I stopped using stats programs that look at the raw stats like AWStats for pretty much that reason. Now I use a mix of Jetpack and Google Analytics. Jetpack for quick stuff and GA when I want to dig a bit deeper.
As far as hits on wp-login, I installed the limit login attempts plugin and let it do its thing. One thing I've noticed is that every single attempt that it flags as invalid is trying to login with the username admin. So, I make sure I'm not using that as a username.