Try this:
On your right leg, do a full range of motion single legged squat (pistol). Here is a guide if you have never done it before.
http://www.powerathletesmag.com/pages/pistols.htm
Now, do it on your left leg.
Does it seem to be easier on one leg than the other?
For some reason, pistols on my right leg are easy, compared to pistols on my left leg, where I often fall off balance or struggle.
I think it may have to do with basketball and jumping. I played basketball A LOT in the past 4 years and I've always been jumping off my right leg. I think that has contributed to the growth of muscles in my right leg and make pistols easier for me. But all that jumping from my right leg has left the left leg behind in development. Thus, making it harder for me to do pistols on my left leg.
This has further implications. If my right leg is stronger than my left, wouldn't that make my running stride less than optimal? Wouldn't that make my lateral movements lean towards one direction? I never noticed it before, but then again I didn't realize my left leg muscle imbalance was severe enough to see a major difference by doin pistols.
What do you think?