Idea: Rating System (ELO?) for VS mode

[tzetze]

The percentage of victories is not a very fair measure of the strength of a team since it forces Top teams to play a lot against weak teams to stay at the Top.

For this reason, I suggest to add a "Rating" real number statistic
besides the number of victories, defeats and win percentage as follow:

-Each registered Team starts with a Rating of 0
-The rating of the "Cookie" unregistered team is assumed to be 0,
for the rating change calculation of the one it attacks.
-Ratings can become negative. 0 is the average reference.

-When a team A with Rating r_A fights a team B with rating r_B,
depending on the result, the following rating change is made:

-If A wins:
A's rating is increased by
2^(r_B/100) / (2^(r_A/100)+2^(r_B/100) )
* 20 / ( 1 + (r_A/100-r_B/100)^2 )
B's rating is decreased by the same amount

-If B wins:
B's rating is increased by
2^(r_A/100) / (2^(r_A/100)+2^(r_B/100) )
* 20 / ( 1 + (r_A/100-r_B/100)^2 )
A's rating is decreased by the same amount


Those numbers have the following properties:

- the total r_A+r_B doesn't change

- Their ratio is 2^((r_B-r_A)/100) which means that:
If A is 100 points above B, A is assumed to be 2 times stronger,
which means that if A win 2 matches for each win of B, their rating
will not change in average.
If A is 200 points above, A is 4 times stronger.
300 points is 8 times stronger, etc
100 points below is 1/2 time stronger (2 times weaker), etc.

-Their sum is 20 / ( 1 + (r_A/100-r_B/100)^2 ) which means that
the amplitude of the rating change is more important between
similar ratings, in such a way that, for example, you cannot destroy the rating of a Top team simply by attacking it with a strong underrated team.

-20 is a parameter that can be changed if one wants to make rating more or less volatiles.
-1 is a parameter that can be changed if one wants to allow more amplitude to larger or narrower rating differences

Also, I think that the restriction of maximum 1 fight per day between the same teams should be kept.

There are a lot of formulas in Stick Ranger.
We, Stick Ranger Team optimizers, are not afraid of one more.



Tze-Tze

[zelkova]

I just skipped over the math part as I don't feel like thinking or checking for errors.

But I would love a real rating system.

[Fringe Pioneer]

It seems you have put an impressive deal of thought into this scoring formula, but I have one question.

Under the assumption that W is the pre-battle rating of the winner and L is the pre-battle rating of the loser, and

2^L/100 / (2^W/100 + 2^L/100) * 20 / (1 + ((W - L)/100)²) = δ

...how do you get that (W + δ) / (L - δ) = 2^{(W - L)/100}?

[ganondorfchampin]

Just so everyone knows you can make exponents with [sup][/sup]. The paraphrases are a little confusing. And since the formulas appear the same, only with the teams reversed, you could have just put them in terms of winner and loser and say "The winner increases by (formula) and the loser decreases by the same amount."

[tzetze]

Aug 29, 2010 23:09:53 GMT Fringe Pioneer said:

It seems you have put an impressive deal of thought into this scoring formula, but I have one question.

Under the assumption that W is the pre-battle rating of the winner and L is the pre-battle rating of the loser, and

2^L/100 / (2^W/100 + 2^L/100) * 20 / (1 + ((W - L)/100)²) = δ

...how do you get that (W + δ) / (L - δ) = 2^{(W - L)/100}?

There is no reason that your formula should be true. It compares the ratio of two ratings with the exponential of a rating difference.

What is true with my formula is that:
-If p_A is the probability that A wins and p_B=1-p_A the probability that B wins, then:

If p_A/p_B = 2^{(r_A-r_B)/100} , then the expected rating change is 0 for A and for B.

If p_A/p_B > 2^{(r_A-r_B)/100}, then the expected rating change is positive for A and negative for B.

If p_A/p_B < 2^{(r_A-r_B)/100}, then the expected rating change is negative for A and positive for B.


Thanks for your consideration. I have indeed thought quite a lot about this rating formula. I also have a master degree in maths.
So, have some faith

TzeTze

[tzetze]

Aug 29, 2010 23:41:13 GMT ganondorfchampin said:

Just so everyone knows you can make exponents with [sup][/sup]. The paraphrases are a little confusing. And since the formulas appear the same, only with the teams reversed, you could have just put them in terms of winner and loser and say "The winner increases by (formula) and the loser decreases by the same amount."

Thanks for your help about writing exponents. And yes, the formula is symmetric. Sorry if I was too long and confusing. I tried to explain it as much as I could. I know this is only my opinion, but it should work well.

[Fringe Pioneer]

Ah, so it's a ratio of the probabilities, not a ratio of the new ratings? I apparently mistook what you meant by "their ratio." Thank you.

I'm also glad that we now have a Master of Mathematics graduate in our midst.

[tzetze]

In fact it was the ratio of the two potential rating changes. But it is related to probabilities.