# Leagues and league score

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## League score

Score delta in Grandmaster league

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 2800 3200
Gold 3100 3500
Platinum 3400 4000
Diamond 3900 4500
Master 4400 5500
Grandmaster 5400 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