Imagine there are 80 dodgeball players in the world. Each of them has played thousands of dodgeball games with the other 79 players in more-or-less random order. This is a world without teams (e.g., every player has a chance of being drafted in either team each game). I know the previous win rate of each player (e.g., one has won 46% of all previous games, another has won 56% of all his previous games). Lets say there is a match coming up and I know who is playing on each team. I also know their previous win rate.
What is the best way to calculate the probability of each team winning based on the composition of the team?
If it requires relatively advanced calculation (e.g., logistic regression) let me know some of the specifics. I am pretty familiar with SPSS, but I rather not need to ask a follow-up question.
Moreover, how would I explore the accuracy of my method using archival data? I know it won't be clear cut since most players hover around 40-60%, but still.
To be specific, what are the odds that team A is going to win?
A – comprised of individuals with previous win rate of 52%, 54%, 56%, 58%, 60%
B – comprised of individuals with previous win rate of 48%, 55%, 56%, 58%, 60%
(this is just a random example for illustrative purposes. Two pretty good teams.)
Edit: Is there a way to start with a very simple algorithm and then see how it works? Maybe we could simply sum the percentages of each team and predict that the one with the highest percentage is going to win. Of course our classification would not be accurate, but over thousands of archived games we could see if we can predict better than chance.
Best Answer
Is it correct that you have not only those percentages but all the individual game outcomes as well? Then I would suggest the r package PlayerRatings. This package not only deals with problems like how to calculate player strength (using algorithms like elo or glicko), but offers functions that can predict future game outcomes as well.
For examples check: http://cran.r-project.org/web/packages/PlayerRatings/vignettes/AFLRatings.pdf