Auto-translated
Check out my rating system:
AmberSoler
Posts from Player rating for tournaments across all installments of Heroes.
Auto-translated
Open
Which rating system should I choose? (see the text for details)
33
voters
Single choice
Sign in to participate in this poll.
Poll results will be visible after you vote or when the poll closes.
AmberSoler
Fireball
Auto-translated
All of this already exists, but few are satisfied with it.
1. The difference in linear ratings between 1st and 2nd place is equal to the difference between 11th and 12th. This not only diminishes the role of the top positions but, with a large number of participants, very quickly fragments this difference between them. And if we are being completely honest, for strong players it makes no difference whether there are 30 or 40 participants. They will be competing among themselves within the top ten at most.
2. The bonus, although dependent on the correct parameters, is truly negligible. It in no way reflects the difference between a warm-up gathering and a WW, nor does it offer any particular clarity.
AmberSoler
Auto-translated
1. The difference in linear ratings for 1st and 2nd place is equal to the difference for 11th and 12th. This not only diminishes the importance of the top places but also, with a large number of participants, very quickly reduces the difference between them.
2. The bonus, although it depends on the correct parameters, is truly negligible. It does not reflect the difference between a warm-up gathering and a BB, and it is not very clear either.
What can be proposed? By default, provide each player with a conditional strength parameter equal to five on a ten-point scale (or 50 on a hundred-point scale - it doesn't matter). Then, from game to game, this parameter will be adjusted up or down. Any newcomer receives exactly the average parameter, not zero. Because the average value of the strength distribution of any set of players will tend towards the median as the sample size increases. Previously, we started from zero; perhaps this is where the mistake lies... It is impossible to underestimate the true strength of unknown players, thereby unreasonably lowering the rating of the tournament... And in each tournament, there are enough players whose rating has not yet been determined...
Next, we calculate the level of relative strength of the opponents in the tournament and take it into account as a parametric coefficient when calculating the bonus. And no numbers should be taken out of thin air! Someone here said that in mathematics and physics, many coefficients are taken from the air, and that's okay... :)
I am not yet familiar with such mathematics...
Kamikaze
Auto-translated
What function do you suggest for building the curve if a linear one doesn't suit you? The function should, in any case, take into account the number of players, even if it is non-linear.
Perhaps we could use the result, rather than the number of participants, as a coefficient.
Sometimes it turns out like this: 1. A - 10 days
2. B - 11 days
3. C - 11 days
4. D - 69 days
5. E - 80 days
The difference in rating between second and third place is equal to the difference between third and fourth :eek:
AmberSoler
Auto-translated
I agree with Fireball, a linear rating is definitely not objective.
However, this component can be somehow distorted to avoid a linear dependence. Hence the question: what function is proposed as a criterion for distortion?
Kamikaze
Auto-translated
For example, there is a biathlon rating.
There, it is calculated for a huge number of participants, but we are not just doing this for nothing. Let's recalculate it correctly. We need to think about it.
Added 10 minutes later
Another function, although I can't write it as a formula.
X - the number in the table, in order, according to the results, of course.
Y - will be the rating.
Y(x) = Y(x-1) - Y(x-1) * 10% - I think something like this.
A non-linear function, and it also takes into account the number of participants.
There, it is calculated for a huge number of participants, but we are not just doing this for nothing. Let's recalculate it correctly. We need to think about it.
Added 10 minutes later
Another function, although I can't write it as a formula.
X - the number in the table, in order, according to the results, of course.
Y - will be the rating.
Y(x) = Y(x-1) - Y(x-1) * 10% - I think something like this.
A non-linear function, and it also takes into account the number of participants.
AmberSoler
Auto-translated
Y(x)=Y(x-1)-Y(x-1)*10%
2. Your formula Y(x)=Y(x-1)-Y(x-1)*10% is equivalent to this - Y(x)=0.9*Y(x-1), i.e., you proposed a geometric progression (instead of an arithmetic one). This is what we are talking about... The only question is, how is the progression coefficient of 0.9 determined? I suggest k=0.85, and someone might say that this is too much and it is better to take k=0.44... We get an infinite number of absolutely equal calculation options...
The goal is to justify the progression coefficient, to link it to other constants (number of players, tournament level, etc.). If we analyze the behavior of the function (on a graph), we can conclude: the more complex the tournament, the more participants, the higher the average rating of all players in the tournament - the smaller the coefficient should be in order to ultimately increase the bonus for the leaders. The question is - by how much?
Kamikaze
Auto-translated
Yes, you are right, 0.9 is a constant, but we need to use a variable value. I need to think about it.
Added 2 minutes later
But, in any case, it is easier, or rather more rational, to justify the coefficient than to use a line.
Added 2 minutes later
But, in any case, it is easier, or rather more rational, to justify the coefficient than to use a line.
Fireball
Auto-translated
What function do you suggest for constructing the curve if a linear one doesn't suit you? The function should, in any case, take into account the number of players, even if it is non-linear.
It will depend on the number of participants.
Then, according to what criteria will you differentiate between a warm-up tournament and a BB (Best of Best)? In my opinion, the only criterion is the composition of the opponents. That's it. What difference does it make to run 100 meters or 400 meters if Ben Johnson is running next to you? And again, we return to our topic - without knowing the strength of the opponent, it is impossible to calculate the relative significance of your victory, and therefore, to correctly take this result into account in your rating.
AmberSoler
Auto-translated
But, still, it's more rational to justify the coefficient... than to use a linear function.
That's why I suggest not overcomplicating things. There's no need for it. We're wasting a lot of time, when we could already be creating tournament brackets, attracting players, and creating motivation for clan battles based on the rating calculation methods that already exist. In my opinion, they are quite acceptable... And mathematics is just a pastime for a few players, while the rest don't really need it...
Maybe we should leave these developments aside? :)
Take the simplest calculation scheme from the ones already proposed and forget about the rest?
And I think I know how to take into account the strength and number of opponents. And the difference between a warm-up match and a main battle will be quite noticeable. And, if necessary, I can present my system to the public for review.
Kamikaze
Auto-translated
I calculated some coefficients here, and if someone can link them to a formula (I think it's possible), it would be great.
Participants - Coefficient
10 - 0.631
15 - 0.736
20 - 0.795
25 - 0.832
30 - 0.858
It's a bit difficult for me to derive such a formula based on five data points.
AmberSoler
Auto-translated
I calculated some coefficients here, and if someone can link them to a formula (I think it's possible), it would be great.
vbn
Auto-translated
Will the formula K = 1 - 3.5 / N work?
There must be more than 3 participants.
The result will be:
N=05, K=0.300;
N=10, K=0.650;
N=15, K=0.767;
N=20, K=0.825;
N=25, K=0.860;
N=30, K=0.883.
There must be more than 3 participants.
The result will be:
N=05, K=0.300;
N=10, K=0.650;
N=15, K=0.767;
N=20, K=0.825;
N=25, K=0.860;
N=30, K=0.883.
Клан Homo homini
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things. Charity never faileth...
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things. Charity never faileth...
AmberSoler
Auto-translated
Would the formula K = 1 - 3.5 / N work?
vbn
Auto-translated
But what do you need? You asked for a formula, right?
Клан Homo homini
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things. Charity never faileth...
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things. Charity never faileth...