That minimum and saturating no. of rounds do only vary between players if there are other influences accelerating the process.
As a TM, it is 50 rounds, as a Legend and TL, 500 rounds each.
+1 to BTB for an unsaturated average, but after saturation the highest scores will be kicked out of the equation by better scores, allowing for a possible average drop even if the new score is higher than the average.
@alexia, the high number of scores might result in average drops so small (third digit) that you won't see it in the two digit display.