*See the [Aura Definitions](https://hackmd.io/-5NhDyekTJWH4NmPD3xBTg) document for more detail on the meaning of the terms used.*

## Overview

Subjects, Players, Trainers, and Managers can achieve levels by being evaluated by Players, Trainers, or Managers.

Levels are team-specific and set by team captains. A team must try to create useful levels to increase their chance of being included in leagues[^1].

Levels are a convenient way to consistently measure quality. For example, "subject level 1" communicates a certain level of quality about the subject. As conditions in the network change, the underlying requirements ([score](#Score), [minimum evaluations](#Minimum-evaluations)) for a subject to achieve level 1 might change, but the quality conveyed by that label will remain constant.

## Level requirements

### Score

Each level defines an *score* needed to achieve the level.

A participant's score is defined as follows.

$$
score = \sum_{n=1}^{num\_evaluators} \max(score_n \cdot confidence_n \cdot sign_n , cap)
$$

* $score$ is the score the evaluator received from their own evaluators, [except in the case of managers](#Manager-energy). An evaluator must have a positive score for their evaluation to contribute to the score.
* $confidence$ is the evaluation confidence given by the evaluator.
* $sign$ is $1$ or $-1$ , indicating a positive or negative evaluation.
* $cap$ is the maximum allowed contribution by a single evaluator to the score. This is defined with the level.

### Minimum evaluations

A level may define minimum evaluation requirements. A requirement may define both a minimum confidence and a minimum evaluator level. Requirements can be combined with logical AND and OR operations.

For example, Team BrightID might attach the following minimum evaluation requirements to its subject levels.

* Level 1: one low+ confidence evaluation from one level 1+ player
* Level 2: one medium+ confidence evaluation from one level 1+ player
* Level 3: one high+ confidence evaluation from one level 2+ player OR two medium confidence evaluations from two level 2+ players
* Level 4: one high+ confidence evaluation from one level 3+ player OR two medium confidence evaluations from two level 3+ players

Player, Trainer, and Manager levels have their own minimum evaluation requirements.

## Manager energy

Energy is a special name for a manager's score, and it's computed differently. Energy flows between managers for a limited number of iterations (usually 2 or 4 depending on the size of the team) using a weighted SybilRank algorithm. The seeds in the algorithm are the team captains. Manager energy flows from one manager to another proportionately to the confidence they have in their positive evaluation. When a manager evaluates a new manager positively, it reduces the energy flowing to other managers they're already evaluating. This is different from trainer and player scores, where one evalution doesn't diminish other evaluations.

Despite the differences in how they receive their scores, managers can still receive levels, including [level -1](#Level--1). To bootstrap manager levels, team captains are exempt from [minimum evaluation requirements](#Minimum-evaluations) and achieve their manager levels based on [score](#score) alone.

## Level 0

Level 0 indicates a provisional role. Anyone can choose any provisional role for themselves, but to achieve a positive-numbered level, they need to receive evaluations and meet the [requirements for the level](#Level-requirements).

## Level -1

It's possible for a subject or participant to receive level -1 if their [score](#score) is negative. [Minimum evaluation requirements](#Minimum-evaluations) aren't used in level -1; only the score is considered.

[^1]: A league is an entity in Aura that aggregates levels from one or more teams to create its own set of levels that are easy for apps to consume. Leagues track the rise and fall in utility of different teams so that apps don't have to. For example, BrightID (League) levels 1-3 might correspond to what were previously called Aura Bronze, Silver, and Gold.