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Posts from Player rating for tournaments across all installments of Heroes.
Which rating system should I choose? (see the text for details)
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Fireball
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well, we could keep the 100-point system... the numbers in the third column won't change because of that...
Thus, in total, the winner will receive exactly 50+50=100 rating
I don't quite like that the figures in this non-linear part (depending on place) were just pulled out of thin air...
That is true. But here there are 2 ways: 1. Take an already existing system (like VDV Forever or some sporting one, for example, motorcycle racing, multiply by 2 and end with a one, 50-40-32-26-22-20-18-16-14-12-10-8-6-4-2-1-1-1... by the way, Alan had already mentioned it before, etc.). 2. Write a formula based on place, and perhaps even the number of participants, like in an oscillator, only to make it more logical. I don't know which of these ways is more suitable.
2. Given a specific number of participants (as a parameter), the linear rating decreases linearly, meaning the difference between 1st and 2nd place is the same as between 11th and 12th, which is not ideal. In VDV Forever, the difference between 1st and 2nd place will be greater than between 11th and 12th.
The idea is sound, but propose a principle based on which this "non-linearity" will be implemented. The only condition is that each number must be logically justified... We won't be taking coefficients "out of thin air."
Suggest a principle based on which this "non-linearity" will be implemented.
For now, there is only one principle: the difference between the places should increase as you get closer to the winners.
The only condition is that each number must be logically justified... We will not take coefficients "out of thin air."
However, this condition is definitely impossible to fulfill. You will inevitably have to resort to making things up, because everything comes down to how quickly the rating curve should decrease with the place. Once this is known, you can simply write some power from 0 to 1 in the formula for the oscillator instead of the expression n-1/N-1 and obtain any curvature of the curve. And this is far from the only way. Therefore, to avoid endless debates that will not have objective arguments, I suggest taking an existing distribution system as an example, using the VDV Forever system as an example.
If you have any other fundamental and specific requirements for the dependence of the rating on the place (i.e., they can be represented as specific properties of a function), please state them. This will narrow the search.
In total, the winner will receive exactly 50+50=100 rating points.
Well, if we leave it as it was: (100+100)/2, the final number won't change..., but a 100-point system is somehow more familiar... But this isn't a critical issue, and it doesn't really matter how it ends up... ;)
Fireball;100465
That's true. But there are 2 ways: 1. Use an existing system (like VDV Forever or some other sport, for example, motorcycle racing, multiply by 2 and end with 1, 50-40-32-26-22-20-18-16-14-12-10-8-6-4-2-1-1-1..., by the way, Alan and others have already mentioned it).
Oh, these "ceiling" numbers... I, by the way, don't like such a large gap between 1st and 2nd place... Fireball;100465
2. Write a formula based on the place, or maybe even the number of participants, like in an oscillator, but so that it's more gradual.
Well... about the logic, you're exaggerating... :D Because the existing linear formula is much easier to understand than:Fireball
writing some power from 0 to 1 and getting any curvature of the curve.
Believe me, only a few of those present on the portal will understand this... :D
With the introduction of this formula, we need to think... but not about the formula, but about the philosophy of our system, i.e., we need to clearly define and understand what we want from the rating! Who should it encourage, and who should it punish. And after that, it will not be difficult to write a formula that satisfies our criteria... ;)
Sincerely.
Кто состоянием своим доволен, тому жить весело. (с)Алекса́ндр Васи́льевич Суво́ров
Fireball
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Ah, these "ceiling" numbers... By the way, I don't like such a large gap between 1st and 2nd place...
This is a motorcycle racing system; the probability of crashing when riding at the limit is quite high. Therefore, the reward for winning should be commensurate. VDV Forever has a difference that is twice as small. Choose, I don't care.
Well... you're exaggerating about the logic... because the existing linear formula is much easier to understand than:
Logic and comprehensibility are not the same thing. A logical function satisfies certain properties that we need. And a comprehensible one... I think it's clear what I mean. It all depends on the mathematical background of those around us. And I mentioned the degree just as an example.
With the introduction of this formula, we need to think... but not about the formula itself, but about the philosophy of our system, i.e., we need to clearly define and understand what we want from the ranking! Who should it encourage, and who should it punish? After that, it will be easy to write a formula that satisfies our criteria...
I completely agree; the main question is precisely about the philosophy of the system, but this question is highly subjective.
Ah, these "top-tier" numbers... By the way, I don't like such a big gap between 1st and 2nd place...
The gap is indeed quite large, as Fireball suggested, but that's how it should be, essentially... After all, it's the first place, and everyone should strive for it. Let's take the blitz situation as an example - the difference between 1st and 2nd place is minimal, but Radik still won... and he received almost the same as the 2nd place... it's not very fair... but here, I think the problem lies elsewhere... the level of the opponents is very different... and only a small number of participants will be able to compete for this first place:(...
If you have any other fundamental and specific requirements regarding the dependence of the rating on the position (i.e., they can be represented as specific properties of the function), please state them. This will narrow down the search.
"We're just reinventing the wheel" here... I deliberately introduced a non-linear component into the oscillator so that it would take into account not only the result but also the player's position – the more players you outperform, the greater the bonus you receive. Then, averaging the linear and non-linear components only smoothed the function, but did not change its essence... And now you are suggesting introducing another differential coefficient. It is much simpler to add a "weight" to the oscillator formula, shifting the arithmetic mean towards the non-linear function, and we will get a greater curvature, which is what you advocate for...
We can experiment with balancing endlessly, but there will be no point in it because there is too little material for analysis, and it will not be possible to see the effectiveness of the formulas for reflecting the real strength of the players. There are no objective criteria that we can use as a benchmark...
I suggest leaving everything as it is. And if we are going to optimize, then let's do it within the framework of the proposed and used calculation methods. As an option, we can put in some effort and choose one single method from all the methods currently in use. But we should not create a new one. Just another one out of many...
We're just reinventing the wheel here... I deliberately introduced a non-linear component into the oscillator so that it would take into account not only the result but also the player's position – the more players you outperform, the greater the bonus you receive.
For a more productive discussion, let's define the terminology. The non-linear component in the oscillator is the one that depends on the number of days, because it is INVERSELY PROPORTIONAL to this number. The part that depends on the position is LINEAR with respect to this position (and non-linear only with respect to the number of participants). Please don't confuse them. And most importantly, don't forget that the number of participants does not reflect the significance of the positions, especially the top ones.
It's much easier to add "weight" to the oscillator formula, shifting the arithmetic mean towards the non-linear function, and we'll get a greater curvature, which is what you're advocating for.
Curvature is determined by the second derivative of the function. Introducing a weight (read: multiplier) doesn't change anything. A straight line remains a straight line, and the second derivative of kx+b is equal to zero.
You can experiment with balancing endlessly, but there's no point in it because there's too little material for analysis, and it won't be possible to see the effectiveness of the formulas for reflecting the real strength of the players. There are no objective criteria that we can use as a benchmark...
I disagree. A rating is needed for a specific tournament on a specific portal. We look at the average number of participants in the Van Caneghem stages and check how the oscillator behaves. The difference between adjacent positions with the same number of days is ALWAYS the same and is approximately 3 points. We think about whether this is good or bad.
I suggest leaving everything as it is.
Not yet. There are several author's, NON-official systems.
And if we're going to optimize, then we should do it within the framework of the proposed and used calculation methods. As an option, make a certain effort and choose one single method from all the ones currently in use.
No offense to the authors of these systems, but none of them can withstand the simplest criticism when applied to a multi-stage tournament.
But we shouldn't create a new one. Just another one of many...
So far, I haven't tried to do that, although maybe I should have. If you read carefully, I just suggested combining the IronAxe and VDV Forever systems. Their linear combination would not contain at least obvious contradictions. Moreover, if a certain system had already been chosen for the tournament, I would not challenge it, considering it part of the rules.
I wasn't even trying to do that, although maybe I should have. If you read carefully, I was just suggesting combining the IronAxe and VDV Forever systems. Their linear combination would not contain any obvious contradictions. Moreover, if a system had already been chosen for the tournament, I would not challenge it, considering it part of the rules.
It might not be worth delving deeply into mathematics, although you are absolutely right in your reasoning... I will try to simplify.
1. Any sequence of values "100-95-91-86-83-...-5-1" is abstract and does not contain anything in itself, because it does not explain why exactly these coefficients were introduced. The goal is to find a method that will generate coefficients each time, depending on objective factors that characterize the player's achievement. What are these factors?
1.1. Map difficulty. In my opinion, it doesn't matter. All participants are in equal conditions, and therefore it is not appropriate to divide them according to this criterion, although, at first glance, it seems necessary to take this criterion into account.
1.2. Number of participants. It matters. And directly proportional - the more opponents you manage to beat, the higher the level of the game. A tournament for five players and a tournament for a hundred are significantly different. But: at the moment, it is customary to award 100 points to the tournament winner, and therefore we initially abandoned this parameter. The only way to take this into account is to give a higher delta to players in the upper part of the table compared to the rest when the number of participants increases... And this automatically leads to a compression of the ranking of players in the lower part of the table.
1.3. Average strength of players in the tournament. This is fundamentally important - even more so than the number of players. Beating the top five strongest opponents in a tournament with only ten participants is more significant than beating a hundred conditionally weak players in a tournament where the strong do not participate. But for this, it is necessary to take into account the current rating of the player, as well as assess the strength of all new participants, which is impossible in principle.
Conclusion. The only parameter that we can somehow optimize is indicated above (highlighted in color). But, against the background of the rest of the balance distortions caused by objective factors, it does not seem particularly significant. In other words, increasing the accuracy of measuring one of the parameters of the system in the case when this [accuracy] is lower than the error of the entire system as a whole (which we are observing in our case) does not make practical sense. We have already discussed this, and I believe that a reasonable solution will not be found.
If we do not take into account the strength of opponents, but only the number of participants in the tournament, the rating will not approach its true value, no matter how hard we try to balance this criterion. That's why I say - it's not necessary. Although, for theory, this issue can be tried to be solved purely mathematically, but whether to apply it or not is a matter for the future...
My bonus directly depends on the average strength of the tournament. It's also not an arbitrary number; it's borrowed from tennis, where a strong player receives a lower rating for winning against a weak player than a weak player receives for winning against a strong player. Starting from the second round of the tournament, this bonus comes into effect. Since the player roster is starting to become more or less defined, there shouldn't be any significant fluctuations in the bonus. Although, for a multi-stage tournament, a slightly different system might be possible. The whole question is what we want to measure. After all, a player who has played more games has a higher chance of achieving a higher ranking. But the thing is, that player isn't the only one. There are several of them. In addition, it was suggested to also calculate and separately recognize the winners for each version.
In other words, increasing the accuracy of measuring one of the system's parameters when this accuracy is lower than the error of the entire system as a whole (which we observe in our case) does not make practical sense.
This statement is true for errors that are statistical in nature (having a variable sign, lucky or unlucky, it was there - it wasn't, etc.). Factors that shift the measured value in a specific, defined direction should be eliminated, because such errors add up with statistical errors according to a linear law, not a quadratic one. Of course, it may turn out that even in this case they can be neglected, but I am not sure that this is our case. However, it is not yet possible to prove or disprove this.
However, we need to talk about the strength of the participants separately. After a certain number of tournaments have been played in a given version, this strength can be reasonably estimated. Each participant will contribute a certain number of points through their participation. This number will be determined by their average rating in this part of the game + some constant addition for everyone, so that even beginners are taken into account. Based on the total points, the tournament will be assigned a category (as in chess), which will then turn into an ordinary multiplier for the overall rating, as once planned, but the category will not be arbitrary, but strictly defined.
A high category can be obtained by both a large-scale tournament and a cool head-to-head competition.
However, all of this is not applicable to determining the winners in the Van Caneghem tournament, in which, by its idea and spirit, all stages should be equivalent.
My bonus depends on the average strength of the tournament. It was also not taken out of thin air, but from tennis, where for a strong player winning against a weak player, the winner receives a lower rating than for a weak player winning against a strong player.
That's why I noticed a familiar expression. Alan already mentioned motorcycle racing, and now tennis has surfaced. The idea of borrowing an already proven system is indeed tempting, but we need to be careful.
AlexeyPank
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Don't just copy a proven system, but take the idea. I only borrowed the idea of calculating the bonus, but the formula is my own.
This statement is true for errors that are statistical in nature (having a variable sign, lucky-unlucky, it happened-it didn't, etc.). Factors that shift the measured value in a specific, defined direction should be eliminated, because such errors add up with statistical errors according to a linear law, not a quadratic one. Of course, it may turn out that even in this case, they can be neglected, but I am not sure that this is our case. However, it is not yet possible to prove or disprove this.
You've said quite a thing... :D I think if a contest were held on the forum for the smartest phrase that doesn't relate to pointless chatter, you wouldn't have any competitors... ;)
Why talk about something simple in such a complicated way? For example, if a car has problems with its chassis, which prevents it from moving at a speed of more than 50 km/h, then increasing the quality of lubricants, fuel, and improving the driver's skills will not help it accelerate above this limit. Because the bottleneck is a malfunction in the chassis... (I said this as a way to lighten the mood - otherwise, we'll go into the wilds of terraforming and mathematical analysis, which we can avoid for now)...
The same applies to us - we are not yet taking into account many significant parameters, which gives a total error in the assessment of the final player rating of +/- 5-7 points per tournament (on average), and therefore, trying to optimize one of the calculation parameters now in order to find one or two points does not make much sense. Excessive complication of the calculation increases the likelihood of errors in its application. And as a result, we may not get exactly the result we are striving for...
I suggest that we do not consider specific tournaments for now, but create an abstract calculation model, which we (possibly) will then adopt. For now, I don't think we should make changes to the existing methods... Time will tell.
You’ve certainly said something… I think if we held a contest on the forum for the smartest phrase that isn’t just mindless chatter, you wouldn’t have any competitors…
I just thought that you were familiar with the theory of errors, and therefore I preferred to use generally accepted terminology.
I suggest that we don’t consider specific Tournaments for now, but create an abstract model for calculation, which we (possibly) will adopt later.
Your position is clear. But for now, we can only consider the categories of Tournaments and their assignment in a completely abstract way.
For now, I don’t think it’s worth making changes to the existing methods… Time will tell.
But, at a minimum, the organizers will have to decide which system to use for the Van Kanighem and justify their decision.
Not to copy a proven system, but to take the idea. I only borrowed the idea of calculating the bonus, and the formula is my own.
Fireball;100689But, at the very least, the organizers will have to decide which system to use for Van Kanigem... It's not that complicated... Just flip a coin and that's it...Fireball;100689...and justify your decisionA monument could be erected for such a feat... :)
You cannot compare the incomparable. A single rating for the VK tournament will be far-fetched in any case, unless, of course, its wording includes a phrase like: "This rating in no way reflects the player's strength in comparison with others. Rather, it is simply for demonstration purposes and shows how well the player navigates the entire diversity of the world of Might and Magic!" :) Well, or something along those lines...
You can only correctly compare players who participated in all VK tournaments. Otherwise, it's like choosing the best soccer player among hockey players... :)
Fireball
