Generally speaking, search engines use algorithms to index websites and rank them in the SERPs. These algorithms run a keyword search on all the sites in their index. They also take into account user experience and engagement.

These systems use different formulas to come up with a final score. They are probabilistic and decoupled development. They are largely based on complex models. These systems are often stacked ensembles of multiple sub-models.

The simplest is the pre-ranking stage. In this stage, Google takes into account site architecture, user experience, and user engagement to determine what each page is about. This includes taking into account the theme of the site and placement of the menu.

The ranking stage is a bit more complicated. It is based on a model that has been trained on logs of query, doc and pair with label as human judged relevance. This model is typically not as accurate as it could be and thus not chosen for impressions.

The multi-stage ranking system is the most complex and most likely to be error prone. This is because of the sheer number of classifiers involved and the fact that training data is expensive. In addition, these systems are a pain to debug because of their chaining of classifiers.

The cascade architecture is a clever way of achieving the aforementioned feat. This design meets the constraints of computational cost and latency. It is also the most elegant of the multi-stage ranking systems.