Why does everyone do 9-overlord, not 10-overlord?

What is the advantage on saving the money for the overlord when you have 9 drones, and not filling your supply first and then getting the overlord?

In my theory, in the first case you get to wait the saving time with 9 drones, and get to wait almost the same time with 10 drones in the second case. Second case should be better, since 10 drones mine faster than 9? So why does everybody go with the first case?

All this is assuming you go 12 pool or something like that, where you will get more drones after the overlord. 6- and 8-pools are obviously different.

Solution 1:

If you do 10 Overlord instead of 9, you'll wait longer to continue producing drones since you're supply-blocked for the time the overlord is "in production". I guess the amount of time you lose outweighs the minerals you gain from one additional drone (10 instead of 9).

Liquipedia clearly states 9OL as the best build economy wise.

Update: Here's the forum post that's quoted in Liquipedia. You'll find all the numbers there.

Solution 2:

The forum post bummzack has linked explains exactly the mechanic mehind this, in a form a a guy using the stareditor and a pc player to model the perfect timings for each build, and see how far does each build gets you if it is executed ideally (because in the test it is executed by a pc player somehow).

And just to put the answer here, here is the spot on extract from the post: (and explains the exact mathematical difference between the two mentioned builds).

There is exactly one point of time where 10OL is ahead of 9OL. From 55.9375 seconds until 71.375 seconds, 10OL has one more worker running, for a gain of about 15 worker seconds. But 9OL finishes drones 11 and 12 almost 10 seconds faster than 10OL, so this 15 second advantage begins to be lost at 88.625, and is completely gone somewhere around 96 seconds in. After that point, 9OL is ahead of 10OL in every way. It finishes the 15th drone 4 seconds faster, and is 15 minerals ahead at the 2:15 mark.