The blog post, "How to Practical BM25 — Part 2: The BM25 Algorithm and its variables," delves into the intricacies of the BM25 algorithm, a widely used method for ranking documents based on relevance in search engines like Elasticsearch. The discussion begins with the mathematical structure of the BM25 formula, breaking it down into components such as query terms (q_i), inverse document frequency (IDF), term frequency (f(q_i, D)), and parameters like k1 and b, which influence how documents are scored. The post explains how IDF penalizes common terms and how document length relative to the average field length affects scoring. It also discusses the role of k1 in determining term frequency saturation, illustrating its impact through examples with varying k1 and b values in different document sets. The results show how these parameters influence the scoring of documents based on term frequency and document length, offering practical insights into optimizing relevance scoring in Elasticsearch. The post concludes by setting the stage for the final part of the series, which will explore considerations for selecting appropriate values for b and k1.