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)?