Relevant showcases 100% accurate search results for any search query, but does not consider engagement data to determine the sort order of the search results. Hence products are only sorted by the keyword relevance and position of the words of the query in the product table.
Bear in mind almost 80% of your visitors will not scroll more than 3 pages at any product listing page, hence showing the best products (Using engagement analytics) for that segment increases your probability of conversion. This visitor behaviour increases on mobile, where they are filled with distractions, hence whats is not on top is not on their mind.
But if you were planning on using an open source engine like Elastic Search, SOLR etc., Relevant Search from Tagalys is a better option as it will save your hundreds of hours of setup, show you 100% accurate results.
You can find our pricing details here - http://www.tagalys.com/e-commerce-search-pricing
Please read our SLA to know our support for Free plans.