Suppose I want to know whether a baseball team's winning percentage the previous season or the Pythagorean expectation of that team from the previous season is a better predictor of next season's win percentage. (I take percentages because the number of games played per season has changed in the past, so it seems easier).
For each of these independent variables, there's good reason to suspect their will be a linear relationship with the dependent variable, so linear regression seems like it would work.
The dependent variable is always within the [0,1] interval, so logistic regression also seems like it would work. But the dependent variable isn't exactly a probability (well, I suppose it's the probability that the team beats an unknown opponent team), and it also never is actually very close to 0 or 1 (it's pretty much without exception between .3 and .7).
So, with all this in mind, which would be the more natural method to use, linear regression or logistic regression? Are they both valid approaches?