Provided are a computer program product, system, and method to use data set copies for recovery of a data set in event of a failure. In response to an update to the data set, a determination is made of an update group to include at least one copy of the data set that was not in a last determined update group to which a previous update was applied and to exclude at least one copy of the data set that was in the last determined update group. The update to the data set is applied to the copies of the data set in the update group and not applied to the copies not in the update group. In response to a failure event, the data set is recovered from one of the copies of the data set in the update group or not in the update group.