Results 1 to 3 of 3

Math Help - r-value > Probability

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    2

    r-value > Probability

    I have two wrestlers who are going to arm-wrestle. I want to try to predict who will win based on their previous fights against other opponents.


    This is the information that I know:


    The outcome of each wrestler’s last 5 fights (win, lose, draw).


    I know that the probability of a win is 0.4, the probability of a loss of 0.4 and the probability of a draw is 0.2 (these are true in the population of arm-wrestlers as a whole).


    If we give 2 points for a win, 1 point for a draw and 0 points for a loss, then I can work out the Average and Standard Deviation for each wrestler’s last 5 fights.


    Using these I can work out the Variance, Degrees of Freedom and the Test Statistic t. I can then work out the r-value (correlation co-efficient). The r-value gives me an indication of who will win the fight, or if the fight will be a draw.


    But the r-value does not tell me: What is the probability of Wrestler A winning, what is the probability of wrestler B winning, and what is the probability of a draw?


    Is it possible from the information I have to work out these probabilities? Can I turn an r-value into a probability (p) value?


    Here is an example:


    Wrestler A last 5 fights: Win, Win, Draw, Loss, Loss
    Wrestler B last 5 fights: Loss, Draw, Win, Loss, Draw


    Wrestler A: Avg Points = 5, SD of Points = 1
    Wrestler B: Avg Points = 4, SD of Points = 0.8


    Pooled variance estimate = 0.85
    Degrees of freedom = 8
    Test statistic (t) = 0.343


    r-value (r) = 0.12


    I know this r-value shows that Wrestler A has a slight advantage in this fight. But is there a way of working out the exact probabilities of each of the three outcomes (Wrestler A wins, Wrestler B wins, draw)?


    Thanks. Marc
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: r-value > Probability

    Quote Originally Posted by cmarkc View Post


    I know this r-value shows that Wrestler A has a slight advantage in this fight. But is there a way of working out the exact probabilities of each of the three outcomes (Wrestler A wins, Wrestler B wins, draw)?


    Thanks. Marc
    Probably not. You could use something like an Elo rating system and the assumption that each wrestler previous opponents represent average opposition.

    Then the Elo system would give a probability of win based on the two players rating difference (or rather the expected score of the game which is not quite the same thing because of the possibility of draws)

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2011
    Posts
    2

    Re: r-value > Probability

    Thanks. I'll look into it next week, post-holiday.

    Anyone else got any other ideas?

    Thanks. Marc
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  2. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  3. fundamental in probability & convergence with probability 1
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 23rd 2010, 09:58 AM
  4. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  5. Replies: 3
    Last Post: December 15th 2009, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum