AlliumCepa: a graph is just a series of results, so my formula could certainly be graphed if you want to show history.

It isn't meant to be clairvoyant, so while doubling the number of games *may* not mean twice as slow, it's the best guess with the available data. Of course you could discount time where no moves are available if you want to be more accurate -
moves made / time with at least one move available, over, say, the last month.

"moves per day" = moves / days. It *is* an average. Otherwise I would say "moves made today" or something like that.

Some considerations:

Whatever metric is chosen, there ought to be one for each type of game, or the games should be broken into categories. Ludo can be played in an instant but chess can take a while to ponder. A moves per day metric could penalise someone who likes to bash out a game or two of Ludo if they ponder long and hard in their chess games.

The metric also needs to be computationally cheap. If, like a moving average, it requires a fair bit of data manipulation per move then it's probably not a good idea. If, like a graph, it requires a lot of storage, ie. values for each move, then it's also very expensive. Bear in mind that the ratings graphs are just a couple of data per match. The utility/cost value for the speed graph would be very low, for all that it's an interesting graph at times.