Not competing, and mostly doing nautilus stuff that doesn't involve getting out from under a bar. I wouldn't want to do squats (or a lot of other free weight exercises) to failure without a spotter. I'm actually glad to hear it's not necessary to go that far to make good progress, because I was a litle iffy about exactly that.
As far as the sports I play, it's absolutely true that quickness is far more important, but that's something you develop with practice at the sport (or exercises based on the sport), mostly. Yeah, if lifting was taking that away, I'd be concerned, but so far that's not a problem. Note, I'm playing at a "rec league" level in both sports, I have never been, nor to I expect to become semi-pro or anything, and I'm coming back from a multiyear couch potato layoff -- still about 40-50 lbs. overweight. My upper body in general is not that strong (my bench 1RM is probably around 170-180 and I weigh 250), and I feel it when I go into the paint in bb, and in my delts and lats in rb. There's a lot of twist muscles there that get strained after a match with good players where I have to hit hard to be competitive, especially in the backhand where my form isn't quite as optimal. I'd like to get some of those strong enough to take the pounding better.
Anyway, suggestions are always welcome, and I'm going to try taking it a little easier and see if I can go back to every other day training. A couple of my exercises were going backward in reps, so I figured I was overtraining and should go less often. But maybe if I'm not pushing so hard it'll be better.