In addition to the default TF-IDF similarity implementation, other similarity implementations are available by default with Lucene and Solr. These models also work around the frequency of the searched term and the documents containing the searched term. However, the concept and the algorithm used to calculate the score differ.
Let us go through some of the most used ranking algorithms.
The Best Matching (BM25) algorithm is a probabilistic Information Retrieval (IR) model, while TF-IDF is a vector space model for information retrieval. The probabilistic IR model operates such that, given some relevant and non-relevant documents, we can calculate the probability of a term appearing in a relevant document, and this could be the basis of a classifier that decides whether the documents are relevant or not.
On a practical front, the BM25 model also defines the weight of each term as a product of some term frequency function and some inverse document frequency...