# Leagues and league score

## Contents

## League score

**The league score of a player is the sum of her score for each game mode.**

Each player starts the game with a league score of 3000 points (1000 points for each game mode). After each ranked match in career a certain amount of score points is exchanged between the opponents. The amount of exchanged score points depends on the result, the score difference between the opponents and the K-factor used in the score range of the players. The score system is a better estimate than the victory ratio, because it rewards victories against strong opponents more than victories against weak opponents.

The elo rating system[1] is used for the calculation of exchanged score points:

### Score ranges and K factor

- For scores less or equal to 1000 points, K factor = 50
- For scores between 1001 and 1200 points, K factor = 45
- For scores between 1201 and 1400 points, K factor = 40
- For scores between 1401 and 1600 points, K factor = 35
- For scores between 1601 and 1800 points, K factor = 30
- For scores between 1801 and 2000 points, K factor = 25
- For scores greater than 2000, K factor = 20

If both players are in different score ranges, the average K-factor is used.

### Examples

If a player with a score of 1623 points (K factor = 30) wins a match against an opponent with 1447 points (K factor = 35) he wins 8 points.

If a player with a score of 1625 points (K factor = 30) wins a match against an opponent with 1493 points (K factor = 35) he loses 3 points.

If a player with a score of 1100 points (K factor = 45) wins a match against an opponent with 1101 points (K factor = 45) he loses 22 points.

K factor = 20 | K factor = 30 | K factor = 40 | K factor = 50 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Score difference | Victory | Draw | Defeat | Victory | Draw | Defeat | Victory | Draw | Defeat | Victory | Draw | Defeat |

500 | 19 | 4 | -1 | 28 | 7 | -2 | 38 | 9 | -2 | 47 | 11 | -3 |

400 | 18 | 4 | -2 | 27 | 6 | -3 | 36 | 8 | -4 | 45 | 10 | -5 |

300 | 17 | 3 | -3 | 25 | 5 | -5 | 34 | 7 | -6 | 42 | 9 | -8 |

250 | 16 | 3 | -4 | 24 | 5 | -6 | 32 | 6 | -8 | 40 | 8 | -10 |

200 | 15 | 3 | -5 | 23 | 4 | -7 | 30 | 5 | -10 | 38 | 6 | -12 |

150 | 14 | 2 | -6 | 21 | 3 | -9 | 28 | 4 | -12 | 35 | 5 | -15 |

100 | 13 | 1 | -7 | 19 | 2 | -11 | 26 | 3 | -14 | 32 | 4 | -18 |

50 | 11 | 1 | -9 | 17 | 1 | -13 | 23 | 1 | -17 | 29 | 2 | -21 |

0 | 10 | 0 | -10 | 15 | 0 | -15 | 20 | 0 | -20 | 25 | 0 | -25 |

-100 | 7 | -1 | -13 | 11 | -2 | -19 | 14 | -3 | -26 | 18 | -4 | -32 |

-200 | 5 | -3 | -15 | 7 | -4 | -23 | 10 | -5 | -30 | 12 | -6 | -38 |

-300 | 3 | -3 | -17 | 5 | -5 | -25 | 6 | -7 | -34 | 8 | -9 | -42 |

-400 | 2 | -4 | -18 | 3 | -6 | -27 | 4 | -8 | -36 | 5 | -10 | -45 |

-500 | 1 | -4 | -19 | 2 | -7 | -28 | 2 | -9 | -38 | 3 | -11 | -47 |

## League promotion and demotion

A player's league is based on her current league score points (sum of score in each game mode), each player starts in the Silver league. The top league is the Grandmaster league.

- When your league score is ≥ your current league promotion score, you get promoted to the higher league.
- When your league score is < your current league demotion score, you get demoted to the lower league.

League | Demotion score | Promotion score |
---|---|---|

Bronze | N/A | 3000 |

Silver | 2900 | 3200 |

Gold | 3100 | 3500 |

Platinum | 3400 | 4000 |

Diamond | 2900 | 5000 |

Master | 4900 | 6500 |

Grandmaster | 6400 | N/A |

### Examples

**Promotion:**

You are in Gold league with a 3490 league score and win a match, earning 15 points.

Your new league score is now 3505, you reached the Gold league promotion score (3500), so you are promoted to the Platinum league.

**Demotion:**

You are in Gold league with a 3105 league score and get defeated in a match, loosing 10 points.

Your new league score is now 3095, you drop below the Gold league demotion score (3100), so you are demoted to the Silver league.

## Interpreting score differences

If a player looses a match against an opponent that has 191 league score points less, then he needs 3 victories against the same opponent to regain the lost league score points. For any known victory-defeat-draw ratio (in the previous example it is +75% -25% =0%) one could calculate the expected score difference after many games between the two opponents with the following formula (Deduction of the formula):

**Observations:**

- The formula doesn't consider changes due to matches against other players.
- There is no dependency of the K-factor, every league behaves the same.
- If a player could choose its opponent there would be someone to maximize the expected score difference. A player with 2300 league score points would prefer playing against an opponent with a league score of 2000 and a victory-defeat-draw ratio of +90% -10% =0% (Expected score: 2382) instead of playing against an opponent with a league score of 2200 and a victory-defeat-draw ratio of +50% -40% =10% (Expected score: 2237).
- If a player plays only a few games the score difference might not reflect the current victory-defeat-draw ratio between him and other players, but either a past victory-defeat-draw ratio or a run of good luck.
- Reaching the expected score difference from a victory-defeat-draw ratio of +99% -1% =0% (Expected score difference: 798,3) or even +100% -0% =0% (Expected score difference: ∞) is limited by the K-factor. With a difference of 637 league score points in Grandmaster there is not a single league score point reward for a victory of the better player anymore.
- If 3 players share approximately the same amount of league score points over a long time one would expect a victory-defeat-draw ratio like +50% -50% =0% or +40% -40% =20% between them. However in
*Gladiabots*there is no transitive relation between the victory-defeat-draw ratio of different players due to possible rock-paper-scissors effects when using different strategies. Here is an example of 3 players sharing approximately the same amount of league score points but with very different victory-defeat-draw ratios between them.- The resource strategy of player A outperforms the defensive strategy of player B by +70% -20% =10%.
- The defensive strategy of player B outperforms the aggressive strategy of player C by +65% -15% =20%.
- The offensive strategy of player C outperforms the resource strategy of player A by +60% -10% =30%.

### Examples

Draws: 0% | Draws: 10% | Draws: 20% | Draws: 30% | Draws: 40% | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Victories | Ratio | Difference | Ratio | Difference | Ratio | Difference | Ratio | Difference | Ratio | Difference |

50% | +50% -50% =0% | 0.0 | +50% -40% =10% | 36.7 | +50% -30% =20% | 78.5 | +50% -20% =30% | 128.1 | +50% -10% =40% | 190.8 |

55% | +55% -45% =0% | 34.9 | +55% -35% =10% | 74.3 | +55% -25% =20% | 120.4 | +55% -15% =30% | 177.5 | +55% -5% =40% | 254.7 |

60% | +60% -40% =0% | 70.4 | +60% -30% =10% | 113.6 | +60% -20% =20% | 166.0 | +60% -10% =30% | 234.5 | +60% -0% =40% | 338.0 |

65% | +65% -35% =0% | 107.5 | +65% -25% =10% | 156.0 | +65% -15% =20% | 217.6 | +65% -5% =30% | 305.4 | ||

70% | +70% -30% =0% | 147.2 | +70% -20% =10% | 203.3 | +70% -10% =20% | 279.6 | +70% -0% =30% | 405.7 | ||

75% | +75% -25% =0% | 190.8 | +75% -15% =10% | 258.5 | +75% -5% =20% | 361.2 | ||||

80% | +80% -20% =0% | 240.8 | +80% -10% =10% | 327.8 | +80% -0% =20% | 492.2 | ||||

85% | +85% -15% =0% | 301.3 | +85% -5% =10% | 426.8 | ||||||

90% | +90% -10% =0% | 381.7 | +90% -0% =10% | 627.3 | ||||||

95% | +95% -5% =0% | 511.5 | ||||||||

99% | +99% -1% =0% | 798.3 |