Calculating a true related posts algorithm in WordPress is often associated with poor performance, but Yoast is introducing a different way in an upcoming release of the commercial version of the Yoast SEO plugin. The method they are using is to utilize the existing browser-based content analysis tool they already have in Yoast SEO, but for internal linking purposes. They've found it reduces, “the heaviness of the queries needed to find related content.”
Internal linking and the related posts algorithm should provide a good additional incentive for Yoast SEO users to upgrade to the commercial version, which thus far is primarily marketed via its redirection tool and user support. It's such a huge plugin that they've done very well without major feature incentives, so I'll be curious how much they improve conversions by adding internal linking to the commercial version.