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 Sage

IronAxe

18 years ago

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Sage;114146

I've done some testing :) In the first tournament, the winner will receive 3000, and the number 6000 was likely chosen to prevent the "tournament strength" bonus from exceeding the base points for the tournament (although this situation is still possible if the tournament only includes players with high ratings). It seems the ideal idea was to provide a bonus from 1x the base points to 1.75x the base points.

Sage, so what can you say in general about this rating calculation system for online tournaments – is it suitable? And during your testing, what did you find out – what does this symbol ^ mean? Is it exponentiation?

Added 1 minute ago

OptiMAL;114139

I'll do a final check, I can't do without it :)
Well, if everything works out, I think we can close the discussion about the rating calculation system and ask a moderator to delete all posts except the first one (so they don't get in the way):) ;)

Nothing needs to be deleted – all discussions should remain. Who knows, maybe someone will have questions and it will all start over again. Let everything stay as it is.

In reply to IronAxe

OptiMAL

18 years ago

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So, here are the results:
The basis for the calculation is:
Number of players = 10, so there are 10 places.
Also, the initial rating for all 10 players is 100.
Here's the calculation:
Using the system proposed by IronAxe:
Player 1 - 416.67
Player 2 - 334.25
Player 3 - 267.19
Player 4 - 213.58
Player 5 - 171.49
Player 6 - 139.00
Player 7 - 114.20
Player 8 - 95.15
Player 9 - 79.95
Player 10 - 66.67

In reply to OptiMAL

Sage

18 years ago

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OptiMAL;114334

(Comment on the IronaAxe system: Player 10 received a rating lower than the starting one by 43.33 units. Why?)

During the tournament, he received 0 points, but lost 33.33 points due to the 2/3 multiplier.
By the way, I calculated the values for the first 9 places not quite correctly (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but this does not change the meaning.

In reply to Sage

OptiMAL

18 years ago

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Sage;114368

He received 0 points for the tournament, but lost 33.33 points due to the 2/3 multiplier.

I understand. I was just asking why it's so unfair. :)
But it would be harsh for someone who didn't show up for the tournament at all.

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114334

I will do the following:
I will calculate the rating according to your system and according to mine. Just for comparison.
And I will use the ^ symbol to denote exponentiation; I think it fits there. I will post everything soon...
Added 3 hours 0 minutes ago
So, here are the results:
The basis is:
Number of players = 10, so there are 10 places.
A round-robin tournament with 10 people was taken, meaning everyone played against everyone else.
Also, the initial rating for all 10 is 100.
Here is the calculation:
According to the system proposed by IronAxe:
Player 1 - 3521.67
Player 2 - 2708.07
Player 3 - 2046.14
Player 4 - 1516.91
Player 5 - 1101.43
Player 6 - 780.73
Player 7 - 535.86
Player 8 - 374.87
Player 9 - 197.79
Player 10 - 66.67
According to my system
Player 1 - 200.00
Player 2 - 185.00
Player 3 - 177.33
Player 4 - 171.50
Player 5 - 166.40
Player 6 - 161.67
Player 7 - 157.14
Player 8 - 152.75
Player 9 - 148.44
Player 10 - 144.20
(Comment on my system: 1st place was taken by the player who played 10 games, 10 wins, 0 losses; 2nd place - 10 games, 9 wins, 1 loss, and so on. If a player who took last place did not win a single game, then he is not awarded a rating, but if he won at least one, then the count begins:) )
(Comment on IronAxe's system: Player 10 received a rating lower than the starting one by 43.33 units. Why?)
P.S. I attached my system just to see:)

If we comment on your comments, it turns out that in your example, player 10 DID NOT WIN A SINGLE GAME. Then I have a question for you - why, according to your system, is a rating of 44.20 points added to the starting capital of a player who did not win a single game - out of pity :)? And did you ask him - does he need pity :)? According to my system, he logically went into the negative from his starting capital. IMHO, you initially wanted it that way, in the very first discussions about the rating. I will say even more. If you calculate further according to my system, for example, he played another tournament with the same participants, but only player number 10 took first place there (won all games), and player number 1 took last place (lost all games), and you don't forget to take the players' ratings earned in the first tournament into account in the calculation for the second tournament, then you will probably be even more surprised. Well, and calculate the second tournament according to your system. Then post the tables again with the results of two tournaments. Here, there will really be something to compare. We will carefully look at how the places in the rating table will change according to the results of two tournaments for players number 1 and number 10.

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114372

If I were to comment on your comments, it turns out that in your example, player 10 DIDN'T WIN A SINGLE MATCH. So, my question is: why, in your system, was 44.20 rating points added to the starting capital of a player who didn't win a single match – out of pity? And did you ask him if he needed pity? In my system, he logically went into the negative from his starting capital. In my opinion, that's what you initially wanted, as in your earliest discussions about the rating. I'll say even more. If you calculate the example further using my system, like he participated in another tournament with the same lineup, but this time player number 10 came in first (won all matches), and player number 1 came in last (lost all matches), and you don't forget to include the players' ratings earned in the first tournament when calculating the tournament rating, you might be even more surprised. Then calculate the second tournament using your system. After that, finally, post the tables again with the results of the two tournaments. This is where there will really be something to compare. We will carefully look at how the positions in the rating table will change for players number 1 and number 10 based on the results of the two tournaments.

So, I wrote that the player at least played, and therefore he should be rewarded. And those who don't show up get nothing.
So, is it okay to simply swap all the players, or just player 10 and player 1?

In reply to Sage

IronAxe

18 years ago

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Sage;114368

During the tournament, he received 0 points but lost 33.33 points due to the 2/3 multiplier.
By the way, he didn't quite calculate the points for the top 9 places correctly (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but it doesn't change the overall meaning.

Sage, :) Well done! I completely forgot about the rating aging. Because this system automatically ages players' ratings by 1/3. The question now is different. Let's say someone got a good rating and stopped attending tournaments altogether. In my opinion, when calculating ratings from a tournament, it seems necessary to age the ratings of all players in the database, with the exception of those who are playing in another tournament organized by someone else - or for organizers to coordinate their tournaments with each other. This will be a bit challenging. But I think a similar problem would occur in any other system (I mean, if a player played in one tournament, took 1st place, and then disappeared from the tournament scene).

Added 6 minutes ago

OptiMAL;114374

So, I wrote that the player at least played, so we should reward him. And those who don't show up get nothing.

Whether they show up or not is not within the scope of the rating system - the reason for not showing up may vary, and you will quickly get tired of dealing with it. What does "reward" mean? :) (Wow, what a reward! 44.20 is approximately HALF of the increase in rating points earned by the leader (100 - for 9 wins)???) Then reward ALL those who SHOWED UP, not just the one who took last place. The one who didn't show up shouldn't have a starting capital, so it will be zero. The starting capital of 100 should be awarded to a player when they register for a RATED tournament for the first time, not as you did. You just took everyone you knew from the previous tournament and immediately gave them 100 points.

OptiMAL;114374

So, it's good. Should I swap all the players or just player 10 and 1?

For clarity, it's better to swap ONLY players 10 and 1.

Added 12 minutes ago

Sage;114368

By the way, he didn't quite calculate the points for the top 9 places correctly (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but it doesn't change the overall meaning.

You better explain why he made that mistake. How do you calculate it yourself? What do you take that ^ symbol in the formula for when you calculate it yourself?

Sage

18 years ago

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I think ^ means raising to the power of 3. Although, for the first place, whether it's 1 cubed or the cubic root of 1, you'll still get 1 ;)

In reply to Sage

OptiMAL

18 years ago

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Sage;114368

By the way, I didn't calculate it quite correctly for the first 9 places (for example, for 1st place: 2/3*100+3000*(1+100/6000)=3116.66), but it doesn't change the meaning.

Doubtful... I calculated it using a program :) And I specifically checked to make sure the result was 3000 for Rold=0 and 1st place :)

In reply to OptiMAL

Sage

18 years ago

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OptiMAL;114457

Doubtful... I calculated it using a program :) And I specifically checked to make sure the result was 3000 for Rold=0 and position 1 :)

I calculated it for Rold=100, also using a program :)

In reply to Sage

OptiMAL

18 years ago

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Sage;114463

I also calculated for Rold=100 using a program.

Okay, then let's exchange programs.
And if we're talking about the results:
Player 1 - 1263.52
Player 2 - 1158.84
Player 3 - 876.57
Player 4 - 654.10
Player 5 - 479.44
Player 6 - 334.62
Player 7 - 241.69
Player 8 - 162.65
Player 9 - 99.57
Player 1 - 277.78

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114473

Regarding the IronAxe system, it turns out to be quite dynamic there.

:) It's not entirely correct to call it my system. There's nothing of mine in it. This system was created by the Planet players. I just suggested adapting it for Heroes in online tournaments.

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114616

:) It's not entirely correct to call it my system. There's nothing of mine in it. This system was created by the Planet players. I just suggested adapting it for Heroes in online tournaments.

I understand) I just call it your system because you suggested it... you know what I mean;)
So, what's your opinion about these two systems?

In reply to OptiMAL

IronAxe

18 years ago

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OptiMAL;114617

Of course) I just call it your system because you suggested it... you know what I mean;)
So, what's your opinion about these two systems?

Currently, the planet system has one advantage: it takes into account the strength of the tournament. Your system doesn't have this. It's one thing for a player with 100 rating points to beat all other players in a tournament who have ratings of at least 3000. It's another thing if a player with 10000 rating beats all participants in the tournament, but none of them had a rating of more than 100. This parameter is very important for online tournaments. That is, in the first case, the sum of the ratings for the entire tournament = 3000*9+100=27100. 27100/10=2710 (this is the tournament strength). And in the second case = 10000+9*100=10900. 10900/10=1090 (the tournament strength is less). How will this be taken into account in your formula?

In reply to IronAxe

OptiMAL

18 years ago

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IronAxe;114627

How will this be taken into account in your formula?

Good question... Considering that the strength of a tournament equals the sum of the ratings of all players participating in the tournament, this formula needs to be implemented correctly, but it will result in a large number, which is probably why they use a coefficient of 6000.
My formula needs to incorporate this in a way that avoids dynamic changes.
Hmm... I'll think about it and post another formula tomorrow, and recalculate the ratings again :) At least it gives me something to do when I have nothing else to do.