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

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Announcement

OptiMAL

18 years ago

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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

In reply to OptiMAL

OptiMAL

18 years ago

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Also, the letter N there indicates the number of players who finished the **game**. How is that? Or does it refer to the number of players who participated in the tournament?

In reply to vbn

IronAxe

18 years ago

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vbn;113628

Actually, the caret symbol (^) is generally used to denote the exponent to which a number is raised, i.e., X^3 = X * X * X.

VBN! Just take a look at the formula; someone should be able to figure it out. You might be right; we should ask a mathematician.

Added 1 minute ago

Ley;113635

Yes, I received all the emails, just in several stages... :) I'll start looking into what Iron is proposing on Monday...

I didn't come up with this. I borrowed it from the Planetfall community. It worked for them about 10 years ago, and it probably still works now.

Added 3 minutes ago

OptiMAL;113636

Also, the letter N there means the number of players who finished the game. How is that? Or does it mean the number of players who participated in the tournament?

In my opinion, it means the number of players who participated. There can be from 2 to 11 players in a game. A losing player is also considered to have finished the game, even if they quit. The other players continue to play, and sometimes they have to break through his planet's defenses, even though the player has already lost.

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;113653

VBN! Just take a look at the formula, maybe someone can help :) There should be some logic there, so it should be clear what's being done.

Yesterday, I was trying to understand the formula, and here's what I came up with: In principle, the exponent is correct. And I have a question. Pparty = (1/N) E Post_game So, does that mean I should just write 1/N in the formula? Rnew = 2/3 * Rold + Rgame * (1 + Rparty/6000) So, would it look like this: Rnew = 2/3 * Rold + (1000*(N-i)/(N-1) + 2*((N-i)/(N-1))^3) * (1 + (1/N)/6000)? P.S. I'm just clarifying.

In reply to OptiMAL

vbn

18 years ago

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OptiMAL;113662

I'm just clarifying.

Take a look at the example of rating calculation according to the formulas provided. In the first formula, X(i) was taken out of the parentheses, so instead of X^3=X*X*X it became X^2=X*X.

In reply to vbn

OptiMAL

18 years ago

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Okay, I understand... but there seems to be a nuance, and it lies in this:
It seems to me that VGAplanet is an online game in which more than two people participate, and therefore, in one match, places are taken, and these places are taken into account in the ranking.
A Heroes 4 tournament (as with all tournaments) involves a 1-on-1 game, and there are several such games (round-robin system). Accordingly, only two people participate in a match (i.e., one game). There will be many matches, but only one place.
Therefore, this formula needs to be adapted for Heroes.

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;113933

Okay... but it seems there's a nuance, and it lies in this:
It seems to me that VGAplanet is an online game in which more than 2 people participate, and accordingly, places are taken in a match, and these places are taken into account in the ranking.

That's essentially how it is. So what? The main thing is that at the end of this match (tournament), we get a distribution of the participants' places, and then, based on the places and the number of participants in the match (tournament), we calculate the rating.

OptiMAL;113933

A Heroes 4 tournament (as well as any other) involves a 1-on-1 game, and there are several such games (round-robin system). Accordingly, only 2 people participate in a match (i.e., 1 game). There will be many matches, but there is only one place.

So what? You run the tournament to the end, where you calculate points for all participants depending on whether they won/lost/did not show up. At the end of the tournament, you calculate the final results for everyone and distribute the places. And how is this different from the final in VGAPlanets? You have the same initial data - this is the distribution of participants' places and the number of participants in your tournament. You take the calculation system and assign a rating to your players for this tournament.

OptiMAL;113933

So, this formula needs to be adapted for Heroes in some way.

And why do you need to adapt anything now? You just need to understand where they get the number 6000 from in the formula. And maybe it will also be suitable for Heroes in online tournaments?

In reply to IronAxe

vbn

18 years ago

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As far as I understand, after looking at the formulas provided, the coefficients of 1000 and 6000 can be changed to your liking. The main thing is that they should be greater than 1 and the proportion between them should be maintained, for example, 10 and 60.

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114106

That's essentially correct. So what? The main thing is that at the end of this match (tournament), we get a distribution of the participants' places, and then, based on the places and the number of participants in the match (tournament), we calculate the rating.

That's exactly what I was talking about.

IronAxe;114106

So what? You run the tournament to the end, where you calculate points for all participants based on whether they won/lost/didn't show up. At the end of the tournament, you calculate the final results for everyone and distribute the places. And how is this different from the final in VGAPlanets? You have the same initial data - this is the distribution of participants' places and the number of participants in your tournament. You take the calculation system and assign a rating to your players for this tournament.

So why do you need to adjust anything now?

It seems you didn't understand me. I was asking about Rparty because it is Rparty that calculates the rating for a match, which in VGAplanet is one, but in Heroes, there are many. Should I calculate all the matches for each player? I'll go crazy.
And in the final formula, it is Rparty that is divided by 6000.
Therefore, it is Rparty that needs to be replaced/changed with something

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114118

It seems you didn't understand me. I was asking about Ppartii because it's Ppartii that calculates the rating for a match, which is one in VGAplanet, but many in Heroes. Should I calculate all matches for each player? I'll go crazy :)

:) Don't go crazy, but approach this creatively. For them, this Ppartii is considered one match that can last from 3 to 6 months. Just call this match a "tournament," and everything will fall into place. In reality, it's an accounting of the "strength of the match (tournament)." It takes the ratings of all players participating in the tournament, adds them up, and divides by the number of participants in the tournament. But why does the formula say that the ratings of players are taken AFTER the tournament ends? It means that a person playing one match in VGAPlanets may be playing a dozen more on other hosts at the same time. And those matches may end earlier than this one for which the rating is currently being calculated. So, this player has already been given a rating for those completed matches. Therefore, when calculating the rating for this match, his new rating will be used to calculate the strength of THIS match.
In other words, you will have this: Ppartii will be called Pturnira and will be calculated as the sum of the ratings of all players in the tournament, which they HAD at its end, and then this number is divided by the number of participants. This is if you want to have a single rating for all online players. Let's say you and Adelaide agree to calculate the players' ratings according to this common system, and you will have two tournaments running in parallel, but her tournament will end earlier. So, when calculating your Pturnira, you will take the ratings that the players have at the moment after Adelaide's tournament.

OptiMAL;114118

And in the final formula, it is Ppartii that is divided by 6000.
Therefore, it is Ppartii that needs to be replaced/changed with something.

Optimal, don't complicate things :) Instead, try to simplify and focus for now on Ppartii in VGAPlanets and Pturnira in Heroes. THESE ARE THE SAME THING !!

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114124

In other words, it will be like this: The "Parties" will be called "Tournaments" and will be calculated as the sum of the ratings of all players in the tournament, which they HAD AT ITS END, and then this number is divided by the number of participants. THIS IS THE SAME THING!!

So, let's summarize:
Parties aka Tournaments = Rold1/n
Where Rold1 = the sum of all Rold of the players in the tournament
n = the number of participants
I think we can agree on this?:)

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114125

So, let's summarize:
Tournament Rating = Rold1/n
Where Rold1 = the sum of all Rold ratings of the players in the tournament
n = the number of participants
I think we can agree on this, right?

Where Rold1 = the sum of all Rold ratings of the players in the tournament, which they had at the end of the current tournament.
In other words, the calculation for the first tournament will be done in such a way that the old rating of each player = 0. Tournament Rating = 0.
And here's what needs to be checked now. I remember that in this case, the player who takes first place will have a rating of around 3000. Why is it necessary to check this? It's because we need to understand what that tricky sign means – raising to a power or taking a cube root – and how the number 6000 will behave in this case. We need to take an abstract tournament, say with fifteen players. Assign them places and, assuming that the old rating of each is ZERO, calculate each player's rating for the tournament. What will the result be? OptiMAL, you can practice ;)

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114128

Where Rold1 = the sum of all Rold points of the players in the tournament, which they had at the end of the current tournament.
In other words, the calculation for the first tournament will be done in such a way that the old rating of each player = 0. Tournament = 0.

So, are you saying that the initial rating for everyone will be 0?
I've already entered an initial rating of 100 into the table. I think we should proceed based on that:)
And since the Summer Tournament is the first tournament for which we calculate the rating, everyone's Rold = 100 :)

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114132

So, you mean that the initial rating for everyone is 0? I've already entered an initial rating of 100 into the table. I think we should proceed based on that:)

Well, it's your right as the organizer of the online rating. Moreover, personally, I don't see any difference in what the Initial Rating will be, given to each player as an initial starting capital, because it is given to everyone equally.

OptiMAL;114132

And since the Summer Tournament is the first tournament based on which we calculate the rating, everyone has Rold=100 :)

However, this doesn't prevent you from calculating the ratings for players in a virtual tournament, as I suggested, and hypothetically setting Rold to 0 for everyone there. This is to test the formula and practice. With these values, I know that a player should be awarded a rating of around 3000 for first place. If you get that number, it means we are on the right track :) Well, and for the real tournament, you can already start calculating with any Rold using the TESTED FORMULAS :)

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114137

However, nothing prevents you from calculating player ratings for a virtual tournament as I suggested and tentatively setting Rold for each player to 0. This is to test the formula and practice. With these values, I know that a player should be awarded approximately 3000 rating points for first place. If you get that number, it means we are on the right track :) Well, you can start calculating the real tournament with any Rold using the VERIFIED FORMULAS :)

I will do the final check, I wouldn't skip it :)
Well, if everything works out, I think we can close the issue regarding the rating system and ask the moderator to delete all posts except the first one (so they don't get in the way) :) ;)

In reply to IronAxe

Sage

18 years ago

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IronAxe;114128

I remember that in such a case, the player who takes first place would have a Rating of around 3000. What is this needed for? It's to check what that tricky sign – raising to a power or taking the cube root – actually means, and how the number 6000 will behave. We need to take an abstract tournament, say with fifteen players. Assign them places and, assuming that the Old Rating of each is ZERO, calculate each player's rating for the tournament. What will the result be? Optimal, you can practice ;)

I practiced :) . In the first tournament, the winner will receive 3000; the number 6000 was probably chosen to prevent the bonus for the "strength of the tournament" from exceeding the basic points for the tournament (although such a situation is still possible if the tournament only includes players with high ratings). It seems that ideally, the bonus should range from 1xBasePoints to 1.75xBasePoints.