FWIW, many 10k+ user organizations are "around the world" as well.

Web apps for server cluster admins have customer bases evenly distributed across every time zone on the planet? Really?

There may not be a perfect time, but there are almost certainly better and worse times.

Maybe the differences are not big enough to justify increasing the probability of mistakes.

Granted. This is a much more reasonable response to the top of this thread than sanctimonious quoting.

See also scottyallen's comment here (http://news.ycombinator.com/item?id=1817378). If Google web search has (or recently had) such a thing as "peak hours," I'll hazard a guess that <your web app> does too.