How can I (Should I?) use logistic regression/the logit function to predict outcome of a tennis match in a simple simulator?

Question

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?

Answer 1

I'm not quite sure I understand your approach or the problem you are trying to solve.

Seems like the only way your "hot streak" effect can exist is if players change their strength level overtime (meaning you can't just characterize their strength by taking an average of their strength). Is this the question you are really asking? Otherwise you need to define the "hot streak" more.

However one thing to note is that you can absolutely extend logistic regression to the multivariate case, so you may not have to do the "difference in strengths" thing. You can actually just have the two strengths as separate parameters.

Logistic regression is really just a form of linear regression. You are finding a function that takes in inputs x, and predicts the output P. The output P represents the two outcomes, win and lose. The logistic function takes the form:

P=\frac{1}{1+e^{-\omega x + c}}

If you extend it the multinomial case, x is just a vector of parameters and you are looking for the weights \omega and c

It seems to me like you need to do the following:

1) Train using existing statistics about strengths of the two players and the outcome of the game to find your \omega and c. You can add more parameters you want even stuff like weather, etc. if you have enough of it

2) Use your random generator to find the strengths of your two players. Not sure if this distribution should be completely normal, since the strength distribution of tennis players is not normal (you have a bunch of people who are mediocre and then a few extraordinary players and not really any terrible players). Then use your logistic function to simulate outcomes of the games.

3) Record the number of hotstreaks

If you provide more information on where you are confused I can try to help more.