You might want to keep some of your stats on a spreadsheet on your own. As you move up in tier, changing tees, green speeds + equipment, the stats are cumulative from the very beginning. They do not differentiate or reset once you start a new tier.
Be aware, too, that your "average" does reset at each tier but it does not not include every round. It is only an average of the best X number of rounds at a tier and high scores will not be considered once that X number has been reached.
I noticed recently that the average distance to the pin stat for CTTH games is also not taking high scores into account.