I agree the two things are probably not related, but I don't really want them separated in terms of the statistics for the player.
Those disruptive situations, like internet problems, doorbells, and the occasional bombs going off, are not the types of issues that cause someone to go over time on a turn-based game. People who run over time on turn-based obviously don't have the time availability to get on here everyday, as opposed to a short delay. And people who run over time all the time on turn-based are more likely to just disappear altogether. And people who disappear either never return to the site, or they don't get what turn-based is and dismiss the game. (In my experience, it's never been because they were losing.)
However, I have no desire to separate the stats. People who are slow on turn-based games really don't have time to be playing them, and while that is a totally different issue than someone who has internet problems, there's still an issue going on there. I'm not much concerned about which issue it is.
Jest is making a good point that anyone can have the occasional problem, and the ones we need to be concerned about are the habitual ones. If it's habitual, what difference does it make why? If your internet connection is that bad, or you find it impossible to ignore the texts coming in, then don't take live games. If you can't be on here, don't take turn-based games. Either way, there's some issue going on that causes it to be more than an occasional problem.
Although honestly, in the end, someone being over-time a bit is really not my biggest concern. If someone gets ridiculously too slow, I'll make a note on them. I'm more concerned about people who abandon games.