# Leagues and league score

## League score

League score delta in Grandmaster league

Each player starts the game with a league score of 1000 points. After each ranked match in career a certain amount of league score points is exchanged between the opponents. The amount of exchanged league score points depends on the result, the league score difference between the opponents and the K-factor used in the league of the players. The league 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 league score points:

### Examples

If a player in Gold league (K-factor 40) with a league score of 1000 points wins against an opponent with 1200 points he gets 30 points:

If the same player draws against that opponent he still gets 5 points, in case of a defeat he looses only 10 points. This example is highlighted blue in the next table.

Grandmaster
K-factor = 20
Diamond
K-factor = 30
Gold
K-factor = 40
Bronze
K-factor = 50
League 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

The player league is based on the league score points, each player starts at the Silver league. The best league currently available 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 K-factor
Bronze none 1000 50
Silver 950 1100 45
Gold 1050 1250 40
Platinum 1200 1450 35
Diamond 1400 1800 30
Master 1750 2100 25
Grandmaster 2050 none 20

### Examples

Promotion:

You are in Gold league with a 1245 league score and win a match, earning 10 league score points.
Your new league score is now 1255, you reached the Gold league promotion score, so you are promoted to the Platinum league.

Demotion:

You are in Gold league with a 1051 league score and get defeated in a match, loosing 5 league score points.
Your new league score is now 1046, you drop below the Gold league demotion score, 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