Answering queries over a federation of SPARQL endpoints requires combining data from more than one data source. Optimizing queries in such scenarios is particularly challenging not only because of (i) the large variety of possible query execution plans that correctly answer the query but also because (ii) there is only limited access to statistics about schema and instance data of remote sources. To overcome these challenges, most federated query engines rely on heuristics to reduce the space of possible query execution plans or on dynamic programming strategies to produce optimal plans. Nevertheless, these plans may still exhibit a high number of intermediate results or high execution times because of heuristics and inaccurate cost estimations. In this paper, we present Odyssey, an approach that uses statistics that allow for a more accurate cost estimation for federated queries and therefore enables Odyssey to produce better query execution plans. Our experimental results show that Odyssey produces query execution plans that are better in terms of data transfer and execution time than state-of-the-art optimizers. Our experiments using the FedBench benchmark show execution time gains of at least 25 times on average.