No, only rated games will affect the time per move statistic.
Unrated games and time/move
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BorgQueen wrote:
On that, if I stop playing for a month, will my time per move go up since I am not playing moves? Or is that statistic actually intelligent enough to not penalise someone's "move speed rating" while they take a break from playing and go and do some study... or play more live chess?
I'm actually quite a fast mover, but because I take non-playing breaks I believe this "statistic" might become very inaccurate.
Time is counted when a move is made.
Unrated games do not change one's rating
Are these games including in the "time/move" calculations?