Can somebody guide me to the source for the number of moves on 19*19, 13*13 and 9*9 boards respectively? From the explanation on the Wikipaedia handicaps page, these are (approximately) 275, 108 and 45. That is, a full-size game lasts 20% longer than a 13*13 and a 13*13 lasts 15% longer than a 9*9 game.

This could be because there are more local situations to be resolved on the larger board but it could also be because the ratio of board sizes is not linear (19, 13, 9). Taking the average (or sum) of the board areas and of the average number of stones played gives a scale factor of 2 (for 13*13) or 4.5 (for 9*9). This is closer to the scheme proposed by Ishikura Noboru which we used in a recent competition..