All of my HHA bows like arrows weaker than you might think. I would start out by checking for spine problems.

I have noticed that if I crank the top of my bow just a little to the right instead of to about 2o'clock position, my arrows go left as well. When you shoot with your bow cranked over to one side or the other, it alters the dynamic spine of the arrows which can result in arrows behaving as if they are too stiff or too weak in spine

4" left is not much.  I never read if they were flying clean or flying loggy.   A slow recovering shaft on a non-center shot bow can have more contact regardless of spine.  The first thing an arrow does on release, with a non-center shot bow, is flex into the bowstring path.  With a slower recovering arrow there is more bend into the bow and sometimes more contact as it goes around the bow.  When an under spined arrow breaks on a longbow, it usually breaks against the belly of the bow, that is a lot of contact. (Some say it is the rolling action of the the finger release, I have seen the same reaction with a caliper release in slow motion video, taken on my own yard.)   Canting may change things some, mostly just the visual.  Arrow maker Bob often refers to checking to a straight vertical line on the target, a friend came up with a one step up from that test.  A bright yellow stretch line from the top center of the target, nail in my garage, down the 5 foot slope of my backyard, to the 22 yard curb, then stand in the middle of the roading lining his arrow to the string with his natural cant.  He was attempting to find where his secondary aiming point would visually land, but it was a great tool to check for arrow  drift. 

If you feel like you are properly tuned up, check your form.  I have a bad habit of overdrawing and then settling down into my anchor.  If I start shooting left, I am usually overdrawing the bow slightly and turning my head back to the string rather than keeping my head straight and pulling straight back to the corner of my mouth.  Any little thing in your form can change things up...

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