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:

League score delta.png

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):

Expected score difference.png

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