It is probably at least that complex - if not more. As early as 2005, Google's Historical Data Patent [webmasterworld.com] detailed many many factors. It was in many ways a ground-breaking patent and it rocked the SEO world.
Here's just a taste:
Consider the example of a document with an inception date of yesterday that is referenced by 10 back links. This document may be scored higher by search engine than a document with an inception date of 10 years ago that is referenced by 100 back links because the rate of link growth for the former is relatively higher than the latter.
While a spiky rate of growth in the number of back links may be a factor used by search engine to score documents, it may also signal an attempt to spam search engine. Accordingly, in this situation, search engine may actually lower the score of a document(s) to reduce the effect of spamming.