Class Timescaling Guide

Introduction

First the definition of what is meant by "class timescaling". It's a rough approximation of how much your mana profits over a single exile should expect to increase over time, due to the buildup mechanics of the different classes.

The purpose of this guide is to give users the ability to be able to quickly reference the timescaling for different classes and builds and also help with the decision on whether it's better to exile sooner or later to maximize mystery accumulation over time.

Assumptions and tweaks

As a quick and dirty approximation that's meant to be helpful, some assumptions have to be made to clean up the math.

• By far the most glaring weakness is the lack of factors describing character and pet exp/level. Perhaps in time this guide will be advanced enough to help develop approximations for this, or you the user will have to decide how much extra wiggle room in the equations to give.
• Just about any build requires at least some set up time and some builds may require bursting several consecutive times and/or for long amounts of time. All the time spent doing this eats into your total exile time, but doesn't yield any bonus timescaling on at least some of your features. This lost time should be accounted for in the cost of exiling.
• Time scaling of Accumulated Spell casts assumes that you have sufficiently more of them than you start with at the beginning of the exile. In practice, this means playing for really long exiles and/or equipping items such as Shadow-Scryer's Crystal Ball and Frosty Ring. Otherwise, you can expect your true timescaling value to be less than advertised.

Note: If the section assumes you're casting a spell that you aren't, either due to level limitations or other shenanigans, simply neglect that factor to timescaling.

Where timescaling differs by phase, the total timescaling (with optimal time spent in each phase) is simply the sum of the timescaling in each phase:
$\sum {\mathrm{\backslash nolimits}}_{P_i\in Phases(I)}Timescaling(P_i)$
E.g. 3 phases with timescaling of 0.1, 5, and 7 results in total timescaling of 12.1.

To approximate logarithmic growth (base 10) about a particular range, use the following:
$1\mathrm{e}3\le x\le 1\mathrm{e}4⟹{\log }_{10}(x)\approx x^{0.15}$
$1\mathrm{e}4\le x\le 1\mathrm{e}5⟹{\log }_{10}(x)\approx x^{0.14}$
$1\mathrm{e}5\le x\le 1\mathrm{e}6⟹{\log }_{10}(x)\approx x^{0.13}$
$1\mathrm{e}6\le x\le 1\mathrm{e}7⟹{\log }_{10}(x)\approx x^{0.12}$

To approximate logarithmic growth (base 1.6), use the following:
${\log }_{1.6}(1\mathrm{e}3)\approx x^{0.39}$
${\log }_{1.6}(1\mathrm{e}4)\approx x^{0.33}$
${\log }_{1.6}(1\mathrm{e}5)\approx x^{0.30}$
${\log }_{1.6}(1\mathrm{e}6)\approx x^{0.25}$
${\log }_{1.6}(1\mathrm{e}7)\approx x^{0.22}$

Exile Timing

In principle, Exile when the profit bonus from Mysteries earned exceeds the profit bonus from continued timescaling.

This point can be identified mathematically. First, find the timescaling rate using the appropriate sections below. This refers to Mana; to convert to Mysteries, we need to take the square root:
$\text{Mysteries Gain}=\sqrt{\text{Mana Gain}}⟹\text{Mysteries Timescaling}=\frac{\text{Mana Timescaling}}{2}$
$t^{9.5}\text{Mana Profit}⟹t^{4.25}\text{Mysteries Profit}$

At any point during the run, you can either choose to Exile, or to continue that run. For simplicity, we'll assume that in the first case the new Exile duration will be equal to the current Exile duration, and in the second case we'll double the current exile duration. With timescaling:
$t^a$
we assume:
$t=2$
to predict gains if we stay in this exile. This means that optimal Exile point (not counting upgrades) is when:
$\text{Mysteries Gained}=2^a$

In the example above, with t^9.5, you should Exile when you would increase Mysteries by roughly 724 times.

Attribute Perks

Some Attribute milestones carry timescaling elements with them. They are all logarithmic and can optionally be neglected, given a conservative estimate of (t^0.10) per perk, or assigned a slightly more precise approximation:
$\text{INS 150}\propto {\log }_{10}\text{Void Entities Collected}$
$\text{SPC 150}\propto {\log }_{10}\text{Spells Cast This Exile}$
$\text{SPC 200}\propto {\log }_{10}\text{Persistent and Accumulated Spells Cast This Exile}$
$\text{SPC 250}\propto {\log }_{10}\text{Spells Cast This Exile}$
$\text{WIS 150}\propto {\log }_{10}\text{Spells Shards Collected This Exile}$
$\text{WIS 200}\propto {\log }_{10}\text{Evocation Spells Cast This Exile}$
$\text{DOM 150}\propto {\log }_{10}\text{Autoclicks This Exile}$
$\text{DOM 200}\propto {\log }_{10}\text{Autoclicks This Exile}$
$\text{PAT 200}\propto {\log }_{1.6}\text{Idle Time This Exile}$
$\text{EMP 200}\propto {\log }_{1.6}\text{Pet Time}$

Apprentice

Apprentice has timescaling on his class ability of 0.2.

Ritual Of Power grows at a rate of 0.45.

Total

Apprentice has a total timescaling rate of:
$t^{0.2+0.45}$$=t^{0.65}$
0.65. You didn't think it would actually be better, did you?

Druid

Class Ability

Druid has a (t^0.75) timescaling to summon efficiency from total autoclicks.

This has a linear effect on autoclicks and the burst spells: Summon Centipede Swarm Summon Deepwood Stalker Summon Evergrowing Forest Summon Woodland Creatures all of which have a linear bonus to profit, with the exception of Summon Woodland Creatures which might be slightly higher (still rounding to linear for sake of simplicity).

This amounts to a total timescaling of (t^3.75) from Druid ability assuming all 4 of these summons are being used.

Summon Centipede Swarm

Summon Centipede Swarm has linear timescaling from total autoclicks this exile.

Rules of Nature

Rules of Nature (active) has linear timescaling from total casts this exile.

Force of Nature

Force of Nature (if used) has (t^0.35) timescaling from total autoclicks this exile.

Summon Woodland Creatures

Summon Woodland Creatures has linear timescaling from total autoclicks this exile.

Summary

Druid can expect a bit over (t^6.75) timescaling overall assuming all spells are in use.

Necromancer

Note: This section is likely to be very experimental. Necromancer scaling is incredibly reliant on pet levels, which are not yet properly modeled.

Class Ability

Necromancer idle profit bonus scales by (log10(t)^3.7). This is approximately simplified to t^0.5. It carries its own bonus directly to profit as well as:

Dreaded Script Of Harvest scales off of idle profit bonus at a rate of (x^.48), yielding (t^0.24) timescaling.

Excluding the idle profit bonus to pet scaling which will be computed in the next section, this sums to a (t^0.75) timescaling.

Pet Bonus

Deserving of their own subsection, Risen Giant and Zombie scale off of (pet level^(log10(idle bonus)). This is a major part of necromancer scaling and can't be neglected.

This section to remain incomplete until pet level is adequately modeled.

Additionally, Zombie receives a linear bonus directly from pet time for the first 14 days, dropping to (t^0.5) afterwards.

Risen Giant receives a (t^4) bonus from pet time, dropping to (t^0.5) afterwards.

Nightfall

Once Nightfall is casting at maximum speed, it timescales at a rate of (t^0.85).

At less than maximum cast rate, it should be assumed to have a higher timescaling, although the author would suggest against exiling on necromancer prior to having achieved this.

Ritual of Power

Ritual Of Power grows at a rate of (t^0.45)

Summary

Necromancer with Zombie scales at (pet leveling factor)*(t^3.0) for the first 14 days, falling off to (pet leveling factor)*(t^2.5) afterwards.

Necromancer with Risen Giant scales at (pet leveling factor)*(t^6.0) for the first 14 days, falling off to (pet leveling factor)*(t^2.5) afterwards.

Arcanist

Arcane Infusion:
$\text{Character Ability Power}\propto {\text{Arcane Infusion Casts This Exile}}^{1.15}$
$\wedge \text{Profit}\propto \text{Character Ability Power}$
$\therefore \text{Profit}\propto {\text{Arcane Infusion Casts This Exile}}^{1.15}$
This scales linearly, yielding timescaling of 1.15.

Jas'Aham's Missile Storm:
${\text{JMS Casts This Exile}}^{1.3}$
This yields a timescaling of 1.3, distinct from its effect on Spells Cast described below.

Radiant Pools:
${\text{Radiant Pools Casts This Exile}}^{0.81}$
Timescales at 0.81 based on the number of times it was cast this exile.

Jas'Aham's Missile Storm casts Magic Missiles, which count as Spells Cast:
${\text{JMS Casts This Exile}}^{1.3}$
Over the whole Exile, this increases the rate of spells cast by:
$\int {\text{JMS Casts This Exile}}^{1.3}={\text{JMS Casts}}^{2.3}$
This feeds into Arcanist's class ability:
${\text{Spells Cast This Exile}}^{0.7}$ $={({\text{JMS Casts This Exile}}^{2.3})}^{0.7}$ $={\text{JMS Casts This Exile}}^{1.61}$
to give 1.61 timescaling.
It also feeds into Karnaphen's Spellshroud:
${\text{Spells Cast This Exile}}^{0.25}$ $={({\text{JMS Casts This Exile}}^{2.3})}^{0.25}$ $={\text{JMS Casts This Exile}}^{0.575}$
for 0.575 timescaling.

Total

Expect to see around 5.5 timescaling:
$t^{1.15+1.3+0.81+1.61+0.575}$$=t^{5.445}$

Prodigy

Class Ability

Prodigy has a (t^2.25) growth rate over the first 10 days, falling to logarithmic afterwards.

Quasi-Incantation

Quasi-incantation Increases incantation efficiency at a rate of (t^1.5).

This has a linear effect on the burst spells: Alter The Laws Primal Power True Sorcery (active) Ley Overdrive all of which have a linear effect on profitability.

Additionally it has a linear effect on Void mana pre-burst Void Radiance which also has a linear effect on profit

Gem Resonance has a complex formula with a log10 scaling of incantation efficiency, but it gives Mana Gems that have milestones (x1.5) every 25 Mana Gems. The formula for this spell says that after the above ~ 7.2e42 Mysteries, it gives 160 Mana Gems for every e1 incantation efficiency. To compare this scaling with other incantation spells:

e1 Incantation efficiency → 1.6 * 100 Mana Gems ≈ 1.5 ^ (160/25) = 1.5 ^ (6.4) = 13.3962751159 ≈ 13.4

Compared with the regular spell scaling which multiplies its profit by 10 per e1 of incantation efficiency, Gem Resonance multiplies by 13.4 per e1 incantation efficiency. To find the power factor value, it needs to calculate the coefficient just found in any logarithm:

ln (13.3962751159) / ln (10) = 1.126984058

log2 (13.3962751159) / log2 (10) = 1.126984058

log10 (13.3962751159) / log10 (10) = 1.126984058

Simply put, Gem Resonance has profit scaling with incantation efficiency (I ^ 1.126984058) and expands with Quasi-Incantation by:

I ^ (1.126984058 * 1.5) = I ^ 1.69047608693

This extends Quasi-incantation's true profitability to be (t^7.5) or ~(t^9.2 with Gem Resonance)

True Sorcery (active)

The active accumulated portion of True Sorcery grows at a rate of (t^0.85)

Ley Overdrive

Ley Overdrive grows at a rate of (t^0.75)

Summary

The total of the above features is ~(t^13.05) over the first 10 days, dropping to ~(t^10.8) afterwards.

Voidmancer

The Voidmancer class ability scales at a rate of(t^0.73) based on void entities collected this exile.

Ebon Truncheon

Ebon Truncheon scales at a rate of (t^0.45) based on autoclicks done this exile.

Ritual of Power

Ritual Of Power grows at a rate of (t^0.45)

Voidterror

Voidterror provides an increase to void mana profits depending on total void mana this exile with a scaling of (x^0.31).

Summary

This adds up to a scaling factor of (t^1.94)

Exorcist

The Exorcist ability scales at a rate of (t^0.84) based on excess Hallowed clicks.

Battle Trance

Battle Trance also scales with excess Hallowed clicks at a rate of (t^1)

Shattering Strike

Shattering Strike scales with the amount of times it has been cast this exile at a rate of (t^1)

Summary

The total of the above is (t^2.84)

Alchemist (void decompression)

This build assumes void decompression to be sole means of void mana production and summoning elixir to be the only elixir with any pertinent bonuses.

Void Decompression

Void Decompression grows itself at a rate of (x^5) based on accumulated casts. This yields (t^5) timescaling just from normal void mana profit alone.

Additionally, the Alchemist summoning elixir benefits from max void mana at a rate of (x^0.21). Combined with the void decompression rate, this means a gain of summoning efficiency at (x^1.05).

Autoclicks scale at a rate of (x), Automatise scales at a rate of (x^1.45) and Artificial Muse scales at a rate of (x^0.4) off of summoning efficiency. Thus, the summoning elixir component finally resolves at a timescaling of (t^2.993)

This means that void decompression casts provide a timescaling of (t^7.993)

Condensed Energy

Condensed Energy scales at a rate of (x^0.45) accumulated casts this exile, yielding character ability power.

This ability power when factored through summoning elixir with a scaling of (x^0.25) yields (x^0.113) summoning efficiency. When going through the computations in the Void Decompression section, this resolves at a timescaling of (t^.208).

Artificial Muse

Artificial Muse scales at a rate of (x^0.4) from gathered resources this exile. This component can be gamed around a bit since resources can be pooled from prior exiles, but assuming consecutive Alchemist runs, this can directly translate as (t^0.4).

Denaturation

Denaturation scales profits at (x^0.6) based on accumulated casts, yielding a simple (t^0.6) timescaling.

Ritual of Power

Ritual Of Power scales profits at (x^0.45) based on accumulated casts, yielding a simple (t^0.45) timescaling.

Voidterror

Voidterror provides an increase to void mana profits depending on total void mana this exile with a scaling of (x^0.31). With the (x^5) scaling of void decompression this results into (t^1.86) scaling.

Summary

Stacking condensed energy in this build sucks and probably shouldn't happen unless you have the VIP 5 to free the slot in your buildup spell bar. Expect to see ~(t^11.3) timescaling.

Alchemist (high mysts)

This build assumes use of pet elixir + Voidterror for void mana pre-burst.

Pet Elixir

The pet elixir scales linearly with max pet level this exile. The level of your Spellhound over time can be approximated withe the equation (5(log2(t*equipment bonus to pet exp)+60) where t is pet time in seconds.

Voidterror/Voidmana

The amount of voidmana given by the voidterror based of the time scaling is(petlevel*maxpetlevel). An approximation of this scaling in power functions is around (t^0.071).

Additionally time as voidterror will provide its own (t^.31) timescaling due to total void mana earned this exile in addition to any leveling bonuses. This must be balanced against the timescaling earned from getting Spellhound to max level, however.

Summoning Elixir

The Summoning Elixir scales at a rate of (x^0.21) based on max void mana this exile which (t^0.015)

Automatise scales at a rate of (x^1.45) and Artificial Muse scales at a rate of (x^0.4) off of summoning efficiency. Thus, the summoning elixir component finally resolves at around a timescaling of (t^0.028)

Condensed Energy

Condensed Energy scales at a rate of (x^0.45) accumulated casts this exile, yielding character ability power.

This ability power when factored through summoning elixir with a scaling of (x^0.25) yields (x^0.113) summoning efficiency. When going through the computations in the Void Decompression section, this resolves at a timescaling of (t^.208).

When factored through pet elixir with a scaling of (x^0.65), it yields (x^0.29) timescaling to pet ability. As Voidterror has (x^1.75) profit scaling from ability power, this resolves at (t^0.51) timescaling.

Therefore, Condensed Energy yields an overall (t^.72) timescaling to profit.

Artificial Muse

Artificial Muse scales at a rate of (x^0.4) from gathered resources this exile. This component can be gamed around a bit since resources can be pooled from prior exiles, but assuming consecutive Alchemist runs, this can directly translate as (t^0.4).

Denaturation

Denaturation scales profits at (x^0.6) based on accumulated casts, yielding a simple (t^0.6) timescaling.

Ritual of Power

Ritual Of Power scales profits at (x^0.45) based on accumulated casts, yielding a simple (t^0.45) timescaling.

Summary

The total time scaling of the alchemist at high mysteries is around (t^2.2) assuming all of the spell involved are being cast.

Shaman

Timescaling before any softcaps is around t^12 and after hitting sofcaps goes down to a minimum of around t^8. (14 days real time -3, 30 days rt -.2, 200 days game time -.5, 7e7 autoclicks ~-.2)

Heretic

Introduction

Heretic time scaling is like the class itself, both on the surface simple but having lots of particulars that makes it far more chaotic. There are two primary phases that have certain variations depending but I'll address those in their subsections. For some simplicity lets start the basics of spell build and void build and work are way from there.

Forsaken Glory

Forsaken Glory Is your primary time scaling spell for longer run burst. It has 2 separate time scaling elements which both build help with spell set being the main bulk of it. Glory receives (t^1.25) to auto clicks from auto clicks preformed, and additional (t^1.15) to click profit for spell casts.

Since both of these can flux heavily over the course of a run the approximate time scale is (t^2.4) across the average of the run. You can judge additional value as of extending of a build (((NT/CT)*(CurAcs/AveAcs))^1.25 * ((NT/CT)*(CurCasts/Avecasts))^1.15).

Excess Hallow Clicks

Chaotic Fervor

With the addition of Chaotic Fervor your ehc gain with be more then ever dependent on it, with more casts over 1e5 the closer your ehc value will approach a value of (t^1.4) which then compounds the scaling of the others.

Character Ability

Character ability is click power (t^.9) for time spent with eHC gain with bulk being spell build time.

Battle Trance

Battle Trance gets (t^1) from ehc to Hallow Click power which is 1 to 1 with profit.

Subtotal

The total time scale for eHC is now at min (t^1.9) and at most (t^2.66).

Void Entities

Character Ability

Your primary mode of collecting VE is through casting the Void Syphon spell, with its value to time being (t^.75) and the effect depending on level.

The Smite Elephant

Oh boy smite, why you have to make it so complicated. Smite has long term 2 scaling factors, and the added fact of being the only scaler for heretic that gets massively effected in the run based on pet choice and upgrades in the run. The primary effect of smite on scaling is the persistent effect of preformed hallow clicksn Voidforged Armaments which is has a (t^.5) based on all casts over the realm. This will naturally pile up with the second pHC scaling, with that being Voidlight Amalgam which gets (t^2.5) to voidmana generation which will be addressed in it own section.

Void Mana

Voidmana generation is important for heretic for a combination of 3 factors giving it its general void scale and its short and long void phase scale. The first is void generation which is (s^.5) to profits up to void stabilization.

Void Elemental

Conjure Void Elemental gets (s^.4) based on max voidmana in exile, so scaling with time up to void stabilization.

Void pets

There are two primary pets for heretic, being Voidterror and Voidlight Amalgam, which both scale off voidmana generated over the exile, giving them a (t^.31) and (t^.36) to time in void gen respectable. In addition voidlight has the scaling off of pHC that comes from the build phase which when combined has a (t^3.15) scaling for the void generation effects.

Ceaseless Hunger

In the case of using Voidterror pet for void mana gathering and bursting legendary Ceaseless Hunger increases pet ability power with time value being (t^.3). PAP directly multiplies VM with ability 1 of VT resulting in (PAP^1.21) profits scalings (.5 + .4 from Void Mana section + .31 from VT ability 2) and mutliplies profits as (PAP^.85) with ability 2 of VT. The total value of pet ability power on profits with Voidterror is (PAP^1.96). Therefore the timescaling for profits is (t^.588).

Pitch-black Cage

In the case of using Voidlight Amalgam pet, VM collection phase is performed using Pitch-black Cage, which has a timescaling of (bats^.5), resulting in profits scalings of (bats^.63). This value is acquired with (.5 + .4 from Void Mana section + .36 from VLA ability 2, multiplied by .5). Thus timescaling is (t^.63).

Enigmatic Parchment

With Voidlight Amalgam as a burst pet and using Enigmatic Parchment, there is an additional timescaling factor of (t^.5).

Totals

Heretic time scaling is a bit all over based on which phase of the game, what spells you use, what offhands you have and their rarity, and other stats you have on top of attributes. The minimum scaling that always applies is the (t^1.65) off of class scaling. When adding in Spells you get a scaling in the range of (t^5.05) to (t^5.55) depending on amount of time and relative stacking of smite in realm, generally leaning to the lower end. Then when going to VLA the time scale for build phase becomes (t^8.2) to (t^8.96) while void phase time is (t^1.26) up to saturation which then its (t^.36). * that the more accurate picture is closer to (ts^5.8-6.56)*(tv^.36)*(tt^2.4) since outside of specific auto click or spell spam phases both build types tend to keep similar average amount of spells and clicks. Ignoring non-polynomial scaling factors, the highest timescaling achievable with VT after void stabilization is (t^6.708), and with Archivist + VLA it is (t^10.09). The effect of heretic's time scale is also effected heavily based on stats since most of his scaling is not off linear sources, with large impacts to evo efficiency and cast rates making It not as cut and dry pure wise.

Oni

Introduction

Oni shifts through different phases of building up and thus these times need to be accounted for. This guide provides a basics of the flow and mechanics. This section will assume that all of your timescaling will come from using berzerker defense stance with furious strike casting at 100% uptime. If furious strike does not yet have 100% uptime, then you should consider your timescaling to be even higher.

Berzerker/FS stacking

This spell/gear set will provide accumulated stacks to everything on the bar. This rate is assumed to be constant with respect to time once furious strike gets 100% uptime.

Ritual of Power

Ritual Of Power grows at a rate of (t^0.45). This is direct to profit and has no further modification.

Enhanced Strength

Enhanced Strength grows at a rate of (t^1.2). This is direct to profit and has no further modification.

Unclean Knowledge

Unclean Knowledge grows at a rate of (t^0.41). This corresponds to pet leveling, and will be fed forward into the pet leveling function.

Iron Blood

Iron Blood grows at a rate of (t^1.18). This corresponds to character ability power, and will be fed forward into that function.

Class Ability

Meditation and Defense stances are neglected, because Meditation is just a tool to set everything else up and Defense incantation duration reduction is obsoleted by Berzerker.

Pet Ability Power

The portion that feeds into pet ability power receives (x^0.5) scaling from character ability power, which is itself timescaled by (t^1.18) from iron blood. This resolves to (t^0.59) timescaling from this portion.

Additionally, it is scaled by pet level at (x^0.8), which is itself timescaled, with its computations in the pet leveling section.

There is a pet time factor of (t^0.8) as well, but be very careful about where you decide to factor this in, as it is completely erased every time you decide to switch pets.

Incantation Efficiency

This scales by (x^0.65) total cast incantations. Total cast incantations accumulates linearly, thus this scales at (t^0.65).

Goblet of Fire, Enhanced Strength, and Ritual of Power all have linear scaling directly into profits.

Possessed Blade has (x^1.3) scaling off of incantation efficiency into evocation efficiency. This resolves to (t^0.85) and feeds into the evocation efficiency section.

Unclean Knowledge has linear scaling from incantation efficiency into pet leveling.

Berserk Stance

Berserk Stance receives linear scaling from total incantations, which itself scales linearly.

It also receives (x^0.5) scaling from character ability power, which is itself timescaled by (t^1.18) from iron blood. This resolves to (t^0.59) timescaling from this portion

This means that Berserk Stance provides (t^1.59) timescaling to evocation power, which will be fed into its respective section.

Evocation Efficiency

Multiple Oni mechanics are based around evocation efficiency, and thus, it deserves its own section.

Summing together the contributions from other sections we have (t^1.59) from Berserk Stance, (t^0.85) from incantation efficiency class bonus through Possessed Blade. Whenever you have archivist up, it converts the (t^.59) pet ability timescaling into evocation efficiency, as well as a yet unsolved pet level timescaling.

This sums to (PetLevelFactor^1.125*t^3) timescaling to evocation efficiency when archivist is running, (PetLevelFactor^1.06*t^3) for interrogator, (PetLevelFactor^2*t^2.65) for Living Sin, and is otherwise (t^2.4).

Burst (Furious Strike)

Burst is only effected by evocation efficiency on Furious Strike which has linear scaling.

Thus on Hungerer, timescaling is (t^2.4).

On Living Sin, timescaling is (PetLevelFactor^2*t^2.65).

Pet Leveling (Hellstorm)

Evocation scaling is one of the primary ways to increase your pet leveling, via Hellstorm which has evocation scaling of (x^0.5).

When leveling interrogator, this provides (PetLevelFactor^0.53*t^1.5) timescaling.

Fill this section in later with other pets.

Pet Leveling

Pet leveling timescaling comes in from two sources: 1) evocation efficiency through Hellstorm, 2) accumulated casts and incantation efficiency through Unclean Knowledge with a timescaling of (t^1.41).

For interrogator (the pet used to achieve max pet level), the timescaling of experience received is (PetLevelFactor^0.53*t^2.91).

Fill in this section when I have the patience and mathemagical insight to resolve the pet level factoring.

Archon

Overview

Archon receives timescaling primarily from 3 different places: 1) Accumulated casts (both for accumulated spells as well as total casts) 2) Total spell shards gathered (either with Tempered Arcanomancy or with Silence as Abolisher and 3) pet leveling.

Jas'Aham's Missile Storm (active)

Jas'Aham's Missile Storm scales at a rate of (x^1.3) casts this exile, yielding (t^1.3) timescaling directly to profit, as well as feeding into any components scaling off of Total Casts this Exile.

Nullzone

Nullzone has (t^0.95) profit timescaling.

Syphon Power

Syphon Power has (t^0.9) timescaling to spell shard generation. This couples through Fire with Fire bonus of (x^1.35) from passive shard generation to yield (t^1.215) timescaling to profit.

Radiant Pools

Radiant Pools timescales at (t^0.81) based on the number of times it was cast this exile.

Karnaphen's Spellshroud

Karnaphen's Spellshroud scales at a rate of (x^.25) total spell casts this exile. Due to JMS increasing the rate of total spells cast, this translates to (t^.575) timescaling.

Tempered Arcanomancy

Tempered Arcanomancy provides (t^1.45) timescaling to character ability power, which is linearly tied to profits, thus providing (t^1.45) profit timescaling.

The component dealing with spell shard costs will be addressed in the Total Shards section.

Class Ability

Total Spells

Archon has (x^0.85) profit timescaling from total spell casts. The longer the exile (and the lower your persistent stacks), the safer it is to assume that all of these casts are coming from JMS. In this instance, the (t^2.3) timescaling from JMS makes this into (t^1.955). In cases where this may be less true (accumulated casts from JMS passive become more noticeable), perhaps this component could be rounded down to a slightly lower value.

Total Shards

Archon has (x^0.85) profit timescaling from total spell shards.

Tempered Arcanomancy passively earns a linear bonus to itself as long as it is on the bar being fed by JMS. However, this bonus is only converted to shards when you have an incantation spell active, ideally using Spellstaff Of Chamaon and several instant evocation spells.

Pre-TA Archon does this as Abolisher with Silence, with the same timescaling although for much less pronounced effect.

This yields (t^1.7) timescaling to profit. Initially this must be stacked in a way that interferes with other forms of stacking, but later can be done simultaneously (once JMS casts are capped with Spellstaff instead of LB).

Soulstealer Level Milestones

Every 25 levels, Soulstealer earns a new ability. Some of these abilities scale off of timescaled features. Cases where character/pet level are a factor do yield some timescaling, but are not accounted for here.

Level 150: (x^0.15) scaling from total spells cast, with (t^2.3) JMS timescaling, this becomes (t^0.345) profit timescaling.

Level 200: linear scaling from enchanting dust collected, with linear profit timescaling (t^1).

Pet Leveling

As with all sections in this guide, computing pet timescaling can be tricky. However, with some assumptions, you can hopefully make good enough approximations.

Assumption: The exile is long enough that differences in raw pet level is not a significant influencer on profit timescaling. That is the biggest observable difference is being able to achieve the next 25 level milestone.

Ideally, this means that optimal Archon exile length will "snap" to one of these milestones. In practice, this isn't always the case, and you may need to linger after one milestone for a while to timescale in other areas while it would still be impractical to make it to the next one.

You can estimate how long it will take for your pet to earn ~5 levels by taking your current pet time and doubling it. Soulstealer will earn a little more than 5, Psychic Cacophony a little less. This also assumes your character experience is the same during this stretch of time, which is slightly untrue - assume you'll get there slightly sooner.

Summary

Assuming SS reaches at least level 200, Archon's normal stacking phase provides a combined total of (t^8.1) for pre-TA, (t^9.55) for TA + LB, and (t^11.25) for TA + Spellstaff.

The shard stacking phase has (t^1.7) timescaling. If stacked independently:

Pre-TA the ideal Ratio for build up is 4 to 1 ~9.5 to 1.

With TA the ideal Ratio is close to 5 to 1. (4.88 to 1) ~5.6 to 1.

Pet level timescales in 25 level increments as well, but this is not easily resolved computationally.

Temporalist

Temporalist scales from a variety of features. He scales from time in exile, time skipped, several accumulated spells, and with t3 pets unlocked Mechanos Apexis.

NOTE: Any bonus to evocation power (including that recursively through the class ability) provides an additional timescaling, since more evocation power makes for more time skipped from Refined Wormhole albeit only on a log10(x) scale, which makes for more evocation power. At an evocation efficiency of 1e30, this approximates out to an additional (x^0.05) timescaling, 1e60 evocation efficiency: (x^0.03) timescaling. This in addition to the standard linear timescaling with casting evocation spells for profit. Various numbers for Temporalist may be rounded/nudged upward to account for this factor.

Class Ability

Time as class

~(t^2.7) timescaling to profit from time as class for the first 30 days, ~(t^.15) afterwards.

Time skipped

~(t^3) timescaling to profit from time skipped.

Character Experience

Not at all accounting for character levels, character experience provides linear scaling to profits. All experience timescaling comes from activity, since Temporalist can instantly max sources on any exile using simulacrum/chimaera. This can be approximiated to (t^0.5) initially, but likely falls off closer to (t^0.25) as the exile continues.

Character Levels

The class ability scales by (L^2) and Kelphior's Black Beam scales by L. This amounts to roughly (t^0.07)

Quasi-Incantation

Quasi-incantation Increases incantation efficiency at a rate of (t^1.5).

This has a linear effect on the burst spells: Converge Timelines Stabilize the Flow True Sorcery (active) Ley Overdrive Superposition all of which have a linear effect on profitability.

Additionally it has a linear effect on Void mana pre-burst Void Radiance which also has a linear effect on profit. This part only applies if you're not using voidterror for void mana production.

If you are using Mechanos Apexis, Gem Resonance will likely also be part of your burst. The Prodigy guide higher up provides the math explanation: Gem Resonance has profit scaling with incantation efficiency (I ^ 1.126984058) and expands with Quasi-Incantation by: I ^ (1.126984058 * 1.5) = I ^ 1.69047608693

This sums up to (t^9.2) timescaling with gem resonance and no void radiance, or (t^9.0) timescaling with void radiance and no gem resonance.

Superposition

~(t^0.12) timescaling through accumulation as well as (t^0.5) timescaling through time skipping.

True Sorcery (active)

The active accumulated portion of True Sorcery grows at a rate of (t^0.85)

Ley Overdrive

Ley Overdrive grows at a rate of (t^0.75)

Mechanos Apexis

Note 1: Mechanos Apexis has some huge timescaling to evocation power. See the above note on how this number is being modified to be slightly higher than linear profit scaling.

Note 2: Mechanos Apexis experience gain is a power function of time, and thus is timescaled itself much more than the typical pet would be. This factor is uncalculated for now, but should not be deemed insignificant.

From 1 day to 3 days: ~(t^3.1) profit timescaling.

From 3 days onward: ~(t^5.4) profit timescaling.

Summary

It is important to note that it is impossible to stack all of Temporalist's timescaling features simultaneously. This is both a curse and a blessing. Curse in that all these features can't simply be summed together for one final number. Blessing in that one can optimize accumulating casts with Shadow-Scryer's Orb in one set, and accumulating time skipped and quasi-incantation with Perfected Kata Bracer's and Temporal Stabilizer in another set.

Accumulated casts should provide (t^2.7) between eachother, with a very approximate additional (t^0.5) possibly being made through attribute milestones.

Time-skipping+QI should provide about (t^12) timescaling w/o void radiance.

Without Mechanos, in either mode, ~(t^3) timescaling should be achieved through time as class and through char exp.

With Mechanos, add another ~(t^5.4) from 3 days onward.

Equipment

Certain equipment gains power accumulated over exile. If you use this equipment in your build, it is yet another timescaling factor to include.

Calculating Character Level

The rate of experience gain on any character is based on the sum of all its individual components.

Sources

This section here can say that when you can rely on Homunculus/Simulacrum/Chimaera/etc to build your sources, it is not important at all to timescaling, since exiling doesn't reset your total mana.

Active

Total mana gained is scaled by log10. At higher mysteries, this number already starts out tremendously high, and thus its contribution should be entirely neglected by timescaling. eg. log10(1e520)/log10(1e500) marks a nice e20 change in profits, but only gives 1.04x more experience than you started with.

Clicks/autoclicks scale by log10. Use the earlier approximations to give an estimate (x^.12 is close to generically accurate)

Void entities/HCs/Liquid Shadow spent scale by ln. x^.20 is a very rough approximation of what you should expect.

Spells cast also scales by ln. For non-Arcanist/Archon classes, x^.20 can be good enough an estimation.

Excluding low mysteries, one should roughly expect to see a timescaling to active experience of (t^0.5). This also means that spending 4x the time should provide 2x the experience.

Putting it together for level

It takes 1.09x the current amount of experience to reach the next character level. What this means is that 2x the experience will yield 8 levels.

Calculating Pet Level

For the purposes of timescaling, the rate of experience gain can be assumed to be constant over time.

T1 Pets

It takes T1 pets 1.16x the current amount of pet time to reach the next pet level. If you like to use time doubling for timescaling, this will yield just under 5 more pet levels.

T2 Pets

It takes T2 pets 1.2x the current amount of pet time to reach the next pet level. If you like to use time doubling for timescaling, this will yield just under 4 more pet levels.