Rating system for online games in Heroes of Might and Magic IV. — Online Tournaments

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OptiMAL

9/8/2007 8:27 PM UTC

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Rating system for HMM4 online games!
The rating will be updated after the completion of each Tournament. The table will be populated by players who have applied for HMM4 online tournaments.
The following rating system has been adopted:
Rnew=2/3Rold+1000((N-i)/(N-1)+((N-i)/(N-1))^3)(1+SumRold/6000) and divide by 10 so it is not too large a number and (+ kGw-k1Gl), where k, k1 are coefficients that will depend on the rating.
N- number of people in the tournament
i- place in the tournament
^- exponentiation.
Rold- old rating
Gw- games won
Gl- losses:)
Rating graduations on which coefficients k, k1 will depend:
Up to 500 units k = 3 k1 = 1
From 500 to 1500 k = 1.5 k1 = 2
from 1500 to 3000 k = 0.75 k1 = 3
from 3000 and above k = 0.5 k1 = 3.5

Rating point graduations with ranks:
0-150 novice
150-500 recruit
500-1000 warrior
1000-1500 Knight
1500-2250 crusader
2250-3000 champion
3000-3500 master
3500-above hero.

№	Player	Current rating	Wins	Losses
1	LeSHiJ-MaX	215,000(recruit)	5	0
2	Lu4ik	149.203(novice)	3	1
3	Арандор	101,296(novice)	2	1
4	Пандора	100,296(novice)	2	2
5	Zybr	38,037(novice)	1	2
6	Starhan	18,129(novice)	1	2
7	Драккошка	-3(novice)	0	3

Player statistics for LeSHiJ-MaX
Games as:	Wins	Losses
Life	0	0
Death	0	0
Chaos	5	0
Nature	0	0
Order	0	0
Power	0	0

Player statistics for Lu4ik
Games as:	Wins	Losses
Life	0	0
Death	0	0
Chaos	0	0
Nature	3	1
Order	0	0
Power	0	0

Player statistics for Арандор
Games as:	Wins	Losses
Life	1	1
Death	0	0
Chaos	0	0
Nature	1	0
Order	0	0
Power	0	0

Player statistics for Пандора
Games as:	Wins	Losses
Life	0	1
Death	0	0
Chaos	0	0
Nature	0	0
Order	1	1
Power	1	0

Player statistics for Zybr
Games as:	Wins	Losses
Life	0	0
Death	0	1
Chaos	0	0
Nature	0	0
Order	1	1
Power	0	0

Player statistics for Starhan
Games as:	Wins	Losses
Life	1	2
Death	0	0
Chaos	0	0
Nature	0	0
Order	0	0
Power	0	0

Player statistics for Драккошка
Games as:	Wins	Losses
Life	0	0
Death	0	0
Chaos	0	1
Nature	0	2
Order	0	0
Power	0	0

Rating calculated after the Summer tournament.
Rating is strictly internal to the portal

Starhan

9/28/2007 8:42 AM UTC

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I'll contribute my ideas now. The top 1/3 of all participating players are selected. (I think there will always be more than 3 players, because if there are fewer, it's no longer a tournament.) 1st place - 12 points 2nd place - 8 points 3rd place - 5 points If there are enough points for the rest (i.e., if there are 18 players), then: 4th place - 3 points 5th place - 2 points 6th place - 1 point Once a month, the rating decreases by (let's say) 1/10. This can be further refined. So, if a player had 20 points, it becomes 18. And that's it. The point isn't about the map or its difficulty. Let's imagine that someone has a winning track, even among biathletes (i.e., it's easy for them, but due to illness, they missed it. Should they still get points?). Added after 3 minutes If there are only four players, then: 1st place - 1 point, and that's it. If there are 10, then (10/3 = approximately 3): 1st place - 3 points 2nd place - 2 points 3rd place - 1 point So, you start by awarding points from the bottom up. If there are 18 players, use option 1. 2. Optimal. You should be doing economic modeling. Added after 3 hours 47 minutes You can even add a dependency of the number of points on the number of players or the difficulty of the tournament. This way, it will be easier for everyone

Каждый может быть героем ...

In reply to Starhan

OptiMAL

9/28/2007 5:19 PM UTC

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To Starhan
Please write down the formula... That is, not step by step, but as a formula, just in case your version turns out to be the most universal, and your formula needs to be automated... So, share the formula :)

In reply to Starhan

IronAxe

9/28/2007 5:27 PM UTC

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Starhan;114703

I'll add my contribution now.
The top 1/3 of all participating players are selected.

This type of system, a "BIATHLON-LIKE" one, has already been discussed, but only in the context of offline tournaments. I don't know exactly how it works in biathlon – maybe the number of participants in the tournament is fixed. It has already been said that it's not a good idea to simply take a sports ranking system and apply it to Heroes 4, because it's a computer strategy game. Why did I suggest the "Planets" system? Because it's also a computer strategy game. With your system, where you propose awarding points from the bottom up, and considering that the number of participants in online tournaments is not fixed, it turns out that one tournament has 10 participants, and another has 20. The attendance at the tournament is not the responsibility of the tournament leaders (they have no control over this; it's more of a problem for the organizers).
It's possible that in the first tournament, the leader won 9 games – the maximum – and didn't lose once. And in the second tournament, the leader has eight wins (losing 12 times) – but is this actually possible? :) And yet, they still get 1st place. But according to your system, would THIS leader from the second tournament get a higher rating than the leader from the first tournament?
So, the question is, why would we have such a flaw in the rating calculation? ;)

Added 2 minutes later

OptiMAL;114895

To Starhan
Please write the formula... That is, not step by step, but as a formula, just in case your version is the most universal, and your formula needs to be automated... So, give us the formula. :)

Are you kidding? :) There is no formula there. :)

In reply to IronAxe

OptiMAL

9/28/2007 7:38 PM UTC

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Yes... Implementing the strength rating in my formula causes significant problems. I will remove it for now and reconsider. BUT:
As vbn correctly pointed out, the coefficients are 1000 and 6000.
We can experiment, for example, by taking not 1000, but 100, and not 6000, but 600. Then the numbers will be less dynamic:)
So, it turns out that after the initial rating of 100, players receive a
starting rating, which will then change. That is, the first tournament game already provides an initial capital.:)
What are your thoughts?

In reply to OptiMAL

IronAxe

9/29/2007 2:45 PM UTC

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OptiMAL;114932

Yes... Implementing the strength rating into my formula causes significant problems. I'll remove it for now and reconsider.

You should rather think about how to incorporate the number of wins and losses for each player in a given tournament into the planet system. In the planet system, there were no one-on-one battles in a match (tournament). They played as a group throughout the game and, after it ended, determined their rankings based on their victory criteria. Therefore, they didn't need to consider the number of wins and losses in the tournament in their formula. But I think that this coefficient would be useful as an additional criterion in Heroes online. That is, the primary parameter in the formula would be the ranking in the tournament, and the secondary, additional parameter would be the number of wins and losses. This is because there will be two different leaders in two different tournaments who took first place. But someone may have won MORE games in their tournament. The secondary parameter could take this into account (ALTHOUGH IT IS NOT NECESSARY). But this secondary parameter should not have an overwhelming influence compared to the primary parameter.

OptiMAL;114932

BUT:
As vbn rightly pointed out, the coefficients of 1000 and 6000.
You can experiment, for example, by taking not 1000, but 100, and not 6000, but 600, and then the numbers will be less dynamic:)
So, it turns out that after the initial rating of 100, players receive
a starting rating, which will then change. That is, the first tournament game already gives an initial capital.:)
What are your thoughts?

But these experiments are not necessary because the figure of 6000 has already been more or less tested by the planet system players. What can be done in this regard? You just need to give everyone a starting capital, either ZERO or 1000. IMHO.

In reply to IronAxe

OptiMAL

9/29/2007 4:02 PM UTC

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Iron, this simply makes the rating dynamic and with large numbers. In my opinion, this is not very convenient. When players have an extremely high rating, the strength of the tournament will also be significant, and as a result, the new rating will be enormous! IMHO. And implementing victories and defeats in the formula for planet rankings is essentially the same hassle as implementing the strength of the tournament in my formula.

In reply to OptiMAL

vbn

9/29/2007 4:17 PM UTC

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IronAxe, the coefficients are there and the coefficients are there, but changing them will not affect the calculation results in any way. For example, you can calculate all ratings using the formulas provided earlier, and then, after the calculation is complete, after you get ratings with 3 zeros, simply divide them by 1000, or 100, or 10, to make them easier to read.

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...

In reply to vbn

IronAxe

9/29/2007 5:32 PM UTC

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vbn;115128

IronAxe, coefficients are coefficients,
and their change will not affect the calculation results in any way.
For example, you can calculate all ratings using the formulas provided earlier, and then, after the calculation is complete, after the ratings with 3 zeros are obtained, simply divide them by 1000, or 100, or 10, so that it is more convenient for the eye to perceive.

Well, if this is the case in this formula, and changing 6000 to 600 doesn't significantly change anything, then let it be. So, what do we choose? Which formula? At least you, Sage, and Optimal should express your opinion, because you have studied the formulas, and Ley has disappeared somewhere.

In reply to IronAxe

OptiMAL

9/29/2007 5:41 PM UTC

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I wanted to clarify something about the coefficients for the planet creatures.
So, we'll change 6000 and 1000 to 600 and 100, or even to 60 and 10. But how should we handle the exponentiation, ^3? Should we also reduce it, or increase it, since X^3 has a maximum value of 1, and numbers less than zero, when raised to a power, result in even smaller numbers...

In reply to OptiMAL

IronAxe

9/29/2007 6:01 PM UTC

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OptiMAL;115163

I still have a question about the coefficients for the planet bonuses.
So, we change 6000 and 1000 to 600 and 100, or even to 60 and 10, but we need to figure out how to handle the exponent ^3? Should we also reduce it, or increase it, since X^3 is at most 1, and numbers less than zero raised to a power result in even smaller numbers...

In my opinion, it's better not to change anything. Because, as I said, that formula has been tested. And if you look at the rating lists, there were players with high ratings, and the tournament strength was sometimes correspondingly high, and nothing bad happened. Because don't forget about the rating decay for each player, which is 1/3. But if you are going to change something, then choose the coefficients yourself at your own risk. Or maybe just do what VBN suggested. Don't change anything in the formula, but after calculating all the ratings for the tournament, just divide the resulting rating of each player by a corresponding number, like 10 or 100?

In reply to IronAxe

OptiMAL

9/29/2007 6:08 PM UTC

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IronAxe;115166

Or maybe just do it as VBN suggested. Don't change anything in the formula, but after calculating all the ratings for the tournament, just divide each rating by the corresponding number, like by 10 or 100?

It's possible. This is correct, and we can round it to, say, hundredths.
But since this is an online Heroes tournament, we also need to include Gw and Gl. That's the question here.
And if we don't include them, then we can consider the formula ready. :)
P.S. The old rating there is not 1/3, but 2/3;). This is significant.

In reply to OptiMAL

IronAxe

9/29/2007 8:13 PM UTC

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OptiMAL;115167

Yes, it's possible. It's also correct to round to, say, hundredths. But since this is an online Heroes tournament, we also need to add Gw and Gl.
That's the question. And if we don't add them, then we can consider the formula complete.

We can add them, but I don't know how. But we can also do without it, although I think it wouldn't hurt to add it, so that this parameter doesn't overly suppress the parameter for PLACE. If you need help, ask FireBall, AmberSoler - maybe they can come up with something, or Sage or Vbn. Maybe after calculating it using the formula, we can then divide by 10, which would give us a rating of several HUNDREDS for the leaders. Then, to the resulting number, already with aging (reduced by 1/3), we can simply add (Gw-Gl)*10. This addition will be approximately equal to about a hundred for the leader in a tournament with 10-11 participants. And for the underdog, this part of the formula will also pull them into the negatives, by about a hundred, if they don't have a single victory in the tournament. I don't think there's anything offensive about this - it's fair. It just increases the gap between the leader and the underdog. But no one prevents the underdog from improving their game and trying to win and take a high place in the next tournament.
The gap can be made less significant if, instead of adding (Gw-Gl)*10 to the result, we simply add (Gw-Gl). Then, to the rating of several hundred for the leader, there will be a bonus for victories (plus 1 for each), and for the underdogs, where the rating will be around ten, there will be a "-1" for each defeat. Although the addition for the leaders is not large, it prevents us from pushing the underdogs into the hundreds of negatives. So, think for yourself - is this necessary or not?

OptiMAL;115167

P.S. The old rating is not 1/3, but 2/3;) This is significant.

I didn't say that the old rating is 1/3 :) I said that the aging of the rating occurs at 1/3, that is, the rating is reduced by 1/3. Because, as you rightly pointed out, only 2/3 of the old rating is taken.

In reply to IronAxe

OptiMAL

9/30/2007 3:05 PM UTC

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You are right in some aspects. It's possible to implement limits for the coefficient based on Gw-Gl. For example, if a player already has a substantial rating, the coefficient could be reduced, say from 10(Gw-Gl) to simply (Gw-Gl). The same applies to players with low ratings. Rating limits could be established, and the coefficient between Gw-Gl would depend on these limits.

Starhan

10/1/2007 8:06 AM UTC

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Points are awarded from the bottom; if there are few players, the winners receive fewer points.

This is evident in the example.

If there were 4 people, the first-place winner would receive one point; if there were 18 people, they would receive 12 points.

There isn't a formula, of course, but one could be devised.

I also suggested determining the points based on the tournament's difficulty, just in case.

By the way, a certain group of players has already formed for each hero, so the number of participants will almost always be the same.

Added after 34 seconds
I just wanted to contribute and give you a little break.

It helps.

Added after 44 minutes

OptiMAL;115315

Although you are right in some ways. You could simply set limits for the coefficient with Gw-Gl. For example, if a player has already achieved a solid rating, the coefficient could be reduced, say from 10(Gw-Gl) to just (Gw-Gl). The same applies to those with a low rating.
Rating limits could be established, from which the coefficient between Gw-Gl would depend.

As I understand it, we're talking about rating decay.

It should be the same for everyone, or it will become impossible to catch up with the leader

Каждый может быть героем ...

In reply to Starhan

OptiMAL

10/1/2007 8:58 AM UTC

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Starhan;115566

I think we're talking about the aging of the rating.
Should it be the same for everyone, or will it become impossible to catch up with the leader later?

Not quite. We're talking about introducing wins and losses into the formula for planet rankings and about a coefficient.
The aging is expressed by the formula 2/3Rold.