# How many orbs for a Vorici craft?

Estimates the chance per chromatic orb of rolling the socket colours you want in Path of Exile, from the item’s attribute requirements, and compares the average cost with Vorici’s bench recipes.

- Page: https://www.acalculator.org/game/vorici-calculator
- JSON spec: https://www.acalculator.org/game/vorici-calculator.json
- Version: babb46051a67

## Default answer

Example with the default inputs (Strength 0, Dexterity 0, Intelligence 0, Sockets on the item 6, Red sockets 0, Green sockets 0, Blue sockets 0, Chromatic orb price 0.5): For 0 red, 0 green and 0 blue on a 6-socket item, the average number of chromatic orbs is 0.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| strength | Strength | The item’s strength requirement, which makes red sockets more likely. |
| dexterity | Dexterity | The item’s dexterity requirement, which makes green sockets more likely. |
| intelligence | Intelligence | The item’s intelligence requirement, which makes blue sockets more likely. |
| totalSockets | Sockets on the item | How many sockets the item has. |
| redSockets | Red sockets | How many red sockets you want. |
| greenSockets | Green sockets | How many green sockets you want. |
| blueSockets | Blue sockets | How many blue sockets you want. |
| chromaticPrice | Chromatic orb price | What one chromatic orb costs, in chaos orbs, to show costs in chaos. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| chance | Chance per chromatic orb | The chance that one chromatic orb rolls at least the socket colours you want. |
| chromatics | Average chromatic orbs | The average number of chromatic orbs to get the colours: 1 ÷ chance per orb. |
| chromaticCost | Average cost with chromatic orbs | Average chromatic orbs × chromatic orb price, in chaos orbs. |
| best | Cheapest on average | The method with the lowest average cost in chromatic orbs: chromatic orbs alone, or a Vorici bench recipe. |
| bestCost | Its average cost | The average cost of the cheapest method, in chromatic orbs. |
| redChance | Red socket chance | The chance that one socket rolls red. |
| greenChance | Green socket chance | The chance that one socket rolls green. |
| blueChance | Blue socket chance | The chance that one socket rolls blue. |

## Method

socket colour chances from the requirements (Siveran’s model); chance per orb = sum of the multinomial chances with at least the wanted colours; average orbs = 1 ÷ chance

## Assumptions

- Each socket’s colour is rolled on its own, with the colour chances from Siveran’s model (X = 5, C = 5, on-colour ceiling 90%), which he fitted to player data. Grinding Gear Games does not publish the formula.
- Averages treat every chromatic orb as independent. In the game a chromatic orb cannot give the same colours twice in a row, which makes hard outcomes slightly cheaper than shown.
- Vorici’s bench recipes and their costs are those from before patch 3.29, which also added white sockets; this calculator does not model white sockets.

## Worked examples

1. strength = 0, dexterity = 0, intelligence = 100, totalSockets = 4, redSockets = 0, greenSockets = 0, blueSockets = 4, chromaticPrice = 0.5 gives blueChance = 82.5%, chance = 46.325039%. Source: Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io.
2. strength = 0, dexterity = 0, intelligence = 100, totalSockets = 4, redSockets = 1, greenSockets = 0, blueSockets = 0, chromaticPrice = 0.5 gives redChance = 8.75%, chance = 30.668357%, best = Chromatic orbs. Source: Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io.
3. strength = 50, dexterity = 50, intelligence = 0, totalSockets = 3, redSockets = 0, greenSockets = 0, blueSockets = 3, chromaticPrice = 1 gives blueChance = 10%, chance = 0.1%, best = Vorici 3B, bestCost = 120. Source: Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io.

## FAQ

### What is the Vorici Calculator?

The Vorici Calculator is a tool for Path of Exile socket colouring. It estimates the chance of getting the socket colours you want with Chromatic Orbs, the average number of orbs you will need, and whether one of Vorici's crafting bench recipes is cheaper on average.

### How do attribute requirements affect socket colors?

Socket colors are heavily influenced by an item's attribute requirements. Strength items favor red sockets, Dexterity items favor green sockets, and Intelligence items favor blue sockets. The calculator uses Siveran's weighted probability model, fitted to player data, to estimate the chance of each color.

### How are the socket color chances worked out?

With one requirement, the on-color chance is 0.9 × (requirement + 10) ÷ (requirement + 20), and each off color gets 0.05 + 0.9 × 5 ÷ (requirement + 20). With two requirements, each on color gets 0.9 × its share of the requirements and the off color gets 0.1. With three, each color gets its share. For example, an item with only 100 intelligence has a 82.5% chance of blue per socket.

### What is the Jeweller's Method?

The Jeweller's Method uses the crafting bench to change the number of sockets so that the remaining sockets keep or change color, which can be cheaper than Chromatic Orbs for hard off-color combinations. This calculator compares Chromatic Orbs with Vorici's color recipes only.

### Should I use the Crafting Bench or spam orbs?

This depends on your risk tolerance and the colors needed. A bench recipe guarantees its colors and rerolls the rest, while Chromatic Orbs are cheaper on average for easy colors but have more variance. The calculator shows which is cheaper on average.

## Sources

- Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io