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In this article I'm going to outline the standard formations; their strengths and vulnerabilities, as well as some useful tactical maneuvers and important marching orders.
Knowledge Level: Intermediate
The concepts here are pretty basic but an intimate understanding can lead to complex in-game applications.
Below you will see a graphic of the primary, fundamental formations.
The Arc Has two Forms: A Concave and a Convex.
The difference between the concave and the convex arc is simple the direction of focus. The concave is considered an extremely offense arc formation and as you will see below it focuses fire into a centralized location and creates a semi-surround on your target. The convex arc is considered a more defensive formation as it is designed to protect the focal point behind it.
We've all heard the casters and high-level strategists say, "Look at that beautiful arc!" Or they will mention that one player has the arc advantage in a certain scenario. Most of us already know that having an arc is good. But do you know why? Have you visualized why? The following examples pertain specifically to ranged units, however adding melee units into the mix creates extremely interesting dynamics pertaining to each formation.
In Fig B.1 the blue player has an ideal arc formation around the orange player. The orange player is in the ball formation. The blue player will win this battle in equal numbers as the concave arc is more cost efficient. You can visualize this by looking at Fig B.2 and seeing how all the firepower is concentrated into a single point. Additionally, the arc maximizes the number of troops able to engage because they are in range of the enemy's front line.
In Fig B.3 you can see the orange player in the ball formation. He will most likely lose this battle. A portion of his troops will not be in range to fire. Move commands must be issued in order for all of the troops to engage the enemy. This is detrimental because the opponent in the arc formation will not need to issue those move commands. In Fig B.4 you see that the firepower is scattered out from the middle.
The Arc Formation's Vulnerabilities
The concave arc is an extremely potent offensive formation but because it is so powerful in a focused direction it is extra vulnerable to flanks and pincer attacks (discussed more below).
Formations: The Spread vs. The Ball in regard to Melee Units
You'll have heard the term "surface area" used by commentators or high level strategists when talking about melee units and forming surrounds on your opponent. This absolutely must be taken into consideration when moving your troops when you know melee units are on the field. This is especially important when fast melee swarms are in play (i.e. in Zerg matchups).
Now, since this game is essentially played in two dimensions, there is no "surface area" as that is a function of 3D space. What we're actually measuring is circumference. Do you know just how much more effective a surround is in certain scenarios? We're going to refer to this exposure is attack area.
In Fig. D. you see blue's troops in the spread formation. The red circles represent the circumference areas of attack by melee units. c = circumference in the equations. In Fig. D you see blue's troops in the ball formation.
In Fig. E. blue's troops are exposed to a total attack circumference of 12.56 while blue's troops in Fig. D., the spread formation, are exposed to an incredible 56.34 attack circumference! The spread formation is 4.49 times more exposed to melee attack. This increase, or decrease, in attack area exposure is directly related to the number of spread clusters and the size of them.
Formations: Spread and Ball in regards to move commands and focus fire
The ball is the most common formation because it is the one that your troops will naturally create when boxed and issued a move command (See Figure F.). In certain scenarios the ball is absolutely ideal, most notable when you want to focus fire one or several units.
TIP: Maintain Formation while moving.
If you have a nice position, such as an arc composition, you can select the formation and issue a move (or attack move) command very far away (such as clicking on the mini-map). Because the formation converges into a ball formation the farther away you click the slower that convergence will take place. You would need to issue a stop command at the desired location. This will help maintain formation while move.
In Fig. G.1 issuing a focus fire command is going to be relatively inefficient. The majority of your troops have to perform move commands (green arrows) before they can fire (red arrows). The potency of using focus fire from this formation, or the arc formation (but to a lesser degree) is not ideal.
In Fig. G.2 you see that in a focus fire scenario using the ball formation is ideal. Move commands and focus fire commands are most efficient in this formation.
Understanding the "Flank" is vital. The above image describes a flank.
Most formations and marching orders you will face will be vulnerable to a flank attack. The flank attack will constrict your opponent's movement and reduce disperse his firepower's focus.
The Pincer Attack is an incredibly powerful tactical maneuver. If you can Pincer your opponent's army (aka the Double Envelope) you will likely create an offensive advantage in the encounter. The Pincer is essentially a double flank attack and can have a dramatic psychological effect on your opponent.
Charge (Full Frontal Attack), Full Surround, Supply Line, and the Ambush
One of the primary reasons I wanted to discuss the Flank, and the Pincer is because the most common attack formation you will see in a SC2 game is the Charge, which is a full frontal attack. This is the most straight forward attack maneuver you can do. I find this interesting because in a relatively even fight you are not creating an advantage for yourself by doing this. The Charge is absolutely a valid attack pattern, but it should be used for a reason, such as to conceal an ambush, or to increase the effectiveness of a flank.
The Full Surround
If you can manage a full surround on your opponent (by combining a charge with a pincer) you may actually find yourself at an incredible advantage in the encounter. Conversely, being surrounded can have a profoundly negative psychological impact on you.
The Supply Line (Reinforcements)
Not all attacks are reinforced, but when they are the supply line is an excellent tactical target. The supply line is the path in between the opponent's production and their army.
To put simply; to attack where they are not looking or not expecting. Because of the attack move command it can be difficult to truly "ambush" your opponent so this tactic is best embodied by the "drop" play or what is commonly referred to as the "multi-pronged harass". Since all units in SC2 can see in all directions simultaneously you have to "draw their attention" in order to create an ambush. If you do not draw their attention you are basically relying on them to make a mistake.
With a firm understanding of flanks, supply lines, and unit formations you can better understand the importance of having structured marching orders. Your army is the most vulnerable when they are moving from one location to another. If you just click across the map your troops will want to travel in a line. It is very important that you have a forward scout and three guards; one for each flank and your rear.
Use terrain to your advantage. You can actually use impassable terrain to guard a flank, or both flanks. If you're utilizing your supply line and reinforcing your march having a rear guard is not that important. A skilled opponent will attempt to attack you while you're army is marching and will likely use one of the tactics described above. You should be guarding yourself from these tactics.
Use this knowledge of basic formations and tactical maneuvering to optimize your defensive and offensive postures. Keep these concepts in mind at all times when moving your troops, or repositioning your troops. Ask yourself, "am I in the best formation for this exact scenario?"
I know this seems like a basic thought process but I'm sure many players will focus too much on the "end goal" of "attacking an expansion," or "defending a rush, or a ramp," and forget everything that occurs in between now and then. Having knowledge of, and utilizing, formations will help you come out on top in more encounters.
Thanks to Saracen for changing the thread title!