Guide to New Raid Bosses

Quite a long title, huh? Well, I've been working mostly on my games homework from university and I'm kinda sick of it right now, haha. xD Anyways, lately I've been asked by a person how we find out so fast on how bosses work so I want to give the people who have no idea some tips.

Brute Force Way

Before I give you some tips let's go most easily: brute force. It basically means, doesn't think too much about keep trying and every time your group wipes try to figure out why and solve the issues at hand. Of course, if you keep this up at some point you survive long enough to kill the boss. Bam, you made it! This doesn't sound too efficient though.

The Basics

Most of the bosses in raids, regardless of the game - yes, you heard right in all games - basically, work with the same mechanics. I mean think about what a game designer can do in a game. Since nearly all MMORPGs work with similar systems like buffs, debuffs, stuns, stun breaks, healing, tanking, collecting, moving and more. Additionally, they inspire each other. Well, since the mechanics reappear throughout different games but mechanics also usually don't change in the game itself and raids are build using the tools already in the game what you have will mostly suit what is needed for a boss.

Just check out the abilities you have and what they do:

• "Deals damage"
• "Stuns the enemy"
• "Breaks a stun"
• "Heals allies"
• "Taunts the enemy"
• "Leaps"
• "Teleports"
• etc.

Boss fights are not designed to be impossible. They're basically a combination of challenge and puzzle. Solve the puzzle, overcome the challenge and they're dead. So, familiarize yourself with bosses, the more you see the easier it becomes for you to figure things out. Especially if you know your class or even other classes. The more you know about what the players can do the more easy it becomes for you to figure out what the developers intended. Know the limits within which you have to work!

Survive, Deal Damage, But Most Important Analyze

The hardest part next to solving the puzzle is the ability to analyze the fight while still doing your job. The less stressful a boss is the easier this is. Basically what you want to look out is the mechanics of the boss. Here you want to answer the following questions:

Buffs & Debuffs

•  Does he have buffs? Does the group have debuffs?
•  Do the boss or the group get these during the fight?
• Where do they come from? What do they do*? 

* Note: It is often wise to post buffs and debuffs to chat or screenshot them in the old-fashioned way to discuss after the try.

Attacks

• What can the boss do? When does he do what?
• Is it time-based? Is it health based? (at 75% or 66%.)*
• Which attack hurts how much?
• Does he have mechanics that instantly kill?
• Are there scripted events? What happens?
• Does he have an attack pattern?

* Note: Game developers love to use these numbers like every 5% every 10% every 20% every 25% or every 33%.

Map Awareness

• Does the map mark something? Does it mark something throughout the fight?
• What symbol is used? What could it mean?

Surroundings

• What's in the boss arena? What is on the ground?
• Is there a pattern matching the fight?
• Are there AoE fields? Does the arena change?*
• Are there minions or adds spawning? Are they bound to an important mechanic?
• Are there visual effects? What do they do?
• Are there sound effects? Where do they come from? What do they mean? Are they important?

* Note: Developers seem to love to destroy the platform or decrease the area the player works with.

Boss Itself

• Is the boss attackable? Is there something that needs to be done first?
• How does aggro work? Does he need CC? When does he need CC? 
• What happens if you don't CC?
• What works/doesn't work well on him?

Grouping

• How many people need to do what?

Achievements

• What achievements are there? What happens if you fail them*?

* Note: Sometimes failing an achievement triggers mechanics that deal with group damage or do otherwise bad things.

Answering these questions together in your group should give you a good idea about the encounter and boost your speed of killing it. I mean you can always leave this to other people but.. hey. Now you have a good idea of how to do it yourself for the next boss you come across or if you wanna faster with your group on a new boss without waiting for a guide.

While this sounds like the end of the post I've got one more thing for you.

Good Game Design & Boss Mechanics

In a game with good game design coming across a new mechanic in a boss fight that hasn't been explained yet often has an explanation of the mechanic beforehand. In the best case, you will have the mechanic or a similar mechanic be played before the boss with some miniboss or enemy that shares this. It could also be possible that the players are told this by an NPC or have to read it which is sloppy, but at least it's explained.

From a game design perspective, you don't want your players to go into a fight completely empty-handed. You always want to at least hint to the solution so that it is technically possible to figure out the fight first try. (Which is rarely the case).

Just look out on whether or not you've seen similar mechanics somewhere else.

There You Go: A Guide to New Raid Bosses

This all should be enough to get you started on having an easier time learning new raid bosses. I'm actually gonna create a quick google form for one simple question. Just wanna know if you'd be interested in me giving examples for this or actually explaining primarily WildStar and Guild Wars 2 raid bosses from a mechanics and/or player guide perspective.

So there you go: >> Towards the questionnaire!

Game Design: Horizontal Progression in MMORPGs

A few days ago I made a post about the vertical progression often seen in famous MMORPGs like World of Warcraft. A different one is the horizontal-progression that has been seen in games like Guild Wars 1 and Guild Wars 2 for example.

Horizontal Progression in MMORPGs

Horizontal progression is something I often compare to "personal" development. I'm not talking about programming or making something new, I'm talking about development as in progress or improvement here. While vertical progression is compared to "player" or "character" development, meaning your character gets better and stronger as described in the vertical progression post.

So how do you as a person improve compared to your character?

Due to the best gear being capped rather early, all the bosses can be matched to this gear level. Since there's no change between content it's rather easy to balance the bosses to each other. This allows for a more precise difficulty curve.

There's no increase in the strength of the character from the end-game on. Without an increase of level, damage and/or gear for the upcoming content these factors cannot compensate for the player's lower skill. Thus generally resulting in an increment of the player's skill and capability.

Idea Behind It

Just like mentioned above a horizontal progression throws out the player's improvement through stats, leveling and gear grind and replaces it with more or less equally difficult but different content. Additionally, this prevents power creep in the end-game content any added content stays relevant. This also means you can play with your friends anywhere at any time, as the gear or level difference does not exist in the end-game. (Lower level areas in these games often work with downscaling resulting in more or less an equal strength allowing to follow your friends even if they're not in the end-game).

Elements of Horizontally Progression

Generally speaking, horizontally progression is something that's not vertical progression. If you remove the vertical progression you basically get horizontal progression. However, something that should be mentioned here is

Build Variety

One of the elements that are common to horizontal progression is to build variety. The reason for this is to allow bosses and areas to require the player to implement certain strategies and requiring the player to think and solve the problems thrown at them.

Disadvantages

Vertical and horizontal progression are both plagued with disadvantages as well, this time we're gonna look at the horizontal progression.

The Loot Sucks

This is one of the biggest issues for people who are used to a vertical progression. The loot you will find will most likely be useless to you. Since there's no vertical progression the gear does not improve and at some point, you will have everything best in the slot. 

No Feeling of Being Overpowered

If there's no power creep you'll never feel overpowered. This is both an advantage and disadvantage but I'll list it as a disadvantage. If you like to feel more powerful than the older enemies to remind you that you have improved then I have to disappoint you. This is not a part of horizontal progression. The least you will get is knowing the enemy, mechanics and having experienced them often enough to know how to deal with them.

Seeking For Missing Character Development

Accumulating all the aspects you will notice one thing that's a big deal. You might not know what to do. Without better loot, no grind and no leveling, you might wonder what you want to do. This is often a reason these seem more like a sandbox MMORPG but that depends on the game's focus and balance in development.

Exponential Work For Developers

Add-ons to MMORPGs add new content and new areas to the game. The old areas need to be taken care of as well in horizontal progression oriented games. This means that over time the game will accumulate more and more content that needs to be taken care of. Thinking about it, this also increases the number of employees you need and thus will result in an exponentially growing cost.

Final Notes

Again keep in mind neither horizontal nor vertical progression are perfect. So far to my knowledge, no one came up with a diagonal progression based MMORPG. Mixing the positive aspects and fixing the disadvantage would result in a bigger game with a bigger target audience. The reason I'm so invested in this is that I have friends who prefer vertical progression and me, to be honest, prefer horizontal progression more. This brings a divide in the games we play. If people move from WildStar they either go to Guild Wars 2 or World of Warcraft (from my experience though there might be exceptions). Besides what's an MMORPG without a big MMO community? Keep in mind that most of the information here is from personal experience, reading a little upon the topic, analyzing the games I've mentioned that seem to implement these game designs and questioning people and talking over this topic. Thus I can't say for certain that the information is 100% reliable or that I might have forgotten information as well as further points and disadvantages. Still, it is important to share this information as it might help other game developers or people to come up with a solution or to better understand these systems and terms.

Natural Diminishing Returns on Critical Hit Chance

Hold up! I can't believe it took so long to notice. This post is actually a misconception about probability I ran into. This is not an actual diminishing return but a perceived one.

A few days ago I explained that linear functions have a diminishing returns if we look at the damage increase we get at higher values. I also explained that it's even worse if you look at how difficult it is to get stats generally in games. Next up I want to talk about the natural diminishing returns on the critical hit chance.

Natural Diminishing Returns

Before I start, a quick reminder of what natural diminishing returns are. Diminishing returns can be broken down into the words diminishing which means a decrease of something and returns stands for the output or the amount we get from something. An example in video games let's say there's an attribute called strength. Each point of strength gives you about 1 damage. Now we put in 50 points into strength and our damage increases by about 47. If we put in 100 points we get 86 damage. Notice that the value you get out keeps decreasing.

The difference between diminishing returns and natural diminishing returns is that normal diminishing returns are programmed into formulas and such. Natural diminishing returns, however, appear due to the way the math works and is often not visible on it yourself. The example we used last time was that you increase your strength by 50 and you get 50 damage. If you double your strength you add 50 more strength onto it and you get double the damage, so plus 50 here too, the damage is increased by 200% or 100% of the damage is added upon it. If you add another 50 strength on the 100 you get 150 strength and 150 damage. The damage increase is only 150% or 50% of the damage is added upon it.

Mathematically: 100 / 50 =  2.0; 150 / 100 = 1.5

For more details on this check out the older post.

Critical Hit Chance is Linear

Just like the older post, critical hit chance is linear as well. For each 1% of critical hit chance, you get a 1% critical hit chance. Using Guild Wars 2 as an example getting 21 precision increases your critical hit chance by 1%. It doesn't matter how much precision you have, this is always the case. To illustrate the linearity here's a graph showing the conversion. The formula used in Guild Wars 2 for critical hit chance is 

criticalHitChance = (precision - 895) / 21;
{precision | precision ∈ R and precision >= 1000}

This means the function of our graph is:

f(x): y = (x - 895) / 21; {x | x ∈ R and x >= 1000}
Keep in mind that: {y | y ∈ R and 0% <= y <= 100%}

I don't know about you, but this definitely looks linear to me.

How Critical Hit Chance Behaves

Critical hit chance is a percentage that tells us how likely it is for an attack to be a critical hit. This that when the amount of your attacks goes against infinity we get an average of how many attacks critically hit. For example, if we say we have 0% critical hit chance, without much explanation this means you'll never critically hit. If we have a 100% critical hit chance, every attack will hit critically (1 / 1).

If we have a 50% critical hit chance this means that if you do infinite attacks against an enemy you will critically hit it 50% of the time. This is about every second hit (1 / 2).

Now you might notice something.

• 0% means no critical hits
• 50% means about every second hit
• 100% means every hit

If you didn't notice it yet, no problem let's just continue then. As the next example value, we're gonna take 25%. When we attack the enemy infinite amount of times you will see, simply, 25% of our attacks will hit. On average that's every 4th attack (1 / 4).

Now about the 0% thing... let's assume we don't have 0% but nearly 0% critical hit chance. That means we could potentially hit critically but it's as impossible as it can be. To remind you of it I'm gonna write 0.0000...%. This is important that it's not 0%.

What we have now is 0.0000...% which means nearly 1 out of infinite attacks hit critically.

• 0% means nearly one out of infinite attacks hits critically (lim x->∞ (1 / x) = 0.0000...%)
• 10% means every 10th attack hits critically (1 / 10)
• 20% means every 5th attack hits critically (1 / 5)
• 25% means every 4th attack hits critically (1 / 4)
• 50% means every 2nd attack hits critically (1 / 2)
• 100% means every attack hits critically (1 / 1)

I only wrote down the rounded numbers. Such a great idea, this illustrates it even better. Just look at how the numbers behave. From 0.0000...% to 50% we went from one out of infinite to every second. Surprisingly from 50% to 100%, we went from every second attack to every attack.

This is definitely a diminishing returns. Let's plot it so everyone sees in black on white. Actually, I use the standard blue line.. so it's blue on white... though the axis is black.

Not so linear anymore. Here you can see it the more critical hit chance you have the less effective it becomes. Using analysis we can determine the exact point where critical hit chance stops to be as effective as it has been up until then. 

Game Design: Vertical Progression in MMORPGs

I play both WildStar and Guild Wars 2 and I am aware that there are still many people playing World of Warcraft. I know both Guild Wars 2, WildStar and WoW - or other MMORPGs for that matter - have their disadvantages and advantages. Still, I see things wrong and things great on their progression philosophy.

Vertical Progression in MMORPGs

Vertical progression is progression by improving your character in strength. Regardless of which role you play:

• A damage dealer will increase their offensive attributes to deal more damage.
• A healer will increase its supportive capabilities to heal more.
• A tank will increase its defensive stats to improve their survivability and durability.

Most often the vertical progression is implemented by adding new content with a higher level and/or increased attributes of their owns. To put it this way: new content means you play against enemies that had a headstart in gaining experience and gear and you overcome these to work your way onto the same level and to the new end-game.

Idea Behind It

The idea behind this is to keep the player engaged by having challenging end-game content since the player always starts weaker than the respective content. Additionally, the improvement of the character's capability and growth gives the player the ability to increase their strength along with the different challenges that lay ahead. Another idea behind it is to have a linear experience, in which you play the content level-wise or difficulty-wise which goes hand-in-hand with the difficulty curve. Another important point is that vertical progression came from RPGs where leveling and gear allowed the player to beat content by equalizing their skill with level grinding or grinding for better gear.

Elements of Vertical Progression

Leveling

Probably the most common vertical progression in games is leveling. For this, the player needs a certain amount of experience gained from different activities most often from killing opponents though. Leveling can be seen as learning progress, however, if used in the end-game or throughout the whole game until the end-game it's vertical progression. Each level increases the player's stats or allows the player to become stronger and keep on getting stronger.

Gear

The second most common vertical progression is gathering better gear. For this one, the player will need to do a certain content or beat a certain challenge one or multiple times to be able to get better gear which will reward the player with higher stats and thus resulting in a stronger character.

Disadvantages

Don't worry horizontal progression has disadvantages as well, but we'll take a look at those later so let's start with the more common vertical progression first.

Power Creep

So, if you never heard the term power creep then you're in luck now. Power Creep describes the increasing irrelevance of older content due to the increasing power of the player. If you ever played a game with vertical progression and you went back to the very beginning of the game you should know that fighting enemies there is probably close to one hit if not already. Additionally, the rewards are also interesting. What happened here is that you progressed through the vertical so much that the older content doesn't reward you anymore and additionally everything falls over by your pure sight. This is an issue as in MMORPGs there is no reason for you to play with your friends who are levels below you.

Throw-Away-Mentality

This works hand in hand with the power creep but adding new harder higher content to the game to keep players engaged in the vertical progression results in a throw-away-mentality for the game developer. New content, throw away the old, new content, throw away the old, etc.. It's the same for the player and their gear, the old stuff is thrown away the new stuff will be kept. The weight of this downside can be argued but it is a disadvantage after all.

No Clean Difficulty Curve

This applies to many games, but due to the varying quality of items and the varying level of your character, you may jump up and down between the difficulty curve. In RPGs, this was used for the player to be able to balance the game themselves (e.g. grind levels if they couldn't beat a boss) in an MMORPG this mentality doesn't work too well though. At least I haven't experienced it yet in my more or less eight years of MMORPG experience.

Weaker Player Progression

Additionally, since the gear and levels play a huge role, a higher level or better gear can balance the player's skill. This sounds positive at first but in the end, it's a double-edged sword. If your MMORPG is skill-based then this is a bad thing. Additionally, if you want your player to improve over time this could also hinder this progress. That's why I count it as a disadvantage here.

Final Notes

I want to mention here that vertical progression isn't perfect, neither is horizontal progression. Having a mix between these designs is not something one could come up with easily. Hence it hasn't been done. There are definitive disadvantages in both designs and solving these flaws would allow MMORPGs to enter a new area and a bigger audience, which MMOs need to thrive. The information I mentioned here is an opinion I have build from experience, questioning people and analyzing these games. This means that information may not be 100% accurate and that I may have skipped points or further disadvantages. Yet, even an opinion is worth reading through and to give a benefit of a doubt, because who knows. Maybe this is exactly what some people needed to come up with the next great idea.

Natural Diminishing Returns on Linear Functions

So, I actually went into a discussion with a fellow guild member on natural diminishing returns. He claimed there are no diminishing returns if the function that relates to the main stat that increases damage and the damage increase is linear. Well, he's right. There are no diminishing returns as we might know it, however, there are a natural diminishing returns. Let's break it down.

Diminishing Returns

First of all, let's clarify what diminishing returns means - in case you don't know, you can skip this paragraph if you do. Diminishing means a decrease and returns means something you get back. Both words together mean you get back a decreased value. In an example, we say we learn a language for one hour and we manage to keep 24 words from this session. Now we learn another hour with no pause in between and we manage to keep 22 additional words from the lengthened session. We keep pushing learning for longer and longer, but at three hours or so we would have only kept maybe 60 words in mind when we expected to have 24 words for each hour for three hours, so 24 * 3 = 72. As you can see there's a trend down, the diminishing returns.

Common Occurrence in Games

From my experience with a handful of people, I've seen that diminishing returns is known by people who are less active or interested in theorycrafting as a mechanic that affects loot drops. The longer you farm the same content the less loot or drops you get. This - of course - is diminishing returns as well. However, in the theorycrafting community, it's more about the damage increase or stat gain.

Damage as a Linear Function

For the purpose of the explanation I'm gonna use the damage calculation from Guild Wars 2:

damage = (weaponStrength * power * skillMod * positiveMods) / (armor * negativeMods)

Now, the fun part is - if you didn't sleep during your physics classes - we know that we're going to keep a few variables the same. If we compare our damage to another example and only change one value the rest becomes constant.

For our purpose, we only change power. Let's say we have the following values:

damage = (1150 * 1000 * 0.35 * 1) / (2597 * 1) = 154.98652291105122

Now, we change the value of power and leave every other value constant:

damage = (1150 * 2000 * 0.35 * 1) / (2597 * 1) = 309.97304582210245

As you can see, we doubled the power and our damage value doubles as well. Do not believe me?
Here you go:

309.97304582210245 / 154.98652291105122 = 2.0

This means, as long as all the other values do not change we can directly modify the value by the factor we change it. To simplify our calculation we can replace any constant values with a 1:

damage = (1 * 1000 * 1 * 1) / (1 * 1) or damage = 1000

Next up let's look at how our damage behaves if we increase our power by one steadily. For this, I'm gonna plot the function. Though we already claimed that our simplified function is damage = power.
Additionally, we started with 1000 and I claimed to steadily increase it by one. It shouldn't be hard to realize that the function we get is linear starting at 1000 and increasing by x:

 f(x): y = 1000 + x

 Nice and big for everyone to read.

Natural Diminishing Returns Behind Linear Functions

Thus far, we haven't seen any diminishing returns. Now let's do the following:

We start off with 1000 power which directly translates to 1000 damage or 1000 * otherFactors damage to be specific. If we add 1000 power to our base of 1000 we get 2000 power or twice the damage. This means if we double our modifier we double our damage. Funny enough we can look at the damage increase for each point of power we get. To calculate this increase there are multiple ways to do it but my favorite way is to calculate:

damageChange = (newStat / oldStat - 1) * 100
damageChange = ((oldStat + change) / oldStat - 1) * 100

We could calculate this 500 times.. or we simply leave that to the computer. Time is too precious to waste anyways.

damageChange = ((oldStat + x) / (oldStat + x - 1) - 1) * 100

Now let's run it for oldStat = 1000.

As you can see the line decreases. This means for each point of power each additional point of power loses in value or worth. Well, yeah, there you have it, diminishing returns in linear functions.

Worse With Min-Maxing

(min-maxing describes the act of more or less pushing and pulling out the last few improvements. It's the difference between 95% of what's possible and ~99% of what's possible. Might write a blog post about that as well... *shrug*)
However, in many games "one does not simply double their main stat". The stat gain in many games behaves like a log function at higher values. This means the more stats you get the harder it will be to get even more of it.

If you do not know what this looks like here you go:

As you can see, it's easy to get power at the start but at some point, if you have your main stat everywhere you can have it, it's just a few sources here and there where you can still get some making it hard to keep ongoing.
***NOTE: This is not a graph that represents the exact way this behaves in any games or in Guild Wars 2.

Guild Wars 2: Danger Level at Desmina's Platform - Part 2

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.