Resource Galaxy Statistics

[c4sc4]

There was some discussion in the 5.031 thread about the average number of resources in a galaxy. I decided to generate a bunch of galaxy and did some statistics about the resources. None of my data includes the 3 homeworlds. Also, these galaxies were generated with no minor factions enabled (didn't look like it changes anything though) and all 3 expansions enabled. I generated 10 galaxies for each number of planets using the grid map type, expect for 25 & 15 planets which used the snake type. Turns out that Grid was a bad choice because of how it is generated, it causes a lot of the different number of planets to spawn the same number of planets (ie, 80 and 70 both generate 80 planets). So, this is currently missing several number of planets(from here on out refereed to as P#).

I tested 120, 100, 80, 60, 40, 30, 25, 20, 15 and 10 P# but the actual number of planets in each P# was: 121, 100, 81, 64, 49, 36, 25, 20, 16 and 10. At the higher P#, the resource statistics are close together between each trial but as the P# decreases things start to break down and the difference between each trial is larger. The statistics for each P# as a whole all tended to be close together though, yay math. Now onto the actual numbers.

Code: [Select]

---120(121) P#---
Average: 4.104237288
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 1.99238985

---100 P#---
Average: 3.958762887
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.012948414

---80(81) P#---
Average: 4.087179487
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.078705468

---60(64) P#---
Average: 3.949180328
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.04683447

---40(49) P#---
Average: 4.136956522
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.029398174

---30(36) P#---
Average: 3.975757576
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.033014786

---25 P#---
Average: 3.922727273
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.073629121

---20 P#---
Average: 3.964705882
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.092234494

---15(16) P#---
Average: 4.238461538
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.145136363

---10 P#---
Average: 4.071428571
Median: 4
Mode: 4
Min: 0
Max: 8
St. Dev: 2.080422397

As you may have noticed, the median, mode, min and max were the same for each P#. The averages all differed but were very close and between all trials I got an average of 4.040939735 resources per planet.

All ten trials in for P# 120, 100 and 80 had a min of 0 and a max of 8. At 60 and below P#, there were several trials who had different mins and maxs. 27 out of 100 trials had a min above 0 while 23 out of 100 had a max below 8.

So it looks like 4 resources per planet is the average for a galaxy of any size.

If anyone wants some other statistics with this data, let me know and I'll try to get it.

[_K_]

Thank you for the research i was too lazy to conduct on my own.

Too bad theres some kind of rule that the more thorough and precise your suggestion for the devs is, the less its likely they will implement it that way. Making a simple and small statement usually works much better. Probably has something to do with psychology and feeling like you are obeying someone's order as opposed to just following someone's hint.

But damn i just love optimising and playing around with excel spreadsheets, and since no flaws have been detected in my suggestion, i still believe that it offers the best possible solution to the current situation with the harvesters.

[keith.lamothe]

Too bad theres some kind of rule that the more thorough and precise your suggestion for the devs is, the less its likely they will implement it that way.

Sir, that wounds me.

[keith.lamothe]

@c4sc4: thanks for actually doing the numbers, I should have done that myself   Will bear them in mind when rebalancing the harvesters.

[Nodor]

Thank you for the research i was too lazy to conduct on my own.

Too bad theres some kind of rule that the more thorough and precise your suggestion for the devs is, the less its likely they will implement it that way. Making a simple and small statement usually works much better. Probably has something to do with psychology and feeling like you are obeying someone's order as opposed to just following someone's hint.

But damn i just love optimising and playing around with excel spreadsheets, and since no flaws have been detected in my suggestion, i still believe that it offers the best possible solution to the current situation with the harvesters.

Most specific "feature suggestions" on this board, are "this feature would be really cool" without consideration for "this would totally destroy the game balance, is completely unreasonable, or take 2,000 hours to code".  For instance, I want beautiful graphics with individually animated turrets on ships.  Ergo, I need everyone in the world to be running their own personal server, so the average computing power needed for that graphic update to make business sense is out in the marketplace.   Requiring the world to be different than it is does not qualify as a reasonable request, even if the desire for more beautiful graphics seems reasonable on the surface. 

To credit the community, I would argue that the suggestions on the board are used/considered more than 25% of the time.  This beats the 1-2% of most other titles.

[Cyborg]

Too bad theres some kind of rule that the more thorough and precise your suggestion for the devs is, the less its likely they will implement it that way. Making a simple and small statement usually works much better. Probably has something to do with psychology and feeling like you are obeying someone's order as opposed to just following someone's hint.

I am undoubtedly one of the most critical customers. I'm the first to point out ego problems, but let's be clear about some indisputable facts of Arcen Games:

1) they incorporate more fan feedback than any company I've ever seen, and I'm an old school gamer.
2) game balance changes are not based on emotional roller coasters but game experience and statistics together
3) it is their game. They own it, they sell it, and they can do with it what they want when it. I think we are pretty lucky that they didn't abandon the game after they released it, and that it has evolved almost biweekly since the day it came out. How many games can you say that about? Zero.
4) They are human beings with emotions and passions for their games just like we are. I have seen both developers get really into these discussions (a little too much maybe) just like the players. I have seen discussion topics on here that turn into giant shi* storms and other topics that are more mundane; the point being, regardless of what happens on here, the game survives and moves forward every single time despite the human element, or maybe because of it. Can you not respect that perhaps they have a human side?
5) There's a huge difference between some individual claiming a broken mechanic with facts and figures and a community doing the same. Remarkably, both hard-core and average gamers get served by AI war. You can't just upset the apple cart over one well-thought-out statistical post. You should present it to the community first, not necessarily Chris or Keith. Back it up with actual game experience. Then you might get somewhere.

I have no idea what particular post has driven these comments, and I'm certainly not a fan boy of Chris or Keith, but I think what they have done with their community is pretty special and worthy of pointing out here.

[keith.lamothe]

I have seen both developers get really into these discussions (a little too much maybe) just like the players.

No 'maybe' about it, I definitely get too into it sometimes.  I'm more of an "amateur that makes money" than a "professional" and sometimes it shows.  The community is pretty good about bearing with us when we go a touch overboard   And we try to cut the players some slack if they're having a rough time for whatever reason, too.

Anyway, I appreciate the objective analysis of the situation: it isn't perfect, but it's sure different than just about any other game/dev community, and mostly in a good way.

[TechSY730]

You balanced the harvesters under the assumption that there are on average 2 metal and 2 crystal deposits on a normal planet on average, right?

The data seems to support that, though technically speaking, stating that X and Y have an expected of N/2 does not necessarily imply that if (X+Y) has an expected value of N, the distributions are the same. Take for example rolling two d6 and taking the sum is NOT the same distribution as rolling one d12 dice, despite the fact that both cases have an expected value of 6.

In you're assumptions Kieth, you measured (well, guesstimated) two variables (metal and crystal spots) separate. In this experiment, the total number of resource spots was measured.
Though the averages matched up, the distributions might differ. So which distribution you should balance for is dependent on how the game generates resource spots.
Does it first determine total spots on a plant, and then determines which spots have which type of resource? In that case, the distribution will look more like the d12 case.
Or does that game determine metal and crystal counts entirely separate? In that case, the distribution will look more like the 2d6 case.

So if you are merely balancing for the average, balancing for 2 metal and 2 crystal and balancing for 4 resources is equivalent.
If you are also considering how the distribution is shaped when determining balance, you should also consider how the game is distributing it.

[c4sc4]

I'm glad this is helpful, it took a bit longer than I expected it would.

I would have measured the individual number of crystal and metal nodes on each planet but the game didn't give me an easy way to see each type individually all at once like it does with total resources (unless I missed it). It would have taken way longer to collect that data.

Also, would anyone want to see my spreadsheet with all of the raw data in it? I could upload it if anyone would actually want to see it.

[Eternaly_Lost]

You balanced the harvesters under the assumption that there are on average 2 metal and 2 crystal deposits on a normal planet on average, right?

The data seems to support that, though technically speaking, stating that X and Y have an expected of N/2 does not necessarily imply that if (X+Y) has an expected value of N, the distributions are the same. Take for example rolling two d6 and taking the sum is NOT the same distribution as rolling one d12 dice, despite the fact that both cases have an expected value of 6.

In you're assumptions Kieth, you measured (well, guesstimated) two variables (metal and crystal spots) separate. In this experiment, the total number of resource spots was measured.
Though the averages matched up, the distributions might differ. So which distribution you should balance for is dependent on how the game generates resource spots.
Does it first determine total spots on a plant, and then determines which spots have which type of resource? In that case, the distribution will look more like the d12 case.
Or does that game determine metal and crystal counts entirely separate? In that case, the distribution will look more like the 2d6 case.

So if you are merely balancing for the average, balancing for 2 metal and 2 crystal and balancing for 4 resources is equivalent.
If you are also considering how the distribution is shaped when determining balance, you should also consider how the game is distributing it.

The expected average of rolling 2d6 is 7, not 6... The expected average of rolling 1d12 is 6 however, and when you roll 2d12, you get an average of 13.

On the plus side, having a lot of resources makes the game flow faster, and I thought that one of the design goals is to reduce wall wait time, and have more playing time.

I know with the new Harvesters, I have reduced my wait time when I drop a new spire city from around an hour to get all the new ships out to about 10 minutes. Then again, I did just move back to 9/9 from 10/10, but what it does mean is that I no longer can just go watch a TV show well I wait for the computer to get stuff built for me to use as much, and for me that is worth the Harvesters being on the strong side. Better to buff the AI in other ways if you think they became too powerful, then to increase the wall clock time waiting for things to get built, by reducing the income flow.

[keith.lamothe]

Better to buff the AI in other ways if you think they became too powerful, then to increase the wall clock time waiting for things to get built, by reducing the income flow.

Basically: yea.  But the current numbers come pretty close to trivializing the m+c part of the game, which is a bit much   When harvesters are roughly equal to econ stations I think we'll be in a good place; normally you'd only unlock one or the other but if you really wanted to reduce waiting you could unlock both (for 6 planets worth of knowledge, but hey; and on FS I imagine if you want knowledge you just go glass a bunch of AI planets and laugh all the way to the bank).

[TechSY730]

Take for example rolling two d6 and taking the sum is NOT the same distribution as rolling one d12 dice, despite the fact that both cases have an expected value of 6.

The expected average of rolling 2d6 is 7, not 6... The expected average of rolling 1d12 is 6 however, and when you roll 2d12, you get an average of 13.

Oops. Apparently my probability and statistics is a but rusty. 

So, is nerfing Econ station now out of the question, now that harvesters can actually pull their weight?

Nerfing both higher marks might help higher tier income rates from getting out of hand while keeping both relatively competitive with each other. And the buff to harvesters means that wait-times would still be less than they were before, even if both get nerfed moderately.

Maybe in return for nerfing the income rate of econ stations, their energy production could go up. Right now even Mk. III econ stations barely put out enough energy (6k) to be noticeable.

[c4sc4]

Graph time!



This histogram uses all 1180 data points I got from the 120 P# galaxies. Interesting it looks almost normally distributed.

[TechSY730]

Normal distribution. Hmm, that would seem to imply that the game determines metal and crystal counts independently.

Anyways, actually, 1d6 has an expected value of 3.5 ((1+2+3+4+5+6)/6 = 21/6 = 3.5) As two dice rolls are independent, it follows that E(2d6) = E(1d6 + 1d6) = E(1d6) + E(1d6) = 3.5 + 3.5 = 7
For 1d12, E(1d12) = (1+2+3+4+5+6+7+8+9+10+11+12)/12 = 78/12 = 6.5. So actually, 2d6 has a slightly higher expected value than 1d12. Interesting.

So on a normal planet, the range for a single resource type is 0 to 4 (both bounds inclusive). What is the distribution of that? (again, on a SINGLE TYPE of resource)

[c4sc4]

So on a normal planet, the range for a single resource type is 0 to 4 (both bounds inclusive). What is the distribution of that? (again, on a SINGLE TYPE of resource)

I would do it but I don't have that data readily available. But it turns out there are overlays for each resource so I may check this out in a bit.