Matrix Games Forums

ORIGINAL: Mike Parker

I found the problem. Given your P0 P1 P2 then

P(150) and P(0) are as you say but

P(100) = P0*P1*(1-p2)+P0(1-P1)P2+(1-P0)*P1*P2 = .4145

P(50) = P0(1-P1)(1-P2)+(1-P0)P1(1-P2)+(1-p0)(1-P1)P2 = .3255

then all the Probabilities sum to 1

Fixed it just 4 minutes before your post [;)] Nice to see someone versed in these matters around.

I noticed that I suppose I wrote down the problem and found the solution while you were editing the post!

Interestingly enough the expected value of tanks produced is just the mean of the three probabilities times the maximum possible production. I suppose there is a theorum there that I once knew from a stats class and have since forgotten!

ORIGINAL: Mike Parker

I noticed that I suppose I wrote down the problem and found the solution while you were editing the post!

Interestingly enough the expected value of tanks produced is just the mean of the three probabilities times the maximum possible production. I suppose there is a theorum there that I once knew from a stats class and have since forgotten!

Yes, it's very similar to the expectation of a binomial distribution:

E(X) = np

where n would be factory capacity and p the average of the three probs.

Here the analysis depended on time and I wanted to get a grasp on the variability of production, so I just applied the following:

P( event ) = \sum_{situation where event holds} Probability( situation )

Yes, it's very similar to the expectation of a binomial distribution:

E(X) = np

where n would be factory capacity and p the average of the three probs.

Here the analysis depended on time and I wanted to get a grasp on the variability of production, so I just applied the following:

P( event ) = \sum_{situation where event holds} Probability( situation )

Yep,[&o] clear as mud. Not sure I get the relevance of the south seas quote ... but an amusing story.

You don't have to understand this math to play the game, anymore than you have to understand all the combat math to be successful.

This is interesting to me because I'm studying business stats, so let me ask some questions, if you care to engage with me to help me understand. I'm always looking for practical applications of my stats classes.

First, where Joel Billings is quoted thusly:

ORIGINAL: Joel Billings
The way it should work, is once a factory is below 50%, the chance it will produce on any given turn is equal to:
100-current damage
So a 30 damaged factory has an 70% chance of producing in any given turn.

This contradicts the manual pg.282, does it not?
If you are at 51% damage or more, the manual says the factory WILL NOT produce (no probabilities, no equations).
Let us assume that what was intended was this:
"When factory damage is 50 percent or less"
(I'm a technical writer, these things drive me nuts.)

The next questions I have is about the Damage 30 Factory:
It has a 70% chance of producing WHAT QUANTITY? It's capacity? A proportional, probability-distributed quantity?
From what I can tell, it's going to produce its original, undamaged capacity. Am I right so far?

ORIGINAL: heliodorus04

ORIGINAL: Joel Billings
The way it should work, is once a factory is below 50%, the chance it will produce on any given turn is equal to:
100-current damage
So a 30 damaged factory has an 70% chance of producing in any given turn.

This contradicts the manual pg.282, does it not?
If you are at 51% damage or more, the manual says the factory WILL NOT produce (no probabilities, no equations).

I read the manual very much like you have done heliodorus, but Joel knew better

ORIGINAL: heliodorus
The next questions I have is about the Damage 30 Factory:
It has a 70% chance of producing WHAT QUANTITY? It's capacity? A proportional, probability-distributed quantity?
From what I can tell, it's going to produce its original, undamaged capacity. Am I right so far?

Yes, it's nothing or full capacity.

ORIGINAL: DBeves
Yep,[&o] clear as mud. Not sure I get the relevance of the south seas quote ... but an amusing story.

Pretty easy. The natives thought that the reason for the planes arriving was the fact that someone had planted an airbase in their atoll... which is and isn't the reason. The actual reason was the war that was raging all across the Pacific, a business the natives didn't really particularly care about nor had the means to reproduce.

What I mean with that is that WiTE design is telling you that you'll eventually get you tanks, but not when and in what amount. Want to "game" the system so you can play optimally? Then reverse-engineer all the formulas under the hood - including those governing Refit mode, and those are black magic to me - and write a program that analyzes the savegames and predicts - with some margin of error - how soon you'll be having those Tank Corps you so badly need for your offensive at 120% TOE.

In my opinion, a sound wargame is one where it's not practical to behave in an "optimal" way. Wars aren't conducted optimally, so neither we should be able to conduct them optimally.

As Mynok says, you don't need to fully understand all these things to play effectively. You just need to know that when factories are damaged the produced items you want so much perhaps will be available in one, two or three weeks. So adjust your planning to account for that slack (which is easier said than done, of course).

ORIGINAL: Bletchley_Geek

Some math on this.

We have a T-34 factory of capacity 50, with damage of 47% at Turn X. Let's see how many tanks it might be producing. Let p be the probability of the factory producing its capacity.

At Turn X: p0 = 0.53
At Turn X+1 : p1 = 0.56
At Turn X+2 : p2 = 0.59

Now we have three independent random events (i.e. the factory produces its full cap of T-34s).

Okay, yeah, I was right before. You produce your WHOLE capacity, or nothing. This will help anyone who wants to understand these equations understand what Bletchley has done.

Probability of producing 150 T-34's after 3 weeks = p0 * p1 * p2 = 0.1751, i.e. in seventeen out of every 100 games with the same situation.

This is the straight-forward multiplication of the original 3 probabilities.
The probability of 150 tanks (which is the factory's 50-tank capacity multiplied by the 3 turns we're looking at) REQUIRES those probabilities to be achieved. These are independent, exclusive probabilities on each turn. Thus, they are multiplied. If any of those probabilities had failed, it is no longer possible to get 150 tanks, and instead you're in one of the situations where you produce 100 tanks (which I look at next), 50 tanks, or 0 tanks.

Probability of producing 100 T-34's after 3 weeks

To understand the equation below, you have to understand what you're looking at in independent events.
To get 100 tanks, ANY 2 of your 3 probabilities have to be true.
So...

= p0*(1-p1)*p2 + p0*p1*(1-p2) + (1-p0)*p1*p2 = 0.4145, i.e. in 41 out of every 100 games.

You're looking at 3 independent equations. These are:
The probability that on T1, the factory fails to produce, which is this equation.
= (p0*(1-p1)*p2)

Explained. Bletchley is showing the scenario where the factory produces on T0 and T2, but NOT T1.

I added the parentheses to the beginning and end of that equation because that is only ONE scenario where you reach 100 tanks produced. For me, these are really important in understanding probability equations.

Note that the equation(1-p1) is the compliment of the p1 probability (specifically it is 1.0 minus .56, which is .44)- in other words, it is the chance that, on T1, the factory FAILED to produce. All probabilities are between 0 and 1 (think of this as a percentage between 0 and 100 percent). So you have a 100 percent chance of the factory either producing 50 tanks, or not producing 50 tanks - those are your only possible probability outcomes for T1.

The probability that the factory produces 50 tanks on T0 and also T1, but NOT T2, which is this equation:
(p0*p1*(1-p2))
Again, I add the extra parentheses to delineate exclusive scenarios. They are exclusive because the only way to get 100 tanks is to have 2 successful production turns and 1 failure.

(Note you have a similar equation for the compliment of T2 failing to produce any tanks).

And finally the probability that the factory produces 50 tanks on T1 and T2 but not T0, which is this equation:
((1-p0)*p1*p2)

Now to note one more point on the equation:
p0*(1-p1)*p2 + p0*p1*(1-p2) + (1-p0)*p1*p2 = 0.4145
Let's abbreviate these raw numbers with what they mean:

The chance of producing 100 tanks equals:
The chance that you produce 50 on T0 and T2
plus
The chance that you produce 50 on T0 and T1
plus
The chance that you produce 50 on T1 and T2.

Each of those equations is ONE possible way to produce 100 tanks, so we add them together to fine the total probability.

The same thing is happening with the other two sets of equations, only in those, we are measuring only the chance of producing 50 tanks (in other words, two failures and one success over those 3 turns), or 0 tanks (all three turns result in failures to produce).

Probability of producing 50 T-34's after 3 weeks = p0*(1-p1)*(1-p2) + (1-p0)*p1*(1-p2) + (1-p0)*(1-p1)*p2 = 0.3255, i.e. in 32 out of every 100 games.

Probability of producing 0 T-34's after 3 weeks = (1-p0 * 1-p1 * 1-p2) = 0.08478, i. e. in 8 out of every 100 games.

You can see that this slightly beneficial to the factory owner, since the probability of getting the full production in those three weeks is about the double of getting none, being the norm to get just 50 T-34s in three weeks.

But this omits one critical fact, and that omission may cause people to mistakenly believe the system favors Soviet production.

What's missing is the fact that at 51% damage or more, a factory produces nothing (100% chance).

If factories with more than 50 percent damage could produce using the same equations as 50 percent or less, you would see that the chance of producing 0 tanks is the same as producing 150 tanks (right, Blethcley?). But the number of calculations would be far, far higher.

As is, the chance of producing 0 tanks in a damaged factory is actually much higher than the chance of producing 150, because at 51% damage or more, you produce nothing.

ORIGINAL: Mynok


You don't have to understand this math to play the game, anymore than you have to understand all the combat math to be successful.

Well - yes - I can play the game - but like anything - its infinitely more enjoyable if you have some idea whats actually going on.

ORIGINAL: Bletchley_Geek

ORIGINAL: DBeves
Yep,[&o] clear as mud. Not sure I get the relevance of the south seas quote ... but an amusing story.

Pretty easy. The natives thought that the reason for the planes arriving was the fact that someone had planted an airbase in their atoll... which is and isn't the reason. The actual reason was the war that was raging all across the Pacific, a business the natives didn't really particularly care about nor had the means to reproduce.

What I mean with that is that WiTE design is telling you that you'll eventually get you tanks, but not when and in what amount. Want to "game" the system so you can play optimally? Then reverse-engineer all the formulas under the hood - including those governing Refit mode, and those are black magic to me - and write a program that analyzes the savegames and predicts - with some margin of error - how soon you'll be having those Tank Corps you so badly need for your offensive at 120% TOE.

In my opinion, a sound wargame is one where it's not practical to behave in an "optimal" way. Wars aren't conducted optimally, so neither we should be able to conduct them optimally.

As Mynok says, you don't need to fully understand all these things to play effectively. You just need to know that when factories are damaged the produced items you want so much perhaps will be available in one, two or three weeks. So adjust your planning to account for that slack (which is easier said than done, of course).

Well no - actually - the natives were just dumb and didnt understand that the airbase wasnt "planted" and planes only arrived there because there was a reason for it. Now thats just because they were dumb or cause no one explained to them why planes land at an airbase. I am not looking nor am interested in "gaming" the system. what I do need however - if I am going to invest the amount of time in a game this requires - is some expectation of knowing what happens and that its somewhere within the bounds of reality. for all I know - 50% damage could mean the factory suddenly switches to producing bananas.

My point is the formulas shouldnt be so obtuse that people have to go through the hoops you yourself just illustrated to understand it. Fine - I could just accept that damage = bad and no damage = good ... but thats hardly the point - the only reason you can say what you said in your last paragraph is because some one worked it out. The manual certainly doesnt explain it like that and neither does the game. Its not the complexity of the formula that matters but the way the result is represented.

As I said in my post I was talking about the game design - and not information gleaned by users from what only seems like hard work to me.

ORIGINAL: DBeves

ORIGINAL: Mynok


You don't have to understand this math to play the game, anymore than you have to understand all the combat math to be successful.

Well - yes - I can play the game - but like anything - its infinitely more enjoyable if you have some idea whats actually going on.

I'm sure the Russians said something similar in the Summer of 41 but they eventually figured it out[:D]

ORIGINAL: heliodorus04

You can see that this slightly beneficial to the factory owner, since the probability of getting the full production in those three weeks is about the double of getting none, being the norm to get just 50 T-34s in three weeks.

But this omits one critical fact, and that omission may cause people to mistakenly believe the system favors Soviet production.

What's missing is the fact that at 51% damage or more, a factory produces nothing (100% chance).

If factories with more than 50 percent damage could produce using the same equations as 50 percent or less, you would see that the chance of producing 0 tanks is the same as producing 150 tanks (right, Blethcley?). But the number of calculations would be far, far higher.

As is, the chance of producing 0 tanks in a damaged factory is actually much higher than the chance of producing 150, because at 51% damage or more, you produce nothing.

Thanks for saving me the work of going over the computations and explaining them, heliodorus

Indeed. I omitted to mention the fact that factories above 50 damage don't produce anything because it is already in the manual, whose truth has not been modified by any statement made on the forums by WiTE developers.

I say I find it beneficial for the factory owner, I see the distribution somewhat skewed towards getting full production. To me the fact that the manual isn't in synch with the game it's a sign that this mechanism was introduced late in the development process, with an obvious purpose of balancing. A bad thing? Not necessarily but would be nice to read the "designer's notes" about this.

@DBeves: I wasn't trying to sound dismissive, but rather humorous. I'm not an English native speaker and what sounds funny or witty in Spanish in English might sound cocky or arrogant. And I don't think the natives were any dumber than you or me. Just in their culture the thought of thousands of men sailing for weeks to meet their deaths over a patch of salt water was as ludicrous as our view of them trying to replicate something that was beneficial to them in the short run, but rather damaging in the long run. I'm afraid nobody took the pains of explaining to them what was happening around them.

ORIGINAL: Helpless

First of all in reality factories were no moving to some empty places. New locations had all kind of facilities already in place. Also not everything and everyone was moving. Only 10% of workers and 20% of engineers from Kharkov factory #183 (T-34) were moved to Urals (Nizhny Tagil)... the rest went to the front.

Another example of the evacuation pace - last echelons with T-34 factory personal left Kharkov on 19 of October and first 25 T-34 were assembled by December 8th 1941 in Nizhny Tagil.

Pavel

Your learning amazes me Sir Helpless

Do you know when Kharkov evacuation started and when full production achieved? This looks like a minimum of 8 weeks without any production.

If this was typical then damage to moved factories should mean, say, 8 weeks no production then perhaps 1/2 production for x weeks (x = ????) then full production after that. Benefit = simplicity+ improved realism and numbers could adjust for different factory types like repair rate does now. Equally simple system for captured factories

David,

Now you are asking an easy answer for complicated task.

Do you know when Kharkov evacuation started and when full production achieved?

It depends what you call full production.

http://www.battlefield.ru/en/tank-devel ... 9-t34.html

For the factory #183 in Kharkov we have such table:

July - 225
August - 250
September - 250
October - 30

If we omit October figures, and say that evacuation happened by the end of September (turn 14-15). We should get average production ~54. Which is close to starting 50 + 1 expansion.

Now we know that evacuated factory produced 25 already in December 1941, which is roughly half rate of what they started with.

Overall in Q1 1941 factory #183 in Nizny Tagil produced 440 - the same as in Kharkov in Q2. Which gives the rate of 32 per turn. To get the idea of the production rate increase - in Q2 1942 the same factory produced 1380 T-34 tanks - 102.5 per turn

Now the most complicated. Since we keep all the production distributed among many locations and we have the same build limit, we can't have factories to produce at the different rates. Therefore all the rates are greatly approximated towards the averages.

Here we speak about just one type and one factory, but there were thousands of them, with different evacuation and recovery rates. So it can get only more complicated if we'll try to model it better.

ORIGINAL: Helpless
Now the most complicated. Since we keep all the production distributed among many locations and we have the same build limit, we can't have factories to produce at the different rates. Therefore all the rates are greatly approximated towards the averages.

Here we speak about just one type and one factory, but there were thousands of them, with different evacuation and recovery rates. So it can get only more complicated if we'll try to model it better.

What I've learned from this factory discussion is what Helpless says, which is that the WitE system approximates factory relocation, factory damage, and factory production toward the historical average.

Looking at the probability distributions (which don't factor damage greater than 50 percent at all), the system works pretty f***in well in that regard, and I'm impressed by that.

DBeves, you seem like a reasonable person. Respectfully, and if you'll pardon my bluntness, you seem to want to take umbrage with systems that are more complicated than your recreational work ethic. You don't want it to be THAT hard to follow. That's fine, but if you don't understand the modeling under the engine, you're going to be out-played by people who do. Almost all of us have to work at understanding the models. It's not a simple game.

Poker is a simple game, but if you're not going to learn the statistics behind it, don't expect to win tournaments.

The vast majority of people playing the game aren't interested in the 'obtuse' statistical formulae behind the engine, and it's hard to find technical writers who can explain them (I'm not all that sure I did a cohesive, efficient, simple job in my attempt above).

But some of it IS in the manual (for example I'm pretty sure it already says: damage bad, no-damage good), and even with a reasonable (for an American) math background, I have to stop and think it through. Most of the time I don't bother, and just play because it's so much easier. Occasionally I go back and it makes more sense after playing a few times.

People here are more than willing to share the product of what you acknowledge is 'hard work' when they decipher a game mechanic. It would be nice if that didn't lead to "this game is too complicated" criticisms. It's a simulation of the largest theater of the largest conflict in human history.

The manual tells you how to play (and pretty well, too). It's your job to figure out how to win. And that is work.

Dangit don't spill all the beans on the maths behind things! How will I keep my advantage

David,

Now you are asking an easy answer for complicated task.
For the factory #183 in Kharkov we have such table:

July - 225
August - 250
September - 250
October - 30

If we omit October figures, and say that evacuation happened by the end of September (turn 14-15). We should get average production ~54. Which is close to starting 50 + 1 expansion.

Now we know that evacuated factory produced 25 already in December 1941, which is roughly half rate of what they started with.

Pavel

If you worked for me you would probably win my 'geek of the week' competition every time.[&o] I should add that winning is considered to be a good thing in my department!

I can see how you get weekly figures, but assuming Nov production was 0, that means only 55 tanks in 3 months Oct-Dec (13 weeks) ie 12 weeks without any production in game terms. If this is typical then the answer might be damage set as 75% with a small variation, or 50 +random (20-30)
or similar. Neither would mean changing the rules beyond a tweak. I assume, and would not make anything more complicated.

That would seem to be better for restart of production but perhaps would mean further recovery too slow after recover back to 50% damage. If so you could have higher initial damage but higher % recovery each turn.

On the other hand, if you say that existing rules accurately reflect TOTAL production loss before get to 0% damage because recovery from 50 -0% damage in the game is slower than historical then I shall stop arguing.

As I wrote earlier, my experience in PBEM is all my factories only getting 50% damage which I though was too generous. If the average is in fact 75% and I just got lucky in my games, then the rules certainly don't need changing except perhaps to reduce chance of variation from 75%. Sorry - I've admitted my occupation here and I could not resist one last argument.....

If you worked for me you would probably win my 'geek of the week' competition every time. I should add that winning is considered to be a good thing in my department!

[:)]



David,

It is considered that moving all the factories should be very difficult. We do not pretend that everything is in perfect balance, therefore in coming patch rail costs are doubled. So to move 60 T-34 factories you will need 84000 RC's which is ~70% of the whole turn rail capacity. That's a big price.

Also believed or not, there is task on the list to randomize factory damage and make it less predictable. Also some bombing damage should be carried over as well. So there could be some adjustments, but in general the idea will be the same - the more you move the less damage on the destination.

ORIGINAL: Helpless
Also believed or not, there is task on the list to randomize factory damage and make it less predictable. Also some bombing damage should be carried over as well. So there could be some adjustments, but in general the idea will be the same - the more you move the less damage on the destination.

That bombing damage is going to be an abstraction of strategic air warfare during Logistics Phase, or it's supposed to be something Axis players actually have to do?

PS: I have only found so far one lonely Axis player who has done this - to actually bomb important factories such as Leningrad and Kharkov. And he had a very nice success since Soviet players usually rip naked PVO strany formations...

EDIT: I again confused Leningrad with Kiev [8|]