Methods, systems, and apparatus for automatic sharding and load balancing in a distributed data processing system. In one aspect, a method includes determining workload distribution for an application across worker computers and in response to determining a load balancing operation is required: selecting a first worker computer having a highest load measure relative to respective load measure of the other work computers; determining one or more move operations for a partition of data assigned to the first worker computer and a weight for each move operation; and selecting the move operation with a highest weight the selected move operation.