123))*((100-Z)/100))-(W*(100-(Y*0.877))/100)

Soulac · February 2015

@ezareth_ESO‌
Well it was correctly written.. :P

((2400 - 10%) - 200) - (21% * 87,7%) is the same as
((2400 * (1 - 10/ 100)) - 200) - (1 - (21 / 100 * 87,7%))

2400 - 10% = 2160
2400 * (1-10/100) = 2160
2400 * 90% = 2160

It´s just a different / easier way to write it.

Anyway, yes it´s a short version i came up shortly after the release of 1.6.2.
Kinda easy to figure out, cause the champion passives and enchants were applied with 100% of the passive and the other percentages not (with 87,7% instead).

Other Calculations:
The calculation of the statincrease based on invested points, which is capped at 1k Points, is kinda similar and same with other stats which get increased by the champion system.

Stats:
((Base * ChampionPercentage) + Flat) * OtherPercentage

The formula for Magicka/Stamina/Health is kinda complicated and the specific championpoint-based modifier doesn´t include buff-food as example.
Stats = max. Stats without bufffood and championpoints

((Stats * modifier) + (Stats + BuffFood)) * PercentageIncreases

Well for the modifier.. look somewhere else in this forum :P

XEVENEX · February 2015

((2400 - 10%) - 200) - (21% * 87,7%) is the same as
((2400 * (1 - 10/ 100)) - 200) - (1 - (21 / 100 * 87,7%))

Yall are makin my head hurt...

(2400 - 10%)

10% of what? This is pseudo math. It's not human or machine readable, and that's not what it says in your java (I hope) else it would blow up in your face.

(1 - 10/ 100)

What the hell is this? lol. You just write 0.9 and be done with it.

If you want 90% of 2400 you write it like this:
2400*0.9

If you want it to be variable then:
2400*x

Both of you are using way more parentheses then you actually need, and making this way harder then it actually is...

Ezareth · February 2015

Soulac wrote: »

@ezareth_ESO‌
Well it was correctly written.. :P

((2400 - 10%) - 200) - (21% * 87,7%) is the same as
((2400 * (1 - 10/ 100)) - 200) - (1 - (21 / 100 * 87,7%))

2400 - 10% = 2160
2400 * (1-10/100) = 2160
2400 * 90% = 2160

It´s just a different / easier way to write it.

Anyway, yes it´s a short version i came up shortly after the release of 1.6.2.
Kinda easy to figure out, cause the champion passives and enchants were applied with 100% of the passive and the other percentages not (with 87,7% instead).

Other Calculations:
The calculation of the statincrease based on invested points, which is capped at 1k Points, is kinda similar and same with other stats which get increased by the champion system.

Stats:
((Base * ChampionPercentage) + Flat) * OtherPercentage

The formula for Magicka/Stamina/Health is kinda complicated and the specific championpoint-based modifier doesn´t include buff-food as example.
Stats = max. Stats without bufffood and championpoints

((Stats * modifier) + (Stats + BuffFood)) * PercentageIncreases

Well for the modifier.. look somewhere else in this forum :P

Well hindsight is always 20/20 and it sure seems "easy" now that it is done. I wasn't happy with a formula that wasn't precise in all scenarios and a big part of the issue was figuring out the issues with the cost reduction tooltip and discovering that the neck enchant was behaving differently than the ring enchants. I'm pretty certain as well that between 1.6.1 and 1.6.2 something changed in those that decreased the neck enchant by 10(to 198).

I also still don't see how subtracting -(21% * 87.7%) works out to multiplying *(1-(21/100*87%) but I've always done math in my head and haven't ever had much success in translating that to something others can easily understand. I also see you're from the EU so maybe it is something lost in literal translation or a representation you guys do differently. (I notice you use ','s in place of '.' multiple times). Hopefully it isn't something to do with the Metric system haha.
I use programming logic and order of precedence to write my formulas and if I didn't already understand how the formula worked I'd never have been able to "correct" it to something I understood.

The enchants are not applied with 100% and that is what made the entire formula difficult and nonsensical for me at least. When I made the formula I broke it into 3 separate parts (enchant, champion, and reduction percentage). I then tested each of those independently and together to determine where in the calculation each portion was being applied. I was able to figure out the .877 factor pretty quickly but because they switched up the enchant reduction numbers between patches and the neck/ring difference thing threw a monkey wrench into the whole thing and I ended having to retest everything after 1.6.2

I'll see if I can look into the rest of the stat calculations.

You don't want to see my calculations on spell penetration....if you think cost reduction looks crazy, penetration is just nuts and nothing behaves as you think it should.

Ezareth · February 2015

XEVENEX wrote: »

((2400 - 10%) - 200) - (21% * 87,7%) is the same as
((2400 * (1 - 10/ 100)) - 200) - (1 - (21 / 100 * 87,7%))

Yall are makin my head hurt...

(2400 - 10%)

10% of what? This is pseudo math. It's not human or machine readable, and that's not what it says in your java (I hope) else it would blow up in your face.

(1 - 10/ 100)

What the hell is this? lol. You just write 0.9 and be done with it.

If you want 90% of 2400 you write it like this:
2400*0.9

If you want it to be variable then:
2400*x

Both of you are using way more parentheses then you actually need, and making this way harder then it actually is...

Parenthesis are needed to determine correct order of operation but I can be somewhat overly verbose with those due to too many broken calculations caused by poor syntax. You can never have too many haha.

I'm glad to see I wasn't the only person confused by his writing style. It sure *looks* simple but there are many formulas inside the simple formula that are implied but are not easily understood.

WarrioroftheWind_ESO · February 2015

Ezareth I still hate your guts and keep an eye out for you in PVP so I can kill you every time I'm on....but out of curiosity are you a math major? I had a guildie in WoW who picked enough nits that all the chimps in the zoo would be very clean indeed. I haven't seen him as much these days because A) I don't play WoW barely ever anymore and B.) he's prob graduated by now and gotten a job.

As for the impossible to achieve 100% spell reduction, I'm wondering if that was done to prevent the sort of situation they ran into with Skyrim where you could stack flat 25% reduction to skill abilities (Destro, resto, conjuration, Illusion etc) and basically break the game. ZOS has mentioned on more than one occasion they want players to have to manage their resources. Which is at least alot more kinder than Blizz saying "we want you to use your mana" and nerfing the crap out of every possible mana gain, even implementing BS "potion lockouts" for fights. I have a God-given right to chug pots until I run out dammit.

I been seeing alot of people screaming over recent sorc changes. I haven't had the occasion to test on PTS PVP because of work and such, but I'll more than likely stick to the same spec I've been using because I feel more comfortable with it. I tried using a template with pets and it just felt clunky. Pet damage basically tickles and the range on most of the associated spells is so bleh even with shields I'd be exposing myself. I don't expect to get top 10% with my spec, but I'll keep playing it because I like it.

There's still at least a good 3-4 weeks to go of testing. I'm assuming they'll tweak things again, but I would like to see more people backing up their complaints with the math you pop out rather than "this sucks I quit".

Ezareth · February 2015

WarrioroftheWind_ESO wrote: »

Ezareth I still hate your guts and keep an eye out for you in PVP so I can kill you every time I'm on....but out of curiosity are you a math major? I had a guildie in WoW who picked enough nits that all the chimps in the zoo would be very clean indeed. I haven't seen him as much these days because A) I don't play WoW barely ever anymore and B.) he's prob graduated by now and gotten a job.

As for the impossible to achieve 100% spell reduction, I'm wondering if that was done to prevent the sort of situation they ran into with Skyrim where you could stack flat 25% reduction to skill abilities (Destro, resto, conjuration, Illusion etc) and basically break the game. ZOS has mentioned on more than one occasion they want players to have to manage their resources. Which is at least alot more kinder than Blizz saying "we want you to use your mana" and nerfing the crap out of every possible mana gain, even implementing BS "potion lockouts" for fights. I have a God-given right to chug pots until I run out dammit.

I been seeing alot of people screaming over recent sorc changes. I haven't had the occasion to test on PTS PVP because of work and such, but I'll more than likely stick to the same spec I've been using because I feel more comfortable with it. I tried using a template with pets and it just felt clunky. Pet damage basically tickles and the range on most of the associated spells is so bleh even with shields I'd be exposing myself. I don't expect to get top 10% with my spec, but I'll keep playing it because I like it.

There's still at least a good 3-4 weeks to go of testing. I'm assuming they'll tweak things again, but I would like to see more people backing up their complaints with the math you pop out rather than "this sucks I quit".

Not a math major but I took enough Calculus(I,II,II), Linear Algebra, Statistics and god knows what else in college that I've *forget* more math than I still remember and have little use for even that.

I've always been a theorycrafter and a Min/maxer. I worked on and coded one of the major maximum DPS tools for my class in my day in WoW and grew to love understanding how by tweaking one part of a formula you can produce a far greater effect than is obvious to most people.

I realize they wanted to avoid situations where players could achieve 100% spell reduction and I'm OK with that goal, but I think they chose the wrong method to do this by making an untouchable percentage of spell cost instead of just putting a hard cap on cost reduction at the end that if exceeded would reset back to the cap.

I really just wanted to point this out in case it was an unintentional mistake that occurred due to whatever formula they're using to "Scale" stats and abilities, or to protest it not necessarily for my sake but in general as a departure from a somewhat easy to understand system to what that practically takes a math major to wrap your mind around.

If I take the Light Armor passive to get a 21% spell cost reduction to my spells, I should get 21% reduction, not 21% *.877

The compounded effect of this nerf is quite significant and I'm curious to find out if this same logic is present in stamina abilities as well. (I supposed I could find out by making a template NB).

RinaldoGandolphi · February 2015

Great post ezareth!

Its a lot of math to to indulge, but you have revealed a lot.

I also noticed it seems they have reduced spell damage enchants a lot compared to their values on live. It seems folks would be better off now going cost reduction over spell damage even with these changes you have figured out with spell cost reduction.