In my previous blog post I wrote that I was feeling the call of the swarm. I feel horrible.
Nevertheless, I've been reading the Zerg strategy section on Liquipedia (because nobody answered my question in the previous blog post about whether or not it was worthwhile to do so, so I assumed that it was)... and when I came across this passage...
When to Build Your Next Hatchery: When a Zerg player has determined that it is best to play with X Hatcheries, (let us say that X is six in this case, and that it's a ZvP in which the Protoss has two bases), the question is, when should Zerg build their next Hatchery? Zerg should always build their next Hatchery as soon as possible, as long as none of their current Hatcheries are at three Larvae. In other words, if the Zerg player lets all of his or her current Hatcheries run idle until all current Hatcheries have three Larvae each, will the Zerg player have 300 Minerals by that time? If so, then the Zerg should make another Hatchery. If not, then the Zerg player needs to build more Drones.
... I decided to find out where this point was with the Zerg in SC2.
The magic number of Drones necessary to get to 300 minerals is 12. 11 Drones will get you to 285.
So by the BW logic, in SC2 the most optimal time to build another Hatchery (note that I didn't say expand) is when you hit 12 Drones. I would guess that Drone #13 goes to Pool and Drone #14 goes to make another Hatchery... or an Extractor then Hatchery.
I don't see the pros do this, though. I watched some Dimaga replays and he always gets his Pool and Extractor on 15.