Projecting Win Probabilities in Fantasy Sports
So, I made it to the finals for my fantasy football league. The winner receives $100 and the runner-up $10 (maybe disregard this runner-up reward for simplification). I wanted to know how to calculate an offer to both teams, based upon the probability of winning, such that any risk-neutral player would accept.
I believe once odds or a percentage of winning the week had been put in place, each team would get the expected value of their winnings. So, if the outcome was 50/50, risk-neutral players would accept a deal of $50 each before the game was every played.
Now computing the odds is where I'm getting caught up. Each week, the league will provide a projected score for each team, which is relevant to players involved, opponents faced, health status, etc. These scores are seldom accurate. So, I noted the absolute value of weekly differences between projected and actual scores for both teams. From there I found the variance and standard deviation of this statistic.
I was thinking that given the variance of the league's projections and given the projection for the championship week, you could ascertain some long-run average score for the week, for both teams. Once you had done that, you could create odds that informed the expected value of winning the $100. (Note: must assume that the league's projections are independent by week and not conditionally updated). Does this sound like it's going in the right direction? Any advice or experience?