I am studying how well Kobe Bryant shoots and to do so I have run a logistic regression. The variable shot_made_flag is 0 if missed and 1 if he scored. And I am running the regression against distance from the basket.
logitshots <- glm(df$shot_made_flag ~ df$shot_distance, family = binomial(link="logit")) Call: glm(formula = df$shot_made_flag ~ df$shot_distance, family = binomial(link = "logit")) Coefficients: (Intercept) df$shot_distance 0.3681 -0.0441 Degrees of Freedom: 25696 Total (i.e. Null); 25695 Residual Null Deviance: 35330 Residual Deviance: 34290 AIC: 34300
As you see the coefficient of distance is negative. So what I do next is to compute the probability of scoring if Bryant is 1 meter farther.
To do so I have done it this way, but I get a positive effect, so I am not sure about it.
(exp(coef(logitshots))/(1+exp(coef(logitshots)))) (Intercept) df$shot_distance 0.5909933 0.4889768
So how would you interpret this? every 1 meter means a 48% more chances of scoring (Lol)? Is this approach the right one? I guess that Kobe scoring from 25 meters is very unlikely (maybe modelling by a quadratic function?)
I'd really appreciate any interesting insight and help! :)