Dead by Daylight Maths

This Article provides an overview and in-depth explanation of the mathematics working behind-the-scenes of *Dead by Daylight*.
It explains how Action Speed bonuses and penalties are calculated in-game.

## Overview

All interactions in *Dead by Daylight* use so-called *"Charges"*.
Some instances are more obvious than others, such as repairing Generators vs. charging a Killer's Power.

When performing an interaction, Charges are added to it.
Once an interaction is completely charged, it is considered complete.

Interactions are usually charged at a default rate of **1 Charge per second** (abbreviated as **1 c/s** on the Wiki).
This equivalent to an Action speed of **100 %**.

*Dead by Daylight's* various Unlockables may impact the Action speed, but never the total amount of Charges an interaction requires to complete.
While it can take longer than **90 seconds** to repair a Generator alone, it will always be completed after it is charged with **90 Charges**, never more, never fewer.

### Progress Bar

The Progress Bar and its colour reflect the current charge progress of an interaction, as well as the Action speed:

 Debuff State: **red** |  | Action speed is **less than 100 % or 1 c/s**.

## Calculations

### Action Speed

In order to calculate one's Action speed, one must first separate any **positive modifiers** from any **negative modifiers**, as in *Dead by Daylight*, positive modifiers are additive, whereas negative ones are multiplicative.
The latter is done so that an Action speed can never reach **0 %**, making an action incompletable, and stacked effects have diminishing returns.

#### Positive Modifiers

*This applies if there are **only** positive modifiers present.*
Convert all modifiers to decimal and add them together, then apply this bonus to the default Action speed of 1.0 c/s:
`0.5 + 0.25 + 0.1 = 0.85
0.85 + 1.0 = 1.85 = 185 %`

#### Negative Modifiers

*This applies if there are **only** negative modifiers present.*
Convert all modifiers to decimal and subtract each of them from the default Action speed of 1.0 c/s, then multiply them together:
`(1.0 - 0.5) * (1.0 - 0.25) * (1.0 - 0.1) = 0.3375 = 33.75 %`

#### Both Modifier Types

*This applies if there is a mix of positive and negative modifiers present.*
Do the calculations of the positive and negative modifiers separately, as detailed in the two previous sections, then combine them using the following formula:

`(1.0 + Σ positive modifiers) * (Π negative modifiers)

(1.0 + 0.85) * (0.3375) = 0.624375 = 62.4375 %`

### Action Time

Action Time is calculated by dividing the Charges required to complete an interaction by the Action speed in Charges per second.

#### Simple Example

* Health State: 16 Charges
* Altruistic Healing speed: 1 Charge per second

`16 Charges / 1 Charge per second = 16 seconds`

#### Complex Example

* Health State: 16 Charges
* Botany Knowledge Healing Speed bonus: +50 %
* Medical Scissors Healing Speed bonus: +10 %
* Personal Healing Speed penalty: -33 %
* Sloppy Butcher Healing Speed penalty: -25 %

Step 1: Sum of all positive modifiers:

`0.5 + 0.1 = 0.6`

Step 2: Product of all negative modifiers:

`(1.0 - 0.33) * (1.0 - 0.25) = 0.5025`

Step 3: Resulting Healing speed:

`(1.0 + 0.6) * 0.5025 = 0.804`

Step 4: Resulting Healing time:

`16 / 0.804 = ~19.9 seconds`

### Efficiency

In *Dead by Daylight*, all Items come with a certain amount of Charges, referred to as their Capacity.
Actively using an Item consumes its Charges over time until it eventually runs out.

An Item's efficiency determines how many of its Charges are used to complete an action.
The higher its efficiency, the fewer Charges it will consume, whereas a lower efficiency will cause its depletion to occur more quickly.

Efficiency is calculated similarly to Action speeds, but by using efficiency modifiers rather than speed modifiers.

#### Example

* Health State: 16 Charges
* Streetwise Healing Efficiency bonus: +25 %
* Personal Healing Efficiency penalty: -33 %

`16 / ((1.0 + 0.25) * (1.0 - 0.33)) = 19.1 Charges`

The information from the example above shows that healing yourself for **1 Health State** with a Med-Kit while having those two Perks equipped will consume **19.1 Charges** from the Med-Kit's Capacity.

## TL;DR

* An Item stores *"Charges"* inside it.
* Action speed makes the Progress Bar of an interaction fill up faster or slower.
* No matter how fast or slow an interaction is completed, it will always require the same number of Charges to be completed.
* Efficiency is the only metric that affects how many uses one can get from an Item.