1. A system, comprising: one or more processors; a memory coupled to the one or more processors; and a plurality of storage nodes; wherein the memory stores program instructions that when executed by the one or more processors cause the one or more processors to implement a distributed database service; and wherein the distributed database service is configured to: receive a request from a client to create a table having a pre-defined amount of throughput capacity for receiving and servicing requests to perform database operations that target the table; create the requested table, wherein each item in the table is accessed using a hash of a respective primary key value for the item, and wherein in creating the table the distributed database service is configured to: divide the table into two or more partitions, wherein each of the two or more partitions is stored on a respective one of the plurality of storage nodes, wherein each item in the table is stored in a particular one of the two or more partitions based, at least in part, on the hash of the respective primary key value for the item; and provision a portion of the pre-defined amount of throughput capacity on each of the plurality of storage nodes on which one of the two or more partitions are stored; receive and service a plurality of requests to perform the database operations that access items in the table, wherein each of the plurality of requests includes a respective primary key value; and send to the client a representation of a skew metric based on accesses to the table during servicing of the plurality of requests, wherein the skew metric indicates an amount of deviation from a uniform distribution of the accesses to the table across the primary key hash space for hashes of the respective primary key values included in the plurality of requests to access the items in the table.