Would it be safe to assume an approximately normal distribution for a given player's APM rating in all/most APM regressions?
For example, from http://www.gotbuckets.com/statistics/apm/2014-apm/, would it be safe to say that the distribution for each player's APM coefficient is normal with mean "Combined APM" and variance "Std. Error"^2? In other words, a 95% confidence interval for each player would then be ("Combined APM" - 2*"Std. Error", APM + 2*"Std. Error").
Or could each players' coefficient distribution be significantly skewed?
My guess is that collinearity could be the biggest factor that might skew distributions. How garbage time and players with very few possessions are handled might skew distributions as well. If so, a way to quantify this effect would probably be very useful, as the value of a player whose APM coefficient is approximately normally distributed with mean +X and std error Y is different than a player whose APM coefficient has mean +X and std error Y, but a skewed distribution for that coefficient.
What does everyone think?