While competitive shooting at the Riverhead range donkeys years ago I noticed a really strange problem with my rifle. The first shot out of a cold barrel would strike about three inches high. Consistently. Every time I competed . The second shot would strike two inches high. Consistently. The subsequent shots would group together just above the crosswire in the middle of the target. Our competition rules in those days allowed us two optional sighters so there was no real issue, you just completed your required shots. It was a pain while you were hunting , you had to remember to allow for it with your aim. Knowledgeable club members had no real answer to the question. 

I happened to be reading an article by Jack O’Connor, the American guru, about hunting in Africa. He said don’t let the gun bearers clean you rifles, do it yourself. The reason he gave was that they would use an English cleaner which would make your rifle shoot inaccurately for the first couple of shots, generally high. I used the cleaner he mentioned in my rifles. I swapped to Hoppes number 9 and the problem went away. Have used it ever since. 

My competition 22 rifle showed a similar problem. My first shot out of a cold rifle would print about half an inch out, usually low and left at 25 yards. Consistently. All subsequent shots would print to point of aim. The rifle was seriously accurate, when you were holding them well there would be one hole for your prone shots. Just that weird first shot displacement. 

I don’t have any issues with my present rifles but I’m very careful to check any rifles I’m using in case they exhibit the same problems.  I think that one of the advantages of competition shooting is that to get maximum points you need to hit the middle. Group size is irrelevant, centre hits count. Issues such as first shot displacement or different methods  of rifle support causing different zeros can be evaluated if you are trying for centre hits.