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Posted: **Tue Sep 13, 2011 12:39 pm**

I was having fun at work this early morning using Brennall's System Generator when I started to notice a strange trend. I was not coming up with any Very Low or Very High systems. So I decided to track 100 systems, then another 100 systems, another and another, and finally a 5th 100 systems, and no Very Low or Very High systems showed up in all 500 that I tracked. So I looked at the Tables in the latest 2E version and immediately saw there are some issues withe the System value table.

A) Very low shows as 7- (seven or less), but the lowest value in the current system is 2 for Capacity and 1 for the 5 other stats which equals 7, so there is no 'less'. The chance of getting a 7 is 3/36*3/36*3/36*3/36*3/36*3/36 (where each 3/36 is chance of rolling a 2 or 3 on 2D6). That give you a 1 in 2.98 Million chance of rolling a 7 for a systems total Value. Incidentally, that is much better than rolling a 42, the highest value (without it being a homeworld of course). There is a 1 in 2.18 Billion chance of rolling a 42, (1/36*1/36*1/36*1/36*1/36*1/36)

B) Findings for Low, Moderate and High.

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Hundreds  very		   	    	      Very	
Batch	High	High	Moderate	Low	Low	Total
1st	   0   	23   	72   	5   	0   	100
2nd   	0   	21   	75   	4   	0   	100
3rd   	0   	20   	79   	1   	0   	100
4th   	0   	20   	76   	4   	0   	100
5th   	0   	22   	76   	2   	0   	100
Total    0     106     378      16  	0  	500
percent  0     21.20   75.6    3.2  	0     100

Only about 3 % of the systems I generated were Low, this seems rather low compared to the 1E generator.

I think the issue is stemming from using stats that are generated using a 2Die system. Systems generated using a single die have a flat value to each # but 2 (or more) die systems give a bell curve weighted values. when you add each of these bell curve values together you make the bell curve distribution even more weighted toward the middle. Also note that the numbers will very slight scew to the top if a player uses the Capacity rule that uses all values from 2 thru 12 and not just the even multiples. I hope you can get someone to work in the statistics so you can find the sweet spot for your 2E edition.

I have a suggestion here that you could think about.

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System  	System   	   Empire
Value    	Importance   Activation
None     	None   	   0%
7 - 10    	Abysmal	   2%
11 - 12   	Very Low	   5%
13 - 16   	Low   	   10%
17 - 25   	Moderate	   15%
26 - 30   	High   	   20%
31 - 33   	Very High	   25%
35 to 42     Epic   	   30%

Hope you have fun with it

P.S. here is the break down of the 106 'High' Value systems I rolled, It might give you insight as to why I made the changes I did.

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High	                percent of
#	Total	Percent	total group
26  	33  	31.132  	6.6
27  	33  	31.132  	6.6
28  	19  	17.925  	3.8
29  	10  	9.434  	2
30  	8   	7.547  	1.6
31  	3   	2.830  	0.6
32  	0   	0.000  	0
33  	0   	0.000  	0
34  	0   	0.000  	0
35  	0   	0.000  	0
Total	106 	100  	21.2

Hope this helps !

Edited several times to try to get tables correct. I'm using the Code trick but it only helped a little, still missing something.

Posted: **Tue Sep 13, 2011 1:32 pm**

Firstly ... OMG I hope I got all my sums right in the program ... or Tyrel will kill me!

Secondly .. use the Code button to wrap around your tables and they become easier to work with because of the default Monospaced font

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Hundreds     
-------------------------------------------------------------------------------------
Batch       Very High    High        Moderate       Low       Very Low        Total
1st            0          23            72           5            0            100
2nd            0          21            75           4            0            100
3rd            0          20            79           1            0            100
4th            0          20            76           4            0            100
5th            0          22            76           2            0            100
-------------------------------------------------------------------------------------
Total          0         106           378          16            0            500
-------------------------------------------------------------------------------------
percent        0%         21.2%         75.6%        3.2%         0%           100%

Posted: **Tue Sep 13, 2011 2:39 pm**

Brennall,

From what I know about dice and bell curves that turn into Mason-jar curves when multiplied, You probably did the stats correct, but go ahead and check, just to be sure. Thanks much for the tip , I just never have ever been a poster before, just a Lurker on the empire building websites for over a decade. This old dog will try to learn that new trick.

I didn't send the excel sheet home (The one with my stats) as I left work so I'll have to wait and modify my first post sometime early tomorrow. Spent 40 minutes just trying to get it readable by adding dashes, hehehe. So hopefully you guys/gals can see why I posted in the first place.

Posted: **Tue Sep 13, 2011 2:44 pm**

If it turns out that this does need fixing, it will be one of the easiest and quickest fixes Tyrel will have to make.

Posted: **Wed Sep 14, 2011 12:12 pm**

Brennall, does it help to keep the tables aligned when I post a small spreadsheet table if the spreadsheet cells are left alligned, or does it make no difference if they are centered in my spreadsheet cells ?

Posted: **Wed Sep 14, 2011 12:19 pm**

Makes no difference ... you will need to do some manual adjustment back and forth using the preview button and the "Code" bbcode.

Posted: **Thu Sep 15, 2011 1:02 pm**

I spent the last 2 nights trying to find the probability values of the 31 possible numbers (12 thru 42) that are the total of Cap, RAW, Orb, Bio, Sci, and Jump. When I got these probabilities, I’d compare them to my suggestion above for modifying the ‘System Importance’ table and see if I needed to tweak a number or two. I do see a need to change the current ‘System Importance’ table but I really have no problem with the system generator system for 2E. If Tyrel wants a wider average distribution he’ll probably need to adopt another system, but I like the current system; it’s just a bugger to get good data on due to:
A) The massive amount of Probability outcomes on a 2D6 x 6 generator, 2,176,782,336 to be exact.
B) The inefficiencies of Excel and Standard computers in dealing with Base 6 ‘Standard Die’ numbers. Even with a Standard Distribution, the total # of each possibility equaled 202.345 less than the actual value of 2,176,782,336 possible die rolls due to inefficiencies with dealing with numbers such as 2, 3 4, and 5 when divided by 6. In a hundred billion star galaxy, we just lost 20,234.5 star system, hehehehe. This gets exacerbated slightly when using weighed values.
C) In the old days, before I used my grey matter, I’d just make a chart with every available variation by putting die results on a spreadsheet then doing a sort by value, but at over a million rows usable by my current version of Excel , I’m about a 1,00th of the way to what is needed to do it that way and even with cyclic cut and pastes, it would take me hundreds of man hours to fill in the spreadsheet. So is there a better way …
D) Welcome to the Internet, where I just look up probability and Dice and what should appear but the Normal Distribution Theorem of Die rolls in Wikipedia and some teaching websites. This is so cool, just use some math to plug in some data such as a Number you are looking for, Sides to your die, and Number of Dice you are rolling and there you go. And I was actually figuring it out, when I looked back at the title and groaned. There it was, that word – Standard; and as we have established, our dice roll results come from a weighed system. Hopefully, 1 or more of our posters (or Lurkers) has more college level math than I do; for I really do want to know what the odds of rolling those dang numbers are. Or ask a professor for a little help if you cannot. For right now, I think I made some adequate guesses for my table above, but I love system generation and want to do it right.

Ihad some more fun with this project but this is too long already.

Posted: **Tue Sep 20, 2011 11:09 am**

Here is the latest on this issue, after I created 100K (100,000) systems to get a better idea of the distribution of System values. Here are the results.

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Total Value	Total	Percent	Current 2E	My Idea	New Idea	Total Value
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
     7       	0    	0     	Very Low	Abysmal  	Abysmal   	7
     8       	2    	0.002 	Low     	Abysmal  	Abysmal   	8
     9       	2    	0.002 	Low     	Abysmal  	Abysmal   	9
     10      	14   	0.014 	Low     	Abysmal  	Abysmal   	10
     11      	38   	0.038 	Low     	Very Low 	Abysmal   	11
     12      	111  	0.111 	Low     	Very Low 	Abysmal   	12
     13      	285  	0.285 	Low     	Low      	Very Low  	13
     14      	641  	0.641 	Low     	Low      	Very Low  	14
     15      	1230 	1.23  	Low     	Low      	Very Low  	15
     16      	2083 	2.083    Moderate	Low      	Low       	16
     17      	3337 	3.337 	Moderate	Moderate 	Low       	17
     18      	4932 	4.932 	Moderate	Moderate 	Low       	18
     19      	6488 	6.488 	Moderate	Moderate 	Low       	19
     20      	8166 	8.166 	Moderate	Moderate 	Moderate  	20
     21      	9654 	9.654 	Moderate	Moderate 	Moderate  	21
     22      	10441	10.441   Moderate	Moderate 	Moderate  	22
     23      	10706	10.706	Moderate	Moderate 	Moderate  	23
     24      	10139	10.139   Moderate	Moderate 	Moderate  	24
     25      	8734 	8.734 	Moderate	Moderate 	Moderate  	25
     26      	7418 	7.418 	High    	High     	High      	26
     27      	5682 	5.682 	High    	High     	High      	27
     28      	3938 	3.938 	High    	High     	High      	28
     29      	2606  	2.606	High    	High     	High      	29
     30      	1666 	1.666 	High    	High     	Very High 	30
     31      	892   	0.892	High    	Very High	Very High 	31
     32      	462  	0.462 	High    	Very High	Very High 	32
     33      	195  	0.195 	High    	Very High	Very High 	33
     34      	91   	0.091 	High    	X - Oops 	Epic      	34
     35      	28   	0.028 	High    	Epic     	Epic      	35
     36      	16   	0.016 	Very High  Epic     	Epic      	36
     37      	2    	0.002 	Very High  Epic     	Epic      	37
     38      	0    	0     	Very High  Epic     	Epic      	38
     39      	1    	0.001 	Very High  Epic     	Epic      	39
     40      	0    	0     	Very High  Epic     	Epic      	40
     41      	0    	0     	Very High  Epic     	Epic      	41
     42      	0    	0     	Very  High Epic     	Epic      	42
						
Total Value	100000	100	Current 2E	My Idea	New Idea	Total Value

So I decided to modify my proposal due to these findings

But first is the 2e data in the latest update. There are some big issues there, but since it is just a table, it is very easy for VBAM personnel to fix (any way they want to). The second table is My modified version, I hope it is considered.

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% Found	2E Value
0.000% 	Very Low
2.323% 	Low
74.680%	Moderate
22.978%	High
0.019% 	Very High

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% Found	My Value    Activation % Chance
0.167% 	Abysmal        2%
2.156% 	Very Low       5%
16.84% 	Low            10%
57.84% 	Moderate       15%
19.644%	High           20%
3.215% 	Very High      25%
0.138% 	Epic           30%

The standard 0% activation chance if the System has no Value. Abysmal and Epic worlds (together) will appear in about 3 of every 1,000 systems generated. I think those 2 value classes could be used for a few special things in the Companion and the Menagerie. I posted this thread a week ago, and hope to hear from VBAM about their fix of this issue soon.

Posted: **Tue Sep 20, 2011 3:10 pm**

Vandervecken wrote:

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% Found	My Value    Activation % Chance
0.167% 	Abysmal        2%
2.156% 	Very Low       5%
16.84% 	Low            10%
57.84% 	Moderate       15%
19.644%	High           20%
3.215% 	Very High      25%
0.138% 	Epic           30%

Well, I came up with very similar numbers when I calculated the chances.

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Value       Range   Found %   Average
Abysmal      7-12    0.172%   1.17-2.00
Very Low    13-15    2.146%   2.17-2.50
Low         16-19   16.995%   2.67-3.17
Moderate    20-25   57.567%   3.33-4.14
High        26-29   19.728%   4.33-4.83
Very High   30-33    3.256%   5.00-5.50
Epic        34-42    0.135%   5.67-7.00

I don't pretend to know statistics (been WAY too long), I calculated mine by just multiplying the odds by the previous tables results in Excel, adding one stat at a time and using your values to sum the ranges. If anyone is interested, I have the spreadsheet saved, as well as the Combat Analysis spreadsheet.

Posted: **Wed Sep 21, 2011 2:22 am**

I also saved my excel sheet, but it has only the last 10K systems I rolled. Statistically, even 100K systems is a small sample, but for all but the ends (both high and low) I think it gets pretty close to what is gonna show up. I was hoping for a 7 or a 42 to show up but the odds were literally '20 to 1' for the 7, and a lot less likely for the 42 to show up in a 100,000 group.

Edit: Odds are actually just a hair under '30 to 1' to have rolled a 7, NOT '20 to 1', I need to refresh my basic math AND/OR stop working on this while at I'm at work.

Thanks Nimrodd, glad the numbers you came up with were so close to my rolled (er ... spreadsheeted) findings.
I originally did my first 500 systems by using the 2E Sys Gen that Brennall made but to get a BIG group to compare , I had to go back to the Excel spreadsheet. I did all 100K in less time than doing 500 manually. Now that I have crunched my numbers, I'll be happy to play around with Brennall's Sys Gen again, it's so much more functional and elegant than a spreadsheet. And even though the total value of the system isn't listed, just the system Importance, I'll keep adding the stats together, looking for my first 7 or 42 !

Posted: **Wed Sep 21, 2011 3:51 am**

Vandervecken wrote:And even though the total value of the system isn't listed, just the system Importance, I'll keep adding the stats together, looking for my first 7 or 42 !

There are 2,176,782,336 different combinations of dice rolls (6^12). There are 729 of those rolls that will give you a 7 (2 or 3 on each 2d6 roll x 6 stats). There is only 1 combination that will give you the 42 (12 on each 2d6 roll x 6 stats).

7 = 1 in 2,985,984
12 = 1 in 2,176,782,336

Posted: **Wed Sep 21, 2011 10:16 am**

Yup,

I said the same in my first post (2nd Paragraph), but I found my wife; so hitting apon a number that has a 1 in 2.176 billion chance should be easy.

Posted: **Thu Sep 22, 2011 4:07 am**

Big thanks to Vandervecken for running the numbers and getting them so cleanly formatted. After looking through the statistical distribution of the results, I think Vandervecken's solution for altering the separation points matches the numbers pretty well. I am not entirely sold on the Abysmal and Epic system importance levels just because they are so extreme, but at the same time I do see their utility for possible local campaign missions or scenario objectives.

Looking over the numbers some more, I am thinking that it might be best to combine the upper and lower bands of system importance so that they encompass a greater percentage of systems, with each eating away at the Moderate total. That leaves us with the following rough breakdown:

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Statistics Total       System Importance        Percentage
         18-                       Very Low                     12.7%
       19-21	                         Low                        24.3%
       22-24	                     Moderate                    31.3%
       25-27	                         High                       21.8%
         28+	                      Very High                    9.9%

This is fairly close to Vandervecken's numbers, but spreads the percentages out a bit so that we have a good distribution of systems of each type. Most systems remain Moderate in quality, with the remainder usually one bracket above or below. Only ~20% of the systems are then left in the extreme bands of being either very good or very bad.

I think my biggest mental block when I look at these numbers is that I'm still conditioned towards the 1E stats where there's only Carrying Capacity and RAW (plus Biosphere, which I used in my own 1E campaigns). The addition of the extra system stats increases the total, and my simple 2D6 rolls make it much easier to find systems that are sitting in the middle of the road stat-wise. Back in 1E that was never the case, as the majority of systems had positively atrocious statistics. 2 Capacity, 1 RAW systems were very common back then, now they are a statistical outlier. That's both good and bad. The upshot is that every system probably will provide a player access to some resource that makes it worth colonizing, so the player's decision making process is going to hew towards the question of "which system is the best colonization option?" rather than the straight binary "is this system worth colonizing - yes or no?" that was prevalent in 1E.

That's another reason that I do like having the Orbital and Science stats in the game even if they aren't very realistic and will probably be home ruled out by most players. It gives systems some other qualities beyond economic production that might make players decide to establish colonies there.

Posted: **Thu Sep 22, 2011 8:10 am**

I originally had the Moderate category a little smaller - like where you have it but decided to thicken it because there was only a 5 point jump from the top low value to the bottom High Value. I wanted my lows to feel LOW and my highs to feel HIGH, so I fattened the Moderates. (and unlike the current US economy, I don't mind seeing the mid-class get expanded, hehehehe). And a 10 % difference in NPE activation will now rest on whether you rolled a '2' or a '6' on a single stat. Ultimately, this is your system so you need to do what you feel is right. I'd just like to give you some insight on why I chose the numbers that I did.

I'm also glad that when Brennall reconfigures his 2E System Generator, I'll get to see Very low and Very High Systems again. Maybe he'll do a special one for me with my Epic and Abysmal values. Cause if you find a system that is worth 8 Points, it truely is Abysmal (7pts to 12pts) or if you find a system that is worth 40 points, that would be Epic (34pts to 42pts). Another reason to possibly add a these is that there are 3 point values associated with each of the 3 middle stats under your proposed system, but 12 point values for Very low and 15 point values for very high. Adding Abysmal and Epic breaks those very large numbers down a bit. If I somehow actually do roll that 41 point system it seems to me to be so very different than the vast majority of Very High sysems that I roll (usually 28, 29, or 30 value systems), why not call it something special.

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System Importance - Issues found in values for 2E

System Importance - Issues found in values for 2E

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Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E

Re: System Importance - Issues found in values for 2E