1. A system comprising: one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising: receiving a query prefix from a user; obtaining query completions for the query prefix, each query completion having a respective ranking score, the query completions having a first ranking based on the ranking scores; obtaining a reference query for the user; identifying matching user activity sessions, the matching user activity sessions being user activity session that each include an occurrence of the reference query; identifying one or more likely queries, the likely queries being queries that occur in the matching user activity sessions, wherein each of the likely queries is associated with a respective likelihood score, wherein the likelihood score represents a likelihood of the likely query occurring in the matching user activity sessions relative to a likelihood of the likely query occurring over all user activity sessions; designating, as a matching query completion, a first query completion of the query completions that matches a first likely query of the one or more likely queries; boosting the ranking score for the matching query completion by an amount based on the likelihood score associated with the first likely query; determining a modified ranking of the query completions using the boosted ranking score of the matching query completion; and providing the modified ranking of the query completions in response to receiving the query prefix.