Okay, I had a change of heart. I'm going to release the Desmina research results now because I still can't find the time to continue and secondly because I want to keep any following data for different research.
Procedure
What I did was the following. I looked at the two wall spawns, three wall spawns and four wall spawns differently and tracks them separately. Then I added them all together but also looked at them added together keeping the duration of their phases in mind, created a weighted result basically.
I also calculated the percentage of coverage using the number of walls appearing at one point and dividing it by the amount of total wall spawns.
The Result
Size of Data
I have accumulated a total amount of 266 two sized waves which means 532 wave parts in the first phase. I've tracked 1201 three sized waves which consist of 3603 wave parts and I have tracked 444 four sized waves which are 1776 wall pieces. In total it accumulates to 1911 waves and 5911 wave parts. The first phase is weighted at 0.1, the second phase takes 57% of the fight assuming constant damage and the third phase is 33%. The weighted count results in 857.69 waves.
Two Wall Spawn
| 108 | 113 | 110 | 122 | 111 |
| 101 | 106 | 103 | 105 | 104 |
| 92 | 97 | 94 | 106 | 95 |
| 104 | 109 | 106 | 118 | 107 |
| 97 | 102 | 99 | 111 | 100 |
|
| 40.60% | 42.48% | 41.35% | 45.86% | 41.73% |
| 37.97% | 39.85% | 38.72% | 39.47% | 39.10% |
| 34.59% | 36.47% | 35.34% | 39.85% | 35.71% |
| 39.10% | 40.98% | 39.85% | 44.36% | 40.23% |
| 36.47% | 38.35% | 37.22% | 41.73% | 37.59% |
|
266 or 532 may not be a big data set, yet it does not seem to try to reach an equal amount in every field. This has been confusing me. If we assume that it is completely random shouldn't each field have the same amount in the long run? That's not the case here though. There are what seems like random oddities all over it. Of course, I might have made some mistake here and there but none that should affect the result by that amount. Apparently, there are a few safer places as shown by the darker green in the percentage view.
Three Wall Spawn
| 732 | 729 | 715 | 711 | 706 |
| 723 | 720 | 699 | 693 | 699 |
| 726 | 715 | 694 | 686 | 693 |
| 692 | 692 | 669 | 672 | 676 |
| 752 | 759 | 738 | 729 | 735 |
|
| 60.95% | 60.70% | 59.53% | 59.20% | 58.78% |
| 60.20% | 59.95% | 58.20% | 57.70% | 58.20% |
| 60.45% | 59.53% | 57.79% | 57.12% | 57.70% |
| 57.62% | 57.62% | 55.70% | 55.95% | 56.29% |
| 62.61% | 63.20% | 61.45% | 60.70% | 61.20% |
|
Looking at this result... okay, seriously. Is this generated using Perlin noise? If you assume this to be a height map, it could be some area straight out of Minecraft. That's soo weird. Nevertheless, it shows the safer places during the longest phase turn out to be in the lower right part of the platform. Now, this might have been the result of how we pulled her, however, I've checked fifteen different days for between half an hour to three hours and our tanks start off with a pattern but switch to going wherever the walls and exploding deads lead us to. Usually, when something is random there is still a pattern behind it. For example, when throwing a dice randomly each side should appear an equal amount of times at some point.
Four Wall Spawn
| 444 | 376 | 366 | 372 | 444 |
| 368 | 298 | 290 | 296 | 368 |
| 361 | 291 | 283 | 289 | 361 |
| 377 | 308 | 299 | 305 | 377 |
| 444 | 376 | 367 | 372 | 444 |
|
| 100.00% | 84.68% | 82.43% | 83.78% | 100.00% |
| 82.88% | 67.12% | 65.32% | 66.67% | 82.88% |
| 81.31% | 65.54% | 63.74% | 65.09% | 81.31% |
| 84.91% | 69.37% | 67.34% | 68.69% | 84.91% |
| 100.00% | 84.68% | 82.66% | 83.78% | 100.00% |
|
Here, we can see that 2 pieces are always forced to spawn in the corners resulting in the corners being covered by each wall that spawns at some point. This also - due to the nature of how the walls or waves move - results in very dangerous corners. This doesn't matter too much since the outer ring should be nearly impossible to touch without dying as the platform has been decreased to more or less a 3x3 area. Obviously, the middle is safer now. Besides from this fixed field, it seems like the corners and edges are yet a tiny bit safer than the middle. Whether or not this matter depends on how much you believe in numbers. I don't think this is the case though. We have three safe fields and two walls will always occupy two of those three safe fields at some point. That means 33% of a lane is going to be safe while the rest - the 66% - are covered by a wave. If this is completely random each area in the middle should end up with a coverage of 66%.
Total Coverage
| 1284 | 1218 | 1191 | 1205 | 1261 |
| 1192 | 1124 | 1092 | 1094 | 1171 |
| 1179 | 1103 | 1071 | 1081 | 1149 |
| 1173 | 1109 | 1074 | 1095 | 1160 |
| 1293 | 1237 | 1204 | 1212 | 1279 |
|
| 67.19% | 63.74% | 62.32% | 63.06% | 65.99% |
| 62.38% | 58.82% | 57.14% | 57.25% | 61.28% |
| 61.70% | 57.72% | 56.04% | 56.57% | 60.13% |
| 61.38% | 58.03% | 56.20% | 57.30% | 60.70% |
| 67.66% | 64.73% | 63.00% | 63.42% | 66.93% |
|
If we sum up all the walls and touched areas we get this total coverage. So, if you're interested in an overall that does not care about the length of each phase this is the result. The safest area in the middle, still. Obviously, since the last phase strictly prohibits us from moving into the outer ring. Is this the reason people came up with the idea that big walls spawn when you go outside? To scare people from staying in the middle without explaining it mathematically? Hmm...
Weighted Coverage
| 623.04 | 576.69 | 563.67 | 567.17 | 612.16 |
| 567.55 | 519.86 | 505.17 | 506.81 | 557.53 |
| 563.25 | 512.12 | 497.43 | 499.21 | 549.36 |
| 560.55 | 514.82 | 498.6 | 505.11 | 553.97 |
| 630.54 | 588.49 | 573.13 | 573.81 | 623.53 |
|
| 72.64% | 67.24% | 65.72% | 66.13% | 71.37% |
| 66.17% | 60.61% | 58.90% | 59.09% | 65.00% |
| 65.67% | 59.71% | 58.00% | 58.20% | 64.05% |
| 65.36% | 60.02% | 58.13% | 58.89% | 64.59% |
| 73.52% | 68.61% | 66.82% | 66.90% | 72.70% |
|
For the weighted coverage, we consider the length of each phase as well. This means the first phase plays hardly to no role and the last phase only a bit. We still get a result similar to the total coverage, however. There are some slight changes in percentages here and there, overall nothing new.
So, There We Have It!
An analysis of which area of the platform is the safest and whether or not there is a pattern to the coverage. The end results show that there's more at play than just randomness. At least that's what it seems like to me. Except for the fourth phase, the total coverage and weighted coverage, it pretty much seems like some kind of noise function.
Fun
I've created this height map from the three-wave data using Python and Matplotlib. It's always fun to do these things. Seriously, Python is awesome.
