Balancing workers

Balancing workers means to redistribute workers among bases.

Maynarding means transferring workers from an active base to a newly-established base.

The point of transferring workers is to allow them to mine faster then they would in a crowded base. This comes at a cost, because while the worker is traveling towards its new base, it's not mining.

First of all, let's note that there is no point in moving a worker that is mining 0.7 m/s, because it is performing already at its best, so you never want to leave a base with less than 12 workers.

Let's assume you have more than 12 workers (and less than 24), and you transfer some to your natural, leaving 12 in your main. When they reach your natural, each of them will mine 0.7 m/s, which is 0.15 m/s faster than they would if you didn't move them to your natural. However, while the workers are moving to the natural, they are not mining. Each second each worker is not mining, you are missing the opportunity to mine 0.55 minerals.

Let Y be the time it takes for the worker to reach the natural, and X the number of workers you transferred. We want to know how transferring to the natural compares to not transferring with respect to the total number of minerals mined. When they reach your natural, you are Y·X·0.55 minerals behind, because X workers did not mine for Y seconds. Y seconds after they reached your natural, you are (Y·X·0.55 - Y·X·0.15) behind, because X workers did not mine for Y seconds, and then they mined at a greater speed (0.70 m/s - 0.55 m/s = 0.15 m/s faster) for Y seconds. 2·Y seconds after they reached your natural, you are (Y·X·0.55 - 2·Y·X·0.15) behind. With some math we can conclude that you will be even (0.55 / 0.15) · Y seconds (which is 3.6 · Y seconds) after your workers reached your natural.

For example, if the transfer time is 20 seconds, you will be behind in minerals for the first 20 seconds (the time to transfer the workers) plus 1 minute and 12 seconds (3.6 · 20 seconds). Then you break even. After 1 minute and 32 seconds, your total mining speed will be X·0.15 faster than if you did not transfer. If you transferred 8 workers, that means 72 minerals per minute faster.

Using this reasoning, you can calculate more-or-less-obvious things like:
 * it is a good idea to transfer 12 workers to your natural when you have 30 in your main
 * it is a bad idea to transfer 6 workers to your natural when you have 12 in your main