Harassment in StarCraft Brood War

Learner

The short version

Hit the things that cannot hit back. Workers and production give you something for nothing.
An army is the only target that charges you for attacking it, which is why it should usually be the last one on your list.
Interrupting mining is damage even when nothing dies. Twenty seconds of a stopped mineral line is a specific number of minerals.
A split army is a free meal, because the attrition arithmetic in T2 is brutally kind to whoever catches the smaller piece.
Harassment is not a personality. It is the highest return on investment available to most players, and it is priced.

The situation

You have eight units spare and a window of about forty seconds. You send them at their army, because that is what units are for, and you trade eight units for six of theirs and feel like you came out ahead.

You did not. You spent eight units to remove six units, which is one column of their ledger, and in the same forty seconds those eight units could have stopped twelve workers from mining and made them pull the whole army home.

The difference is not aggression or caution. It is which target charges you for the privilege.

Three targets, and only one of them shoots

Lesson 4 walks through this as a series of questions, and the questions are worth keeping because the answers are obvious once they are asked in order.

If you hit their economy, does it fight back? No. Workers have a weapon and it is a joke, and using them to fight costs the mining you were attacking in the first place. Damage done to economy reduces the rate at which they gather.

If you hit their production, does it fight back? No. A gateway does not shoot. Damage done to production reduces the rate at which they convert what they have gathered into things on the map. In lesson 1's vocabulary, you are attacking a transformation resource, which is the machine rather than the output.

If you hit their army, does it fight back? Yes, at full price.

So the first two get something for nothing, and the third does not. That is the whole principle and it is not a subtle one. What is subtle is how consistently players ignore it, because the army is the target that looks like a target.

Interruption is damage

The part that does not show on the score screen.

A harassment run that kills nothing at all still did work, in three ways. It stopped mining while the workers ran. It spent their attention, which T1 says is the scarcest thing they own and T10 says is a fixed budget. And it may have pulled their army out of position, which is the most expensive of the three.

Put a number on the first one and it stops feeling like a consolation prize. Twelve workers stopped for twenty seconds, at roughly forty minerals a minute each, is about a hundred and sixty minerals. That is a zealot and a half, for free, from a run that killed nobody.

And that is the floor, not the ceiling. The ceiling is that they pull the army home, in which case you have bought the map for ninety seconds, which is usually worth more than the entire harassing force.

The working

Show the maths

What a dead worker is worth. A worker mining at $m$ a minute, killed at time $t$ in a game that has $T$ left, costs its owner the mining it will not do plus the money to replace it:

V_{\text{worker}} = m\,(T - t) + c \quad\text{if it is replaced, or}\quad m\,(T-t) \quad\text{if it is not}

(1)

Linear in the time remaining. A worker killed at five minutes is worth several times one killed at fifteen.

This is the same shape as the early actions argument in T10 and the early worker argument in T1, and for the same reason: anything that compounds is worth more the earlier you touch it.

What an interruption is worth. Stopping $k$ workers for $\Delta t$ costs them

V_{\text{stop}} = k\,m\,\Delta t

(2)

Twelve workers, twenty seconds, forty a minute: about 160 minerals, with nothing killed.

What a production building is worth. From T9, the bank grows whenever income exceeds what production can consume. Killing production buildings does not reduce their income, it reduces their ability to spend it, which means the money piles up and does nothing:

\frac{dB}{dt} = I - P\,\bar{c} \;\longrightarrow\; I - (P - 1)\,\bar{c}

(3)

One fewer gateway does not make them poorer. It makes their money useless for a while, which is the same thing later.

Why a split army is a free meal. Straight from the square law in T2. If they have $B$ split into a piece of $\theta B$ and a piece of $(1-\theta)B$ , and you catch one piece with your whole $A$ , you come out of the first fight with

A_1 = \sqrt{A^2 - \theta^2 B^2}

(4)

and then fight the rest at that strength. Catching an isolated tenth of an army with all of yours puts you deep in the regime where the fight is over before the smaller side has delivered anything at all. Which is why splitting is not merely inefficient for its owner: it creates a target that pays better than any building on the map.

And the converse, which is the practical version: when you are deciding whether to chase, ask whether the thing you are chasing is a piece of something bigger or a whole thing. The piece is worth chasing. The whole thing usually is not.

Choosing the target, in order

A rough ranking that survives most situations. It is a starting order, not a rule.

Workers, as early as you can reach them. Highest compounding, lowest resistance.
An isolated part of their army, if you can bring everything and they cannot. This is the only army target that is genuinely cheap.
Production, when you cannot reach workers. It converts their income into a float.
Tech and support buildings, when a single building is the reason a branch of the game exists for them.
Supply, which sounds trivial and stalls production for a surprisingly long time.
Their army, in a fight you chose, which is T2 and T3's subject.
Their army, in a fight they chose, which is what happens when you skip the list.

The connection back

This guide is the map-scale version of T7's target selection. Inside a fight, you pick the unit whose death most reduces the enemy's output. Across a map, you pick the thing whose death most reduces their output, and the answer is nearly always something that is not shooting at you.

It is also the reason T5's probing works. A small force sent at something undefended is simultaneously a harassment run, a scout, and a question about their judgement. Three returns on one purchase is why it is the best value in the game.

What the lecture said

The principle is taught from 47:00 to the end of the lesson 4 lecture. The board lists the targets under a heading of raw resources: minerals and gas, buildings, units.

The lecturer tied it straight back to the attrition model: catching an isolated ten supply with fifty supply puts you in the regime where the fight ends before the smaller side deals meaningful damage, so a split army is not just inefficient for its owner, it manufactures a free meal for the opponent. He distinguished an army's units from its sub units, which was his shorthand for whether the thing is together or scattered.

He closed on Sun Tzu, and read the old advice against his own model. His gloss is the part worth keeping, and here it is in our words: every line in that passage is the same rule seen from a different distance, which is to fight where he cannot hit you. Running away preserves your force and denies him damage. Defending uses terrain and micro to minimise what he can deliver. Both are the same instruction as attacking what does not fight back.

He also pointed back to a replay the class had studied. A drop of about a dozen hydralisks and fifteen zerglings into Terran space met nothing that could fight back and did a fortune in damage. The same player then engaged the Terran army head on and lost hydralisks to splash. Same units, same game, opposite results, and the only thing that changed was the target.

A common mistake. You drop, the workers run, and you chase them across the mineral line into the turrets. The moment you chase, you have swapped a target that cannot shoot for one that can. Hit what is in reach, then leave, and come back from another side.

Lesson 8 turns this into a harassment plan: which targets pay, and how much the defender should spend to stop you.

Still true today

Checkpoint

Your harassment killed nothing. What did it do?
Why is killing a production building not the same as killing income?
You see a fifth of their army alone on the map. You have your whole army nearby.

Sources for this page

Lesson 4 lecture, on YouTube, channel VioleTAK What to attack runs from 00:47 to the end, where the recording cuts off mid sentence
David Sirlin's write up of week 8 Week 8, on the techniques of scouting and anti scouting, was not filmed