Performance difference between day and night

We are in the utility industry and every outage, we do a copy and a baseline of our outage project once daily and once overnight. The problem is that our nightly baseline and copy consistently takes 2-3x as long to complete as the daily baseline and copy. Why is this?

Our DB Index and stats jobs generally run in the early evening, before the overnight baseline and copy. Maybe that's it, but I'd think it would be faster AFTER the index and stats are run, not slower. We monitor database traffic through Oracle EM and this will happen even with no difference in db traffic. We have moved competing jobs to other times. We had the database server guy monitor one night and found nothing unusual. We checked network traffic - nothing unusual.