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.