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I effectively want to model the probability of a player winning his service point (a point in which he is the server) based on the values of explanatory variables (namely court surface and opponent world ranking)

Can this be done using a binary response logistic regression?

Consider the fact that I can view my response variable as number of successes out of a total number of trials (for which I have the data). Will it work considering I have both categorical and numerical explanatory variables?

Any feedback on why this will/won't work or how I can make it work would be hugely appreciated! I am doing the analysis in R, so pointers on functions or packages would also be welcome!

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  • $\begingroup$ What does "service point" mean? $\endgroup$ – Sycorax says Reinstate Monica Jul 30 '15 at 17:12
  • $\begingroup$ You may want to separate "offensive ranking" and "defensive ranking". John Isner vs. Novak Djokovic would be an interesting duel: the latter tends to win his return points rather than his service points, and that's what makes him a huge outlier relative to his service performance (on which Isner would beat Djokovich). $\endgroup$ – StasK Jul 30 '15 at 17:26
  • $\begingroup$ @user777 by a player's service point (or game) I mean a point in which the player in question is serving. $\endgroup$ – Stevie Kvothe Jul 30 '15 at 17:30
  • $\begingroup$ @user777: For a given player, I have the point by point data for hundreds of matches. So take Nadal: 250 matches, each with on average 100 total service points i.e. trials, with (on average) 75 winning points i.e. successes. Does this affect the logistic regression? Specifically, i'll have approx. 25000 observations in total for my dependent variable, each with an outcome of win/lose (0/1). My worry is, each group of 100 of these observations will relate to a certain combination of dependent variables: court surface and opponent world ranking. Does this affect the validity of logistic? $\endgroup$ – Stevie Kvothe Jul 31 '15 at 8:46
  • $\begingroup$ Include court surface as a feature... Not sure about ranking, though. $\endgroup$ – Sycorax says Reinstate Monica Jul 31 '15 at 12:48
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It appears that there are only two outcomes in this situation: either the server gets a point or he doesn't (yes/no). As long as the Response Variable only has two possibilities (yes/no, 0/1, etc), logistic regression will work (under most conditions).

The explanatory variables don't have any restrictions, they can be either numerical or categorical. Just make sure you're sample size is large enough to provide accurate results (it's good practice that each yes/no in the response have a number >10*(p-1), where p is the number of covariates + 1 (for the intercept)).

There requires some set up in R to get your data transformed into usable form for glm to read it, but the glm(,data, family = "binomial") is a good starting point.

Here is a good tutorial/article on how to set up Logistic Regression in R Here

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  • $\begingroup$ For a given player, I have the point by point data for hundreds of matches. So take Nadal: 250 matches, each with on average 100 total service points i.e. trials, with (on average) 75 winning points i.e. successes. Does this affect the logistic regression? Specifically, i'll have approx. 25000 observations in total for my dependent variable, each with an outcome of win/lose (0/1). My worry is, each group of 100 of these observations will relate to a certain combination of dependent variables: court surface and opponent world ranking. Does this affect the validity of logistic? $\endgroup$ – Stevie Kvothe Jul 31 '15 at 8:46
  • $\begingroup$ In logistic regression, your response variable/dependent variable has to be categorical, AND the response must have exactly two categories (i.e. its binomial). There are cases where it can be multinomial, and a quick search on here or google can help you find some information. I think in your last sentence you meant to say "independent" variables. Assuming you did, this is the whole purpose of a logistic regression: to take in a combination of independent variables (categorical or numerical) and to give you the probability/odds of success or failure. Does this help at all? @StevieKvothe $\endgroup$ – Jake Jul 31 '15 at 13:19
  • $\begingroup$ I actually realised after posting that I was pretty much describing the function of a logistic regression, so apologies for that. Was just confused by some differences between my case and examples I have seen elsewhere, but I get the picture now. That helps greatly, thank you so much for your help! $\endgroup$ – Stevie Kvothe Jul 31 '15 at 13:28
  • $\begingroup$ No problem! Glad to help. $\endgroup$ – Jake Jul 31 '15 at 15:43

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