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Reflection Symmetry vs. Rotational Symmetry
This is a discussion of the use of reflection symmetry vs. the use of rotational symmetry in the making of 4 player 1v1 maps. We will discuss the differences and their advantages and disadvantages in balancing. First of all, let's examine what Reflection Symmetry and Rotational Symmetry mean and how they pertain to map making.
Reflection Symmetry (Wikipedia entry)
Reflection symmetry, also known as mirror symmetry is when a figure (or map in this case) is reflected along an axis such that both sides appear the same. If you'd like to tell if a map is symmetrical by reflection, then all you must do is find the axis of symmetry and draw a line down it. If you then mentally fold the image along the line, the two halves should match up where they touch. You can see this type of symmetry in maps such as Lost Temple or Metalopolis.
Example of Reflection Symmetry: + Show Spoiler +
Lost Temple with highlighted axis of symmetry: + Show Spoiler +
Rotational Symmetry (Wikipedia entry)
Rotational symmetry, I've seen described as "pinwheel" symmetry, is when a figure can be rotated by a certain amount and appear the same. If you'd like to tell if a map is symmetrical by rotation, then all you must do is rotate it at the center until it matches the original. Generally in 4 player maps, you just rotate the map by 90 degrees and the everything should be the same. You can see this type of symmetry in maps such as Delta Quadrant.
Example of Rotational Symmetry: + Show Spoiler +
Delta Quadrant with lines to highlight rotated sections: + Show Spoiler +
How does this affect map balance?
Here comes the discussion part and where I'll share with you my opinion on the subject.
The way that this affects map balance is in 4 player maps, is with positional balance with regard to spawn locations. With a 1v1 game played on a 4 player map, the spawn locations of the players are variable. Therefore, balance consideration needs to be taken into account such that all possible variations of spawn locations for the two players are equally balanced. When using one of the two types of symmetry we've seen earlier, the considerations are different, and rotational symmetry is considerably more difficult to balance. The biggest area of concern, in my opinion, would be expansion placement when considering expanding patterns.
When using reflection symmetry, the designer is actually inherently given a balanced map. When looking at Lost Temple, if it were perfectly reflected, then no matter where the players spawn, they are both given the same advantages and disadvantages. If they spawn close positions, they both have to contend with being unable to easily expand to a third base. No matter where the players spawn, they are given the same choices for expansions and their expansion patterns are the same.
When using rotational symmetry, the designer must contend with inherent imbalances. Unless the players spawn in cross positions there are going to be imbalances. Much care and consideration are needed in order to make it balanced. It may look balanced since it is symmetrical, but don't let that fool you. In order to discuss some of these imbalances I'm going to use an example map.
I chose the Starcraft 2 remake of Fighting Spirit by prodiG because it's good but you can still see some of these imbalances. An image of Fighting Spirit for reference: + Show Spoiler +
With spawn positions at 2, 5, 8 and 11 o'clock, let's use the top spawns at positions 2 and 11 for our examples. From the very start of the game, you'll notice the positions of the natural expansions. When spawning at the 2 o'clock position, taking your natural expansion, you expand towards your opponent at the 11 o'clock position, while they take their natural and expand away. This does not seem like much of an imbalance yet, but when looking at the air attack paths, a straight attack path from 11 to 2 has the player traveling over the 1 o'clock natural, where it does not travel over the 10 o'clock natural. Of course, this wouldn't stop you from expanding at your natural since the benefits of the close natural outweigh these imbalances.
But when choosing a third expansion, this may not be as easy a choice. The player at the 1 o'clock position could take a third at the 3 o'clock position and they would safely be expanding away from their opponent. Unfortunately, the player at the 11 o'clock position could not expand to the same relative base at the 12 o'clock position and gain the same safety. They would be expanding towards their opponent and decreasing the opponent's attack distance. Fortunately, there is another viable third expansion for our 10 o'clock player would be the third at the 9 o'clock position which is of similar distance away from the natural.
Fortunately, the designer of Fighting Spirit is quite good and was able to account for the inherent imbalances with good expansion placement, but in the hands of inexperienced map makers, rotational symmetry's imbalances could be amplified. When doing rotational symmetry, there are a lot more things to consider other than just giving each player the same number of expansions. The positions of these expansions and how they relate to each spawn point needs to be considered.
These are my thoughts. I would love to hear yours.
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I believe that Starcraft needs maps that are both rotational and mirrored. It looks like you covered all of the points I was going to make
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As prodiG said, both rotational and mirrored should be in the map pool.
That said, I have a very hard time bringing myself to make a rotational map for all of the reasons you just exaplained.
In fact, I really love mirror symmetry in 4 player maps. I'm pretty certain my next few maps will be 4-player mirror symmetry.
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I agree. Both types should be used when making maps. I hope I didn't sound too harsh when speaking about rotational symmetry. I believe it's more challenging to balance, but that does not mean it shouldn't be done.
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Dude, Rotational is so much more pimp. Seriously, the X, Y, XY symmetry gets so boring. In Brood War, the Paranoid Android symmetry was the most pro because it's so hard to execute but not so in SC2 where mirroring is eternally more annoying but better.
tl;dr: Reflection symmetry is balanced, Rotational symmetry is so much more fun.
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Isn't this an issue of the past?! When BW mappers did positional balance for rotational symmetry either they are geniuses, VERY careful mappers, or they had a secret tool to help them.
For SC2 we have the map analyzer--and balancing interesting symmetries (or lots of asymmetry) is exactly what this pig is for! Case in point: the map analyzer says adjacent spawns on prodiG's iCCup Fighting Spirit are quantitatively balanced, positionally.
+ Show Spoiler [Fighting Spirit] +
Boom!
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@dimfish I luvz u, but I really doubt I can be convinced that rotational symmetry maps are nearly 100% positionally balanced.
In the case of Fighting Spirit, the position of the third bases in same-side positions is really what gets me. Mostly the ramp. It is so much easier for a terran player to push a zerg player when the zerg is at 2 and the terran is at 5, as opposed to the other way around. Furthermore, the way the natural is much closer to 2 when you're at five (as opposed to vice versa) makes it much more vulnerable to air harass. In 2 and 5 positions, the distance from 2's natural to 5's third is much much farther than the distance from 5's natural to 2's third.
I'm pretty sure that when you take the entire map into consideration is what makes the analyzer give such a high score. While the close positions aren't really that balanced, (once you're moving into the late-game) expanding to the other half of the map kind-of is (I am pretty sure this would not be the case with all rotational symmetry maps). I would be very very interested to see a map analyzer picture of fighting spirit when it's only analyzing half of the map.
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I also want to point out here that there are pretty much two 4-player maps in the map pool that are generally considered the most balanced. Lost Temple (in my recent experiences most people are agreeing that the cliff over the natural is plenty fine. Once a zerg can get through that point the map is really good for them) and Metalopolis.
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It seems the "best" maps currently are Reflection maps with two pairs of parallel ramps (Lost Temple, Metal). This creates very diverse games, with three different possibilities, Cross, close ground, close air.
However, I think Rotational maps with their two possibilities really help give a player a fallback if they aren't very comfortable with having to adapt to the map based on spawn location.
In short, both are needed.
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@dimfish, I'd love to know the algorithm that you use to calculate "influences" and what factors it takes into account.
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What your analysis fails to take into account is that on a rotational symmetry map, you're equally likely to be "upwind" as "downwind." This produces some problems when it comes to things like muta harass, which is rough on FS's natural with an upwind Zerg against downwind Terran, but much less so with Zerg downwind.
Still, rotational symmetry produces interesting maps and situations, and should be part of the map pool.
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An explanation of influence --> positional balance.
Admittedly, the analyzer model has parameters, so adjusting them adjusts the overall balance. Here's the gist of it:
The analyzer finds all the bases on a map and calculates, for each starting location, how far away is that base by ground, cliff-walking and by air? Using this data we can calculate influence as inversely proportional to some weighted combination of those values. Example: my natural is close by ground, cliff-walk AND air when compared to another start location, so the combined distances are LOW and the resulting influence is HIGH. It is expressed as a percentage, and you can alter that percentage by playing with the influence weights in the map analyzer constants.txt. At the moment ground is weighted heavily, air is important and cliff-walking is generally low.
Okay, so you consider each pair of starting locations at a time (a possible spawn for both players in 1v1) and decide which start location influences which base by how much. Now you have to choose an attribute of the bases to balance by. It doesn't matter if I have 99% influence over a base with one mineral patch as much as a lots of influence over a gold base, right? So the analyzer gives you two positional balance scores at the top of the image: one by total resources per base and one by openness per base. If my natural is more open than your natural, even though they are positioned fairly, then the overall balance will come out off.
The algorithm can be tweaked and perfected and I have plans for more base attributes (think cliffable versus a non-cliffable base, very different bases), but I think the overall idea is very, very useful for deciding if a rotational symmetric map is "in the ballback" of positionally balanced.
And yeah, Barrin, the analyzer can only do this taking the entire map into account. How about this: suppose the influence calculation ALSO says "bases that are closer to BOTH spawns are more important to the calculation" so the variations between your spawns are taking more into account? Do you think that would better show the balance?
edit: Mango, the air distance takes into account "upwind" and "downwind" but if muta harass is very important when compared to ground distances, then the analysis constants should be altered to reflect that.
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I don't like rotation maps. While it adds a nice twist in 2v2, it makes 1v1 imbalanced. I say this in all of my posts in the map threads.
Delta Quadrant isn't affected by this largely because there's almost a line of semetry in the middle horrazonally and vertically. On close positions, one player is closer to the natural and the third than the other player is to his. The position of the gold doesn't play a huge role because a player can opt to take the one farther away from his opponent as it is nearly the same distance as his own.
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@MangoTango, I'm sorry but your terminology confuses me. Instead of upwind/downwind do you mean north/south or counter-clockwise/clockwise?
@dimfish, The analyzer seems to work well to provide good general results. I thought it was only taking into account the ground distance between spawn points and expansions, so it's good to know you also take into account cliff and air distances. There are some more complicated factors that I can think of that could be taken into account but would make the calculation much more difficult, such as high ground vs. low ground expansions, ramp widths, and destructible rocks. Destructible rocks seem to be a difficult thing to analyze at the moment. Perhaps an option to run the analyzer where it would ignore destructible rocks would be good, so we can compare the analysis of the map with and without them. (This is perhaps the wrong thread for this discussion.  )
Edit: @DamageInq, This is why I chose not to analyze Delta Quadrant in my original post. It does a good job of factoring the imbalances of rotational symmetry by aligning itself with the center. Meaning, the naturals go towards the center and the gold expansions are between each base. The biggest imbalance is probably the backdoor third blocked by rocks.
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What your analysis fails to take into account is that on a rotational symmetry map, you're equally likely to be "upwind" as "downwind."
You are correct. This is very important and should not be forgotten.
At the same time it just bothers a "perfectionist" (undiagnosed OCD ^_^) like me to no end when even then close positions can be so incredibly ambiguous.
cliff-walking is generally low.
This is entirely why Fighting Spirit has such a high position score.
Before you said this, I totally thought this must be the answer I just couldn't really put it into words lol. You made it sound simple though.
And yeah, Barrin, the analyzer can only do this taking the entire map into account. How about this: suppose the influence calculation ALSO says "bases that are closer to BOTH spawns are more important to the calculation" so the variations between your spawns are taking more into account? Do you think that would better show the balance?
Woah.
Yes. I think it would not only help rotational maps, but also not affect 100% mirror at all. (edit: on second thought, it would help "imperfect" mirror).
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1. Positional balance has nothing to do with Racial balance.
2. Rotational symmetry can still be relatively balanced while being far more pimp than reflectional. Katrina was probably the most problematic in regards to rotational in the Brood War pro map scene, where the mains were more vulnurable one way than in another, but even there, people cared far more about the racial balance than the positional.
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I think rotational versus reflection symmetry for the high-level layout (let's call it macro symmetry) is less important for positional balance than micro symmetry.
Consider that reflection symmetry maps usually have some asymmetry.
Metalopolis has some weird spacing and size asymmetries, even though it is deceptively reflection symmetric.
+ Show Spoiler [Metalopolis Asymmetry] +
But the overall effect on Metalopolis is that major distances between key points are balanced, and the fine details are exact (the center has perfect symmetry for instance). And apparently the community at large believes Metalopolis is fair.
Other maps with reflection macro symmetry have more problematic micro asymmetries: on Scrap Station the choke between the natural and the third base is tighter for the southern spawn. And I believe on Lost Temple (maybe patched in 1.1?) that Thors on the natural cliff can kill hatcheries at 3 o'clock and one other spawn, but not the other two. So in a ZvT where Zerg spawns in a Thor-cliffable spawn it might influence whether the player expands to the natural, which is a significant imbalance.
As long as the asymmetries are within reason, I think rotational macro symmetry is far less of a factor than the exact shape of main chokes or natural layouts or whatever.
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@dimfish yes I agree with all of that.
I also want to state that I really hate the Blizzard maps for all of the little nuiances like that. Noob mapmakers imo lulz. They have gotten a lot closer to true symmetry since the beta though.
As long as the asymmetries are within reason, I think rotational macro symmetry is far less of a factor than the exact shape of main chokes or natural layouts or whatever.
Particularly distances from certain entrances/chokes to corresponding entrances/chokes IMO. This is my biggest problem with Fighting Spirit when it comes down to it. A 2 o'clock spawn's third base ramp is much much closer to 5's main entrance than 5's third base is to 2's main entrance.
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Oh yeah now that I think about it, anyone who likes this topic might find the following link interesting. It's a post I made in the beta about my idea of "perfect" reflection symmetry.
http://www.teamliquid.net/forum/viewmessage.php?topic_id=137143
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Lost Temple is not the best example of a reflectionally symmetrical map being balanced. If you and opponent are at 7 and 8 bases air rush distance is tiny, which to me is worse than your natural taking you closer to an opponent.
With rotational symmetry you're not going to see any of the mains right next to each other like that (barring some weird 2 way only rotational symmetry on a 4 player map, but I've never seen one of those)
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Lost Temple is not the best example of a reflectionally symmetrical map being balanced. If you and opponent are at 7 and 8 bases air rush distance is tiny, which to me is worse than your natural taking you closer to an opponent.
With rotational symmetry you're not going to see any of the mains right next to each other like that (barring some weird 2 way only rotational symmetry on a 4 player map, but I've never seen one of those)
I'm not sure what you're trying to say. The whole point of 4player reflectional symmetry is that each of the positions that your opponent spawns on influences the game very differently, which is kind of similar to rotational. The difference with reflection maps is that each of those spawn points still splits the map perfectly.
A concept here really should be underlined. Basically, Blizzard maps are not perfectly symmetrical. Not a single one of them. I don't know about the rest of you, but when I use their maps as an example of symmetry (again, they're just not symmetrical), I'm really using the IDEA or CONCEPT of that particular map, with all the tiny little positional imbalances aside.
The tiny little positional imbalances should not be a part of this discussion at all, IMO.
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OP was saying with rotational the distance from your natural to their main will be different depending on whether they are located clockwise or counterclockwise to you (ignoring cross positions). This is true, but how is it worse than the distance between mains being greatly different on a reflectionally symmetric map like Lost Temple (again, ignoring cross positions)?
True, in Lost Temple the variability applies equally to both players. On a non mirror match though it can make a big difference. Like in BW, a closer air distance between mains, even though it's the same for both players, greatly benefits a Zerg.
But yeah, reflectional symmetry does mean the distances will at least be the same for both players, while it won't be with rotational (main to natural)
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EPT![[image loading]](http://upload.wikimedia.org/wikipedia/commons/2/2d/Symmetry.png)
![[image loading]](http://i214.photobucket.com/albums/cc256/BoomStevo/Lost_Temple_Symmetry.jpg)
![[image loading]](http://upload.wikimedia.org/wikipedia/commons/d/d7/Wallpaper_group_diagram_p4.png)
![[image loading]](http://i214.photobucket.com/albums/cc256/BoomStevo/Delta_Quadrant_Symmetry.jpg)
![[image loading]](http://img96.imageshack.us/img96/6751/fightingspiritsc2.jpg)
![[image loading]](http://static.curseforge.net/thumbman/images/25/519/552x600/iCCupFightingSpirit-influence-5-2.png.-m1.png)
![[image loading]](http://static.sc2mapster.com/content/images/22/571/Metalopolis-asymmetry.png)
