Do search engines produce better results because their algorithms are better or because they can access more data from past searches? We document that the algorithm of a small search engine can produce nonpersonalized results that are of similar quality to those of the dominant firm (Google) for certain types of search queries. Overall differences in the quality of search results are explained by searches for rare queries, which constitute 74 percent of the traffic in our data. We conduct an experiment in which we keep the algorithm of a small search engine fixed and only vary the amount of data it uses as input. Our results show that giving small search engines access to more data about rare queries improves the quality of their results. This suggests that mandatory data sharing by large search engines is a necessary condition, yet probably not a sufficient one, to increase competition in the search market.