Your average score is calculated from your best x number of ranked rounds in your current tier.
Pro : *20 rounds
Tour Pro : *25 rounds
Master : *40 rounds
Tour Master : *50 rounds
Legend : *500 rounds
Tour Legend : *500 rounds
Therefore once you have played the aforementioned number of rounds your average will no longer increase, it will either remain static or go down.
When you move up to a new tier, your score will reset and your first round in the new tier will reflect that, sometimes it might change by a large amount depending on your first round score and that is what confuses some people.
* the values quoted in this post may not be correct.