Looking at my rankings through the API and by web, I notice that changes in ranking often "stutter" between valus, and then "settle in." So, for example, I'll be 9 for two weeks in a row, then 4, then 9, then 5, then 9, then 4 for two weeks. Sometimes it goes on for much longer than that. API results also often differ from web results; immediately re-requesting by either medium does not cause the results to change.
My question is: What is known about Google propagation? How long does it usually take? Is it a predictable process? Are API results biased toward the future, or past? Do certain areas of the country see changes sooner?
What's the current state of knowledge?