| ryanvn23764 | Tuesday, January 15, 2013 - 02:11 am 
I have the following education indexes of.
elementry schools 86.00
high schools 92.00
universities 125
It says my overall education index is 83
when it should be 101?
86+92+125/3=101 |
| Aries | Tuesday, January 15, 2013 - 02:25 am
Your calculation method is invalid. From Docs:
The education index depends on the balance between the three partial indexes for Schools, High schools and universities. The index is in fact the lowest of these three indexes. It is computed every month by taking the lowest of the three partial indexes, adding to it 4 times the current education index and dividing the result by 5. |
| Andy | Tuesday, January 15, 2013 - 07:06 pm
Aries,
Thank you.
Exactly that. |
| Michael VII | Saturday, January 19, 2013 - 11:08 am
Why make it muddy? An average would be simple and to the point. If the player does not want to improve indexes, then s/he will lose out on employment personnel, etc.
It all depends on the management of your country. |
| Aries | Saturday, January 19, 2013 - 03:21 pm
An average would allow an unrealistic scenario where an advantage would be gained by purchasing the least expensive schools to raise the index, especially with teachers who can fulfill roles in elementary or high schools. Why purchase high schools if the elementary schools happen to have a cheaper market price? |
| Crafty | Saturday, January 19, 2013 - 08:26 pm
Actually without doing the math I'm not sure about that Aries. The number of elementary schools required for 100% is far far more than unis, so to raise your index by buying the cheaper schools may cost more because you'ld need to buy so many more of them. Totally agreed about teachers though.
Michael likes a moan, dont you Mike, man after my own heart  |
| Laguna | Saturday, January 19, 2013 - 11:11 pm
"taking the lowest of the three partial indexes, adding to it 4 times the current education index and dividing the result by 5."
Edu_t = (min{A_t,B_t,C_t} + 4*Edu_t)/5
(=) Edu_t = min{A_t,B_t,C_t}
83=/=86
Maybe I suck at interpretation and/or math, or, crazy thought here, the text is badly written and they actually mean that Edu_t is a moving average with constant and equal weights. |
| Laguna | Saturday, January 19, 2013 - 11:43 pm
That reminds me, I finally have an excuse to shove a sigma into a message. They meant:
Edu_t = (min{A_t,B_t,C_t} + S4 i=1 Edu_(t-i))/5 |
| Mizore | Sunday, January 20, 2013 - 12:39 am
Too bad I forgot what the sigma meant. That's just a big S though. |
| Jiang Hu Warrior | Sunday, January 20, 2013 - 01:29 am
ha ha lol we got lost at the /5 of the equation let alone the sigma.
this is how we work this equation out
education index = whatever* randomness/32.18% of randomness = 1.214976 of a high school index + 1.25 of a universal index * 21/86 +4/5*sigma = the answer |
| Crafty | Sunday, January 20, 2013 - 05:53 pm
You suck at math Laguna.
You have to annontate the different sets of A_t, B_t and C_t, also Edu_t.
Therefore the seemingly random statement (=) Edu_t = min{A_t,B_t,C_t}
83=/=86
is completely meaningless.
As for your S4 i=1 Edu_(t-i), allowances made for lack of character availability, the written word does not say a sum of the last (presume thats what you mean) 5 Edu_t. That equation would make sense to the education index, but I think the initial explanation makes a simpler sense.
Either way, keep your minor edu indexes approx the same is the advice. Likewise the transport indexes. |
| Lorelei | Sunday, January 20, 2013 - 06:08 pm
Well you all lost me at Edu.... lol |
| Crafty | Sunday, January 20, 2013 - 06:18 pm
edu was what you were supposed to be getting while you were gazing out the window dreaming of shoes Lorelei. |
| Rick | Sunday, January 20, 2013 - 07:30 pm
For the mathematically challenged:
Edu index = Get all Edu indexes even + Continue building evenly + stop building when you reach desired index. |
| SweetPea | Sunday, January 20, 2013 - 07:42 pm
lols@ Rick.
I just use this, if you want an index of 180 then all three categories need to equal 180. All three need to be 200 to get 200 and so on. Never failed me yet.
Math makes me think, therefore, I won't use it. I like my hair on my head. |
| Laguna | Sunday, January 20, 2013 - 09:32 pm
My point is this: the documentation is being misleading. The way it is written implies:
Edu_t = min{A_t,B_t,C_t}
That says the education index depends only on current information - t -, and it equals the lowest of the sub-indexes. That is obviously false.
Now, what I wrote is the lazy way of writing:
Edu_t = (min{A_t,B_t,C_t} + Edu_(t-1) + Edu_(t-2) + Edu_(t-3) + Edu_(t-4))/5
That says it depends on the current information - the smallest of the sub-index, and on the indexes of the previous four months, not five.
Why should this matter?
1. If someone comes up and says "I've taken the lowest of the three partial indexes, adding to it 4 times the current education index and dividing the result by 5, but I'm still getting the wrong number", they'll know why. It's not their fault, but they are doing it wrong.
2. The second one is more interesting, and concerns a bit of an odd fact if people think about it.
Someone looking at that might think "since the index depends on the four previous indexes, if I don't do anything and the targets don't move for fours months, the index should plateau in four months".
Actually, no. While the "oldest" factor is Edu_(t-4) in that equation, Edu_(t-4) itself depends on Edu_(t-5) to Edu_(t-8). Edu_(t-8) in its turn depends as far as Edu_(t-12). And so on ad infinitum.
So, Edu_t in fact depends on all previous information. So, when should the index plateau? To be precise, never. Luckily for us, the number of decimal places that can be store is finite, and hopefully small, so there are rounding errors that can bring the process to a stop.
As long it takes, depends on the precision with which numbers are stored, the magnitude of the changes, and the coeficientes, which I assume all to be 1. I imagine that if someone is building a country from a C3 and bringing the index to 200, it'll take some 5 to 6 game years for the index to settle, when all the sub-indexes are at 200.
The short and rough of it:
1. Re-write that bit about adding four times the current index.
2. The indexes take forever to reach their "true" value. |
| Laguna | Sunday, January 20, 2013 - 09:38 pm
Look at that, it really has been a while since I've posted something that big.
While you guys may not understand the "sigma thingy", I hope you do understand the "short and rough of it" and the why as well. |
| Crafty | Sunday, January 20, 2013 - 11:35 pm
I still cant see whats wrong with Edu_t = (min{A_t,B_t,C_t} + 4*Edu_t)/5
It's a simple average, not a convoluted integral.
But I do understand you economists need to play with your numbers until they are meaningless. |
| Laguna | Monday, January 21, 2013 - 12:42 am
Let us write that as: X = (Y + 4X)/5
With little manipulation, it can be shown that yields: X = Y
Also, there's an underdeterminacy problem if you try to calculate it exactly the first way. |
| SweetPea | Monday, January 21, 2013 - 02:08 pm
it'll take some 5 to 6 game years for the index to settle, when all the sub-indexes are at 200.
Yes I do understand the weights on the averages take some time to catch up to their true values.
It is even worse for Health index,,,, takes waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaay too long to catch up.
What does the formula for the Health index look like LG? I appreciate the detailed explanations that I'll never figure out, even if I had a real year to brush up on math lol. |
| Andy | Monday, January 21, 2013 - 06:36 pm
The health index has only one component which is hospitals.
The index is initially converging to the number of hospitals you have divided by the number needed. (5x + old index)/6.
However, It is assumed that just adding hospitals will not increase the health care in this way (linearly) for ever and that the cost of increasing quality will become higher at higher levels.
This slower growth starts at 120.
if you double the number of hospitals you had when the index was at 120, (and assuming nothing else, like population has changed)
the index will not reach 240 but rather: 180 or so.
reaching 150 is easier and it is probably high enough. |
| SweetPea | Monday, January 21, 2013 - 06:40 pm
oh yeah not complaining Andy just pointing out the lag when compared to the edu index.
But yeah since I have you here, I have an interesting question.
If you do go to double the amount of hospitals, once you get to say 140-150 can you drop back down to 1.5 times the Hospitals needed to hold the 140-150 index value? |
| Laguna | Monday, January 21, 2013 - 09:03 pm
Give me a hand here, are you saying that X is the value to which the index is converging to? And you are saying that in the weighted average, it's coefficient is 5/6? Then the index should reach X in one game month or something. Is this what you people see? |
| Borg Queen | Monday, January 21, 2013 - 10:01 pm
Andy, got a question btw: If you have to double your hospitals to get from 120 to 180 does that slower rise is at least linear or is it even more increasing? So do you have to quadruple your Hospitals to get from 120 to 240 or do you need even more? And if you need more than 4 times your hospitals from 120 to 240 then how many more is it to 280?
Health index of 150 is maybe enough but for Peacefull lvl 10 you allready need 160 ^^ |
| Andy | Monday, January 21, 2013 - 10:11 pm
SweetPea
I understand what you say but it does not work like this.
if you reduce the number of hospitals, the index will decline.
I also realized the difference in the "lag" when I looked into the formulas.
there is no good reason for this. I will change health to 4/5 too.
will be part of the update tomorrow.
Laguna,
X might be the value the index will reach at the end.
5/6 is used to set the pace of convergence.
4/5 is a bit faster. |
| Andy | Monday, January 21, 2013 - 10:14 pm
borg queen
The increase in the index slows down gradually and slows even more at higher levels.
The message is in fact:
Don't go in there. It makes no sense. The advantages do not weigh against the increasing cost. |
| Jiang Hu Warrior | Tuesday, January 22, 2013 - 02:00 am
in other words, put simply, DONT GO SPENDING MORE THAN YOUR COUNTRY CAN AFFORD..if a=b which equals a value of c, keep it real it makes no sense, the advantages do not weigh against the increasing COSTS! |
| Laguna | Tuesday, January 22, 2013 - 03:13 am
Might be?...
Here's what I'm thinking now.
While the docs says: "It is computed every month by taking the lowest of the three partial indexes, adding to it 4 times the current education index and dividing the result by 5."
Edu_t = (min{A_t,B_t,C_t} + 4*Edu_t)/5)
It probably means something like this: "It is computed every month by taking the lowest of the three partial indexes, multiplying it by 4, adding the previous education index and dividing the result by 5."
Edu_t = (4*min{A_t,B_t,C_t} + Edu_(t-1))/5)
That last one is in line with what you wrote for the Health Index.
I have a hard time believing those are the equations being used, as they correct much faster than what I think is going on. But this would be compatible if the function that gives X, the value to which the index is converging to and depends on hospitals/schools, exhibits lag itself. In that case, let me tell you that is complicating things needlessly.
I haven't bothered to actually have a good, measured look yet, but I like to think I have a nice feel on this. Then again, I may not. So, if anyone has data to share, that would be nice. |
| Laguna | Tuesday, January 22, 2013 - 03:27 am
By the way, the closer the coefficient is to 1, for the set of information of time t, the faster is the pace of convergence. So, no, 5/6 is actually slightly faster than 4/5. Take this example:
Y_t = aX_t + bY_t-1
As a + b = 1, if a is 1, then only one period is needed to converge to it's new value. If a is 0, it doesn't converge to it's new value, it stays at the previous one indefinitely. a is giving the percentage at which the gap is being closed consecutively.
If you are going to change that, remember that the sum of the coefficients needs to be 1, in order to have a nice behaviour. So, that "5x" better become "4x". |
| Lorelei | Tuesday, January 22, 2013 - 03:57 am
I'm about to throw a shoe at you, Laguna lol |
| Laguna | Tuesday, January 22, 2013 - 01:12 pm
I bet it's a shoe coloured with all kinds of theorems on it. |
| Laguna | Wednesday, January 23, 2013 - 10:22 pm
So... Today I had a little experiment to put my assumptions and the information the GameMaster provided to the test. Guess what? I do have a nice feel after all.
I measured how much current information weighs on the education index, and it came up as being 1/5. It's amusing, because I was excepting 4/5. Seems like the information provided on this thread was switched, so that "4/5 is a bit faster" thing now makes sense. He just wrote the equation wrong. Its' actually:
Y = (X + 4*Y_(t-1))/5 |
| Crafty | Thursday, January 24, 2013 - 09:52 pm
Do be quiet Laguna, you are babbling inanities. |
| SweetPea | Thursday, January 24, 2013 - 11:02 pm
My head wants to explode haha. |
| Laguna | Thursday, January 24, 2013 - 11:33 pm
Not so me as I am babbling, it is that not even once the index was reported correctly. I've corrected that. |
| Crafty | Friday, January 25, 2013 - 12:50 am
Great, I'm sure everyones so much more the wiser for that.
If any people playing out there are wondering, the edu index will follow the lowest of the 3 individual indexes. Simples, no? |
