Mathematics of Facets and Scaling

[Konrad]

The Maths of Facets

A brief note: Patch 1 (build 28175) on 2026-03-18 changed facet numbers and nerfed enchantments related to crits in a major way. As a consequence, my happiness has increased greatly. The maths below are for build 26973 of the game.

A post with updated calculations can be found here: [> link].

Preface(t)

In this post, I will calculate optimal weapon facets for expected damage values (that is, average over many hits, not maximum possible).

TL;DR: Use something with a 20% overall damage boost, not a crit facet.

For damage, there is a clear best group of facets and it’s the same in all circumstances. My analysis ignores benefits not related to damage, though I comment on them in a dedicated section.

Further discussion in this topic explores why current ‘multiplicative’ stat scaling can lead to systemic balancing issues, especially in view of numbers-based and skill-based difficulty (broadly, ARPG vs Souls).

Before Enchantments

Weapons fall in these categories:

10% chance to deal 200% damage
20% chance to deal 150% damage
25% chance to deal 140% damage
40% chance to deal 125% damage

These are balanced and all have an expected damage increase of 10%, which pleases me greatly. Choose a reliable or a swingy weapon!

Facets can provide, amongst others, the following choices related to damage:

40% increased crit damage for 10% less overall damage
10% increased crit chance for ‘free’^[1]
20% increased overall damage for ‘free’^[2]

I will select optimal cases for the first two to show why they are subpar choices.

The 40% crit damage boost should be optimal for weapons with a 40% base crit rate. It is not. Expected damage is 116% (60% chance for 90% + 40% chance for 90% of 165%). The facet with 10% bonus crit chance is worse at 112.5%. The 20% increased overall damage is best (expected damage of 130%).

Boosting crit rate should be suited to weapons with 200% crit damage. It is not. With 10% bonus crit chance, expected damage is 120%. With 20% increased overall damage, expected damage is 130%. Bonus crit damage is last with 114%.

For all weapon types, the 20% increased overall damage is best. It will remain so as enchantments are added.

Enchantments: Crit Chance vs Crit Damage

Optimal combinations of crit chance and crit damage are achieved if crit damage is two times crit chance, until the cap of 100% crit chance. At this point crit damage takes over.

Enchantments provide five mutually exclusive bonuses of 10% crit chance or 20% crit damage, doubled with enchantment power (a pox on it). To keep maths manageable, I will not consider exalting for now.

(Armour penetration of 100% can be achieved without exalting, as can a bonus of 100% to any one element. I will not consider these for my calculations, but for anyone curious, it is marginally better to invest in crits over damage-type bonuses.)

The optimal number of crit chance enchantments for weapons with a facet granting a 20% overall damage boost is thus:

10% chance to deal 200% damage: 3 or 4, for 271.2% total
20% chance to deal 150% damage: 3, for 244.8% total
25% chance to deal 140% damage: 2, for 244.8% total
40% chance to deal 125% damage: 2, for 259.2% total

The optimal number of crit chance enchantments for weapons with a facet granting a 10% crit chance boost is thus:

10% chance to deal 200% damage: 3, for 244% total
20% chance to deal 150% damage: 2, for 219% total
25% chance to deal 140% damage: 2, for 220% total
40% chance to deal 125% damage: 2, for 230.5% total

The optimal number of crit chance enchantments for weapons with a facet granting a 40% crit damage boost at the cost of 10% overall damage is thus:

10% chance to deal 200% damage: 4, for 235.8% total
20% chance to deal 150% damage: 3, for 212.4% total
25% chance to deal 140% damage: 3, for 212.4% total
40% chance to deal 125% damage: 2, for 223.2% total

In this build completely focused on crits, the crit facets still do not catch up. The winner continues to be 20% increased overall damage.

The difference between facets’ expected damage is around 16%. I am unsure whether to consider this a sign of good design or of a lack of choice.

Facets Not Directly Related to Damage

I am not considering the relative merits of focus-generating facets over damage-boosting facets (Ritualistic vs Heavy). I believe this to be a moot point: The optimal strategy consists of a focus-generator (or life-as-focus set-up) paired with a damage-optimised focus-spender (like a one-handed hammer).

I cannot quantify the undoubtedly enormous non-numerical ‘benefits’ of Quick. Though the facet represents a meaningful choice compared to pure damage, I believe attack speed modifications should not exist in their current form, or at least be less accessible. There is no ‘commitment combat’ with the current 35% attack speed boost.

The elemental facets are flexible for build-crafting, but should never be considered for damage: A flaming sword with a mottled ruby is outdamaged by an unfaceted sword with a chipped ruby, even in its own element, but especially on all other elements if accessed by runes. Less damage at the cost of a facet is a poor deal. Use oils.

Poise facets are hard to quantify. I personally think they’re great and the damage trade-off is well worth it. Reliable is an early-game powerhouse.

On Armour Facets

Rapid should be removed.

Facets that trade focus for stamina regeneration (or vice-reversa) feel good, though due to additive stacking with certain Echos can lead to situations where characters cannot recover stamina over time.

The Dense facet is a rough deal, especially compared to its elemental brethren. 5 armour at level 30 is a rounding error, even if 5 weight can often fit into a loadout. The stacking of elemental resistance enchantments, elemental resistance facets, and rings is intransparent.

Durable makes me wonder what its design goal is. Weapon and armour durability, as a system, was intended to provide a delayed punishment and nudge players away from difficulty walls. Currently durability provides no real forced break if one dies repeatedly, a pathway to excessive power (deserved nerf incoming), and no trade-off to hardcore players. Bonus durability could be attractive on tools, but currently resources-per-harvest enchantments would be superior since repairs are a non-issue.

Afterword: Systems and Scaling

Wicked feels initially great to play. The early balance is excellent.

In the long term, however, some systems feel like they scale too strongly. This is not a matter of ‘optimising the fun out of the game’, but of simply playing the game beyond the ten-hour-mark without deliberately ignoring its systems. I do not need the above maths to be too strong.

A build with 100% damage to a beneficial element and 100% armour penetration will do, against an enemy with 50% damage resistance, 1084.8% of the damage of a plain weapon. Exalts can roughly double this (1948.8%).

I personally would prefer a game less focused on numerical power and more focused on player skill; a narrower band, ‘bounded accuracy’. This could begin with the removal of attack speed, armour pen, and percentile boosts to damage of one element.

In addition to the multiplicative damage scaling, some other systems that feel mathematically unsound are armour weight classes, damage reduction enchantments, stamina/focus management past the early game, and bonuses to overall speed.

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1. Reduced durability is practically free. ↩︎

2. Stamina cost and focus gain can be massively overcompensated for by other systems; stamina consumption is irrelevant if using the weapon as a rune stick. ↩︎

[Hubristic]

this is an excellent summary of the current state of stats scaling, thank you

it’s useful to see everything in one place

i too think that scaling shouldn’t blow out of proportion

i think the “easiest” solution is to use linear scaling instead of multiplicative

i also think that stats shouldn’t determine everything and leave room for skill

so i would like stats to be like this:

+10 weapon damage after dodge for 5s
+5 physical damage

instead of

+15% damage after dodge
5% physical damage

and stats that change how you play instead of just “number go up”, for example:

• after parry, charged attack is 0.5s faster
• after taking more than 30% hp in one hit, add 15 poise damage for 5s
• your dash deals 20 damage to enemies it passes through
• stuff like that

P.S. just to contradict myself:

there are plenty of players who simply like the stats based power curve and it feels good to obliterate the game with a press of a button. they should be able to enjoy the game too. i think Wicked is more flexible in that way.

by flexible i mean, like we talked about SSF regarding self-imposed difficulty: you can always play the harder version if you want it harder.

for example: my latest run is using full cloth, no runes, one sword, no shield, and no durability based resists. the game is hard because everything one-shots me. but i enjoy that kinda thing. it’s even fun to farm pestilence when you can die from a sting of a bee. if i add the dura/resists, all of the sudden the game is irrelevant and i’m just mowing down pixels.

[Konrad]

Thank you! I feel that we have similar wishes for game feeling.

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Re: Wicked Is Flexible

Power-fantasy players can have their cake without warping the game. What this means is that challenges should not require big numbers. Reducing skill-based difficulty with stats is fine. That’s when we can gimp ourselves and have fun.

I am warning against designs warped by big numbers at the expense of skill, or copy-and-paste content with bigger numbers. I’ve seen this happen before (Elden Ring, many ARPGs). Pestilence and Cyvion debatably already fall into this trap.

Thomas said the current power levels might feel excessive, but upcoming challenges will require them. At other times, he has emphasised that Wicked will absolutely fall on the side of commitment and deliberate combat. I suppose we can trust, wait, and see.

Tangent

On a personal note: I desire a fair, skill-based game that disallows cheating and cheesing. This may be a form of escapism into a just world. I do not think there is an inherent contradiction between minmaxing, stats giving strong benefits, and skill-based gameplay. And yet.

Wicked is between Souls and ARPG, where two cultures clash. It’s a discussion oft poisoned by mutual derision and name-calling: Challenge-seekers are derided as gate-keepers, elitists, or no-lifers. Power-fantasy players are accused of ruining games, seeking instant-gratification, called meta slaves, netdeckers …

Since I think the conflict is completely avoidable, I am always searching for designs that harmonise both sides’ wishes. Wicked has the chance to straddle the line, and so I have high hopes.

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Re: Enchantment Design

I agree that good enchantments change playstyle, not just numbers.

Numbers bonuses should mostly be tied to risk or opportunity cost. If they have no trade-off or the trade-off is meaningless, you have uninteresting minmaxing (Indestructible and Unrepairable, though that at least has a minuscule opportunity cost).

Conditional bonuses should be skill-based, not just synergistic. Positive examples:

• Your parry-into-charged-attack suggestion is great because parrying is inherently risky and the bonus only allows a slightly safer retaliation.
• Attacks on heavy weapons with ‘guard points’ that permit aggression to act as a timing-based defence.
• Allowing a longer-distance dodge if you roll into a wall to push yourself off.
• The Dawn Never Comes is brilliant in my eyes.

Negative examples:

• MonHan has weapons that are stronger after gathering. If implemented poorly, weapons like this make tedious buff cycles optimal.
• Lifesteal vs. bleeding. Trivial to build around and set up, just free bonuses.

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Stacking Models

Additive and multiplicative scaling have their place. For instance, you can’t stack elemental resistance (or dodge %) additively without a sensible cap or drop-off. It makes sense that every piece reduces the remaining elemental damage multiplicatively.

Nor am I sure that linear growth should be the goal. On the plus side, it is a very predictable option for players. For instance, if every point of armour represents a consistent increase in effective HP, armour never becomes worthless. The danger is that multiple linear boosts can become multiplicative of each other (like hp–dodge–armour, or base damage and crits).

Solutions in action and pen-and-paper RPGs tend towards diminishing returns or caps. Breath of the Wild simply has a maximum number of attack boosts. In early drafts of D&D 5E, you were relatively strictly limited to ability + proficiency.

These solutions can make buildcrafting too simplistic (or solved, often with hard or soft caps), make items that merely boost stats redundant, or make it too easy to reach a cap if player retention through gear grinding is the goal.

I wonder if the current loot system is compatible with non-incremental gear, and if there is enough design space for conditional boosts.

[Hubristic]

if i understand correctly:

you’re saying that optimally the design should avoid runaway numbers and allow the challenge to be “how well you read the enemy” vs “how high my weapon level is”

i think that is already the situation though. being able to clear some of the challenges (the savage pair, weeping sisters, even the mad fire witch prisoners quest) requires an upgraded weapon, otherwise you’re in for a battle that lasts 15 minutes and needs you to parry the same attack 50+ times. (fighting the Torn Colossus from the side quest with a level 1 weapon comes to mind)

the game ceases to be fun when you do 0.5% damage to an enemy per hit. you can still do it. but the message is very clear: get the blacksmith the things he needs to upgrade your weapon or farm a higher lvl one.

@Konrad

I am warning against designs warped by big numbers at the expense of skill, or copy-and-paste content with bigger numbers. I’ve seen this happen before (Elden Ring, many ARPGs). Pestilence and Cyvion debatably already fall into this trap.

in order to avoid that - and stick to lower numbers - much scaling would have to go extinct already.

@Konrad

Thomas said the current power levels might feel excessive, but upcoming challenges will require them.

this would mean that exponential scaling of stats is intended and future challenges will indeed have badass numbers. i don’t think there is a way of avoiding that !

the ARPG element of this game is the number scaling i guess. the power creep as you get/craft better equipment that allows you to go into harder zones and clear more easily, to get better equipment, to clear harder zones, etc, etc, etc.

and as a long-time ARPG player i gotta say i identify fully with “crafting the awesome perfect relic for my build” it’s a great moment.

can that exist without massive number ramp-up? i don’t know, struggling to see it.

look forward to hear your thoughts on this, particularly about how the game already expects you to have an adequate weapon to solve most of the serious challenges

[Konrad]

Wicked should require both skill and item progression. I do not want one to make the other superfluous. (Great question, thank you. My answer went through a few iterations.)

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Game Too Hard? Use Numbers!

I’ll use a ‘bad’ challenge as an example. The current difficulty of Cyvion is so high (in numbers and skill: damage, stagger, combo speed, run-back time) that players are pushed into ARPG-style one-shot ‘builds’ or unintended enchantment combinations.

The margin for error is too low without them, especially on leather/cloth. It is natural to see the fight as an unfair challenge. This pushes players not towards upgrading and preparing, but towards minmaxing (immortality or oneshots).

While the high difficulty can be excused to a point (rogue-like environments can generate ridiculous perk combinations; it’s a placeholder wall in Early Access), there are two counters: Cyvion can be one-tapped without any echoes and the difficulty on the path to the boss is rather low. As a consequence, a Cyvion-killing build will trivialise the run to him.

Use Numbers? Game Too Easy!

Player power level is currently degenerately high. This is not, as Thomas claims, because we do not have the later challenges yet, but a systemic flaw. If I upgrade carelessly right now, I destroy my fun.

If I only use what the game lays at my feet – common, store-bought weapons, random blues – the game provides a pleasant challenge during progression. If I upgrade regularly, get mats, pick sensible enchantments, or use oils and vials, the game becomes faceroll-tier easy. That’s not hardcore grinding or minmaxing, that’s engaging with the basic systems.

Shields, groups, enemy mages and such should make me pause to think. Right now, depending on your weapon and armour weight choice, players can button-mash and heal-spam even through bounty targets and bosses.

I am not nudged to upgrade, I am forced to be careful not to do it too much.

Born to Skill, Forced to Number?

Upgrading should be mostly necessary. It funnels me into other systems that I also enjoy.

The 15-minute parrypaloozas are a nice example. I think everyone would agree they’re not fun, but it’s no harm at all if they’re possible, right? While I do some of the bounties you mentioned at level 3 on HC with starter gear, I know that’s not a healthy difficulty and even I wouldn’t want the entire game to be like this.

With infinite time and perfect play, the game can be beaten without any numbers progression. I contend that this should always be the case in this genre.^[1] At the same time, it is perfectly desirable that challenges eventually outscale me: otherwise, to exaggerate, the entire upgrade system is pointless.

But a good upgrade should play catch-up, not make the game easier. Otherwise, as I play more, my skill increases and my relative numerical power increases. The game gets doubly easier.

I don’t mind being nudged to upgrade, I just want challenges to remain relevant when I do.

Progression and Solutions

Current Wicked scaling design is that you become strong within the current difficulty, then it is replaced with a new one as you progress. This works well enough if you don’t make optimisation-like choices (or can’t, pre-Sacrament).

To preserve this good challenge past the five-hour mark there are several routes:

• increase enemy stats as you progress, make optimisation choices necessary
• keep enemy stats (or even reduce for Cyvion), make optimisation increase player power by a smaller amount

Is it contentious if I suggest that many ARPG moments of the ‘perfect build-defining relic’ are degenerate in terms of challenge? Is the joy of a really good item not diminished if it trivialises the game? I think it’s nice to have a short-term burst of power, but would items not need to lose effectiveness in the next zone?^[2]

Curious what you feel about these as an ARPG player. I feel that upgrading should remain relevant and items should never be perfect; or that progression should be horizontal instead (appearance, options over strength).

The class system might end up re-balancing this automatically. From some of the comments, it seems to tie incoming/outgoing damage to character level to an extent. I’m just unclear what the desired experience is. If I want to play Souls instead of Path of Screenwipe, I have to skip a part of the game I’d want to enjoy too.

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1. But not every genre – numbers should be strictly required in, say, Fire Emblem. ↩︎

2. It has never sat right with me that the legendary Excalibur is vendor trash two zones over. ↩︎

[Hubristic]

getting/crafting a perfect relic in this game feels good because the item isn’t necessarily breaking the game.

it’s so hard to get the correct affixes on the right looking piece, with the right facet, that it’s a cause of celebration “YES THIS IS PERFECT FOR MY BUILD” - does not have to mean “YES I NOW DELETE THE BOSS IN 0.2s”.

i feel like the game does that well, up to a point. it also doesn’t end the journey. the journey is “what’s gonna be the next cool encounter?” not “when do i get the super-mega-legendary win-sword?”. that’s why i sing praise for the current deterministic crafting system - it’s “play and the RNG will eventually give you what your build needs”. amazing. we are pretty much completely off the endless treadmill of chasing stats. getting embers doesn’t seem like such a big deal. fine

that’s why i say that the problem comes in the shape of multiplicative scaling.

if i have 4 pieces of armor with +10% physical damage, those do not multiply with each other — they sit in an additive bucket. so that becomes:

40% physical damage → 1.40x multiplier

NOTE: phys% from gear stacks additively, not multiplicatively.

if i have 50% CSC and 200% CSD that’s another (averaged) ~1.5x multiplier.

that in total is a ~2.1x multiplier for my base weapon damage.

now add that to an expensive rune attack, which has a 10x multiplier, we’re at ~21x.

if my base damage was 150 with no facet this rune now hits for ~3.1k

let’s say i’ve just got a plain 10% damage affix on a weapon, that ~21x becomes ~23.1x.

new rune hit: ~3.4k

then i grab the rune ring with a low 20% roll (1.2x) — my total multiplier for that rune attack is now ~27.7x

new rune hit: ~4.1k

… and so on. we are now miles away from the 150 base damage. your naked starter warrior has no business in this game anymore if killing the boss requires 10 of those attacks.

(if i had one of the aforementioned superior facets that avg hit would now be ~5k+ — massive difference)

NOTE: facets increase base weapon damage, which is particularly powerful because base damage is multiplied by all later systems (phys bucket, crit, rune multipliers, etc.)

now every tiny increment will add a huge chunk to my damage. at the game’s current state, that invalidates all the content.

if future content is expected to match that level of power, it completely leaves in the dust the player who didn’t optimise.

however, optimising requires:

• player knowing that there are 3-4 “king stats” which are the ones that get you to the max damage, everything else is… flavour

so, optimising is inherently a boring thing to do when the game is so full of awesome animations, rich environments, interesting enemies. but it’s a part that’s fun for a lot of people, and it’s nice when you can feel like you have ownership of your build “clicking” into place. it should IMO enable you to clear content faster. i think we are fully in agreement here, the system is fun and we want to take part in it.

my point: if the scaling wasn’t multiplicative, but instead linear, we wouldn’t be so far away from the base 150. optimisers could still optimise without orbit-nuking the content and hardcore naked warriors could still go into each fight with a cathedral-sized eldritch bear holding a butter knife for a weapon and a dinner plate for a shield, wet napkin for armor, and do their thing.

linear scaling will still multiply by parallel stats, but it be subject to runaway damage much less than it is now. linear can be end-game too: 5,10,15,30,60. much easier to control than increasingly big multipliers

at the moment this game multiplies most stats which is guaranteed to blow the system with massive numbers under current construct. a few more increments, another multiplier, and we are in millions.

p.s. i realise this goes back to your initial post about facets - that extra base damage due to a facet is HUUGE in a system that multiplies most stats

but is this system guaranteed to blow out of proportion ? what if they never scale base damage numbers up any more ? they said that currently we are playing ~1/3 of the content. if i’m doing 10 damage on the starting beach and 5k by the time i’m schooling 10x curses pestilence cyvion, that suggests an exponential rate of exactly… too much.

so the concern here is real and in my eyes the design choices for future content become:

• add more power
• or make future loot/progression feel flat
• or hard-reset/rebalance systems

those are real non trivial forks

so i guess my next question is: what design tools could possibly control the unbounded power curve ?

completely off rails & in parallel universe: it would be refreshing to have 6 hearts like Link in a game like Wicked

p.p.s. forgot to answer:

having a perfectly crafted piece of gear doesn’t mean it has to be obsolete in the next level because we have incremental upgrades. i think those work well. they increase base value by a small amount.

but yes the good item only works if it doesn’t delete the game you looked forward to playing so much. another good example next to Dawn Never comes: Wind of Death. tradeoffs are great

edited to reflect the additive bucket reality of elemental damage from multiple sources - thanks Konrad

[Konrad]

Assuming your preferences can be generalised, I am now convinced that a stat scaling model exists which can harmonise ARPG and Souls preferences. I also agree that it’s great to be off the treadmill.

I’m not sure we are completely in agreement as to the meaning of linear and multiplicative scaling, so for the sake of argument I will present several mathematical models. This might become a two-parter.

Tangents, Caveats, Miscellanea

Apologies in advance if I’m preaching to the choir, or if it seems like I’m splitting hairs on what isn’t linear. I just want to define terms to avoid misunderstandings.

I’m really unsure what maths level I should pick for this discussion.

Hearts in Zorldo are a great system! It’s fractional as all damage is by nature (all the floor and ceiling functions below), so despite the abstraction from the numbers the math is much more readable.

I also think minmaxing can be fun in itself, completely separately from gameplay, but that’s a separate discussion.

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The Maths of Scaling

In the current state of the game, not everything is multiplicative. Four pieces of armour with +10% physical damage currently stack additively as far as I’ve tested, so not 1.4641 but 1.4. Elemental resistance from rings is additive. I will show that additive isn’t linear.

What stacks multiplicatively is % dmg from facets, % dmg per element from enchantments, rune dmg modifiers, and crit calculation. We are in complete agreement that this will escalate.

Before I even get into multiplicative stat interactions, I want to clearly define terms for the various scaling effects of increases to single stats. I’ll also show good and bad scaling models.

Part 1: Linear Stat Increase, Non-Linear Scaling

Example 1.

For this example, I will assume a (mathematically pleasant) baseline enemy with 100 effective hp, against whom a player deals 20 damage per strike, so five hits to kill. As damage increases linearly, the number of hits to kill drops in steps.

The following diagram shows the number ‘f’ of hits to kill as a function of the damage ‘x’ done per swing. Green (or f) is the number of hits to kill, while pale yellow (or g) is a continuous function so the qualitative scaling becomes more apparent.

As damage increases linearly (on the x-axis), the benefits per point diminish hyperbolically. In other words, more points are needed to achieve the next reduction in number of hits-to-kill (the green lines become wider; after the first 5 points you need 8 to make a difference, then 17).

I’d argue that this is good behaviour in the sense that the effect of linear stat-increases actually diminishes with increases stats.

I’ll call this (hyperbolically) diminishing returns.

Does this lead to healthy scaling? – At the extreme end of this, oneshots become possible, which I consider unhealthy (or degenerate). The correct number of hits if you overpower a region is up to personal taste, but could be two to four attacks, depending on the speed of your weapon.

Note also how small increases are much less worthwhile for weapons with large base damage, so this may be unfair towards two-handed weapons, which already receive fewer stats in total.

Example 2.

Now I will assume the enemy hits back. My sample player has 50% damage resistance initially, which I will increase linearly again. Let’s say an incoming hit has 70 raw damage. I’ll now show the reduced damage ‘d’ for this hit as a function of resistance ‘x’.

This is a linear decrease in damage, but I’d argue it doesn’t lead to linear scaling in actual survivability – instead, a better question would be how many hits of this strength the player can survive.

I’ll assume the player also has 100 hp. Initially, the player dies on the third hit of 35 damage. In now familiar fashion, I’ll show the number ‘n’ of survivable hits as a function of resistance ‘x’. In pale yellow, I’ll show what this looks like continuously.

A small initial boost allows surviving the third hit, then the stat has a long interval of limited benefit, and as we approach 100% the number of survivable hits grows (to infinity at full damage immunity).

Unfortunately, this is also hyperbolic in mathematical terms; but effectively the function is defined by the asymptote at the 100% mark. If I had to name this form of scaling, I’d term it asymptotic for that reason.

Obviously this is ridiculous and no defensive stat should scale like this. Small numbers are irrelevant and stacking is extremely worth it. Multiplicative effects like enchantment-power gems are especially horrifying.

Example 3.

Let’s return to the enemy of the first example. His 100 effective hp were secretly 50 hp with 50% damage reduction. Let’s hit him again with 40 raw damage.

This time, we’ll add linearly increasing armour penetration. Armour penetration is a percentile reduction to his percentile damage reduction. This is a linear decrease, and resistances can’t be reduced below zero.

In the following diagram, as a function of our armour penetration ‘x’, we have the real damage (‘dmg’) and the remaining damage reduction (‘dr’).

Not very enlightening – I’m mostly including it so we’re on the same page for armour penetration maths.

The next diagram will display the number ‘n’ of hits to kill the enemy as a function of armour penetration ‘x’, again with a pale-yellow continuous version ‘f’ to compare:

What does this mean? – Armour penetration scales hyperbolically, even if rather gently here. What’s new is the hard cap: No armour penetration lets me kill in fewer than three hits.

This is an extremely useful property if you are with me in the idea that enemies should have a ‘minimum’ number of hits required to defeat them. In this case, this number is the enemy’s raw health divided by our raw damage, rounded up. No amount of overgearing gets us under that.

Maybe this type of scaling could be called hyperbolically diminishing returns with a hard scaling cap. Hardly rolls off the tongue, so I’m open to suggestions. This is a good scaling model, but I’d like to explore its properties more in …

Example 3a.

Same as ex. 3 with one small change: We’ll increase the enemy’s damage reduction to 80%. This has drastic consequences for the number of hits to kill:

Now if I am still wielding my trusty 40-raw-attack weapon and have no armour penetration, I need 13 hits. Yet no matter how much I stack armour pen, I still never need fewer than three.

Benefits: The existence of this minimum achieves our desired goals of strongly rewarding gear, yet never trivialising fights. Low values have sharp benefits, so there’s a built-in catch-up mechanic. There is a sizeable interval near the top in which ‘complete’ builds can fall without requiring absolutely perfect rolls.

Flaws: This scaling still has an (exclusively human) issue in that enemy DR and player armour pen could conceivably approach 100%. Once numbers get high, increasing armour pen by 0.5% will seem to players like a small increase, but actually have huge effects. It just won’t look that way when comparing two items, which is why fake ‘linear’ stats like the current armour are used instead.

As an afterthought, I’d consider an item tooltip complete if it provided the following information (ideally more succinctly; while the ‘linear’ numbers below are asspulled, the percentages make sense):

Currently equipped item: 400 linear AP, equivalent to 90% reduction in enemy defences.

Item being previewed: 450 linear AP, equivalent to 92% reduction in enemy defences; defences reduced by a further 20% compared to the equipped item; equivalent to a damage increase of 1.74% of against foes with 80% damage reduction.

Systemic concerns: If there are many stats where small increases have strong benefits, the correct buildcrafting solution is to spread stats widely rather than specialise. I believe specialising should be encouraged; or in other words, the 50% model is great for early game and the 80% for mid-late game.

I’ll continue in a second post once I find time.

[Konrad]

Part 2: Achieving Linear Scaling

I have shown in the first post how linear stat increases lead to non-linear effects, usually hyperbolic in some way.

In this second post, I would like to design a type of scaling that keeps giving the same benefit with every added point to a stat (which I’ll daringly call linear scaling, even though the term is somewhat overloaded by now).

Example 4: Linear Defensive Stats

There is something inherently sensible to a stat which keeps giving consistent benefits as it is increased. Calling this linear scaling is somewhat contentious.^[1] I’m open to better suggestions (hyperbolic decay?), but I’ll run with it for now.

I’ll model an ‘armour’ stat in which every point of armour is equivalent to the same additive increase in effective hp. I’d like every 15 points of armour to effectively add 100% of my base hp. Linearly, therefore, I want my effective health to increase by around 6.67% per point of armour.

To achieve this, the percentage of received damage ‘d’ can be expressed as a function of armour ‘x’ as follows (indeed, it’s hyperbolic again):

The reduction can be expressed as x/(x+15), which mathematically is a saturating hyperbolic curve. Just mirror the curve above at a horizontal line at y=0.5, it’s the same idea. It turns out that armour in Wicked nearly works this way – see the bonus section below.

This type of scaling is not inherently bad – in fact, I think it is intuitive in that players can eyeball the effectiveness of armour once the 15-armour-to-double-hp figure is known – but tends to have multiplicative effects:

Consider, for example, that as you take less damage, regeneration or lifesteal can more easily recoup the fewer points of damage dealt. For higher values of regen to be permitted, incoming damage must scale so strongly that increasing just armour won’t cut it – you need to be forced to also increase maximum hp. If armour instead outpaces incoming damage, recovery stats become too strong.

Since the increase in effective hp is percentile, this way of designing armour (compared to subtractive armour) does not warp the scaling of maximum hp. The same amount of armour will always extend your life by the same relative amount.

What this means is that the model works great if, at every level, there’s an expected armour number corresponding to an expected incoming damage number, expected max hp and recovery. Alternatively, resistance (or heavy armour) would need to decrease healing received. This is why armour classes in Wicked don’t work.

(The well-behaved armour penetration scaling from the previous post has similar constraints: it requires the ratio of base weapon damage to enemy base health to remain relatively constant. In the current version of the game, base damage outpaces hp.)

Bonus: Wicked’s Armour-to-Resistance Scaling

Disclaimer: If you are reading this in the future, I expect this to have changed. My tests were done on build 26973 in February 2026, before Patch 1.

At level 30, all resistances scale with points in armour. This scaling can be modelled as follows:

• For the first 200 points of armour, all resistances increase linearly by roughly 0.1% per point of armour (around 20% at 200 armour).
• Between 200 and 800 points of armour, every point linearly increases resistances by around 0.05% (to 51% at 800 armour).
• From 800 points to the limit of my testing (1275; I didn’t test how shield armour stacks), every further point increases resistances by roughly 0.025%. Not as linear since I have limited data points and there is rounding.

An interesting system. There are clear breakpoints that the game does not reveal. Here’s my data represented visually:

Note how the slope of three piecewise linear intervals halves from one to the next (1/10, 1/20, 1/40). The data looks clearly piecewise linear, but there are rounding artifacts so I do not have the exact function.

Now let’s see damage taken in % as a function of armour (mauve segments below), and I’ll throw in a logarithmic approximation as well as a hyperbolic one (for the logarithm, I just eyeballed the parameters, this isn’t a proper least-squares fit):

Despite the weird piecewise definition, I think this is good design. There are diminishing returns, there’s a scaling cap in that armour is not infinite, and resistances from armour are additionally capped to 70%.

There are just a few very minor details that tarnish the system, like the multiplicative scaling with health totals, the unbalanced armour weight classes, the additive stacking with ring resistances, the fact that enchantments can be stacked on top, the unfortunate existence that is the Dense facet …

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1. Mathematicians have their own ideas of ‘linear’ and ‘proportional’, but I hope you’ll agree the name is sensible in the context of the scaling discussed. ↩︎

[Hubristic]

thanks a lot for taking the time to explain. the visuals help a lot !

so the damage reduction system is sane (provided the bug of going over the resist cap is fixed)

what is not sane is the massive leaps in player damage with every stat, namely:

• 1.3x damage to large enemies / 1.4x damage after fatality
• 1.3x rune damage ring
• 1.2x after being hit damage ring
• 1.4x from elemental damage on gear
• being able to reach 90-100% crit chance and 200% crit damage easily
• easily get 100% armor penetration
• using the villainous multiplier gems

seems to me if instead of swimming in a multiplier soup they joined the additive bucket of increased damage, the damage scaling would be a lot more tame because then diminishing returns kick in

perhaps that’s a solution?

because otherwise you just have to increase the HP of further content to match player power levels

which then only means - same fights, but longer

requiring you to play perfect for longer OR stack gear as much as you can

if i have to stack every possible mathematical advantage i can, in order to progress in the game, fair enough. that’s the ARPG side of NRFTW.

the problem is not the having to put stats on, as we already discussed, is that the stats skip the content

essentially the better your gear is, the less you can enjoy the game because you delete the boss before it can stand up

[Konrad]

Yeah, exactly! There are even more modifiers than you’ve listed, like vegetable cake and the damage-surge spell. I’d cautiously guess that additive stacking of this number of modifiers (within their current range) works well.

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But guessing is silver, calculating is gold, or however that saying goes.

Let’s add your first four modifiers, cake, damage surge, and completely disregard armour pen and crits for the moment. That’s 1+(0.3+0.3+0.2+0.4+0.1+0.2) = 2.5.

Doing 250% base damage against an enemy with 100 effective hp and a weapon that deals 10 raw damage per attack takes me from 10 hits to kill down to 4. If my base damage is higher, such as 20, the number of hits drops from 5 to 2. This is sensible.

But before I’m willing to hail the Great Additive Bucket as the new overlord of offensive scaling, I’d like to give it a thorough test. The knobs we can turn in this model are as follows:

• the ratio of our base damage to enemies’ effective health
• the number ‘n’ of different effects we can stack
• what bonus ‘b’ each effect provides

I’ll try something hopefully fun: Here’s a link to an interactive simulation which displays the number of hits to kill an enemy as a function of base damage. Additionally, you can control the values ‘n’ and ‘b’ above and see what happens.

Hits-to-kill scaling with additive damage enchantments

The way I’ve set this up is that every effects has the same strength. I could’ve simplified it as a total bonus in percent, but I wanted to preserve the feeling of ‘number times strength’.

It’s a nice toy if you’d like to answer balance-related questions. For example, to ensure a weapon will not kill in under three hits, with six distinct effects of 20% each, base damage must not be higher than 22.5% of enemy effective hp.

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Now to evaluate.

Every model remains fine as long as enemy hp grows proportionately to the (expected) modified damage at this level. What is different is how impactful deviating from this expected number is.

In our case, in order to go down to ‘three hits to kill’, a weapon with 17.2% base damage could have anywhere from 5 to 9 effects of 20% each. This is a wide margin. One could argue that this is great (stable), or complain that getting four additional effects achieved nothing.

I expect the number of distinct effects to remain relatively constant through the game. Exceptions like vegetable cake and damage surge should be watched. They’re much more problematic in multiplicative models, and I recall Thomas off-handedly says Moon wants to avoid adding ‘one more floating damage boost to keep track off’ or similar.

So that leaves effect strength as a potential problem. In the example above, if I manage to collect all 9 distinct effects, they can have up to 51% effect strength before I get into oneshot territory. The diminishing effect is strong.

The flip side, again, is that small variations in individual effects fail to have a noticeable impact. Let’s say, in the same 17.2% example as before, that damage-boosting effects could have rolled from 15 to 35%. We have piss-poor rolls of 20% on five pieces of gear, then use 9000 Radiant Embers and still kill enemies exactly as quickly, in three hits.

In other words, multiplicative systems encourage chasing the last few percent, which is why they’re used for perfect-roll chasing.

The flip side to this flip side is that refusing to use any enchantments means I’d still kill in six hits of 17.2%, which is totally doable. Might even say that this doesn’t force me into upgrading enough, but that just means 17.2% is relatively early in the game.

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In summary, the model is robust. Not sure you’d like it (or rather, ARPG perfect-roll chasers) due to how sharply returns diminish. Would you?^[1]

As a final comment: In the current system, some runes have ridiculous damage multipliers (up to 10×). No matter how these stack, they’re ridiculous. If they stack additively, the bonus from the rune is more important than the entirety of item-based damage.

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1. I would. I’d upgrade the weapon until it’s perfect for absolutely no benefit, just so it gets a funny max-roll border or the numbers become golden or nicely round. I don’t know enough about player psychology to know if this is the case for everyone though. ↩︎

[Hubristic]

@Konrad

I’ll try something hopefully fun: Here’s a link to an interactive simulation which displays the number of hits to kill an enemy as a function of base damage. Additionally, you can control the values ‘n’ and ‘b’ above and see what happens.

that is fun. i was playing around with it when the patch 1 hit. the answer the developers used was not to throw everything in the holy grail of additives, but to massively cut the big multipliers.

I feel like that directly answers pretty much everything we’ve been discussing here. need to play a bit more to see how exactly it impacts various builds. my guess is that everything is a lot more balanced and power creep is a lot slower but the 10x runes still screen-delete.

i can’t even pin-point what is the biggest win of this patch. all of the contenders seem very valuable:

• crit chance now can’t be stacked to oblivion - fantastic (max you can stack from gear is now 25% * 1.5 i think ?)
• modifier gems seem pretty much on par with other gems - this invites thinking “what is good for my build”, instead of “obviously slot in the multiplier and nuke the boss”
• increased endgame enemy HP - seems like it hits the spot so far, but i haven’t played extensively much. will be able to more next week

@Konrad

In summary, the model is robust. Not sure you’d like it (or rather, ARPG perfect-roll chasers) due to how strongly returns diminish. Would you?

personally i’m jarred by the infinite scaling because i’ve played ARPGs for so long. i welcome sanity based scaling with open arms and especially love bounded power numbers and more interesting solutions to problems in games than “just add maths until the boss explodes”

seems i discovered the souls genre a bit late but in my defense i was stuck in the blizzard bubble for a very long time and don’t regret it, dota1 and d1-2 are only full of fond memories for me. i wouldn’t do that diablo grind again though, i’m too old for that.

which is why i love the enchantments system of NRFTW - all drops are possibly valuable - because you can cannibalize the items. there is no point where all the loot is just vendor trash. and it’s quite interesting.

now that the stats have had a nerf perhaps i can engage more with the systems i like, like enchantments, and maybe i’ll start using runes again as well.

look forward to hear your impressions on the nerf patch

[Konrad]

How’s The Nerf?

In build 28175, facets were adjusted as follows:

• crit chance down from 10% to 5%
• crit damage down from 40% to 30%
• all damage adjustments from facets decreased by 75%; this is not represented in my calculations, which incorrectly assume a 20% overall damage boost

Enchantments were adjusted as follows:

• mottled black pearl adjusted down to 50%
• crit chance halved to 5%
• crit damage halved to 10%
• armour penetration down to 10%
• physical damage unchanged at 10%, other elements down to 5%

Crit facets are worth even less and physical is the ‘best’ damage type now.

Before exalting, the optimal number of crit chance enchantments for weapons with a 20% damage facet has changed as follows (calculated with 120% base; multiply by 1.6 for physical damage boosts):

10% chance to deal 200% damage: 5 (out of 5), 177% total
20% chance to deal 150% damage: 3, for 160.8% total
25% chance to deal 140% damage: 2, for 160.8% total
40% chance to deal 125% damage: 1 (or 0), for 168.45% (or 168.0%) total

Exalting is hard to evaluate. Since armour penetration no longer passively hits 100% (it is 60% instead), to evaluate it I would need to know average enemy DR by damage type. In addition, there is a bug which makes exalting triple rather than double crit enchantments. This means they are worth more than physical damage.

I’ll ignore the option to exalt armour penetration for now. A good chunk of previously optimal builds should not have exalted armour penetration.

On 10% crit chance weapons, optimal damage is 477.6% base when exalting crit chance and damage to maintain a 1:2 ratio (compared to 389.4% if exalting physical damage exclusively).

Against enemies with 50% DR, expected damage has changed as follows:

• without exalting: from 10× base to 2.3× base
• optimal exalting: from 20× base to 3.8× base

Rune damage multipliers, cake, damage surge and some multiplicative enchantments (vs Large, rune damage) appear unchanged. A handful of specific lightning runes do less damage due to fixes to multi-hits (notably Stormpiercer). This is before enemy health adjustments. We’ll do maybe one fifth of our previous engame damage.

My expectations match yours. I need to play more before I can give a subjective opinion as well (too busy PvPing), but T4 Pestilence sure has grown a little chest hair. This might be the patch for us.

[Hubristic]

i wanted to test whether it’s definitely true that physical damage wins now

so i broke it down into base vs int scaling (was surprised the icebreaker took so much more extra bonus from INT than gnarled staff) applied the actual bonus buckets as if i had 4 pieces of gear with +5% fire or +10% physical (total fire 1.2x, physical 1.4x), and compared real output and efficiency

i wanted to compare a 2h magic weapon and a 2h physical weapon so i picked gnarled and icebreaker because they both scale off int. fused coronet is just something i had so i threw it in there.

in this test fused coronet has a quick facet so less base damage
both gnarled staff and icebreaker - no facets

setup

46 int, no gear, no crits

fire bonus: 1.2
physical bonus: 1.4

coefficient = raw / total weapon damage
damage per focus uses multiplied damage

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weapon	base	+int	total	attack	raw	bonus	final dmg	coeff	focus	dmg/focus
staff	48	86	134	armageddon	829	1.2	994.8	6.19x	150	6.63
staff	48	86	134	fire nova	603	1.2	723.6	4.50x	100	7.24
wand	40	72	109	fire burst	184	1.2	220.8	1.69x	100	2.21
wand	40	72	109	fire nova	490	1.2	588.0	4.50x	100	5.88
wand	40	72	109	hellfire	674	1.2	808.8	6.18x	150	5.39
icebreaker	112	200	312	slashing spin	698	1.4	977.2	2.24x	100	9.77
icebreaker	112	200	312	tremor slam	799	1.4	1118.6	2.56x	100	11.19
icebreaker	112	200	312	juggle strike	599	1.4	838.6	1.92x	100	8.39

this shows wildly different coefficients than the db claims:
correction: DB numbers are correct, i forgot about dummy DR
armageddon listed as doing 1000% of base damage
fire burst listed as 200%
fire nova listed as doing 300% if instant and +200% if fully charged
hellfire listed as 1000%

and i guess the real advantage of elemental damage is that it’s mostly ranged, has a big AoE, and doesn’t lose focus upon interruption unlike melee skills. plus the status effects of course. burn damage is still pretty crazy. lightning aoe still nuts. frost requires a very particular set up or group. plagued ? maybe best when combined with fire / bleed ?

funnily enough i played the whole game with that character using fire burst and thinking “damn, this is OP”. from the numbers it really doesn’t look like it is.

[Konrad]

Nice testing! I’ll try to make sense of these numbers. I hope you’ll agree afterwards that the coefficients in the database are consistent with your data.

Physical Damage

I don’t know which enemy you were fighting, so I’ll calcuate DR first. Expected damage of Slashing Spin is 350% base for 1.4×3.5×312.5 = 1531.25. You tested against an enemy with around 36.2% physical resistance, as (1-0.362)×1.4×3.5×312.5 = 976.9375.

Using this resistance figure to predict Juggle Strike at 300% base, we arrive at (1-0.362)×1.4×3×312.5 = 837.375, matching your data.

I can’t calculate Tremor Slam since I haven’t figured out the precise scaling of shockwaves, traps, kicks and other ‘weapon-independent’ effects. Sorry.

Fire Damage

Determining DR first. The gnarled staff casting Armageddon with a 1000% boost does 11× damage. This leads me to assume 43.725% fire resistance. Expected damage would now be (1-0.43725)×1.2×48×2.79×11 ≈ 994.8.

As you are writing, fire Nova does 400% damage at base and 800% fully charged. Expected damage becomes (1-0.43725)×1.2×48×2.79×8 ≈ 723.49, closely matching your data.

The wand does

• (1-0.43725)×1.2×109×8 ≈ 588.9 with fire nova
• (1-0.43725)×1.2×109×3 ≈ 220.8 with fire burst
• (1-0.43725)×1.2×109×11 ≈ 809.7 with hellfire

Note that in practice, fire burst does its damage with an explosion, not the weak impact you were testing. It does slap.

Note for Re-Testing

From my testing, the dummy should have around 40% physical resistance and 48% fire resistance. What enemy were you hitting?

If it was the dummy, I’ll have to test a few more things. The damage resistances in your testing had the same ratio (5:6) as the dummy, so there may be level-dependent effects or a stacking model I hadn’t considered.

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Misc. Notes

@Hubristic

armageddon listed as doing 1000% of base damage

1000% additional for 1100% of base damage. Just in case you’re misreading the multipliers.

Unrelated: There are two Armageddon runes for some reason, and one is much worse than the other. I was really confused when testing it until I figured this out.

@Hubristic

was surprised the icebreaker took so much more extra bonus from INT than gnarled staff

You may be similarly surprised, then, that all attribute-based damage is a percentage of base damage. At 46 Int, you get a 179.0% damage increase. Icebreaker gets 112×1.79 = 200.5 points, the gnarled staff gets 48×1.79 = 85.9 points.

I expected two-handed weapons to scale better or, from Souls, weapon-specific scaling, so I was surprised about this at first.

@Hubristic

frost requires a very particular set up or group. plagued ? maybe best when combined with fire / bleed ?

Since shatters scale off physical damage, the frost-physical set-up is one of the easier oneshot builds left. The frost-specific armour pen enchantment is now better than universal armour pen.

Plague is great defensively. The lifeleech and slow are crippling. Wouldn’t count on it for damage though; the fire-lightning combo is much better.

[Hubristic]

it was the dummy

i forgot about the dummy resists D :

yes in that case the damage matches the DB completely

sorry, DB

[Konrad]

It has occurred to me to retest some facets. Balancing has taken place.

Both Quick and Sharp decrease damage by less than before, somewhere in the order of 2% to 3% instead of 10% as was previously the case. Heavy increases damage less than before, around 5% instead of 20%.

Assumption: Damage modifiers have been set to one-fourth of previous values. This is massively healthy. My appreciation for the patch grows daily.

[fishypixels]

Yeah I switched off sharp weapons for clumsy and didn’t notice a massive difference. Still better, but not leagues.

[Konrad]

@fishypixels

Still better

Now I felt obliged to check.

If I’m right(*) and all damage adjustments are reduced by 75%, Sharp (.975 base?) is ever so slightly better with perfect (bugged) exalts. For example, 10%ers would be at 421.98% with Sharp vs 415.38% with Clumsy.

Otherwise, once exalts are fixed or if exalts are slightly off, base damage wins by a slight amount. Since base damage has drawbacks and numbers are close, it’s very balanced. The devs definitely did the math this time.

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(*) Just in case anyone is reading this in the future, I wasn’t right: Damage-adjusting facets in 28175 seem to be relative to base damage, not multiplicative to final damage. Exalts also provide the unnerfed bonus for all enchantments, tripling not only crit, but also elemental damage. Doesn’t change the analysis much.

[fishypixels]

Yeah perhaps it’s more fair to say it “feels” better. I know I am partial towards consistent damage rather than spikes, which is why I pushed crit cap before nerf, even if it wasn’t optimal compared to being below cap and going for more crit damage.

It does sound like the balancing is going to make facets more like a flavor rather than build defining.

Poise damage facets are still pretty defining though. Gotta get dat stagger.