A data processing apparatus has processing circuitry for performing processing operations including high priority operations and low priority operations, events occurring during performance of those processing operations. Prediction circuitry includes a history storage having a plurality of counter entries for storing count values, and index circuitry for identifying, dependent on the received event, at least one counter entry and for causing the history storage to output the count value stored in that at least one counter entry, with the prediction data being derived from the output count value. Update control circuitry modifies at least one count value stored in the history storage in response to update data generated by the processing circuitry. The update control circuitry has a priority dependent modification mechanism such that the modification is dependent on the priority of the processing operation with which that update data is associated.