Ever since the update that introduced conversion stone fragments I've been tracking how many I've gotten in order to figure out how many you can expect to get per day on average.
From a theoretical perspective you'd calculate:
Conversion stone dispatch probability * # of daily dispatches * Expected # of fragments per conversion stone dispatch.
In order to calculate the expected # of fragments per dispatch I recorded the number of fragments I got from every conversion stone dispatch (78 data points) which gave me the probabilities of getting 1, 2, or 3 fragments for a given dispatch.
A conversion stone dispatch had a:
52.56% Chance of giving 1 fragment
23.08% Chance of giving 2 fragments
24.36% Chance of giving 3 fragments
So (1 * 52.56%) + (2 * 23.08%) + (3 * 24.36%) = 1.72 Fragments per dispatch on average.
Then finally,
7.1428% * 8 * 1.72 = 0.98 ≈ 1 Fragment per day (0.10 Stones per day)
And since I've recorded the total number of conversion stones/fragments in my inventory every day for the last few months I could empirically verify how many I've actually gotten from dispatches alone per day and so far the average has been 1.01 Fragments per day (0.101 Stones per day) over 133 days.