That's a pretty common phenomenon with rifles that have some recoil.

In many years of building and shooting big rifles, I have to say, I have seen this kind of thing quite a bit. It’s a good idea to hold them firmly whenever you are shooting.

The rifle is starting to move as the bullet does. Don’t believe that old tail that “the bullets gone before the gun ever moves”. It’s not true!

So if you feather the rifle, or hold it gently, it’s possible to get good groups , if you are 100% consistent, but the group won’t be at the same point of impact as when the rifle’s held firmly.

As a rule, you should hold all hunting rifles snugly, from a 30-06 and up, in my openion..

Get a nice grip on them and develop the habit of doing the same thing every time.

I have a 375 that will outshoot most of my other rifles but it hits about 5” higher at 100 yds if you don’t hold on. I get much better results and tighter groups too (under 3/4 every time, and manytimes under 1/2” so this rifle is a real shooter) if I hold it firmly. If I don't I get about 2" out of it, and a hight group.