Constellation36: In order to be clear about my:
like the tendency of "moves per day" (and yes this is an average obviously :-) ) when the number of games change, which is what you want.

"Moves per day" is an average as it is just a sample arithmetic mean(average) if we don't use all the active days the player has played games.

I guess your argument comes because actually when we speak about "moves per day" for a specific day and this is how you meant it i guess, that you mean "moves per 1 day" or moves that have been played in a specific day, so actually we divide by 1 so there is no actual average(mean).
And indeed if we speak about 1 day there is no real point for speaking about average, BUT mathematics are mathematics and definitions are definitions. :-) So "moves per day" for a specific, 1 day, it is an average(arithmetic mean). A trivial one.

It becomes non-trivial and worthful when we speak about "moves per day" over a period of time so if we have played 500 moves over 50 days we find the average 500/50 = 10 moves per day.