X3: Sector Planner v1.2 sp1 Released (19 March 2006)

[LordSuch]

jlehtone,

Have you actually validated your formula under X2 or X3? I validated mine under X2 but have only had a very brief check in X3 and the values looked pretty much the same - also the game files seem to back this up.

On the Sector Planner FAQ there is a formula for converting cycle time (prod_time) to yield which is:

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yield = (96 / prod_time) * 25

If we rearrange this to get cycle time from yield we get

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prod_time = 96 * 25 / yield

Where prod_time is the time taken to produce one silicon wafer.

This certainly held true in X2 and therefore there was no diminishing returns from larger yields. Also it means that a 25 yield mine will feed exactly 1 factory (ignoring M / L variations).

My concern about your formula is there seems to be a number of +1's that seem to have no logical reason. For instance when coding you would normally guard against a divide by zero rather than arbitrarily adding 1 which effects the calculation, particularly at the limits. i.e. adding 1 to a yield 2 asteroid is adding 50% to its yield.

In terms of this mathematical examination, I am going to ignore the multiplier from your formula as whether a station creates 2 products in 90 seconds or 1 product every 45s is irrelevant when working out normalised factory units.

If we take your formula (modified to remove the multiplier) as we only want to know how long it takes to produce one unit (set up for silicon)

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BASETIME = 2400

Basic_cycletime = rounddown( BASETIME / (Yield + 1) ) + 1 seconds 

If we think about this as if we're writing code so we guard against divide by zero without adding a factor

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BASETIME = 2400

if (Yield > 0) 
{
Basic_cycletime = rounddown( BASETIME / Yield ) + 1 
}
else
{
Basic_cycletime = -1 // -1 to signify that the cycle time is infinite
}

Guess what? If you ignore the rounding which may or may not be valid (but should be irrelevant anyway) we get:

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Basic_cycletime = 2400 / Yield 

Which is the same as

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prod_time = 96 * 25 / yield

Q.E.D.

On a final note in a mathematical sense 2400 / yield is valid even for zero as the cycletime would then be infinite which is the correct outcome!

If you read all of that well done!

If you have any questions or want to tell me I'm wrong please let me know.

[jlehtone]

jlehtone,

Have you actually validated your formula under X2 or X3? I validated mine under X2 but have only had a very brief check in X3 and the values looked pretty much the same - also the game files seem to back this up.

I dare to disagree.

I have shown X3 in-game values that I did look up myself here. Since we are now mainly talking about the Silicon, I repeat that table:

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Silicon mine L:
Yield/Time/Products
0  40:01  5  *
5   6:41   5
6   5:43   5
13   2:52   5
21   1:50   5
26   1:29   5
31   1:16   5   *
64   1:14   10

* Observations by others, the yield 0 is a case, where the Silicon mine was erroneously built on an Ore asteroid.

I fully agree with you that both multipliers (mine_size and never-under-60s) are mere obfuscation that can mostly be ignored. In the above table, only yield 64 has multiplier 2 and the raw prod_time is 37s.

I just checked my X2 game, and the cycle times are exactly the same there too. I did saw a version of my equation initially in some ancient thread for X2, and have verified it along my X2 game. At least every single case have fitted exactly.

On the Sector Planner FAQ there is a formula for converting cycle time (prod_time) to yield which is:

Code: Select all

prod_time = 96 * 25 / yield

Where prod_time is the time taken to produce one silicon wafer.

This certainly held true in X2 and therefore there was no diminishing returns from larger yields. Also it means that a 25 yield mine will feed exactly 1 factory.

Now allow me to show the table from above again, but this time with raw times in seconds and with prod_time from your equation. I'll even add couple datapoints from my X2 Silicon mines that I just looked up.

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Yield	Cycle	prod_time
0	2401	Inf
5	401	480
6	343	400
9	241	266,67
12	185	200
13	172	184,62
17	134	141,18
21	110	114,29
26	89	92,31
31	76	77,42
45	53	53,33
64	37	37,5

You have validated your data. I have validated my data. Does Egosoft have a random number generator?

My concern about your formula is there seems to be a number of +1's that seem to have no logical reason. For instance when coding you would normally guard against a divide by zero rather than arbitrarily adding 1 which effects the calculation, particularly at the limits. i.e. adding 1 to a yield 2 asteroid is adding 50% to its yield.

Yes, there are two. First is adding to the yield, and the other is just one annoying second more. The odd thing is, which I did realize only recently, that with my equation, Ore mine yield 25 has cycle time to exactly match one factory. The logic for both is beyond me.

If we take your formula (set up for silicon)

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BASETIME = 2400

Basic_cycletime = rounddown( BASETIME / (Yield + 1) ) + 1 seconds 

If we think about this as if we're writing code so we guard against divide by zero without adding a factor

Code: Select all

BASETIME = 2400

if (Yield > 0) 
{
Basic_cycletime = rounddown( BASETIME / Yield ) + 1 
}
else
{
Basic_cycletime = -1 // -1 to signify that the cycle time is infinite
}

Guess what? If you ignore the rounding which may or may not be valid (but should be irrelevant anyway) we get:

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Basic_cycletime = 2400 / Yield 

Programming-wise, it is more efficient to compute than to test for conditions. I would assume that the yield is an unsigned integer, since we really do not need any other values than 0 and positives. Thus, the 0 is the only special case. There is no asteroid with yield 0. Except when you build a mine of wrong type on it. Then it apparently has yield 0. Now, how to show in the game that you have made a mistake. It would be nice, if they would simply deny building on wrong type. However, I could then fly around with a mine in my TL and test where I can build, without scanning the roid first. The mine could have infinite cycle time, but that is a big number to put in there. The mine could just show "Disabled", put that too is a "special" number to place somewhere and requires a way to show it. What they obviously have chosen, is that every mine produces. Yield 0 produces only half of what yield 1 produces. 2 is 50% faster than 1 and 3 is 33% faster than 2. The effect is clear in low-yield roids. You can hardly see it on "normal" ones. 50-yield roid is still ~100% faster than 25-yield one, which is intuitive. The explanation for yield 0 producing is probably that every roid contains some traces of all minerals. This would explain the fisrt "1" in my equation.

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prod_time = int( 25.0*96/(yield+1) )+1

That can always be computed, and there is no reason to test the special condition, because its result has acceptable effect in the game and requires no special handling, ie extra code.

The extra second. Ore mines have obviously a different constant. Thus:

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prod_time = int( 25.0*24/(yield+1) )+1

Without that extra second, yield 24 would be the "fab equivalent". With the second, it is too slow. Yield 25 in there

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25.0*24/(25+1) = 23,08
int( 23,08 ) + 1 = 24

creates the illusion of "exact match". Thus, the "rounding" is not indifferent, but crucial for the logic and very simple in the code too.

The lack of exact match in the Silicon case - no yield matches "fab equivalent" - could be intentional. After all the 100% SPP is intentionally (I presume), "one second off" too.

My equation is not utterly complex. It does fit the observed data perfectly. All that I can do is to rest my case and let the jury do their work

If only the judges would not have NDA ...

[LordSuch]

jlehtone,

This is an interesting set of data. Unfortunately I'm pretty certain I don't have my data from X2 any more and even if I do, its on a machine with a broken graphics card! However I am willing to entirely trust your data and can therefore only assume that either something changed at some point in X2 or that I deliberately decided to use an approximation. It was getting on for two years ago now when I did the original calculations

However if what you are saying is correct (which given the data you have provided, it seems to be) then Sector Planner will underestimate *slightly* the number of factorys that a single mine can support.

For instance (assuming silicon mine L to emphasise the difference):

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Yield   Actual Facts  SP Facts
  12            2.6          2.4
  64            12.95       12.8

Of course the there will be a point at above 64 yield where you can actually support one more factory (with L) than Sector Planner states.

Once I have a working graphics card in my development machine I will address this. I suspect that it never came up in X2 as there were not the M, L variants and therefore the difference would always be less than a factories worth.

Ultimately I concur!

On a final note - purely to be picky - If I was writing the code for X3, I would not be calculating the production time for a mine repeatedly I would calculate it once when the mine is built - the yield is an invariant in this context. And I would probably prefer the one assembly instruction overhead for the clearer code (and probably a correct calculation)! However it would appear this is not what happened!

Thanks for you input I will address this once I have a new graphics card.

LS

[jlehtone]

I sincerely hope that I have presented you the "real" data and no misconceptions of mine. (pun unintended)

It is not that bad to underestimate the production. The opposite would be. Everybody having unexplainable lack of wafers.

I agree that the production time is probably computed exactly once and stored in the station description. I do not think they do it in assembly. Optimization is the source of evil, etc. It is still tricky, because every mine can have different cycle time, apart the NPC ones, while the other station types are more homogenous. Memory vs cpu cycles. Both are valuable and used by X3

I got into this, because I wanted to get the most out of the few roids in X2. Now I practically mine everything, regardless of cost. Hence the knowledge. And I wanted to know how much is much. Being a late convert, I naturally use version 1.4 of X2. Was there economy adjustments in those patches?

The L-mines in X3 practically multiplied the amount of asteroids by 5. Where is the challenge, if one can set up 13 self-sufficient weapon factories with just 3 well placed mines (in Ore Belt)?

Now I remember. You corrected the NPC mines to have yield 40 in the latest X2 SectorPlanner. I assume that the data for that is relatively recent?

BTW, Burianek wrote in S&M that factories, I assume High tech, can have different cycle time for player than for NPC. The example was that player fab is faster than the NPC one. It was a description of some T*-file. Thus, I do not know how the ware amounts are affected.

PS. I know the feeling about gfx. Had mine broken in the summer. Took one month to even get the warranty replacement. The replacement occasionally "disappears". Does not consume power either and does not show in the PCI(-E). Had a trusty 2MB Matrox Millennium card in use in the summer.

[LordSuch]

Now I remember. You corrected the NPC mines to have yield 40 in the latest X2 SectorPlanner. I assume that the data for that is relatively recent?

This was based upon information from Rapier (the person who created the Utopia spreadsheet for X-T).

To be honest I have never spent that much time investiagting NPC production times as you have to monitor over a significant period of time and allow for the actions of traders coming and going which means that it is never an exact science. Particularly secondary resources - X3:SP assumes a rate of 1/3 but that is an educated guess, purely because it seems about right, however depending upon when you monitor you could come up with figures from 1/6 -> 1/2.

BTW, Burianek wrote in S&M that factories, I assume High tech, can have different cycle time for player than for NPC. The example was that player fab is faster than the NPC one. It was a description of some T*-file. Thus, I do not know how the ware amounts are affected.

I'm intrigued as the T-files don't distinguish between NPC and player fabs - unless I have overlooked a field or two. Similarly the production (or consumption - not certain which) rate is in the various TWare files (it was rolled into the price in X2) but again there is no distinction between NPC & player.

It could be internal to the game as it does a number of things that aren't defined in the game files, i.e. NPC stations that require things as primary resources, but the player equivalent does not.

I suppose I really should get round to signing that NDA I printed about 6 months ago and then I would probably know!

[jlehtone]

BTW, Burianek wrote in S&M that factories, I assume High tech, can have different cycle time for player than for NPC. The example was that player fab is faster than the NPC one. It was a description of some T*-file. Thus, I do not know how the ware amounts are affected.

I'm intrigued as the T-files don't distinguish between NPC and player fabs - unless I have overlooked a field or two. Similarly the production (or consumption - not certain which) rate is in the various TWare files (it was rolled into the price in X2) but again there is no distinction between NPC & player.

It could be internal to the game as it does a number of things that aren't defined in the game files, i.e. NPC stations that require things as primary resources, but the player equivalent does not.

It probably was about TWare Relvalue fields. There are two of them and they represent the production time in seconds. The latter one is for player. The (average) price of ware ought to be Constant*Relvalue. I think that the Constant is about 80 for ships, or at least for some classes of ships. Thus, the Constant depends on ware class, and is hidden somewhere. I have no idea, how different rates for same product are handled nor what is the benefit, but I assume that only high-end products are affected by this. No idea yet Explore, Think, ...

[LordSuch]

It probably was about TWare Relvalue fields. There are two of them and they represent the production time in seconds. The latter one is for player. The (average) price of ware ought to be Constant*Relvalue. I think that the Constant is about 80 for ships, or at least for some classes of ships. Thus, the Constant depends on ware class, and is hidden somewhere. I have no idea, how different rates for same product are handled nor what is the benefit, but I assume that only high-end products are affected by this. No idea yet Explore, Think, ...

X3: SP gets its all its values from the TWare* files, however I had assumed that the second "Relvalue" field was cycle time related and the first was price related mainly because seperation of price from cycle time was wanted by several modders. I haven't tried modding them and checking the outcome in game so I can't validate either viewpoint.

[jlehtone]

Ho hum, went digging ... real deep ...

This was the post I referred to.

[LordSuch]

Yeah that was the one I found today also!

At some point when I have some time, I need to do a bit of testing on this as I really haven't had the time since the beta of X3: SP was released back in early November. However it shakes down, SP is not that far off the mark at the moment. Ultimately SP will can never be 100% accurate as its model is based upon the average case i.e. if you set buy price to 15 for energy it assumes you always buy energy at 15, whereas in reality you'll sometimes buy it for 12!

Anyway, looks like I've got plenty to do when my development machine is back in working order!

[Apocholypse]

Actually, you always buy at 12!

Anyhoo, LordSuch, I been looking at your sector Planner, and found a few errors in the Station profits and resources.

Quantum Tubes:
1.Ore cannot be bought at 49 credits
2.The profits per hour is way off

MicroChips
1.Profits per hour again off by 20-30,000

Solar Power Plants
1.Profits Way way off lol
2.(XL can earn nearly 300,000 more than you puit in

Weapon Component Factory
1.Earns to little
2.At Average Price selling, and at lowest Price buying, it nets only 28,000 but should be getting 46,928.57

Ore Mines
1.Cannot sell at 49 credits!

Alpha PSG's
1.90,780 profit, not 15,124

Alpha Hepts
1.101,536 profits not 22,000

Bliss Place
1.Swamp Plant can be baught for 36 at lowest price
2.It makes 24,000 more profit than you have specified.

Ammunation Factory's
1.84629 is it's profits per hour buying at lowest price not 15,000
2. Again ore cannot be bought at 49 credits

I won't rant any further, but you see my point. Now either I'm terribly terribly wrong, in which case you have my sincerest apology. Or you need to redo some of your figures.

Now, I know I'm not your beta tester but I'm just so dam helpful

Basically:

1.Change that ore pirce lol
2.As far as I can see, most if not all of your weapons statistics are inaccurate (you haven't based it on X2 to have you )
3.High Tech Fabs need to have a breeze over
4.As far as I can see, all food fabs are okay, except for the slight inaccuracy on space weed.

If you want it, I would be willing to help you out on your statistics.

I was going to PM you, but didn't think you would answer.
If you want me to Beta Test..... (If I'm right of course)

On a positive note, a side from a few miss calculations, your sector planner is truly work of exelence! Nice work!

[X-it]

Sorry to bring this to you Apocholypse, but this is all mentioned on the known issues page (well at least the parts with the hi-tech fabs). SP for X3 is still beta.

[Apocholypse]

Yeah, I didn't realise, sorry bout this...

However I have all the SPP statistics now if you want them Lordsuch!

Infact, I solutions for all of your stations if your willing...

[Rapier]

This was based upon information from Rapier (the person who created the Utopia spreadsheet for X-T).

And if I may offer my thoughts... (a bit late due to office Christmas party )

This value was calculated using both observation of the cycle time of NPC mines and the equations discussed above. I had arrived independantly at the equations LordSuch uses through my own obseravations like those of jlehtone. The observations were done originally in X-Tension for UTOPIA. The same equations held for X2 against about a dozen checks (I'm sure other people did more). The equation;

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prod_time = 96*25/yield

is not quite correct as in many cases the result must be rounded to make it a whole number of seconds. Even then, in X-Tension one had to be careful becuse a given prod_time of 1:45 acted as 1:46 because the factory only updated every 2 seconds (I believe this was fixed for X2).

If we don't have the gamecode to work from, we must use the scientific method of observation to try and understand what is happening. Based on these observations we can put forward theories about what the rules (i.e. the game code) might be. This will satisfy our need for things to be neat and easy to work out. In fact, what we need in this case is different from what we want. We don't need a neat formula, a table of production times for all yields will give us all the information we need.

I did something similar for my ship data spreadshet, most of the data was observed but some was calculated from other information. These calculated values were overwritten if and when I discovered the actual values. I'll knock up a spreadsheet for yields and production times after I've had lunch and those that want can set about filling in the data. Drop me a PM if you'd like to help.

[Dgn Master]

Looking forward to this when it is finalized, your sector planner for X2 was invaluable to me and, i'm sure, other empire builders out there.

Thanks for putting the effort into this for us!

[X-it]

Yeah, I didn't realise, sorry bout this...

However I have all the SPP statistics now if you want them Lordsuch!

Infact, I solutions for all of your stations if your willing...

Well you would probably be the perfect beta-tester for this like you mentioned above, seeing as you have done some great guides and built extensive complexes etc. I think LordSuch is considering implementing a 'complex simulator' as well, so that you can clearly see what will be the end products etc. That would be truly great.

About the SPP statistics, those are not correct in SP as of now? I've been planning to set up XL SPP loops scattered around, and according to SP they would bring in 788,000 credits an hour (or so) if I manage to sell the surplus energy cells at average price. But you are saying that they actually make more than that?

[jlehtone]

Even then, in X-Tension one had to be careful becuse a given prod_time of 1:45 acted as 1:46 because the factory only updated every 2 seconds (I believe this was fixed for X2).

I have never seen X-Tension. Therefore I never realized that the interval in the simulation could be that long.

We don't need a neat formula, a table of production times for all yields will give us all the information we need.

I disagree on two points:
(1) I can always generate the table from the equation in a minute. Besides, it is more convenient (for me) to calculate than to look from a table. I trust the equation which I use Besides, if it turns out to be wrong, I change that one thing and then I immediately have more correct values. No erroneous tables lingering around. One can make the table more compact if one includes only the yields, which really exists in the game, but then it will not help scripters.
(2) We do not really want those production times. We want to know how much the mine produces, and "factory unit equivalent" is the most practical dimension for that value.

Wolf pointed out a bit older message by Birdman. That mine production table is for X2, but I bet it is a valid table for X3 too.

PS. I was interested in NPC mine production data, because it is now assumed to be yield 40 in X2 SP. Or more precisely I assume that the yield have chosen as such that with the SP equation it reflects the observed rate of production. Since I use a different equation, the yield could be different too. But 40 sounds like easy choice and could very well be the best possible answer anyway.

[Rapier]

The standard unit in UTOPIA was the production/useage of a standard factory. NPC mines produced enough to supply 1 3/5 factories, using a table or working a formula backwards gives the equivalent yield used in UTOPIA and Sector Planner.

I'm not saying a formula isn't a good thing. It can be used to generate a complete table which can then be used to calculate the production and profit per hour. The production and profit follow directly from the cycle time and amount produced per cycle, but this is exactly what we need to hypothesize our formula. A few observations should indeed enable us to gererate an pretty accurate formula. But developing perfect formula will require a complete set of observations, thus negating the need for a formula in the first place.

I take your points about practicality, and agree. I'm arguing here from the purely scientific perspective.

[RavenIII]

Wow wish I tried this in my X2 days... just found out how profitable the SPPs are... jeez! Anyway, great work LordSuch.

My Empire will now grow and grow

Cheers,
RavenIII.

[jlehtone]

It is rare indeed to obtain complete and accurate observations in empirical sciences. Hence the working hypotheses.

Reading more closely the message of Birdman, I noticed that he had actually copied it from French thread and only validated it in some points. I did comparison of my equation(s) against that data, and apart from yields 63&64 in silicon and about ten points of higher yield ores, I did obtain a perfect fit. Not only to the production time, but for the "multiply-by-integer-to-keep-cycletime-gt-60" too. The Sil 64 was a known typo anyway, and I assume that the rest are typos in the table too. Never type, if you have an equation, script, or program to do it for you systematically

Thus, I have pretty good confidence on my equations. But then again, there have not been many complaints about the equation in SP either? There is a huge difference between "perfect" and "good enough". I think we are already passed "good enough", but do enjoy everything that we reach beyond that point. Infinite Improbability Drive.

Yields 40 and 41 in Ore supply 1 3/5 factories, but in Silicon yield 39,5 woud do the same - by my calculus. Thus, 40 is definitely appropriate yield for NPC mines.

[Dual Nihil]

Wanted add some remarks here.

First of all - mines and SPP of NPC. They have fixed rate of production

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Factory       |Cycle Time |Prod. Units | Consumed EC
Ore Mine M    |     60    |      8     |          48
Ore Mine L    |     60    |     20     |         120 
Silicon Mine M|    118    |      4     |          96
Silicon Mine L|    118    |     10     |         240
SPP M         |     60    |    132     |         ---
SPP L         |     60    |    330     |         ---
SPP XL        |     60    |    660     |         ---   

As for differend RelValues - for NPC and player they are different. Player RelValues are less for goods like Rockets and Microchips, and they are greater than NPC - for Lasers and Shields

For example:

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Ware         | NPC RV |Player RV 
Quantum Tubes|  120   |  100
Fighter Drone|  144   |  132
AIRE         |   48   |  104
25 MJ shield | 1320   | 2520

NPC Relvalue are used to calculate Average Price of product and cycle time (so resources needed) on NPC fabs.

Average Price for ware is counted as Const/60*RelValue
There are 4 groups of products with their own const+one for EC.
For EC C=240.
First group - basic food (Argnu Beef etc) C1=312
Second group - advanced food (Meatsteak Cahoonas ets) C2=728
Third group - high tech and rockets C3=1684
Fourth group - shileds and lasers C4=3895
C_{i+1}/C_{i}~2.3
So are observations.

Player Relvalue is used only to calculate Cycle Time of factory and resources needed.

As for secondary consumption there is not fixed rate of 1/3 or 1/6 or other for all products. I didn't manage to find mathematical function for calculating it, but found some results, observing TS and ED for disappearing goods at them.

So, I've got that there is nonlinear function between RelValue and Ratio of Consumption/Production times. I give here some examples:

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Ware            | RV | RoCP
Firefly Missile |  8 | 36,7
Warheads        |  8 | 34,67
Computer comp   | 48 |  2,47
Quantum tubes   |120 |  1,59

These were values only for consuming wares by ED/TS
It is likely that
RoCP(RV)=C1+ C2/RV+C3*RV^{-2}+C4*RV+C5*exp(-T)
where
C1=10.41, C2=-393, C3=5255, C4=-0.069, C5=-17858.
I can't see any hidden sense in those numbers, but at least for third group of wares it gives somewhat "not bad" approximation. Only for consuming by TS/ED.

For example, Swarm Missile Production Complex consumes Warheads approximately at 1/12 of rate they are normally produced, and Image Recognition Missile Complex - at 1/6.
Need more time to explore this aspect of in-game economy.