1. A computer program product to control event logging and error recovery in a system including adapters, ports, and channels, the computer program product comprising: a computer readable storage medium having program instructions embodied therewith, the program instructions readable by a processing circuit to cause the processing circuit to perform a method comprising: storing, in a memory device, a recovery threshold for each event type among a plurality of event types, each event type indicating a type of error or interrupt, each recovery threshold for each event type representing a first number of events of the event type; storing, in the memory device, a level-specific logging threshold for each event type, each level-specific logging threshold for each event type representing a second number of events, a third number of events, or a fourth number of events of the event type, respectively, at an adapter-level, a port-level, or a channel-level; implementing event handlers for each of the channels, the ports, and the adapters of the system, each event handler being associated with one of the channels, one of the ports, or one of the adapters, each event handler identifying events corresponding to the respective channel, the respective port, or the respective adapter; and implementing a threshold manager for the events identified by the event handlers based on the level-specific logging threshold and the recovery threshold for each of the respective event types of each of the events, wherein, for any identified event corresponding with a given event type, the implementing the threshold manager includes considering the recovery threshold and the level-specific logging threshold at every level regardless of a level at which the identified event is identified.