[G] Walling Mechanics

Roughly speaking, there are 2 kinds of walls:
1. wall between a building and a map feature such as ramp/cliff/doodad/edge etc.
2. wall between a building and another building
This thread is all about the latter, and the former isn’t discussed. This is because ramps/cliffs/doodads/edges are fairly map-dependent so that one example at a particular place on a particular map doesn’t apply to other cases, which makes drawing meaningful conclusions impossible. On the other hand, the relationship between a building and another building is completely map-independent so that test results are consistent. For example, in the image below, it doesn’t help much outside of this particular ramp on Entombed Valley to know that A and E are tight walls because this exact shape of ramp/cliff doesn’t appear anywhere else. Instead, it is more meaningful to note that B and D are tight walls and C is what I later call semi-wall because the only factor in question in these cases is the relative positions of two adjacent buildings regardless of the map (or race for the matter) played.

Most buildings can be categorized into 4 groups by their sizes: 2x2 (spine/spore), 2x2 (normal), 3x3 and 5x5.
2x2 (spine/spore) includes only spine/spore crawlers. To distinguish from 2x2 (normal), this size is defined as SxS in this thread. SxS is slightly smaller than 2x2.
2x2 (normal) includes all the other 2x2 buildings. 2x2 refers to this size from here on.
3x3 includes all 3x3 buildings except for refinery/extractor/assimilator.
5x5 includes CC/hatchery/nexus and their variants.
Sensor tower and creep tumor are hardly ever used as a part of a wall, so 1x1 is not relevant enough here.

There are 10 combinations in choosing 2 buildings for a wall:
SxS and SxS [S-S]
SxS and 2x2 [S-2]
SxS and 3x3 [S-3]
SxS and 5x5 [S-5]
2x2 and 2x2 [2-2]
2x2 and 3x3 [2-3]
2x2 and 5x5 [2-5]
3x3 and 3x3 [3-3]
3x3 and 5x5 [3-5]
5x5 and 5x5 [5-5]

Because buildings use symmetric footprints, test results in 0-45 degrees account for the entire 360 degrees. Therefore, for the sake of easier notation, bottom left corner of the smaller building of the two is taken as the origin, then x-y coordinate of bottom left corner of the other bigger building is defined as the relative position these two buildings have.




By reflection and rotation, any relative positions in 45-360 degrees ultimately end up with one in 0-45, so it doesn’t matter bottom left corner seems to be somehow more favored, if you will, than the other corners.






This notation system allows us to clearly denote all relative positions. I hope it makes enough sense. I wish I knew a better way to explain this concept.

There are primarily 5 different types of walls. 7 if minor differences in rare cases are taken into account.


Loose wall Lv.0 is not walled at all. All units can pass between 2 buildings that form loose wall Lv.0.

Loose wall Lv.1 blocks only 2 units:
Terran: thor, (siege tank)
Siege tank is blocked even with loose wall Lv.0.5 which is seen very rarely.

Loose wall Lv.2 blocks additional 2 units:
Zerg: ultralisk
Protoss: archon

Semi-wall (or loose wall Lv.3 in a sense) is the most important type of wall at least here in this thread. Just like semipermeable membrane for osmosis in chemistry, semi-walls block big units but allow small units to pass. This selective feature is very useful in some situations. Of course, loose wall Lv.0.5~2.5 work in a similar way, but they block too few units to be useful compared to semi-walls. Additional units blocked by semi-wall:
Terran: hellion
Zerg: queen, roach, infestor
Protoss: stalker, immortal, (colossus)
Colossus is blocked by rare loose wall Lv.2.5 as well.

Tight wall (or you could call it loose wall Lv.4) doesn’t allow any unit to pass between 2 buildings. We usually call this type “wall” and everything else is not wall per se. Most of the time, this tight wall is what we want to make with 2 buildings. These small units are finally blocked with tight wall:
Terran: SCV, mule, marine, marauder, reaper, ghost, viking (assault mode)
Zerg: drone, zergling, baneling, hydralisk, broodling, changeling, infested terran
Protoss: probe, zealot, sentry, dark templar, high templar

Colors are chosen for their role similarity to the corresponding traffic light color. Green - sea green - light green have relatively small differences among themselves.

Enough with prerequisites. What we want to know is, “Which relative position has which type of wall?”

[S-S]
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[S-2]
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[S-3]
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[S-5]
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[2-2]
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[2-3]
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[2-5]
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[3-3]
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[3-5]
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[5-5]
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ALL
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ALL (simplified)
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Never use these 7 relative positions when you want a tight wall. Some of them might be counterintuitive, but workers, zergling, zealot etc. will laugh at the wall and run by between these 2 buildings. I don’t often see a pro fail with these semi-walls because they already know from their experience that a tight wall has to look tighter, but I’m sure some of the ordinary players here have failed miserably before… at least, I have T_T. For example, when you CC first at ramp in TvZ, make sure the wall doesn’t include [2-5 (2,1)] or [3-5 (3,2)] so that you can hold an early pool. Or, when you FFE in PvZ, make sure your forge and gateway don’t look like [3-3 (3,3)]. Green loose walls look wide open rather obviously, but these yellow semi-walls sometimes look deceivingly tight enough, so be careful.

Semi-walls are not always bad. There are some practical applications especially against hellions. As explained in “Type of Wall” section, a semi-wall blocks hellions while it allows passage of workers/zergling/marine/marauder etc. Some sim city can take advantage of this fact.

TvT
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ZvT
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PvT
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Ever since I posted [G] Zerg Sim City for Spire protection in ZvP 4 months ago, I have always wanted to do a comprehensive research on walling mechanics that explains “incomplete wall-in hole examples” in that thread. I am easily distracted and have written several other articles/guides, but finally here it is. With a bit of compromise in quality, I managed to publish this research before 2013. When I started this research, I was hoping to find more practical applications than just presenting facts and data. Also, it would have been nice if I could include analysis on units filling the gap between 2 buildings. (hold position zealot, queen etc.) Well, I guess the content is in-depth enough as it is, nevertheless. As far as I know, the only difference in HotS is that spine crawler is bigger than that of WoL (same size as other 2x2(?)) There might come other changes in future, but majority of basic walling mechanics explained in this thread must remain relevant enough even after LotV. If I find time and passion again, I might follow up with HotS and LotV versions of walling mechanics. As always, thank you for reading. Any feedback is much appreciated.