Over this hill

My hill repeats went fairly smoothly today. I found myself cramping after the first lap so I had to stop and stretch. I think my pre-run stretching routine needs a little work. The last few times I've run outside, I've had to stop to stretch again after the first mile or two. I timed my laps today since I had some sort of reference point. It was an average 10min/mile pace and my laps got quicker as I got the hang of it. This hill will be perfect for the majority of my hill repeats over the next few weeks. Unless I get bored, of course.
Why is it that once I get close to or past the halfway mark in my workout, everything just seems to get easier? I start to open up my stride and pick up the pace. It seems more like liberation than torture. This is when I love running. My legs/joints will be a little sore and I'll feel like I want to stop, but with every step I take, my confidence grows. I find myself at the end of a run sweaty, sore, fatigued and wanting more (just a little).
I'm pretty sore, but it's only muscle aches (no knee pain!), so I'll just have to stretch more before tomorrow's early morning run. I found a dynamic stretching routine on the Runner's World website and I can't wait to try it out!