For a given team of 6 individuals, calculate the probability that this particular configuration of 6 will defeat a different, known, team based on how well each of the chosen 12 individuals have performed in past matches within different teams.
Breakdown of rules and clarifications:
2 teams compete against each other.
For each competition, team configurations differ.
6 individuals are randomly assigned to each team from a large pool of N individuals.
Each "match" will result in either a win, draw, or loss.
Rows of raw data display: the individuals within both teams AND the match result
what is the best way to go about solving this problem? Initially, I thought about using a modified Elo system for each individual. Is this the correct path, and what else could be used instead? I would love to read some papers on the subject.
I'm developing a multiplayer game with a Glicko-based ranking system.
I started creating a system that assign one of 12 ranks out of the decimal rating of the player.
The rank boundaries are determined by the percentiles (https://en.wikipedia.org/wiki/Percentile)
But I don't know to which percentiles can I set the boundaries to keep a smooooth distribution of the players in the ranks like in games like CS:GO.
Your game's real distribution of players' rating comes from your games' features and characteristics, including (but not limited to) teams's size and number, scores, victory conditions, and more.
Only if you know the real distribution of players' rating you can set a smooooth distribution of the players in the ranks, as per your question.
In rankade, our multipurpose free ranking system for sports, games, and more, we noticed significant differences in rating scores' distribution for type of game and/or for 'families', mechanics, factions' set-ups, and more.
I am trying to automatically generate a schedule for a volleyball tournament I am organizing. It is mainly for fun. The rules are as follows:
Teams that sign up consist of 2 players
There are 36 such teams
For a match, 3 such teams get put together to a "game team", so a match consists of 3 teams vs. 3 teams
Every team plays 5 matches
There are 3 courts than can be played at the same time
Thus, a total of 10 rounds will be played (18 teams can play at the same time, so that is 36/2*5 rounds = 10 rounds)
Games are officialled by teams
Additional constraints are:
Every team officials at most once
If possible, a team should not play with another team that it already played with before (if it played against, it is fine)
There should not be more than 2 rounds break in between games for each team
Now I thought that this sounds like a problem that prolog is a good choice for. Unfortunately, I only have theoretical experience with it. It would be great if anybody could give me a good starting point with this, especially on how to fulfil constraints like "official at most once" and "every team plays 5 times". Also, a more compact representation of teams than
team(A).
team(B).
....
would be great. I already tried implementing this in Java,but came to the conclusion that it is not a well suited language. I'd like to do this in prolog now.
I am looking for a rating system similar to the elo rating system in chess.
The problem I have is that the ELO system depends on the order games were played.
eg.
Player A starting Elo 1000
Player B starting Elo 1000
If Player B wins over A he will have lets say 1015 points and A 985.
If A keeps on playing and wins against other people, he will have a higher ranking than B, if B stops playing.
I don't want that. B should still be stronger than A.
How can I realise that?
From this link:
Whole-History Rating (WHR) is a new method to estimate the
time-varying strengths of players involved in paired comparisons. Like
many variations of the Elo rating system, the whole-history approach
is based on the dynamic Bradley-Terry model. But, instead of using
incremental approximations, WHR directly computes the exact maximum a
posteriori over the whole rating history of all players.
It's a rating system without order of game played, like the one you asked, but it doesn't solve your issue with Elo.
On the other hand, many post-Elo ranking systems, as Glicko (for chess), or TrueSkill (for X-box games), or rankade (our multipurpose ranking system) have some 'activity dynamics feature' to avoid 'parking the bus' approach (a player gets a high level in ranking, then he stops playing), indeed.
There are a number of schemes which amount to writing down the win/lose/draw record as a matrix and then typically calculating the largest eigenvalue of some matrix related to this. One summary is at http://java.dzone.com/articles/ranking-systems-what-ive, which points to more technical papers including https://umdrive.memphis.edu/ccrousse/public/MATH%207375/PERRON.pdf - "The Perron-Frobenius Theorem and the Ranking of Football Teams".
If you can get more information out of the game than just win/lose/draw you might do better by using this. Some work on soccer has used the number of goals for and against at each match to try and work out the strengths of each team's offense and defense separately (and I do realise that soccer doesn't have separate offensive and defensive teams). In soccer it is reasonable to model the number of goals scored as a Poisson process. One deduction from this, by the way, is that soccer is inherently a pretty uncertain game, and that predicting score draws, as required in some gambles, is especially uncertain. I try and remember the inevitable uncertainty every time England play a game :-).
I am working on an algorithm to score individual players in a team-based game. The problem is that no fixed teams exist - every time 10 players want to play, they are divided into two (somewhat) even teams and play each other. For this reason, it makes no sense to score the teams, and instead we need to rely on individual player ratings.
There are a number of problems that I wish to take into account:
New players need some sort of provisional ranking to reach their "real" rating, before their rating counts the same as seasoned players.
The system needs to take into account that a team may consist of a mix of player skill levels - eg. one really good, one good, two mediocre, and one really poor. Therefore a simple "average" of player ratings probably won't suffice and it probably needs to be weighted in some way.
Ratings are adjusted after every game and as such the algorithm needs to be based on a per-game basis, not per "rating period". This might change if a good solution comes up (I am aware that Glicko uses a rating period).
Note that cheating is not an issue for this algorithm, since we have other measures of validating players.
I have looked at TrueSkill, Glicko and ELO (which is what we're currently using). I like the idea of TrueSkill/Glicko where you have a deviation that is used to determine how precise a rating is, but none of the algorithms take the random teams perspective into account and seem to be mostly based on 1v1 or FFA games.
It was suggested somewhere that you rate players as if each player from the winning team had beaten all the players on the losing team (25 "duels"), but I am unsure if that is the right approach, since it might wildly inflate the rating when a really poor player is on the winning team and gets a win vs. a very good player on the losing team.
Any and all suggestions are welcome!
EDIT: I am looking for an algorithm for established players + some way to rank newbies, not the two combined. Sorry for the confusion.
There is no AI and players only play each other. Games are determined by win/loss (there is no draw).
Provisional ranking systems are always imperfect, but the better ones (such as Elo) are designed to adjust provisional ratings more quickly than for ratings of established players. This acknowledges that trying to establish an ability rating off of just a few games with other players will inherently be error-prone.
I think you should use the average rating of all players on the opposing team as the input for establishing the provisional rating of the novice player, but handle it as just one game, not as N games vs. N players. Each game is really just one data sample, and the Elo system handles accumulation of these games to improve the ranking estimate for an individual player over time before switching over to the normal ranking system.
For simplicity, I would also not distinguish between established and provisional ratings for members of the opposing team when calculating a new provision rating for some member of the other team (unless Elo requires this). All of these ratings have implied error, so there is no point in adding unnecessary complications of probably little value in improving ranking estimates.
First off: It is very very unlikely that you will find a perfect system. Every system will have a flaw somewhere.
And to answer your question: Perhaps the ideas here will help: Lehman Rating on OkBridge.
This rating system is in use (since 1993!) on the internet bridge site called OKBridge. Bridge is a partnership game and is usually played with a team of 2 opposing another team of 2. The rating system was devised to rate the individual players and caters to the fact that many people play with different partners.
Without any background in this area, it seems to me a ranking systems is basically a statistical model. A good model will converge to a consistent ranking over time, and the goal would be to converge as quickly as possible. Several thoughts occur to me, several of which have been touched upon in other postings:
Clearly, established players have a track record and new players don't. So the uncertainty is probably greater for new players, although for inconsistent players it could be very high. Also, this probably depends on whether the game primarily uses innate skills or acquired skills. I would think that you would want a "variance" parameter for each player. The variance could be made up of two parts: a true variance and a "temperature". The temperature is like in simulated annealing, where you have a temperature that cools over time. Presumably, the temperature would cool to zero after enough games have been played.
Are there multiple aspects that come in to play? Like in soccer, you may have good shooters, good passers, guys who have good ball control, etc. Basically, these would be the degrees of freedom in you system (in my soccer analogy, they may or may not be truly independent). It seems like an accurate model would take these into account, of course you could have a black box model that implicitly handles these. However, I would expect understanding the number of degrees of freedom in you system would be helpful in choosing the black box.
How do you divide teams? Your teaming algorithm implies a model of what makes equal teams. Maybe you could use this model to create a weighting for each player and/or an expected performance level. If there are different aspects of player skills, maybe you could give extra points for players whose performance in one aspect is significantly better than expected.
Is the game truly win or lose, or could the score differential come in to play? Since you said no ties this probably doesn't apply, but at the very least a close score may imply a higher uncertainty in the outcome.
If you're creating a model from scratch, I would design with the intent to change. At a minimum, I would expect there may be a number of parameters that would be tunable, and might even be auto tuning. For example, as you have more players and more games, the initial temperature and initial ratings values will be better known (assuming you are tracking the statistics). But I would certainly anticipate that the more games have been played the better the model you could build.
Just a bunch of random thoughts, but it sounds like a fun problem.
There was an article in Game Developer Magazine a few years back by some guys from the TrueSkill team at Microsoft, explaining some of their reasoning behind the decisions there. It definitely mentioned teams games for Xbox Live, so it should be at least somewhat relevant. I don't have a direct link to the article, but you can order the back issue here: http://www.gdmag.com/archive/oct06.htm
One specific point that I remember from the article was scoring the team as a whole, instead of e.g. giving more points to the player that got the most kills. That was to encourage people to help the team win instead of just trying to maximize their own score.
I believe there was also some discussion on tweaking the parameters to try to accelerate convergence to an accurate evaluation of the player skill, which sounds like what you're interested in.
Hope that helps...
how is the 'scoring' settled?,
if a team would score 25 points in total (scores of all players in the team) you could divide the players score by the total team score * 100 to get the percentage of how much that player did for the team (or all points with both teams).
You could calculate a score with this data,
and if the percentage is lower than i.e 90% of the team members (or members of both teams):
treat the player as a novice and calculate the score with a different weighing factor.
sometimes an easier concept works out better.
The first question has a very 'gamey' solution. you can either create a newbie lobby for the first couple of games where the players can't see their score yet until they finish a certain amount of games that give you enough data for accurate rating.
Another option is a variation on the first but simpler-give them a single match vs AI that will be used to determine beginning score (look at quake live for an example).
For anyone who stumbles in here years after it was posted: TrueSkill now supports teams made up of multiple players and changing configurations.
Every time 10 players want to play,
they are divided into two (somewhat)
even teams and play each other.
This is interesting, as it implies both that the average skill level on each team is equal (and thus unimportant) and that each team has an equal chance of winning. If you assume this constraint to hold true, a simple count of wins vs losses for each individual player should be as good a measure as any.