Rick says that if your off arm swings down and away from your body on the side, that will force your shoulder to open up too early; and you will get less wrist snap on the ball.
He says watch most all the pros “tuck” that off arm toward their chest, which allows them to stay closed longer and get more snap.
I tried it this morning and, while pretty distracting early on, my opponent said that my serve did have a lot more pop to it. Note: in this picture, you can see that i have another problem that Newk has pointed out to me at camp … i open up my hips too early!
Ask a friend to watch when you take warm up serves and tell you where your off arm is going. Worth a try.