ELO Scoring in ENSL

The Idea

I'm sure many wonder how the pointing system works. Basically the idea is to make sure that teams' skill-difference affects the score. That means, you get more points from a draw against a better team than from a draw against a team of your own skill level.

You can use easily find how much any team would get with any score against its opponents in a ladder, by clicking "Scores" under any ladder contest.

Normal a player doesn't have to worry about the math behind it but here's the manual for those of you who are curious.

ELO Scoring is a scoring system that is used in soccer, chess, badminton etc. It is also used in the Clanbase ladders.

 

The Formula

 

The formula to calculate the awarded (or lost) points is following:

P = Points Change
K = Base modulus (affects general scoring level, usually 30)
G = Modulus for different scores (usually even=1.0, 3-1=1.25, 4-0=1.5)
R = The result of the match (0 = loss, 0.5 = draw, 1 = win)
D = Points difference before the match
W = "Weight"
e = The expected result = 1/(1^(D/W)+1)

 

The formula works by subtracting the expected score (e) from the actual result. The expected score will close to 1 (win), more there is chance to win the round. This is basic statistical mathematics.

 

Example

 

Let's suppose Tem A wins Team B by 3-1, the base modulus is 30, and 3-1 score will have modulus 1.25, and the Team B had 40 more points than team A. The result will be:

In this case, the likelihood of a win for Team A is 17%. This means that result will be:

Thus Team A gets 31 points while Team B loses 31 points.

jiriki on 18 September 09 15:04

Comments

1643

Blank Miglecz++

how ensl uses this system now is WRONG!

  • teams initial scores should be positive, not zero
  • score gaining can me manipulated by choosing opponents, it should be random and fixed (sequence determines result)

letters not matching in article and pictures, the example is incomplete (what are those 60, and 1- numbers)

and P is rounded to integer

huge article here

22 September 2009, 03:39

176

Blank jiriki | old people

Nope.

The initial scores don't really matter - just read the formula. The only thing affecting the scoring is the relative score difference, not the absolute score. Also in our system, teams cannot go negative, because that would just ecourage people either fold their teams or go inactive (if they are blocked from re-entering the ladder). However we're still considering allowing negative points though.

P is rounded to an integer, or how many decimals have you seen in the ladder recently?

Score gaining can always be manipulated with a ladder system (prisoner's dilemma and hawk-dome game's for example), but if its random and fixed, we might aswell have a league. Score deflation is always an issue with ladder. However In our ladder, upper teams have to play against lower teams, and every game awards 3 points. Its not a perfect solution, I know the drawbacks, but its a fine compromise.

We've had too little games to worry about manipulated games. One solution would be to allow playing only against 3 ranks up or down, but imo. we've too scene for that.

And what "1" are you talking about?

60 is the weight (w) which has the same affect on the scoring curve as changing K. I could change K but that would drastically change scoring for even games, and break up the scoring level for the existing ladder.

Interesting article though.

However the asusmption of fixed performance is an issue with the simple ELO form, and the fact that ELO is aimed for player-based ladders, not team-based ladders. We could possibly make use of game statistics and and Gaussian distribution of performance.

I'm actually going to ask a few finnish mathematicians that I know, who know more about the subject.

22 September 2009, 04:35

1643

Blank Miglecz++

why R is 1?

22 September 2009, 05:03

176

Blank jiriki | old people

Its an example and 1 means a victory, 0.5 draw and 0 means a loss. And oh, sorry about it, I had it marked W (which was already used for weight) in the addendum.

Also, I updated my previous post. I just realized that how useful server statistics could be to calculate the expected result, but this math goes over my skills.

If there's anyone with great (university-class) understanding of probability mathematics and NS dynamics, feel free to contact me!

22 September 2009, 05:25

1643

Blank Miglecz++

i think that picture should be like this, to match your description:
  (  
1
 
 
)
P = K * G * R -
   
10
D/W
 
+ 1

 

:)

22 September 2009, 06:19

1643

Blank Miglecz++

lol html insertion not working

22 September 2009, 06:20

1643

Blank Miglecz++

P = K * G * { R - [ 1 / ( 10 ^ (D/W) + 1) ] }

22 September 2009, 06:22

176

Blank jiriki | old people

I hate curly brackets. :)

But check this out. New ENSL Scoring system!

22 September 2009, 06:25

1643

Blank Miglecz++

 just implement it :), u have a lotof time it seems J, no school or workplace?

22 September 2009, 06:35

176

Blank jiriki | old people

Yeah I'm in uni, but courses are just starting, and half the lectures are useless, great time for web browsing.

22 September 2009, 07:12

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