Difference between revisions of "Leagues and league score"

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(Interpreting score differences)
m (we don't need the formula if we settled on images. In the case we can recover it from the history. It is a wiki!)
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[[File:League score delta.png]]
 
[[File:League score delta.png]]
<!-- The formula below is commented out because of loading time. It was replaced by the image above.
 
 
<math>
 
Score\ delta_{player} =
 
round
 
\left (
 
  K \cdot
 
  \left (
 
    \begin{Bmatrix}
 
      {victory:1} \\
 
      {draw:0.5} \\
 
      {defeat:0}
 
    \end{Bmatrix}
 
    -
 
    \frac{1}
 
    {1 +
 
      10^{
 
        \left (
 
            {Score_{opponent}} - {Score_{player}}
 
        \right )
 
        / 400
 
      }
 
    }
 
  \right )
 
  \cdot
 
  \begin{Bmatrix}
 
    {draw:0.5} \\
 
    {else:1}
 
  \end{Bmatrix}
 
\right )
 
</math>
 
 
-->
 
  
 
=== Examples ===
 
=== Examples ===
Line 45: Line 12:
  
 
[[File:League score delta example.png]]
 
[[File:League score delta example.png]]
<!-- The formula below is commented out because of loading time. It was replaced by the image above.
 
 
<math>
 
Score\ delta_{player} =
 
round
 
\left (
 
  40 \cdot
 
  \left (
 
    1
 
    -
 
    \frac{1}
 
    {1 +
 
      10^{
 
        \left (
 
            {1200} - {1000}
 
        \right )
 
        / 400
 
      }
 
    }
 
  \right )
 
  \cdot
 
  1
 
\right )
 
=
 
round
 
\left (
 
  40 \cdot
 
  \left (
 
    1
 
    -
 
    \frac{1}
 
    {1 +
 
      10^{
 
        0.5
 
      }
 
    }
 
  \right )
 
\right )
 
=
 
30
 
</math>
 
 
-->
 
  
 
If the same player draws against that opponent he still gets 5 points, in case of a defeat he looses 10 points. This example is highlighted blue in the next table.
 
If the same player draws against that opponent he still gets 5 points, in case of a defeat he looses 10 points. This example is highlighted blue in the next table.

Revision as of 22:03, 24 September 2017

League score

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 deploying player.

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

League score delta.png

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:

League score delta example.png

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

Grand Master
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.

  • 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 1400 35
Diamond 1350 1600 30
Master 1550 1800 25
Grand Master 1750 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 120 league score points less, then he needs 2 wins against the same opponent to regain the lost league score points. For any known victory ratio (in the example above it is 2:1) one could calculate the expected score difference after many games between this two opponents with the following formula:

[math] Expected\ score\ difference = 400 \cdot log_{10} \left ( \frac{Victory\ count_{player}} {Victory\ count_{opponent}} \right ) [/math]

Observations:

  • The formula doesn't consider draws or score 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 ratio of 90% instead of playing against an opponent with a league score of 2200 and a victory ratio of 55%.
  • If a player plays few games the score difference might not reflect a current victory ratio between him and other players, but either a past victory ratio or a run of good luck.

Examples

Victory ratio Victory percentage Expected score difference
1:1 50.00% 0.0
5:4 55.56% 38.8
6:4 60.00% 70.4
7:4 63.64% 97.2
2:1 66.67% 120.4
3:1 75.00% 190.8
4:1 80.00% 240.8
5:1 83.33% 279.6
10:1 90.91% 400.0
100:1 99.01% 800.0
1000:1 99.90% 1200.0
10000:1 99.99% 1600.0