BiS Guide

## What is "BiS"

BiS refers to "Best In Slot". The BIS calculator automatically tests items in every slot, at several different enchant levels, and mathematically determines what items are best for a particular task. The result is an always up-to-date build for your character, for specifically what you're doing, generated in minutes, instead of hours of comparisons and testing.

## How to Use

The BiS calculator is actually an added function to the WikiWizard bot, in the Idle Wizard Discord, and can be used in #automaton-chamber. The root command is:

```
w!it bis calc

```

All queries to the calculator must start with that, and more rules are specified afterwards. For example, in order to get a build for maximizing Hallowed Clicks as Exorcist, use this command:

```
w!it bis calc Class=Exorcist Score=HC

```

*\*Note: Rules can be listed in any order. In this case, "w!it bis calc Score=HC Class=Exorcist" is equally valid.*

As you can see, we're specifying 2 rules for WikiWizard in this command:

1. We're using the Exorcist class.
2. We're using the score "HC" (Abbreviation of Hallowed Clicks), and so items are to be ranked based on how much mana from Hallowed Clicks we're earning.

That's the basic query. Specify your class, and what you're trying to maximize. Available classes and scores are listed below, as well other, more advanced rules.

## How to Read

The BiS calculator will always output an image, like this one:

*\*Note: Unfortunately, most non-wiki guides only include this image, which can be intimidating for new players, but with some experience playing the game and looking at these BiS's, it'll become familiar. If you're having difficulty recognizing these items, the easiest way to compare is to go to the items screen in-game, check the "grid" option to see pictures like these, and change your sorting to "Sorting by Type". Then you can scroll to all the belts, for example, and see them side-by-side to compare with the belts in the BiS.*

There's several things going on here, and I'll cover them from top to bottom. Everything with the black background is telling you about the command used to generate this BiS. This can be useful when looking at a BiS in a guide, for example, to see if this BiS is applicable, or if you should generate one for yourself and your specific setup. I'll cover the black part here:

1. At the very top, are the class and pet portraits. In this case, I'm using Archon and Soulstealer, respectively.
2. Right beneath that you can see I've also specified all the spells I have equipped.
3. This BiS also includes a "passive". Passives, for the purposes of the calculator, are spells with a lingering effect that doesn't need to be on the spell bar to work. In this case, that's . Passives you may be more familiar with are  or . Other information that can display here may be an Ironsoul stance, or an Alchemist elixir.
4. Beneath the white divider line, the first item is Score. That's what this BiS is trying to maximize, such as Void Mana or Hallowed Clicks. In this case, I'm trying to maximize Mana earned while casting , so the score shows a picture of that spell.
5. After that is the formula. This has little practical use to a regular user, but it's interesting to note! It's the mathematical formula BiS has used to compare each item.
6. And then we have "Values". This is a full list of all the remaining rules, including attributes, incantation efficiency, current character and pet XP, etc. These have sensible defaults, so you shouldn't have to worry about them in most cases. Just know you can always customize a BiS even further!

Finally we're at the meat of the BiS. At the bottom of the BiS, we have our recommended item builds.

Along the left side, you'll see "Enchant 0", "Enchant 2", etc. These are recommended builds at different Enchant levels. BiS actually calculates an ideal build at every enchant level up to at least 40, but only displays enchant levels where something changes. For example, at enchant 2, you can see  becomes more efficient than .

*\*Note: Enchant costs scale multiplicatively, therefore enchant levels 1-5 are quite affordable, while enchanting anything to above level 10 takes a great deal of time and dust. When powering up items to match a BiS set, you'll likely want to target the highest enchant level below 8 or so. In this case, I've gone for the set at enchant 2, and will upgrade to the enchant 8 or 10 set when I start doing experiments after e400.*

Along the right is each actual set of items. Items are laid out in rows, showing each slot. Note the slots on the right may not be available at your Paragon level, as Ring, Weapon, and Cape slots are unlocked later. These are the 4 slots on the very right, so don't worry if you can't find those items for now.

## On the Wiki - BiS Embeds

In the "How to Read" section, we used the output image as an example. However, on the Idle Wizard Wiki, we actually have a powerful "BiSEmbed" template, which looks like this:

*\*Note: The BiSEmbed also includes an extra row: Command. This gives the exact command run to generate this BiS, so that future editors can update the BiSEmbed when new updates are released! If you're looking at an older guide, I encourage you to re-run these BiS commands, and update the BiSEmbeds. To learn how to update a template, please read the Guide to Guides.*

These embeds are laid out similarly to the image in "How to Read". The key difference is that it's connected to the wiki itself. Each item and spell actually links to its page, and hovering over any of them brings up more details. This information is designed to make it easier to read, and to understand why items are recommended, so you can make your own educated decisions about what to equip for your situation.

To embed one of these yourself, look at the Guide to Guides to see how to use templates, and get bis\_data directly from the BiS calculator itself with the special rule "wiki=1":

```
w!it bis calc wiki=1

```

*\*Note: As with all rules, "wiki" is an abbreviation. You can also use "Wiki=1", "WikiExport=1", and "wikiexport=1".*

This causes the BiS calculator to output "export.txt" directly after the BiS itself. This file contains exactly the data you'll copy/paste into the "bis\_data" value.

## Shortfalls

Unfortunately, Idle Wizard is an incredibly complicated game, and lots of factors affect the "optimal" build for you and what you're trying to accomplish. In this section I'll give some examples of cases where you'll want to use your own discretion, rather than blindly following a calculator.

### Item Quality

For most players, all items won't be legendary. And many items exhibit drastic differences between levels. For example,  has an incredible effect that makes it critical to many classes Build-Up phase, where it decreases incantation duration by 75%. However, before upgrading  to Epic, it doesn't decrease incantation duration at all!

In consequence, a BiS recommended item may not even have the effect you're supposed to be using it for at a lower quality. In this case, the BiS makes a great starting point for your build, and gives a solid recommendation of what to upgrade later, but might not be ideal with your current equipment.

### Weapons

Each weapon has a custom effect, usually relating specifically to a class or spell in some way, and often scale off their own value entirely, such as  scaling off collected bats this exile. As such, the BiS recommendations for weapons are generally worthless, as the only practical value to track is the enchantment. The result is that most BiS calculations will just recommend  for it's powerful enchant, even though the weapon effect barely applies.

As a result, weapon recommendations from BiS should be almost entirely ignored, in favour of recommendations from the community or your own judgement. However, Spazou has stated he's working on this, but it's a complicated problem to solve, and you shouldn't expect a fix for a while.

### Defaults

The BiS defaults are great for most cases, but sometimes fall short. If you're writing the command for yourself, these shortcomings can be overcome by specifying more rules to tailor it to your needs, but this can't always be counted on in guides.

For example, when trying to maximize Void Mana gathered by Voidterror, he gets stronger the more Void Mana is gathered, creating a moving target for the BiS calculator.

Other examples include attributes, which are assumed to all be at 175 unless specified, and paragon levels, where by default BiS assumes you have all equipment available.

*\*Note: As covered in "How to Read", you can see what these values were set to when the BiS was calculated, and see if these approximations are satisfactory for your situation.*

## Basic Rules

You'll want to have an understanding of these rules before writing your own BiS queries. Knowing these is enough to get good advice on almost any build question you might have.

### Class

The most basic rule, this is how you set which class you're looking to generate a BiS for.

### Pet

If it's relevant, you can also specify what pet you're using. For example, to calculate a BiS for earning Void mana with Voidterror, you can use:

```
w!it bis calc Pet=Voidterror Score=VT/VM

```

Or if you just wanted to account for the fact that you're using Anima Construct as your pet while collecting Hallowed Clicks, you could use:

```
w!it bis calc Pet=Anima Construct Score=HC

```

### Score

Scores are the most important rule in a BiS. This is the rule that defines how items are compared.

*\*Note: In the case of trying to maximize Mana, there is no "Profit" or "Mana" score. This is because classes profit in different ways, and most of them have a custom score you'll want to maximize to get the best burst and mysteries out of that Class. For example, Prodigy bursts using a spell called , which has an abbreviation "KBB", so to generate a Prodigy burst set, we use the command:*

```
w!it bis calc Class=Prodigy Score=KBB

```

#### Generic Scores

These are scores that relate to any class, such as autoclick profit, or evocation efficiency.

#### Pet Scores

These are scores that relate to a specific pet, such as Voidterror's earnings of void mana.

 Voidfiend - Void Mana
```
Score=VF/VM

 Voidterror - Void Mana
```
Score=VT/VM

 Daemon - Mana
```
Score=Daemon/Mana

 Pit Lord - Mana
```
Score=PLord/Mana

```

#### Other Scores

This section is just for scores that don't fit into any of the other categories

 Liquid Shadow Income
```
Score=LSI

```

#### Spell Scores

The most effective way to collect something is in most cases, a spell. For example, for many classes the best way to collect void mana is by casting . So to maximize void mana for those classes, your BiS might start with:

```
w!it bis calc Score=Void Radiance

```

These spells are divided into Common, for spells most classes can cast, or by the T1 Class that has that spell.

```
Score=MM

```
Score=GR

```
Score=Synthetic Entity

```
Score=VR

```

  - Mana
```
Score=FB/Mana

  - Pet Experience
```
Score=FB/Experience

  - Mana
```
Score=HS/Mana

  - Experience
```
Score=HS/Experience

```

```
Score=PZ

```

  - Mana
```
Score=LB

  - Spell Shards
```
Score=LB/Shard

```
Score=JMS

```

```
Score=KBB

```

```
Score=Voidbolt

```
Score=VS

```

```
Score=Smite

```
Score=Rel

```
Score=HF

```

```
Score=FF

```
Score=DIN

```
Score=SIS

```

```
Score=VD

```
Score=Cry

```
Score=AS

```

```
Score=FS

```
Score=TTS

```
Score=FoW

```

```
Score=CS

```
Score=MD

```
Score=Deb

```

*\*Note: Is a score missing? To have WikiWizard send you the raw scores list, just run:*

```
w!it bis pro scores

```

## Advanced Rules

Advanced rules provide a higher level of customization, allowing you to tailor a BiS to your current setup.

### Paragon

By default, BiS assumes you have access to all equipment, as if you were max paragon level. However, if that's not the case, the other recommended items aren't useful, and may even be affecting the optimal outcomes for other slots. For example, if you're paragon level 15, and therefore haven't unlocked the ring slot yet, you can start your BiS with:

```
w!it bis calc Pro=SubParagon18

```

*\*Note: You can't put your current paragon level here. Instead, list the lowest paragon level that's above your own, which unlocks new items. For a list of valid paragons, reference the table below:*

 12
```
Pro=SubParagon12

 18
```
Pro=SubParagon18

 24
```
Pro=SubParagon24

 28
```
Pro=SubParagon28

```

### Attributes

By default, BiS sets all attributes to 175. This rarely affects the outcome of the BiS, but it's easy to imagine an outlier situation where two items give comparable end results, but by buffing different things, and an attribute bonus causes the weaker item to give a larger end result.

Each attribute can be adjusted individually, and has its own rule. Here's an example where I set all attributes to 150 instead of 175.

```
w!it bis calc Int=150 Ins=150 SC=150 Wis=150 Dom=150 Pat=150 Mas=150 Empathy=150

```

*\*Note: Just a reminder that rules can be listed in any order, and that if an attribute is actually 175, it can simply be excluded.*

### Spells

In a lot of cases, spells matter to helping you achieve your goal. And buffing a particular spell's effect may be the main reason to equip an item that's critical to your build. Here's an example of a BiS for maximizing Void Mana as Archon:

```
w!it bis calc Class=Archon Spells=JMS, Void Radiance, Nullzone, Radiant Pools, Syphon Power Score=VR

```

*\*Note: Spells can be listed as "comma-separated" like the example above, or the Spells rule can actually be "packed", where you set the rule multiple times, and the BiS simply understands that means you're using multiple spells, like so:*

```
w!it bis calc Class=Archon Spells=JMS Spells=VR Score=VR Spells=NZ Spells=RP Spells=SP

```

*\*Note: Alchemist Elixirs and Ironsoul Stances have also been included here for simplicity. Please note that they aren't used exactly like spells. Just look at the examples to see their usage.*

*\*Note: Passives - Many spells are "Passives", meaning (for this caclulator) that they have a lingering effect after completing that applies even while not on the spellbar. These spells should always be listed alongside the ones you're casting, even if you're not currently casting them. Passives will be noted with each class they apply to. This should not be confused with spells having a passive side-effect, like Temper The Steel.*

 Evocation Elixir
```
Elixir=Evocation

 Summoning Elixir
```
Elixir=Summoning

 Pet Elixir
```
Elixir=Pet

```

 Meditation Stance
```
Stance=Meditation

 Defence Stance
```
Stance=Defence

 Berserk Stance
```
Stance=Berserk

```

 Meditation Stance
```
Stance=Meditation

 Defence Stance
```
Stance=Defence

 Berserk Stance
```
Stance=Berserk

```

 Evocation Elixir
```
Elixir=Evocation

 Summoning Elixir
```
Elixir=Summoning

 Pet Elixir
```
Elixir=Pet

 Shadow Elixir
```
Elixir=Shadow

```

*\*Note: Is a spell missing? Most likely, that's because the spell has no effect that matters to BiS. If you think otherwise, you can have WikiWizard send you the raw spells list by running:*

```
w!it bis pro spells

```

*If the spell still isn't there, and you need it, feel free to bring it up in the discord at* #arcaneum-suggestions.

## Expert Rules

Expert rules are the most advanced set of rules, and should be unnecessary in most cases. These rules allow you to redefine some of the BiS's most specific defaults, which are only used in specific situations. This section is also far less guiding, and will leave it to your discretion whether or not a particular BiS would be aided by setting these values manually. In addition, this section is totally complete, including even values that should really never be set, and may require intensive calculations beyond what the game provides as statistics to set correctly.

*\*Note: The "values" section of a completed BiS shows all the rules used in that BiS's calculation. However, just because a rule is used in a calculation doesn't mean it can affect the result. In this case, the BiS will detect this, and set the value to 1. This will even overwrite manually set values. You can use this as a guide to determine if adjusting an expert rule may do something, if it's present in values, and not equal to 1, it has at least some effect (which may or may not be consequential).*

### A Note on Values

Expert rules are more complex than regular rules, and may require specific formatting of values.

If a value is a percentage, it's to be represented as a whole number. For example, 100% is 1, and 50% is 0.5.

If a value is very large, scientific notation may be used. For example, 1e300 and 2.95e287 are valid inputs for a rule.

### Click and Autoclick Rules

These rules allow you to specify some values pertaining to click and autoclick profits, such as your critical rating. Here's an example of setting your critical rating, perhaps because you have too few mysteries to afford an upgrade:

```
w!it bis calc CR=9000

```

 Click Profit
```
Click=1.00e10

 Critical Click Profit
```
CM=1.00e10

 Critical Rating
```
CR=10000

 Percentage of "Mana per Second" given by a Click
```
MpSpC=0.05

 Autoclick Profit
```
AutoClick=1.00e10

```

### Spell Rules

These rules allow you to specify things like Evocation Efficiency.

 Evocation Efficiency
```
Evo=1.00

 Incantation Efficiency
```
Inca=1.00

 Summoning Efficiency
```
Sum=1.00

```

### Character Rules

These rules allow you to specify values relating to your character, such as Ability Power, or XP.

 Character Level
```
CLvl=100

 Character Ability Power
```
CharAP=1.00e4

```

### Pet Rules

These rules allow you to specify values relating to your pet, such as Ability Power, or XP.

 Pet Level
```
PetLvl=100

 Pet Ability Power
```
PetAP=1.00e4

```

### Resonator

Resonator is a special rule, used to exclude . Since resonator ring raises the enchant level of all items, it significantly changes the output, and actually has to be calculated similarly to another BiS. Thus, disabling it can boost performance significantly, and is also the only way to get more accurate results for low enchant levels if you don't have the item yet. Here's an example BiS with Resonator Ring disabled:

```
w!it bis calc Resonator=0

```

### Invalid

Invalid is a special rule, used to exclude a slot or slots. With Invalid set, no BiS will be calculated for those items, greatly reducing the number of permutations and making the BiS run faster. It's primary usage for now is to exclude weapons, which currently aren't useful recommendations anyway, as covered above in the Shortfalls section. Here's how to do that:

```
w!it bis calc Invalid=Weapon

```

Interestingly, the Paragon rule is actually just shorthand for this one. For example, the BiS calculates "Pro=SubParagon24" as though you'd used "Invalid=Back, Wrist, Weapon".

### Other Rules

This section is for any rules that don't fit into the other predefined categories. They're listed here, in a loosely alphabetical order:

 Offline Production
```
Off=1.00e4

```

## Internal Rules

These are rules that are not actually intended for you to use, but are technically modifiable, and listed here mainly to help users who want to know about the values they don't recognize. These rules are also the most likely to be outdated, and are subject to change, due to their nature. If you find yourself using these rules for a BiS you're intending to follow, you're almost certainly doing something wrong, or missing a more practical way to achieve the same goal.

*\*Note: Rules that start with "Additional" are not what they seem. Rather, they are the modification to the base bonus. The best way to calculate these values for yourself is to go through your upgrades, and add the bonuses by hand.*

*\*Note: If a rule is split into Additional and Multiplicative versions, the additional is the total of upgrades which add to a bonus, and the multiplicative is the total of upgrades which multiply that effect.*

*\*Note: No support will be given for any BiS using these rules.*

### Building Profit Rules

This rule describes the percentage of profits each building takes. It's used when spells affect the profits of a particular building, for example.

### Other Internal Rules

*Note: These rules are in roughly the same order as Expert Rules, wherever possible.*

## How it Works

For those interested, this section is going to do its best to describe the internal workings of the BiS calc. Obviously, this is not all-encompassing, and changes and upgrades will be made in the future.

To start with, BiS generates a formula based on the rules given, to determine how item effects will affect the score. Then it filters out items that have no effect on the formula. At this point, it moves to calculating each enchant level.

At each enchant level, items go through 2 more layers of filtering (Items which passed the filter described in the last paragraph are tested anew at every enchant level).

1. Each item is scored at the enchant level, in a "best case" way. It's calculated every set effect is an effect on just that item. Then, for each slot, items are sorted by this score, and items are taken until the first non-set item (2 non-set rings are taken). This results in an item list over-favouring sets, and the best item for each slot that doesn't include set effects for each slot.
2. Now, for each set, we test every permutation of a set ({head}, {ring}, {shoulder}, {head, ring}, {head, ring, shoulder}, {head, shoulder}, {ring, shoulder}, etc.) and score these permutations (properly calculating set effects now) as compared to the equivalent non-set items. Any permutations that beat the optimal non-set items for their slots have all their items included for the final calculation.

*\*Note: In filtering phase 2, only set items that passed the first filter are included. This results in smaller versions of the sets being tested.*

At this point, filtering is complete, and every possible combination of the remaining items is scored with the formula, and the highest scoring one is the recommended item set.

*\*Note: Every enchant level has a calculated BiS, but the output image only displays enchant levels where the recommended set changes.*

This process is repeated for a minimum of 40 enchant levels. After the 39th level, a check is run to see if the BiS is complete. To finish, 2 parameters need to be met:

1. There must have been no change in the last 15 levels. This means that for every BiS, at least 15 more enchant levels were tested than the last one you see a recommendation for!
2. The "growth" of the second best set must be less than the "growth" of the currently recommended set. Mathematically, "growth" can be represented as such:

```
Score(Enchant N)/Score(Enchant N-1)

```

This is done to ensure that each BiS lists the set that scales best with enchant level, even if that only occurs at an exceedingly high enchant level.

### Formula Generation

*\*Even more credit goes to Spazou here, as this section was originally written by him in it's entirety. I didn't even know what infix notation WAS.*

Unfortunately, to begin understanding how the formula generation works, we first need to grasp some heavy mathematical stuff. It may be tempting to skip this, but it really is core to how this works! That said, let's begin with some mathematical notation:

You've probably never considered this, but the way we write our math everyday is actually something called "infix notation". Infix notation basically means that operators (+, -, \*, etc.) are placed "in" between our operands (numbers or values). Which is great for readability. In this case though, we use a notation that's better for making changes, called "postfix notation". Postfix puts are operators "post" or after, our operands. Postfix allows us to write without using parentheses (ex: (1+3)^6), and to more easily add more operators to the formula as we go. Let's get into some examples to help show you what I mean:

To keep things simple initially, I'll do these example with variables like "A", "B", "C", instead of using "Evocation Efficiency", "Production", or "Building Profits". The ideas we learn here will still hold though!

So let's try and read the following postfix expression:

```
A 3 + B *

```

We read postfix from left to right, as you'd expect. Each operator affects the previous two terms, so "A 3 +" would read as "A + 3" in regular notation. Continuing, the \* affects B, and the term before B is the one we just converted, "A + 3". In total, this means our expression reads as "(A + 3) \* B" in infix notation. You can already see how postfix notation spares us the messiness of parentheses.

Now let's convert a more intimidating expression, from the next example:

```
A C * 3 + B C * *

```

In this case, we start from the left again. "A C \*" is equivalent to "A \* C". Adding the "3 +" gets us to "(A \* C) + 3". Now we reach something more interesting. "B C \* \*" has two operands in a row! In this case, we continue to follow the rule that each operand affects the previous two terms. So "B C \*" converts to "B \* C", and the last \* affects both of our combined terms, resulting in a final "((A \* C) + 3) \* (B \* C)".

Alright, now that we understand how to read postfix notation, let's look at why we're really using it: To combine effects. For this, let's look at calculating a BiS formula in a heavily simplified environment.

In-game, our Score is determined by this formula:

```
A 3 + B *

```

But since lots of different values go into determining the value of A and B, we need to take more than just these values into account. In this simplified example, the only effects that change the value of A and B are these 3:

1. A is multiplied by C
2. B is also multiplied by C (For example, a spell like  causes production to be multiplied by your incantation efficiency)
3. B has an additive bonus of 2 (For example, the 25 Insight perk that adds 12% to void mana profit)

In postfix, we can represent these effects like this:

```
A C *
B C *
B 2 +

```

Thanks to postfix notation, it's easy to combine these separate effects with the simple in-game formula to get a final unified result we can use for a BiS. So, let's start again with our in-game formula:

```
A 3 + B *

```

Because postfix handles our order of operations without a mess of parentheses, we can simply replace terms with their more complex representations as an effect. (This is like replacing "Evocation efficiency" with "Evocation efficiency \* The effect of  \* Incantation efficiency).

*\*Note: It's important to resolve multiplicative effects, before moving on to additive ones. Doing otherwise won't work.*

Let's start with replacing our "A"'s with "A C \*":

```
A C * 3 + B *

```

And replacing our "B"'s with "B C \*". Watch how this one automatically resolves order of operations between the "+" and the "\*" at the end:

```
A C * 3 + B C * *

```

And finally we resolve our additive effects, by replacing "B" with "B 2 +":

```
A C * 3 + B 2 + C * *

```

Converting this to infix gives us:

```
(A * C + 3) * (B + 2) * C

```

Which is correct! You can see how handling this entirely in infix notation would've required a much more complex approach.

Now, since we added a new value to the formula (C) for our Score, we would search for effects that change the value of C, and repeat the process until everything was accounted for.

Now let's actually take on the full example of a real BiS. We'll use the Score "Magic Missile", which can be described as trying to maximize the profits given by .

Magic Missile gives X seconds of production, where X is determined by the Evocation efficiency (simply called "Evocation" from now on). And production in this case is the profit earned from all buildings, so the basic Score formula for Magic Missile is:

```
AllBuildingsProfit Evocation *

```

Then we start adding in our other effects. Now each attribute point in Spellcraft gives 2.3% bonus evocation efficiency, which looks like this in our notation:

```
Evocation 1.023 Spellcraft ^ *

```

So we replace Evocation in our formula with that, and get this:

```
AllBuildingsProfit Evocation 1.023 Spellcraft ^ * *

```

Now, let's say we're playing Necromancer, an idle class. This means that all sources have their profit increased by our Idle bonus, resulting in this formula:

```
AllBuildingsProfit Idle * Evocation 1.023 Spellcraft ^ * *

```

But we also have Zombie as our pet, who increases our profit by this formula:

```
AllBuildingsProfit Pet.Level Idle log10 0.6875 * ^ * 1 Pet.AbilityPower + 0.6 ^ *

```

This goes on and on, as you might imagine. The BiS calculator has a massive list of effects, and conditions for when they apply (such as when we're using a certain pet, or how many attribute points we have), and will continue to apply them until all effects have been accounted for.

Then, for each item comparison, a copy of the formula is made, and item effects are applied in the same way.

Now, if you've been paying very close attention, you may be asking "But wouldn't item effects break the rule of applying multiplicative effects before additive ones?". And you'd be right to ask. When generating the "Base formula", before items are applied, the BiS calc actually saves locations where multipliers might be added by items, so the formula is always modifiable later while avoiding this pitfall.

For example, if an item had the effect "A C \*", but we had already applied the additive effect "A 2 +" earlier, we would skip replacing "A" with "A C \*", and simply insert "C \*" after the "A 2 +". This results in:

```
A 2 + C *

```

And if we'd calculated the multiplicative effect first, we'd be replacing "A" with "A 2 +" in "A C \*", which is:

```
A 2 + C *

```

Or exactly the same result.

The resulting equation gives us a complete calculation of the final score, taking into account every effect and how it's affected by other things. We can then replace these values with the ones given by our particular build, and see exactly how it performs at maximizing the Score.

Et voila.