[mikeash]

That makes no sense. It's never advantageous to ditch the first stage while it's still producing thrust. At some point when designing a rocket, it's better to add performance to the second stage rather than the first. But when presented with an existing rocket, you'll achieve maximum payload capacity by burning all fuel in the first stage before staging. Every second it burns is more delta-v imparted to the payload. The only reason you'd stage early is if you want to save fuel for e.g. a landing attempt, if the first stage is too powerful and the acceleration or speed would become too great, or if you simply don't need the extra performance to get the payload to where it's supposed to go.