Smoke mentions wet feathers and that's true. More than likely you're going to shoot with a form problem sooner or later and a perfectly tuned arrow (bare shaft) is going to fly closer to the spot.
Matt mentions form problems and with this issue it could be the problem, but we can't address that without seeing the shot and maybe the hook. And I wouldn't rule three under out on a bad hook.
"I have my nock set at 3/8's." What the heck does that mean? And more importantly does it mean the same thing to 75% of us or a 100%. The following explanation should mean the same to 100% of us.
Put the t-square on the string and rest. Put your finger on the spot that's perpendicular to the rest. Put a nocked arrow on the string above your finger and then tie in your nocking point 1/8 inch above the nock. Now move the nocked arrow up to the just tied in nocking point. Tie in another below the nock just so there's a little up and down play. Leave the tag ends long, so they can be moved up or down. Then tightened and glued, when in the proper spot. For my style of shooting this is almost always good. Note almost.
Paper tuning is OK and it might be a time saver, but it won't tell you if the rear of the arrow hit the shelf.
Go to www.fenderarchery.com/blogs/archery-info/basic-tuning.
One of the things you'll see is the bell curve of a tuned arrow. If your arrow is at the top of that curve it will be more resistant to your form mistakes.
Back to nocking points. Look at the first picture of arrows in the target. It shows bare shafts above fletched. **This is important.** The nock on the bare shaft is below the point. This means your nocking point is too low. Here's the really important point. If the bare is above the fletched and the NOCK IS ABOVE THE POINT, the rear of the arrow hit the shelf making it kick up. Lower the nocking point.
YOu can shoot a 1000 shots through paper and it will never tell you that. One more point. If you have that point above the nock on the bare shaft, your really close. Move the nocking points up one strand of serving at a time.
While we're at it, go to the end of the link and read the best broadhead tuning advise I've ever found.
Bowmania