I don't do on-call any more but I use to be on-call at night with the rest of my team incase the servers went down or had any issues. The hardest part about this was there was no schedule or communication, so if someone was already starting to fix the issue(s), you may not always have known it. My piece of advice for on-call teams is to make sure you have some form of schedule and communication about these issues. It can make a huge difference when working together to solve problems.
A rotation with a schedule and a plan for communication are critical.
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