Normally a stiff arrow will fly tail right, weak tail left (for right hander). Sounds like you may be left handed by your description of your bow. If the strike plate is getting excessive wear that points to a stiff arrow. Problem with a stiff arrow is that it may fly nock left for you or may deflect off the shelf and actually fly nock right indicating weak.
If it is flying right sometimes, left sometimes, sometimes perfect...then there may be some issues with your form that need to be worked on first.
Maybe you are dropping your bow arm, collapsing on release, plucking the string...maybe you are so frustrated with tuning that you are doing all of these (ask me how I know
) What bow and arrow setup are you using?
Mike