What is the economic effect of the extractor trick at 14 supply in Legacy of the Void?
Solution 1:
According to Resources - Liquipedia a drone gathers 55-60 minerals per minute. Let's take the average of that and say it is 57.5. This equals to ~ 0,96 minerals per second.
One worker on one mineral field gathers 55-60 minerals per minute (80-85 for gold minerals), depending on distance.
As you said the cost to delete an extractor is 6 minerals (~25% of 25) + the lost mining time for let's say a second. => so the cost in total is ~7 minerals.
Let's have a look on the first situation that you could use the extractor trick. Let's assume that we do it one time with the above cost. When we start our build like you described above (which is standard) [13 drone, 14 overlord, 14 drone], the hatchery is idle for around 9 seconds. Since we need the minerals for an extractor and the drone (25+50), which takes around a second to collect, we could get a drone out for (9-1) 8 seconds faster then it would usually appear (as soon as the 14 overlord arrives). In those 8 seconds the drone could collect 8 * 0,96 = 7,68 minerals.
Just looking at the resources 7,68 is higher then the cost of 7 and if you want to get as many resources as fast as possible, you should do that trick. The problem is that the 6 resources, that you lost by deleting the extractor, are gone for ever. So with perfect execution you gain around 0,68 minerals for the price of removing 7 minerals permanetntly from your main base. In my opinion this is not really worth it.
Taking larva production into account, as I see it, you don't lose larva production time, since the 13 overlord comes out just in time when the hatchery reaches a larva count of 2. So you don't gain anything from it either.
I took a look at Scarlett's, Dark's, Serral's POV and none of them are using the trick in your above described hatch first build. So I wouldn't bother to much with that question.
Edit: Generally speaking I would only use this trick if you already have 3 Larva on your Hatch and want to use them as soon as possible. This usually happens if you make some kind of macro mistake.