Google average calculation
How the Google average calculation is defined can be found in the Webmaster Tools utility support page, it is stated as follows:
To calculate average position, we take into account the top ranking URL from your site your site for a particular query. For example, if Johan's query returns your site as the #1 and #2 result, and Janne's query returns your site in positions #2 and #7, your average top position would be 1.5. You can view up to 90 days of historical data. However, you can only see change data for time periods of 30 days or less.
Due to this rather surprisingly limited window of data made that Google provides, any long term analysis is a challenge. Sure one could export the data each month, but then is it a bit of a hassle.
The simple, yet perhaps not obvious, automated solution is to use the data provided in the referrer string of each entry from Google SERPs to the landing pages of the website and store it in the web analytics solution used on the website. Each browser clicking on a link in a Google SERP will provide the positional data in one of the referrer parameters, that is if they are not using secure search on Google.
Decline of SERP rank over time
Based on the decline in SERP rank for the word webbanalys for the past 9 months (due to lack of website updates) the decline assumption appears to be correct as seen in the image below.
But that conclusion is easily proven wrong as the click frequency does matter, decline of SERP rank is not the same across all search terms. The more the search term is clicked the slower the decline is, analysis of larger number of search terms makes this evident.
However it is obvious that once the rank drops to ~7th position and lower, the decline increases as it turns out at that rank position being below the fold means your link is not visible and without the user scrolling it will not be visible.
Thus the odds of a search term being clicked on become minimal, any search term below the fold will have a far harder time getting a click than those above it.
Google secure search limits visibility on SERP rank
It has been for a while, ever since Google secure search appeared, impossible to obtain correct data on SERP rank of an increasing volume of search terms as the referrals from a secure search contain no useful data. Apparently only websites using Google Adwords have that information, this making it apparent that the claim that secure search provides user privacy is bogus. But as things are currently this is not likely to change.
But there is still enough data flowing in to allow for analysis of SERP rank for now. Perhaps it is time for all website owners to start sending Google a message for each "search term not provided" referral...