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Math Help - finding the "best" player of a game.

  1. #1
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    Question finding the "best" player of a game.

    Hi there,

    I've been looking for a formula to find the "best player" of a certain boardgame. Let me give an example:

    Game name: X (3 player game)
    player A has won 9 out of 10
    player B has won 90 out of 100
    player C has won 49 out of 50
    player D has won 5 out of 5
    ...

    You can see that the winning % of A and B is equal both that doesn't mean that they are equally good in the game does it? Since my guess is that if someone wins a game 90 out of 100 he is better then someone that wins 9 out of 10? I think that the number of players also might have an impact, since a 2 player game gives a 50% chance of winning and a 3 player game a 33.3% chance...

    Anyway the point is I'm trying to come up with a formula that calculates this and gives me the "best" player, and the worst

    Is it even possible to calculate this on people with an unequal number of games played? I can imagine I could order the data so I get a number 1 player in each categorie (less then 10 times played, between 10-50, etc.) but I'm not really interested in that, on the other hand, I am too, so a formula of some sort for that would be cool too. But I'm drifting...

    A formula for the "best" player in a game, with each player having played a different amount of games.

    Many many thanks in advance,
    Kind regards,

    Walter

    SIDENOTE:
    Just thought about this, extra factor: draws (f.e. a player who won 8 out of 10, lost 1 and drawed 1)
    Last edited by Juggala; May 31st 2009 at 02:51 PM. Reason: typo, sidenote
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  2. #2
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    Quote Originally Posted by Juggala View Post
    ...
    I've been looking for a formula to find the "best player" of a certain boardgame. Let me give an example:

    Game name: X (3 player game)
    player A has won 9 out of 10
    player B has won 90 out of 100
    player C has won 49 out of 50
    player D has won 5 out of 5
    ...

    You can see that the winning % of A and B is equal both that doesn't mean that they are equally good in the game does it? Since my guess is that if someone wins a game 90 out of 100 he is better then someone that wins 9 out of 10? I think that the number of players also might have an impact, since a 2 player game gives a 50% chance of winning and a 3 player game a 33.3% chance...

    Anyway the point is I'm trying to come up with a formula that calculates this and gives me the "best" player, and the worst

    Is it even possible to calculate this on people with an unequal number of games played?
    ...
    A formula for the "best" player in a game, with each player having played a different amount of games...
    With wins and losses only -- I'd say that you're success in predicting the outcome of a game won't make you a rich person.

    IF you have the win/loss/tie record of the opponent(s) then you have a much better basis for predicting the outcome.

    If not then you will need to "weigh" the numbers of games. That is, as you indicate, a person who has played more games has more experience and thus has a much more reliable indicator of results.

    It may be that a person who has won 9 of 10 is a far better player that one who has won 90 of 100, but one assumes that experience is worth something.

    The ranking method used for basket ball teams appears to be a likely format for what you are attempting.

    How much data can you get for each player?
    Number of wins/losses/ties.
    The actual time length or number of moves per game.
    The opponents statistics.
    The total number of players who play.
    Is there a home/away statistic.


    Get ALL possible data for each player, then generate a correlation coefficent for each facet for each player. The more indicators you have, the more reliable they become in predicting probabilities.


    How much data can you acquire?
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  3. #3
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    Thanks for the response, I'm not sure what you mean with the "correlation coefficient" though (English is not my native language), although I do think I understand a bit.

    The thing is, there aren't so many factors I can get, like numbers of moves etc, simply because some boardgame don't work like "you make a move then I make a move" etc.

    The only things I've got really is a database of people and games and data like "game X played by player A, B and C was won by player A, player C was second and player B ended last". No length of games, number of moves, etc.

    The hard thing is, like you say: "one assumes that experience is worth something". But is it possible to insert this into a formula? (I'm not a math-wizard in any way by the way, this is just a project for fun).

    Is it even possible or relevant AT ALL to compare 2 people to each other, one who played the game 10.000 times and one who played it 50 times?
    For example it's easy to say that if somebody won 9999 out of 10000 he is better then somebody who won 100/100, but is he REALLY better? Where is the line in between those 2 players that decides which one is better... can math help, or is it simply not possible to compare these to each other.

    And this all gets even more complicated if you add draws, or even games which are played with teams of 2 or more players... but let's not think about that, for now

    By the way: I'm not looking for predictions of any kind, just the rankings of players for a game. So the games are already played (project is a website for a boardgame-club who input the scores of the played games, for fun and statistics)

    (edit: the prediction of the outcome you are talking about sounds interesting too, maybe something for later. So two players could sit down at a table and there would be a percentage of winning chance based on their wins/losses/draws in that game and maybe against each other. Haven't even thought about that, but that sounds even more complex then finding the best player for already played games I'm gonna write it down though, seems interesting)
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  4. #4
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    There is the Elo Rating System used by Chess, Chinese Chess and Go.
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  5. #5
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    Quote Originally Posted by cl85 View Post
    There is the Elo Rating System used by Chess, Chinese Chess and Go.
    The rating system used by the United States Chess Federation gives/takes points from your rating based on the rating of your opponent you play.
    Thus if your rating is far lower than your opponent you may only lose 2 points, but if you win you will pick up many times more that 2 points.

    If you have a high rating and you play a much lower rated player you may only win 2 rating points if you win, but you could lose 50 or more points if you do not win the game.
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