# A Regression to predict tennis player's service point win percentage - Which of these two models makes more sense?

I am conducting a regression in order to predict a tennis player's service point win % i.e. the percentage of points he wins when he is the server. Model 1 If my DV data lies in the range 0.3-0.9, does it make sense to use a logistic regression? If using logistic I would endeavor to build a model with serve win % as my DV and my IV's as:

+average serve win % of last n matches (maybe n=5 or 10) to account for form

+surface

+player ranking

+opposition ranking

..... Would this be a good model to use? Preliminary logistic regressions just involving serve win % regressed on surface + player ranking + opponent ranking ... are showing some strange results so im losing faith in logistic for this data.

An alternative I'm considering is to use raw variables in a linear regression type model with interactions.... Along the lines of Aiken & West 1991 My dependent variable will be number of service points won in match, and my independent variables will be:

+no. service points played in match +the surface the match played on

+the player's ranking points +the opponents ranking points

+an interaction between player and opponent ranking points

+an interaction between surface and no. points played

+average service points won in last n matches

+average % of service points won in last m matches

Do either of these models stand out as smart or appropriate ways to model this data? For context, for each player I have between 100-350 matches worth of data. I would love to hear what you guys think, or if you have any other suggestions on how to predict serve win % using the stated variables I would really appreciate it. I'm conducting this analysis in R so any code/package suggestions would also be great

• What are the strange results you are referring to? Also, you may wish to link to the paper you cite. Aug 11, 2015 at 3:56
• @ChristophHanck For my avg. serve win % in last n matches variable, I wanted to standardize serve % based on surface and player rank/opponent rank for all of my data, for better accuracy - so I needed to gauge the effect of surface/rank I ran simple linear and logistic regressions along the following lines: serve win % = surface + player ranking + opponent ranking I also ran these IV's in regressions of their own. The linear model results were pretty much as expected and were accurate/in line with tennis knowledge/theory. The logistic regression results were pretty wild and inaccurate. Aug 11, 2015 at 9:15
• @ChristophHanck when I say wild and inaccurate, I mean that implied huge swings in the effect of each surface.... Coefficients that didn't really make sense with the data..... For example - mean clay court serve % is 60% and mean overall serve % for all surfaces included is 63% The logistic regression that when all other variables = 0, the clay category (reference) would equal 40% or so.... This is way off. I think I'm interpreting the coefficients correctly... Is there any issue with binary dependent variable and categorical + numeric independent variables in logistic reg? Aug 11, 2015 at 9:19