Difference between revisions of "Leagues and league score"

Latest revision as of 11:01, 4 June 2020

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

@@ Line 1: / Line 1: @@
 == League score ==
-[[Image:League score delta in Grand Master.png|thumb|League score delta in Grandmaster league]]
+[[File:League score delta in Grand Master.png|thumb|Score delta in Grandmaster league]]
-Each player starts the game with a league score of 1000 points. After each {{Tooltip|ranked match|There are no league score points exchanged after unranked, private and tournament matches.}} in career a certain amount of league score points is exchanged between the opponents. The amount of exchanged league score points depends on the {{Tooltip|result|Victory, draw or defeat.}}, the {{Tooltip|league score difference|The score of the deploying player is determined at the time he creates the match. The score of the other player is determined when he joins the match. When creating several matches at once the result of the first match doesn't affect the score used for the second one.}} between the opponents and the {{Tooltip|K-factor|The higher the K-factor is, the faster league scores evolve}} {{Tooltip|used in the league of the players|If both players are in different leagues, the average K-factor is used.}}. 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 league score of a player is the sum of her score for each game mode.'''
-The {{Tooltip|elo rating system|The elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess.}}[https://en.wikipedia.org/wiki/Elo_rating_system] is used for the calculation of exchanged league score points:
+Each player starts the game with a league score of 3000 points (1000 points for each game mode). After each {{Tooltip|ranked match|There are no score points exchanged after unranked, private and tournament matches.}} in career a certain amount of score points is exchanged between the opponents. The amount of exchanged score points depends on the {{Tooltip|result|Victory, draw or defeat.}}, the {{Tooltip|score difference|The score of the deploying player is determined at the time he creates the match. The score of the other player is determined when he joins the match. When creating several matches at once the result of the first match doesn't affect the score used for the second one.}} between the opponents and the {{Tooltip|K-factor|The higher the K-factor is, the faster scores evolve}} {{Tooltip|used in the score range of the players|If both players are in different score ranges, the average K-factor is used.}}. 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 {{Tooltip|elo rating system|The elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess.}}[https://en.wikipedia.org/wiki/Elo_rating_system] is used for the calculation of exchanged score points:
 [[File: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 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 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.
-[[File:League score delta example.png]]
+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 the same player draws against that opponent he {{Tooltip|still gets 5 points|The player is rewarded as he draws against a stronger opponent}}, in case of a defeat he {{Tooltip|looses only 10 points|The amount of league score points a player gains for a victory against a stronger opponent is higher than the amount of league score points this player looses on a defeat against the same strong opponent.}}. This example is highlighted blue in the next table.
+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.
 {|class="wikitable"
-! !!colspan="3"|Grandmaster<br>K-factor = 20!!colspan="3"|Diamond<br>K-factor = 30!!colspan="3"|Gold<br>K-factor = 40!!colspan="3"|Bronze<br>K-factor = 50
+! !!colspan="3"|K factor = 20!!colspan="3"|K factor = 30!!colspan="3"|K factor = 40!!colspan="3"|K factor = 50
 |-
-!League score difference!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat
+!Score difference!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat!!Victory!!Draw!!Defeat
 |-
 |{{R}}         | 500||{{R}}|19||{{R}}| 4||{{R}}| -1||{{R}}|28||{{R}}| 7||{{R}}| -2||{{R}}         |38||{{R}}         | 9||{{R}}         | -2||{{R}}|47||{{R}}| 11||{{R}}|-3
@@ Line 30: / Line 44: @@
 |{{R}}         | 250||{{R}}|16||{{R}}| 3||{{R}}| -4||{{R}}|24||{{R}}| 5||{{R}}| -6||{{R}}         |32||{{R}}         | 6||{{R}}         | -8||{{R}}|40||{{R}}|  8||{{R}}|-10
 |-
-|{{R}} {{Blue}}| 200||{{R}}|15||{{R}}| 3||{{R}}| -5||{{R}}|23||{{R}}| 4||{{R}}| -7||{{R}} {{Blue}}|30||{{R}} {{Blue}}| 5||{{R}} {{Blue}}|-10||{{R}}|38||{{R}}|  6||{{R}}|-12
+|{{R}} | 200||{{R}}|15||{{R}}| 3||{{R}}| -5||{{R}}|23||{{R}}| 4||{{R}}| -7||{{R}} |30||{{R}} | 5||{{R}} |-10||{{R}}|38||{{R}}|  6||{{R}}|-12
 |-
 |{{R}}         | 150||{{R}}|14||{{R}}| 2||{{R}}| -6||{{R}}|21||{{R}}| 3||{{R}}| -9||{{R}}         |28||{{R}}         | 4||{{R}}         |-12||{{R}}|35||{{R}}|  5||{{R}}|-15
@@ Line 53: / Line 67: @@
 == 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.
+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 &ge; your current league promotion score, you get promoted to the higher league.
@@ Line 59: / Line 74: @@
 {|class="wikitable"
-!League!!data-sort-type="number"|Demotion score!!data-sort-type="number"|Promotion score!!data-sort-type="number"|K-factor
+!League!!data-sort-type="number"|Demotion score!!data-sort-type="number"|Promotion score
 |-
-|Bronze     ||{{R}}|none||{{R}}|1000||{{R}}|50
+|Bronze     ||{{R}}|N/A||{{R}}|3000
 |-
-|Silver     ||{{R}}|950 ||{{R}}|1100||{{R}}|45
+|Silver     ||{{R}}|2800 ||{{R}}|3200
 |-
-|Gold       ||{{R}}|1050||{{R}}|1250||{{R}}|40
+|Gold       ||{{R}}|3100||{{R}}|3500
 |-
-|Platinum   ||{{R}}|1200||{{R}}|1450||{{R}}|35
+|Platinum   ||{{R}}|3400||{{R}}|4000
 |-
-|Diamond    ||{{R}}|1400||{{R}}|1800||{{R}}|30
+|Diamond    ||{{R}}|3900||{{R}}|4500
 |-
-|Master     ||{{R}}|1750||{{R}}|2100||{{R}}|25
+|Master     ||{{R}}|4400||{{R}}|5500
 |-
-|Grandmaster||{{R}}|2050||{{R}}|none||{{R}}|20
+|Grandmaster||{{R}}|5400||{{R}}|N/A
 |}
@@ Line 80: / Line 95: @@
 '''Promotion:'''
-You are in Gold league with a 1245 league score and win a match, earning 10 league score points.<br>
+You are in Gold league with a 3490 league score and win a match, earning 15 points.<br>
-Your new league score is now 1255, you reached the Gold league promotion score, so you are promoted to the Platinum league.
+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 1051 league score and get defeated in a match, loosing 5 league score points.<br>
+You are in Gold league with a 3105 league score and get defeated in a match, loosing 10 points.<br>
-Your new league score is now 1046, you drop below the Gold league demotion score, so you are demoted to the Silver league.
+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 ==

Difference between revisions of "Leagues and league score"

Latest revision as of 11:01, 4 June 2020

Contents

League score

Score ranges and K factor

Examples

League promotion and demotion

Examples

Interpreting score differences

Examples

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