Population Density: Guestimations

Tapman · 2012-03-12, 07:52 PM

CAUTION: MATH AND WORDS AHEAD.

Before I begin, let me first request clarification from a developer. My calculations below are based on my understanding that each CONTINENT would be able to host thousands of players, meaning a minimum of 667 players per faction. The PC Gamer article indicated that it would be 666 v 666 v 666 per SERVER, meaning those numbers would be spread across four continents. I really hope that my assumption is correct, if not then I'll have to re-do my calculations. [/Caveat]

The AGN broadcast and lots of folks have discussed how nobody really has any idea what gameplay will be like once the populations approach the starting maximum, we've seen a few demo scenarios that looked roughly scripted but Higby even stated that they have a hard time knowing how the dynamics will change when the battlefield fills up. There is concern over the "Following" system as Planetside has what is described as the "Zerg" and the few coordinated outfits that really make shit happen. My goal was to try to get a more accurate picture of what the numbers will truly scale up towards, based on the mathematical parameters given.

EDIT: Apparently the math and words below needed a more concise summary. TL;DR: everyone needs to chill the fuck out and wait until Beta to see if it's too spaced out/crowded, and try not to focus on the commanding system becoming a popularity contest based on politics because results won't lie.

My first step was to get estimated distances of the actual front lines. I counted the number of edges each empire had with an enemy on the other side based on the GDC map that we saw, their totals are as follows with T=(length of one hex edge):

VS: 50T
TR: 40T
NC (Main): 42T
NC (Secondary): 26T

In order to find out the actual distance, we have to find T. We solve for it using the equation for the area of a single hexagon, the total area of the continent, and the approximate number of total hexes on the continent. I attempted to count the number of raw hexes each empire controlled from the GDC footage, the VS may have more because we never saw a full view of the north end of the continent but I approximated that there weren't too many more as you can see the VS foothold. My counts were as follows:

NC: 112
VS: 90-95
TR: 96

This gives us 298-303 total hexes for this continent, I rounded that to 300 as we aren't working with that many significant figures. The total (assumed) area of this continent is 64 square kilometers, so therefore:

64km^2/300 hexes = 0.213 square km per hex

Plug this directly into the equation to find the distance of one edge of a hex:

(3/2)*(3^0.5)*T^2 = 0.213

T = 0.286km

Plug T into the front-line distances I noted earlier, and you get the following:

VS: 14.3km
TR: 11.4km
NC (Main): 12.0km
NC (Secondary): 7.4km

I wanted to create a mathematically "Normal" scenario where you have every single soldier at their front lines either attacking or defending with as equal distribution as possible. Assuming each empire has 667 people on the continent, the front-line density is as follows:

VS: 46.6 players/km
TR: 58.3 players/km
NC: 34.3 players/km

Breaking it down even further, you get:

VS: 13.3 players/edge
TR: 16.7 players/edge
NC: 9.8 players/edge

At first glance, these numbers seem low. Looking at the map though, you will note that the contestable edges of hexes varies from one to four, one generally being on the edges of the map and four being towards the middle. Not only that, but there will be times when you have a large hex group that is mostly surrounded, i.e. the southernmost VS territory has 13 edges that are immediately adjacent to enemy territory, meaning that territory would have about 173 players defending it. Another interesting figure to look at is the average distance between friendlies along that front line:

VS: 21.5m
TR: 17.1m
NC: 29.2m

We have been told that 0-20m is close range, 20m-100m is medium range, and 100m+ is long range, assuming you are on foot. I can only imagine the madness that it will be when you throw vehicles and MAX units into the mix.

What I take away from this is that the "Zerg" will most likely become an obsolete and easily countered strategy. It became the standard in Planetside because there were preset pathways to enter continents and often times there were few bases that could be targeted even after you managed to get a foothold on a new continent. In Planetside 2 there will be plenty of fights with hundreds of players on each side in the larger hex groups but any leader who relies on having the biggest swarm will ultimately end up hurting their empire overall, a check and balance to the potential abuse of raw numbers.

Feel free to poke holes in or make fun of my math. I promise to re-do it if I get more specific numbers from a Dev and/or if anyone finds errors or something I didn't notice/account for.

Mirror · 2012-03-12, 08:00 PM

I thought it was figgy posting again when I looked at the wall of text and calculations.

/not reading this either.

NewSith · 2012-03-12, 08:04 PM

Italize the main ideas, so it's easier to read.

EDIT: I read it and, well, thanks for sharing your thoughs, now I have some food for my brain

EDIT2: Also fights will always be concentrated, this is where objective value and landscape specifics step in.

KALU · 2012-03-12, 08:14 PM

sorry dude, agree to much to read. Please simplify.

Should be very interesting in beta to see it all play out and stress test the shit out of it though. I bet everyone at SOE and PS dev team cant wait for us all to get in and see how it goes.

Aurmanite · 2012-03-12, 08:16 PM

And they say this generation can't focus on any one thing for more than a minute...

VioletZero · 2012-03-12, 08:22 PM

This is why I hate working in game design. Because I hate math.

Tapman · 2012-03-12, 08:22 PM

My apologies, physics major in college so I didn't think that algebra and unit conversions would be too involved, working up some simpler points to put in the intro.

NewSith · 2012-03-12, 08:27 PM

Originally Posted by Tapman

My apologies, physics major in college so I didn't think that algebra and unit conversions would be too involved, working up some simpler points to put in the intro.

It's not about the complexity of terms, it's about text indescreetness.

VioletZero · 2012-03-12, 08:28 PM

Ever consider working in game design?

They love producing charts upon charts upon charts of this ****. How long does it take to walk two paces. How long does it take to walk up a flight of stairs. How many enemies in a room before they kill you in two seconds. God damn it, it is so boring. But you'd love it.

Aurmanite · 2012-03-12, 08:31 PM

Originally Posted by NewSith

It's not about the complexity of terms, it's about text indescreetness.

The what?

On topic:

Looks like there will be a lot of see-sawing across the front line. The empire best able to mobilize the front line and respond to openings/threats will be dominant.

Get to hex 4!
Back to hex 3! Hex 3!
OMG Hex 4!

Tapman · 2012-03-12, 08:33 PM

Originally Posted by NewSith

It's not about the complexity of terms, it's about text indescreetness.

I highlighted and size-changed the important bits, better?

NewSith · 2012-03-12, 08:35 PM

Originally Posted by Aurmanite

The what?

As in "monochromy".

Originally Posted by Tapman

I highlighted and size-changed the important bits, better?

Well, I already read it, though, what I meant was highlighting general phrases (maybe with bolds, not italics even) so you can glue them up into one much shorter text. Your text (unlike Figgy's) leaves room for that.

Death2All · 2012-03-12, 08:37 PM

Did they really say 666v666v666 per server? I was under the impression that that that was a continent based population cap and the servers themselves could grow way larger.

Fortress · 2012-03-12, 08:37 PM

I wouldn't count out the zerg just yet. I can imagine most players caring less about the hexes and more about the larger facilities (and the larger fights they will guarantee), resulting in one large blob charging towards the closest base while smaller teams push out the flanks.

But again, wait4beta etc.

Tapman · 2012-03-12, 08:39 PM

Originally Posted by VioletZero

Ever consider working in game design?

They love producing charts upon charts upon charts of this ****. How long does it take to walk two paces. How long does it take to walk up a flight of stairs. How many enemies in a room before they kill you in two seconds. God damn it, it is so boring. But you'd love it.

I would have applied for a job at SOE while I was still on the west coast if I had known Planetside 2 was being developed. I'd be open to consulting in my spare time if they were interested, brainstorming ideas for Planetside 2 is one of my favorite things to daydream about.

I'm not the biggest fan of doing math but if I have the tools at my disposal I can enjoy extrapolating new information out of raw data when it comes to stuff I am passionate about.

Originally Posted by Fortress

I wouldn't count out the zerg just yet. I can imagine most players caring less about the hexes and more about the larger facilities (and the larger fights they will guarantee), resulting in one large blob charging towards the closest base while smaller teams push out the flanks.

But again, wait4beta etc.

Like I said, there will be larger battles for the large hex groupings (largest I counted was seven hexes!) so that will naturally attract large groups, but since there will be multiple capture points throughout those facilities I think it will force leaders to micromanage their swarms a lot more which will impose its own limitations on how many people one person can manage.

Originally Posted by DeeTwoEh

Did they really say 666v666v666 per server? I was under the impression that that that was a continent based population cap and the servers themselves could grow way larger.

First paragraph of the article after the main introduction. This guy was also the one that stated Galaxies were 12-man transports, I thought that Higby had mentioned they would hold 10 as it was directly related to squad size.