falker1976 wrote:

I am not sure about run away scores.  In my case I have a 3.4 ratio vs a 1000 rated player.  Which means if I play him 10 times and win 8 times I win about 40 points and lose 60 points in the capped system.  I would have to win about 85.7% of my games vs him with a cap of 30 in order to maintain 3400 vs a 1000 rated player.  In the current system I have to maintain a 93.1% win record vs the same player. 

I'm getting a (slightly) different number - 92.04% in duel situations to maintain 3400. If you have a probability p of winning, some algebra gives Sqrt(p/1-p) times their rating as the equilibrium.

Let's give you the 30 point cap. Against 1000, the cap applies every time you lose. Now your equilibrium is found via 30*(1 - .92) = 20*.92*(1000/E). Some algebra gives E ~ 7,667.

Against a 1500 player, we have 3400 stabilized at an 83.7% win rate. The 30 point cap still applies, so the new equilibrium, against 1500 only would be E ~ 5135.

So, with caps, not only is there inflation, but the inflation is better against lower rated players. In summary, tom was spot on: the equilibrium changes. If scores don't runaway, it's because it's too much effort to reach 7667.

By contrast, consider an industrial-grade system like Elo:

http://en.wikipedia.org/wiki/Elo_rating_system

There are caps. The caps limit how much is gained or lost in any single game. (Sounds great, right? It's not.) So, if 32 (standard in some places) is the cap, then two evenly matched players are playing for +16 versus -16. However, if it's two very unevenly matched players, it's +0 versus -32. Or, if the web site is feeling generous, it's +0.2 versus -31.8.

Name the rating system - if it's worth it's salt, it gives high rated players very little incentive to play lower rated players. In reality, lower rated players should feel the same disincentive because they will most likely lose, but, they get to dream while the high rated player gets ulcers.

SquintGnome wrote:

I agree that win rates of more than 80% occur.  I offer these counterpoints.

* Win rates higher than 80% are more likely when less than 10 games have been played on a board.  Just as likely are players with win rates lower than 20% in this situation. 

*Win rates higher than 80% on boards with more than 10 games played are likely uncommon (outliers).  We can check this.

As tom stated, win rates exceeding 80% are entirely possible on two player boards, and especially those that minimize the luck of the dice.  Five and Go-Geared are examples of this.  The only reason Hugh isn't 90+ on GG is that we pick on each other and I steal a few from him.

and when we include luck factor (dices, position, card sets), half of the obtained results throw into the water :)
I do not believe that the better ranked player can win four times lower ranked player in 5 games.

I challenge the best ranked player in wargear warfare to play 10 games with me (my current rank is 1470) and I am confident that I will finally be the one who will have benefit.

Vidoviti Milan wrote:

and when we include luck factor (dices, position, card sets), half of the obtained results throw into the water :)
I do not believe that the better ranked player can win four times lower ranked player in 5 games.

I challenge the best ranked player in wargear warfare to play 10 games with me (my current rank is 1470) and I am confident that I will finally be the one who will have benefit.

It is also true that rating systems are best applied to a single type of game.Within a single type of game, dice or not, rating systems do make sense in the long run. At the very least, success is measured, if not skill.

If we were to be purists, we'd separate dueling on WGWF from 4-player. Because you're right, no one is getting 80% on WGWF duels. But, someone might reach an 80% H-Rating in multiplayer.

However, separating all that would be very complicated.

Vidoviti Milan wrote:

and when we include luck factor (dices, position, card sets), half of the obtained results throw into the water :)
I do not believe that the better ranked player can win four times lower ranked player in 5 games.

I challenge the best ranked player in wargear warfare to play 10 games with me (my current rank is 1470) and I am confident that I will finally be the one who will have benefit.

But then eventually you're score will rise, and as it rises, the best ranked player won't have to win so many games to break even.  So maybe the problem, is more that many of the goodish players have yet to play enough games to rise to their equilibrium point.

Also in terms of score inflation, we basically already have a limited form of that, right?  Players join all the time, lose a couple of games and then never come back.  For all intents and purposes, they basically acted like an outside source of points that get added to the system.

(learned something new today - 'goodish' is a real word)

Ozyman wrote:

So maybe the problem, is more that many of the goodish players have yet to play enough games to rise to their equilibrium point.

Indeed! I brought this up long ago - this particular rating system makes it difficult to reach equilibrium. (There is a good reason why this happens for this system and not others.) It's not as noticeable for maps where a 70% win rate is as good as it gets, but it's really bad for multi-tiered maps. I would identify this as the main weakness of the current calculation.

(Side bar: Math makes my brain hurt.  Now back to the argument....)

Can someone generate some facts from our database?  For example, from my previous post, how many players, and what percentage have a higher than 80% H rating on a board where they have played more than 75 games?

I say 75 games becuase , starting on a new board at a rate of 1000, you would have to  play about this many before a 40 point cap kicks in.  We don't need to consider the cases where people have player a few games with a high rating.  I am guessing that this number is very low.

After we have this fact we can have a more meaningful discussion I think based on what is actually happening.

Can anyone get that info easily?

Hugh,

Can you redo you calcs based on a 40 point cap.  This is what I am proposing.  Also, can you offer results for different win %'s.  As I posted above I feel that the vast majority of boards will have win% of 80 or less when a significant amount of games are played.  So I would like to see the result at an 80% win rate.  Lastly, could you run the calcs for the high player's rate of 2000 or less, I think this is closer to a range most players will have.

Lastly (again), I haven't mentioned this up to now because it further complicates matters, but there is a big difference between board and global rankings.  I think that global rankings will have a tendency to be much higher and also a much larger range so these will be affected more by a cap.  My concern is mostly about board ratings and not global rating.

The cap you suggest might regularly be applied to the top players on these maps:

http://www.wargear.net/boards/view/Axes+and+Allies/Rankings

http://www.wargear.net/boards/view/Ancient+Isles+of+Kjeldor/Rankings

One of the issues I have with what you are suggesting is that a cap rarely applies. But, once a player reaches a certain level on a map, it regularly applies. So, on the whole, no one will see these caps in action, but the top players on maps like these get their equilibrium inflated through a cap. 

SquintGnome wrote:

Can you redo you calcs based on a 40 point cap.  This is what I am proposing.  Also, can you offer results for different win %'s.  As I posted above I feel that the vast majority of boards will have win% of 80 or less when a significant amount of games are played.  So I would like to see the result at an 80% win rate.  Lastly, could you run the calcs for the high player's rate of 2000 or less, I think this is closer to a range most players will have.

80% win rate against a fixed rating corresponds to twice the rating. So, 2000 is equilibrium versus 1000 at an 80% win rate. Suppose the edge is x-to-1 against a fixed rating. The result is that sqrt(x) times that rating is the equilibrium. So, 66% win rate over a 1000 player is about 1400. etc.

Maybe I should state my case this way: It is true that 500-rated players will look like a ticking bomb to some players. And it isn't entirely unjustified. Often that is just a regular player playing like a lot of 1000 rated players play. It's just that they stuck around. And now you face the possibility of losing your hard work to some bad rolls. I understand. But, caps are dangerous. There is a better way to deal with this.

(Not to go on and on... but, just so we use a "real" point of data):

The A&A example, running the numbers with a 40 cap, assuming 85% win rate against 1000, we get a 2830 equilibrium versus 2400. It's not a devastating example. However, I like to worry about the future. Here is an example of a win rate where if either one of the top two players decides to keep going, an already magnificent equilibrium will be ridiculous with a 40 cap:

http://www.wargear.net/boards/view/Octagons/Rankings

The current equilibrium at 95% (low estimate of 1000 for opponent) is 4360 versus 9500 with a 40-cap.

Hugh, thanks for taking the time for the last two posts, it is appreciated.

It is true that to me, the 500 rate player is what gives me the most concern and motivated my suggestion.  You mention another way to deal with this scenario, what do you recommend.

As to your second post, I agree that if win rates go over 80% for a board in the long run then this would be a problem.  How often does board like the one you presented occur?  I agree that if that happens often then a 40 point cap is not a good solution, but perhaps it is rare? Not sure.

I only see 37 players with 500 or less score.  And only 4 of them had an H rating over 20%.  My guess is that most players at that level have some fundamental misunderstandings about how to play.  

I bet your average 2000 ranked player would win 9 out of 10 games against a 500 ranked player.

I'm barely following some of the math here.  This is all really just a scaling issue, right? Ok, thinking to myself..  You want to maximize the range of the ratings range while preventing runaway ratings.  Going with a cap that is based on an average doesn't work because of outliers, so you want to err on the conservative side and sacrifice range. 

How about something like this..

What kind of a cap would keep equilibrium under 5000 for a player playing at 95%?

M57 wrote:

I'm barely following some of the math here. 

Certainly it's worth checking - I can make mistakes. The worst part of it is the amount of parameters.

However, it's all just algebra. Every calculation I did is of the form "Expected rating change = 0". Each of these breaks down as "probability of losing * |rating loss| = probability of winning * rating gain".

After that it's just plugging in the formula we use to calculate the ratings, or the suggested cap.

SquintGnome wrote:

It is true that to me, the 500 rate player is what gives me the most concern and motivated my suggestion.  You mention another way to deal with this scenario, what do you recommend.

One option, discussed elsewhere and mostly rejected if I remember correctly, is a ratings filter. There's not much one can do to change the low incentive of a large ratings mismatch, so some gaming communities choose to allow filters. (Chess.com defaults at +/- 200, though it's a different system.)

A purely mathematical solution would be to change the multiplier based on rating difference. Currently, we multiply the ratio of the ratings by 20 to get the change in rating. If we decrease that number for large rating differences, we could avoid the "bomb effect" of playing a low rated player. At the cost, however, of making the gain in a win smaller. Unlike caps, equilibrium stays the same under such an approach. (Note that the 20 cancels in the equilibrium calculation.)

On this point, this was a recent post by Playdom on their forums for the Facebook Game Marvel: Avengers Alliance.  They are tweaking the PvP rankings system using a similar ranking system as here (to my understanding) and speak on the filter of higher ranked players vs lower ranked players.  Now, in this case the Higher Ranked players are probably stronger and hence have a distinct advantage which is not true here, but I saw the post and so I'm sharing because I'm a giver.

What is the Elo Rating System?

The Elo rating system was designed by Arpad Elo to solve the problem of how to measure a player’s relative skill in chess. The simple and elegant system first implemented in 1960 has withstood the test of time and variations on the Elo system have found their way into everything from mahjong to Scrabble to video games such as World of Warcraft and League of Legends.

The general way this system works is as follows:

• Each player has a numeric rating which roughly corresponds to their skill or power relative to other players.
• A player with a rating of 1500 is more likely to win in a matchup against a player with a rating of 1200.
• After each match, the player who wins gains rating points, while the other player loses the same amount of rating.

The amount gained or lost depends on how favored the winner was to win. Winning against someone with a rating higher than you grants far more rating points than winning against someone with a lower rating than you. Similarly, if you lose to someone with a higher rating, your rating points won’t go down as much, but losing to someone with a lower rating score will reduce your rating by much more.

In this way, simply winning isn’t enough to maintain a high rating. Players need to also win against higher rated players to gain and maintain their awesome rating. The matchmaking system should find you a group of players to challenge who are not only close to your level range, but also close to your rating.

The players with the highest rating will be able to climb to the top of the leaderboard. We hope this change will help make the way the leaderboard works more transparent and competitive for players who wish to aspire to the highest echelon of SHIELD recognition.

The amount gained or lost depends on how favored the winner was to win.

Seems like this illustrates the problem right here.  What we want is some better way to give odds in a match.  The root of the problem is that a simple ratio of ratings doesn't give a good estimate.

Is there a better formula we should be employing.  Maybe something that gives more weight to H rating, or something?