Given that google records a history of a browser and changes your serp results on that , it changes on your proximity ( yes even for organic results ) and that google also traces an ip ( this can be your own or a tools proxy ) that is constantly checking your site , it does whats called Google dance, it will throw up your rankings , and see your reaction if you try to spam it with new links or do nothing.
Google HATES automated tools especially rank trackers , they can track time btween queries , if it follows human behaviour ect ect.
Lastly google results also work on trends if you are searching rock celebrities today you might get a article on oprah ( because for some reason a ton of people looked oprah up directly recently ) The next few days that can change. THere is absolutely no certian way of saying i rank one two or 20 . Even the device used affects your ranking. Your best bet is to filter results to your country , or town on gwt and use that average position. Traffic is always also a very good indicator of ranks.