I am trying to create a tennis simulator. Specifically I am trying to make a 'random' simulator so that I can see how many times streaks of wins or losses occur, and then compare this to historical data to see if 'The Hot Hand Effect' exists or not. i.e. Do streaks of wins or losses occur more or less often than would be expected by chance.
I create a pool of players and assign them a strength score between 0 and 10 from a normal distribution of mean 5 standard deviation 2.
When I come to matching up players and deciding the outcome, my supervisor suggested using a logit model/logistic regression. I am not quite sure how this would work practically/mathematically though. I thought to somehow use the difference in strength scores of the two players with the logit function to give me a probability to put into a cointoss, with the probability of a head, i.e. a win for Player A, being equal to the logit model output. 'Somehow' is obviously very vague as I do not know how this would work, or even if it mathematically makes any sense. Does what I intend to do sound valid conceptually? How do I use the strength scores with the logit function to get the probability?