This is an interesting thread....
I don't group that well either but then I have only been shooting archery for 2 going on three years. A couple of things I've learned are:
1) Do not squeeze the bow as you're ready to shoot. I was always gripping tight and my brother noticed this and told me hold the box steady but not squeeze the fingers tight.
2) This year I learned that I sometimes pull my string towards me with the release - not just straight back. This explains why I would constantly shoot to the left. (I'm left-handed by the way) I kept thinking this was caused by my sight so I kept adjusting it and got the same results. Now I know not to 'pull' the string and the arrows fly straight.

Just my two cents...let's hear more from others.....