StarCraft economy and expansion calculator

The short version

A worker pays for itself in about seventy five seconds and then keeps paying for the rest of the game. Nothing else you can buy does that.
An expansion costs 400 minerals and puts you behind. The interesting number is not the cost, it is the minute you get back to level, and it is usually sooner than people think.
Patches saturate. Two workers a patch is full rate; the third adds about a quarter of a worker; the fourth adds nothing. This is why more bases beats more workers once you are full.
The gap between expanding and not expanding does not stay the same size. It grows, because the extra income buys workers, which buy more income.
Every rate on this page is an assumption, and you can change all of them.

When the expansion has paid for itself

The same position twice: one of you expands, one of you does not. The gap between the curves is what the decision was worth.

2.5min

Paid for itself after

Counted from the minute you put it down.

9262minerals

Ahead by minute 20

714a minute

Mining now

17 workers' worth, after saturation.

1.2min

A worker pays for itself in

And then it keeps going for the rest of the game.

Expanding at minute 5 costs you 400 minerals and puts you behind until minute 7.5. From there it never stops paying: by minute 20 you are 9262 minerals ahead of the version of you who stayed home.

You expanded You did not Minerals mined, less what the expansion cost

Minute	Expanded: minerals	Expanded: workers	Stayed: minerals	Stayed: workers
0	134	21	134	21
2	1464	24	1464	24
4	2976	24	2976	24
6	4130	33	4488	24
8	6249	47	6000	24
10	9215	48	7512	24
12	12239	48	9024	24
14	15263	48	10536	24
16	18287	48	12048	24
18	21311	48	13560	24
20	24335	48	15072	24

What the model does

Two versions of you start from the same position. At the minute you choose, one of you spends 400 minerals on a hall and keeps making workers into it; the other saturates what they have and stops. Nothing else about the two of you is different: no army, no harassment, no losses.

The curve that matters is the difference between them. It starts negative, because a hall is 400 minerals of nothing. It crosses zero, which is the payback. Then it bends upward, which is the whole argument for expanding: the lead is not a fixed 400 minerals, it is an income.

\text{lead}(t) = \int_{t_0}^{t} \big(r_{\text{two bases}}(\tau) - r_{\text{one base}}(\tau)\big)\,d\tau - c

(1)

Show the maths

The integrand is not constant, which is the part that catches people out. The expanding player's income keeps rising after the expansion, because the new hall gives new patches for new workers, and the worker that pays for itself in seventy five seconds is now a worker that has somewhere to mine. The staying player's income is flat: their patches are already full, so every worker after that adds a quarter of a worker and then nothing at all.

Saturation, and why it is the reason to expand

A mineral patch takes two workers at full rate. A third can mine it, but it queues, so it adds about a quarter of a worker's income. A fourth adds nothing you can measure.

With eight or nine patches a base, that is sixteen to eighteen workers at full rate, and about twenty four before the base is genuinely finished. Build past that on one base and you are paying 50 minerals a time for a quarter of a worker.

This is the sentence the lectures kept coming back to and which is worth carrying: macro is not a bank, it is units you can use. A big bank is a sign that your income has outrun your production, and the answer is more production or more army, not more workers.

What this lab assumes

Assumption	Value	Why, and how sure we are
Minerals a worker a minute	42	Our figure for a worker on a close patch with room to work, and the single biggest thing we have not measured. It is a field: set it to what your own replays show.
Patches a base	8	A typical main. Some maps give nine, some give seven, and a mineral only expansion changes the whole shape.
Third worker on a patch	a quarter	Our estimate of the queueing loss. The direction is certain, the size is not.
Expansion cost	400 minerals	The hall, and nothing else. No defences, no creep, no pylon, and no worker travel time, all of which make the real payback later than this.
Nothing ever dies	no army at all	This is an economy model, not a game. The reason to expand late is that you might be attacked, and that reason is not in here.
Not measured against the engine yet	pending	Validating the mining rate against a headless engine run is on the list. Until it is done, treat these as arithmetic on assumptions you can see.

Economy Lab