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Emud
22-10-2009, 17:36
I have been developing a small application where you calculate the expected combat results for different types of units, with different types of equipment.

I need some help verifying the results. This is not a big job, but I need help from someone else to double check if im doing something wrong in my equations.


What I need is the expected combat result for the following situations (considering 5 models are fighting in the front rank)

1.a Goblin spider riders charge orc boyz
1.b Goblin spider riders fight orc boyz in second round of combat.

2.a Nightgoblins with spears charge longbeards
2.b Nightgoblins with spears fight longbeards the second round of combat

You can make own examples too if you want to (it would be greeatly appriciated), although of the special rules i have only poison and hatred implemented. Ill add stuff along the way though.

Izram
22-10-2009, 17:41
Ask Avian, his works pretty well.

I assume he won't mind posting it here, as he has it in his sig:

http://www.avianon.net/calculations/unit_combat.php

Emud
22-10-2009, 17:44
Ask Avian, his works pretty well.

I assume he won't mind posting it here, as he has it in his sig:

http://www.avianon.net/calculations/unit_combat.php

Thanks, but I dont think he has poison or hatred in that calculator

EDIT: now I found it. Although posion and mounts dont seem to work that well. Thanks anyways!

narrativium
22-10-2009, 18:18
They do... but the problem is, when you say the expected result, you mean if rolls are average. What you might try to do, which would be more complicated, is to show the distribution of a result. It's nice knowing that you ought to kill two and he ought to kill two back, but if you kill only one, is that disastrous or just unfortunate?

Midevil216
22-10-2009, 19:03
Do we really need this? When I make an army I don't worry about all this math/calculation crap. I just want to play and have fun. Who cares how many models on average my guys can take out if I roll the averges. And thats is, Its all up to the ramdomness of the dice roll, some silly calculator is not going to predict that.

I was playing my girlfriend the other day and wounded like 4 or five of her guys and shes needed sixes to save and she rolled at least 4 sixes. Even though that is rare I'm sure some dumb calculator is not going to predict that.

Sorry if this seems harsh but I just think there a waste of time. Just play the game and have fun.

Condottiere
22-10-2009, 19:08
Maths does come in hand in making tactical decisions like which unit to attack, and when to run away.

AFnord
22-10-2009, 19:09
It's not a waste of time, for those who want to compare units, and see which one works best under which conditions. While there is a bit of randomness in die rolls, it's usually not nearly as random as some people make it out to be. You will usually end up near a statistical average, and knowing that statistical average (and being able to calculate it on the fly) really helps when deciding what to charge and when to charge it, or if you would rather stay away from that combat altogether. It's because of lack of understanding of how statistics work that you see people rear charging chaos knights with wolf/spider riders when there is a tougher unit in the front, like black orcs. The result is often that thanks to how much easier the goblins are to kill the orcs lose by even more, and thus have an even greater chance of breaking. So to answer your question Midevil216: Yes, it's needed, at least on a competitive level.

As for the math requested in the original post, it's really easy to do it on your own. Simply take chance to hit*chance to wound*chance to not save then take this result and subtract it from the amount of models with lower I and repeat the process. I don't know all the stats for those troops by heart, so this might be a bit off, but here are the calculations (made easy to follow):
Spider riders charge (if they have spears, I think they do, but i'm not sure, and i'm also not sure about the S value for the spiders), and taking for granted that the orcs don't have shields:
5*(1/2)(1/2)(6/6)+5*(1/3)(1/2)(5/6)+5*(1/6)(5/6)=2,64
Goblins attacking....Spiders attacking(-poisoned hits)..Poison hits.
I'm sure that you will be able to do the rest of the calculations on your own. As you can see, it's very basic math.

Lijacote
22-10-2009, 19:53
Statistics do not lie. Statistics work. To quote someone's brilliant signature, technically correct is the best kind of correct... etc.

jullevi
22-10-2009, 20:05
Sorry if this seems harsh but I just think there a waste of time. Just play the game and have fun.

Some people enjoy crunching numbers and solving mathematical problems. In many cases, solving the problem is more satisfying than the actual result.

Avian's gadget is nice and simple. The maths behind it show how we usually approach problems like this - using expected values and probabilities. While expected values give a good hindsight of what kind of results are to be expected, they are often misleading.

Personally, I find probabilities of different results more interesting than expected values, but maybe it's just me.

Midevil216
22-10-2009, 20:05
Well I don't need a bunch of calculations to tell me not to charge wolf/spider riders into chaos knights, front, flank or rear.

Common sense can tell you when to charge and when not to, or when to flee, It's a *******' GAME, the fate of the world dosen't depend on "well if roll 15 dice, 7.5 should be 4's and x should be 6's blah blah blah - waste of time.

Avian
22-10-2009, 22:26
One man's fun is another man's boredom. You can't dictate what other people find interesting. :p

Tarian
22-10-2009, 22:33
Fate of the world? No, no. Fate of your unit? Oh yeah. Besides, I like crunching the numbers so I can reasonably predict what *should* happen.

Besides, a lot of people I play would definitely benefit from a little "Mathhammer" now and then... and prevent some charges that should never really happen.

catbarf
22-10-2009, 22:38
Well I don't need a bunch of calculations to tell me not to charge wolf/spider riders into chaos knights, front, flank or rear.

Common sense can tell you when to charge and when not to, or when to flee, It's a *******' GAME, the fate of the world dosen't depend on "well if roll 15 dice, 7.5 should be 4's and x should be 6's blah blah blah - waste of time.

We do the math because common sense is often wrong. Besides, having hard numbers makes it a lot easier to figure out how much you can rely on a unit beyond 'might work, might not'.

Tarian
22-10-2009, 22:51
I have been developing a small application where you calculate the expected combat results for different types of units, with different types of equipment.

I need some help verifying the results. This is not a big job, but I need help from someone else to double check if im doing something wrong in my equations.

2.a Nightgoblins with spears charge longbeards
2.b Nightgoblins with spears fight longbeards the second round of combat

Realized I missed the entire OP...

Anyhow, this is working off of memory, I'm sure people will correct if wrong.

2.a) Goblins: 3/6 Hit, 2/6 Wound, Dwarves will armor 4/6, so 2/6 leak through... 6 Attacks (assuming champ) 3 hit, 1 wounds, .2777 wounds after armour.

Assuming that .2777 failed, 6 Attacks from dwarves, 4/6 hit, 4/6 of the misses hit due to hatred, 3/6 wound, Assuming LA/S, 4/6 leak through armour., so... 4 hits, 2*4/6 for hatred, so 1.3333 more hit gives 5.333 hits, 2.6666 wounds, 1.77777 wounds, or thereabouts.

2.b) Goblins: 3/6 Hit, 2/6 Wound, Dwarves will armor 4/6, so 2/6 leak through... 11 Attacks (assuming champ) 5.5 hit, 1.8333 wounds, .6111 wounda after armour.

Assuming that 2/3 succeeded, 5 Attacks from dwarves, 4/6 hit, 3/6 wound, Assuming LA/S, 4/6 leak through armour., so... 3.3 hits, 1.65 wounds, 1.1 wounds.

Brothersir
22-10-2009, 23:49
Well I don't need a bunch of calculations to tell me not to charge wolf/spider riders into chaos knights, front, flank or rear.

Common sense can tell you when to charge and when not to, or when to flee, It's a *******' GAME.

Aaaaaaand why is it common sense not to do so? It's because the probability of your goblins benefiting/costing the combat. While you may not care about the actual numbers in this situation, you are recognizing that the Chaos Knight's odds > the Goblin's odds. Just because you don't realize you are doing the math, doesn't mean you aren't doing it. The human brain is an amazing tool.

Where the calculations come in handy game time are when the situations aren't quite as obvious (and much harder to come up with examples for). Some people enjoy that edge, some people don't. It really depends on your risk management.

Its all about setting limits for yourself on what kinds of risks you take. If you don't like to take risks, stick to the numbers. If you like to take big risks at the prospect of big rewards (ex. the Goblins actually defeating the Chaos Knights) then you'll be willing to put yourself in situations where the numbers are against you. Either way, it never hurts to know the numbers.

And I'll stop there as I feel like I'm writing a paper for class.

Emud
23-10-2009, 07:45
Ok. Thanks for the responses.

About if this is needed or not:
I can inform that i need it very much. I do not intend to compare unit to unit, I want to compare ALL possible combinations of units. The reason is that im working on a mathematical model on how to calculate a units power. This model will include more than raw combat power (depending on tactical values, like holding ground or charging), but for now what is most importat is to calculate combat results accuratley.

About statistics and mean values:
Yes, I might do statistics later. It is not complicated at all. But the amout of extra information often confuses things more than the mean values. For example if the mean value is positive or negative says very much.

About the calculations:
I know the math. It is very simple. I need someone else to do it just to double-check if I am doing something wrong. When you program stuff it is very easy to mess up, especially when you are handling every thinkable off-case in the same equation, thats why I chose units with hatred and poison.

Guanyin
23-10-2009, 07:52
Do we really need this? When I make an army I don't worry about all this math/calculation crap. I just want to play and have fun. Who cares how many models on average my guys can take out if I roll the averges. And thats is, Its all up to the ramdomness of the dice roll, some silly calculator is not going to predict that.

I was playing my girlfriend the other day and wounded like 4 or five of her guys and shes needed sixes to save and she rolled at least 4 sixes. Even though that is rare I'm sure some dumb calculator is not going to predict that.

Sorry if this seems harsh but I just think there a waste of time. Just play the game and have fun.

By this reasoning, a models statline wouldn't matter, since it's so random ;)

When you compare statlines before you decide to charge, for example, (and I do mean YOU) you have some idea of the result expected. So you also do this, but far less detailed.

Avian
23-10-2009, 08:38
Ok. Thanks for the responses.

About if this is needed or not:
I can inform that i need it very much. I do not intend to compare unit to unit, I want to compare ALL possible combinations of units. The reason is that im working on a mathematical model on how to calculate a units power. This model will include more than raw combat power (depending on tactical values, like holding ground or charging), but for now what is most importat is to calculate combat results accuratley.
This sounds interesting. Would you like to tell us more about it? :)

ChaosVC
23-10-2009, 09:19
2x2=6...fail

Emud
23-10-2009, 09:34
This sounds interesting. Would you like to tell us more about it? :)

Well I'm only started, but I can try and tell what im trying to accomplish. I am going to revise unit points for my own house rules. But the program could be used for several other things too. Optimization of army lists, and balancing new armies comes to mind.

Basically I want make a program that can calculate all possible combinations of units and equipments for units, depending on of the unit is charging, is charged, or is fighting in following rounds of combat.

Once I have the ability to generate data accuratley I will start and generating a score for the unit and see how well these corresponds to the unit price. For now I am generating the score by taking a unit and adding the combat result against all other units, then dividing by total amount of units (to get the score back to a comparable combat result). This will give its mean performance against all other units.

Its too much to explain everything here, but examples of what I will do is to calculate a units score while charging, recieveing a charge. Both are fairly strightforward.
More advanced stuff might be to use a combined charge-recieve charge score weighted by the units movement. Where 1 in movement diff gives 75% of charging, and 2 diff gives 87,5%, and so on. This is calculated by a formula, so non integers ar ok, and this makes it possible to estimate the power of animosity for example. At least it get reflected by the score.(This might seem obscure, but I would say its more accurate compared than compared to how GW handles it).
Also the score of holding ground in following rounds, depending on stastistical outcome of CR and Leadership is possible.
Another possibility would be to include units rank bonus based on price difference. If unit A costs half of unit B, a fair comparision, points-wise would be for onit A to have +1 CR from ranks.

All these scores could also be generated with filters, like comparing a unit against costlier units, or less priced units, or against cavalry.

Here is a small example of units power for recieving a charge. (that might be completley wrong by the way)
+0.819 Big'Un______ 11.0 ,light armour,choppa,additional
+0.589 Big'Un______ 11.0 ,light armour,shield,Spear
+0.311 orc________ 7.0 ,light armour,choppa,additional
+0.287 Goblin______ 15.0 ,Giant wolf,light armour,shield,Spear
+0.287 Goblin______ 14.0 ,Giant wolf,light armour,shield
+0.237 NightGoblin__ 4.0 ,shield,Spear,netters
+0.205 Goblin______ 5.0 ,light armour,shield,Spear
+0.199 Goblin______ 13.0 ,Giant spider,shield,Spear
+0.135 Big'Un______ 10.0 ,light armour,shield,choppa
+0.123 orc________ 7.0 ,light armour,shield,Spear
-0.063 orc________ 6.0 ,light armour,shield,choppa
-0.098 NightGoblin__ 4.0 ,shield,Spear
-0.374 NightGoblin__3.0 ,shield,netters
-0.375 Goblin______ 14.0 ,Giant wolf,light armour,Spear
-0.375 Goblin______ 13.0 ,Giant wolf,light armour
-0.403 Goblin______ 4.0 ,light armour,Spear
-0.450 Goblin______ 4.0 ,light armour,shield
-0.476Big'Un______ 9.0 ,light armour,choppa
-0.584orc_________ 5.0 ,light armour,choppa
-0.754NightGoblin__ 3.0 ,shield
-1.058Goblin______ 3.0 ,light armour

Avian
23-10-2009, 11:52
Interesting. Is this one guy of each type fighting one guy of each other type? I can see there being a fair bit of work being put in at the start to calibrate the system to give meaningful output, but once you get it working I can see the potential. :)

Emud
23-10-2009, 12:07
Interesting. Is this one guy of each type fighting one guy of each other type? I can see there being a fair bit of work being put in at the start to calibrate the system to give meaningful output, but once you get it working I can see the potential. :)

Thats exactly how it is right now. Every possible combintaion of unit combination tested against all others.

The data must be combined and sorted of course. Otherwise it would grow out of proportion quite fast.

I dont believe it will be that much work building the app and generating the data though, most of it is done already. Analyzing it might be what is the real pain :)

narrativium
23-10-2009, 12:28
Well, you need some form of conclusion. e.g. one unit is pretty self-sufficient in combat, another unit works better as part of a multiple combat.

Midevil216
23-10-2009, 12:54
One man's fun is another man's boredom. You can't dictate what other people find interesting. :p

Hey I get it. I'm not saying anything bad about the persons who like doing this stuff.

I'm just saying that I know what my unit does and I know what your unit does, I know what could happen if I charge you. I dont need lists of calaulations to tell me this.

It just seems so silly. I could just picture you guys sitting there by candle light with a calculator and a load of crumpled up paper on the floor trying to figure out if unit "a" could take unit "b". Quite comical.

At the end of the day it is just a game. Do you really need to win that bad?

Avian
23-10-2009, 12:58
Analyzing it might be what is the real pain :)
I started fiddling with something similar when I was bored at work a little while ago, which rated specified units' performance in three specific scenarios. IIRC one was getting charged by a unit of Knights of some type, another was charging a Dwarf unit and I can't remember the third but it was an ongoing combat. The score would be the average combat results in the sum of those three cases, divided by the unit's cost. Sadly the project didn't really get very far.



Hey I get it.
<...>
Do you really need to win that bad?
If you actually "got it", you wouldn't be asking questions like that. :D

Midevil216
23-10-2009, 13:03
By this reasoning, a models statline wouldn't matter, since it's so random ;)

When you compare statlines before you decide to charge, for example, (and I do mean YOU) you have some idea of the result expected. So you also do this, but far less detailed.

Of course statlines matter. I could charge your goblin unit with my swordmaster unit and I could roll all 1's and 2's to hit and the goblins get lucky and kill one guy and I flee. This outcome would be the same weather or not I have a detailed calculation list in front of me or not.

I know what the outcome "Should" be with or without calculations but ultimataly it comes down to dice rolling.

So is it random: absolutly
Do stat lines matter : absolutly

Midevil216
23-10-2009, 13:04
I started fiddling with something similar when I was bored at work a little while ago, which rated specified units' performance in three specific scenarios. IIRC one was getting charged by a unit of Knights of some type, another was charging a Dwarf unit and I can't remember the third. The score would be the average combat results in the sum of those three cases, divided by the unit's cost. Sadly the project didn't really get very far.



If you actually "got it", you wouldn't be asking questions like that. :D

Huh, I don't get it :)

Avian
23-10-2009, 13:06
Huh, I don't get it :)
My fun is not your fun. Go away and have your own fun. :p

Midevil216
23-10-2009, 13:13
My fun is not your fun. Go away and have your own fun. :p

Well my fun is reading what you think is fun and wondering why you think it is fun.:wtf:

Midevil216
23-10-2009, 13:14
I'm at work, what else am I supposed to do?

yoshimo
23-10-2009, 13:22
Someone who's playing mathammer with a mirror army of someone playing carebearhammer will win 99.9% of the time, there's another interesting statistic :p

Midevil216
23-10-2009, 13:27
Someone who's playing mathammer with a mirror army of someone playing carebearhammer will win 99.9% of the time, there's another interesting statistic :p

Is there really a stat on that? Do you have a link or some proof to back that up?;)

Avian
23-10-2009, 13:31
Well my fun is reading what you think is fun and wondering why you think it is fun.:wtf:
These things are fun to me because I think these things are fun. :p You can't explain taste. You can't rationalise to someone who doesn't like, say, fried liver why they should like it.

To quote Wash: "Some people juggle geese!"
:D

Midevil216
23-10-2009, 13:38
These things are fun to me because I think these things are fun. :p You can't explain taste. You can't rationalise to someone who doesn't like, say, fried liver why they should like it.

To quote Wash: "Some people juggle geese!"
:D

I'll agree with you there fired liver is disgusting :)

Knock yourself out with all the numbers, if you think its fun go for it, I am not trying to discurage anyone from doing it, I am just trying to see what the point of it is in such a random game, thats all.

Juggle Geese, now that sounds like a party !:p

Lijacote
23-10-2009, 13:58
If we go into psychology and whatnot, we can explain why Avian finds these sort of calculations fun. I'm sure Freud would have something interesting to say. :D

Emud
23-10-2009, 14:03
It just seems so silly. I could just picture you guys sitting there by candle light with a calculator and a load of crumpled up paper on the floor trying to figure out if unit "a" could take unit "b". Quite comical.

Oooh a story! Please continue, I want to hear the ending too



At the end of the day it is just a game. Do you really need to win that bad?
YEA! And thats not the end of it. I sacrifice animals to the dark gods before each game. And then I send a prayer to the good side too, just in case.




Knock yourself out with all the numbers, if you think its fun go for it, I am not trying to discurage anyone from doing it, I am just trying to see what the point of it is in such a random game, thats all.
If you knew about probability theory you might see the point

Midevil216
23-10-2009, 14:06
Oooh a story! Please continue, I want to hear the ending too


YEA! And thats not the end of it. I sacrifice animals to the dark gods before each game. And then I send a prayer to the good side too, just in case.

You sir have issues :eek:

Emud
23-10-2009, 14:10
You sir have issues :eek:

:) In reality i really dislike powergaming. Thats why I am doing this. to balance stuff so that powergaming will be more difficult.

Midevil216
23-10-2009, 14:15
See, now if you would of told me this 10 posts ago you would not of had to endure my rants :)

Emud
23-10-2009, 14:26
See, now if you would of told me this 10 posts ago you would not of had to endure my rants :)

Well, it is hard explaining so that nobody make false assumptions.

wilsongrahams
23-10-2009, 14:45
I am a player that sits on the fence. Usually I will look at the stats and judge in a second or so whether a unit is better or not. But when it comes to a pre-arranged game (eg I know my next one will be against Dwarves, and they will have a cannon and 20 handguns minimum) I like to look at the probability of said outcomes. For example, only by looking into the probability can you compare several different WS, S, enemy T, Save, and see which option is best point for point against your likely opponent. For example, should I take Swordmasters or Phoenix Guard? Both are Xpts per model so will cost the same, but one is better against Dwarves whilst the other will be better against say Vampire Counts.
The stats themselves don't actually show which is most likely to fare better against what you are expecting to face, because different rules and wildly different stats come into play. I think maybe you are concentrating more on thinking about a whole army of say goblins, where all have spears and there is very little to work out as all have the same stats, same weapons, same chances (lose) whatever they face.

I hope you get your project to succeed Emud however I don't believe you will manage perfectly as some abilities (Frenzy and Hatred come to mind) have a fixed cost but will have a wide degree of influence depending upon whom you are fighting. If you spend three turns walking towards the enemy gun line your 1pt shield will be of more use than say 3pts of hatred or whatever it is costed at for that unit. And, also, on that line, an ability costs the same usually even when given to different troops where it will have different effects. Imagine a Frenzied Chaos Warrior and a Frenzied Goblin (just imagine it, don't try finding it in the books!).

Best of luck to you however, and I hope I haven't made anything more complicated for you. I just wanted to help you look at some things now rather than later.

Emud
23-10-2009, 16:41
I am a player that sits on the fence. Usually I will look at the stats and judge in a second or so whether a unit is better or not. But when it comes to a pre-arranged game (eg I know my next one will be against Dwarves, and they will have a cannon and 20 handguns minimum) I like to look at the probability of said outcomes. For example, only by looking into the probability can you compare several different WS, S, enemy T, Save, and see which option is best point for point against your likely opponent. For example, should I take Swordmasters or Phoenix Guard? Both are Xpts per model so will cost the same, but one is better against Dwarves whilst the other will be better against say Vampire Counts.
The stats themselves don't actually show which is most likely to fare better against what you are expecting to face, because different rules and wildly different stats come into play. I think maybe you are concentrating more on thinking about a whole army of say goblins, where all have spears and there is very little to work out as all have the same stats, same weapons, same chances (lose) whatever they face.

I hope you get your project to succeed Emud however I don't believe you will manage perfectly as some abilities (Frenzy and Hatred come to mind) have a fixed cost but will have a wide degree of influence depending upon whom you are fighting. If you spend three turns walking towards the enemy gun line your 1pt shield will be of more use than say 3pts of hatred or whatever it is costed at for that unit. And, also, on that line, an ability costs the same usually even when given to different troops where it will have different effects. Imagine a Frenzied Chaos Warrior and a Frenzied Goblin (just imagine it, don't try finding it in the books!).

Best of luck to you however, and I hope I haven't made anything more complicated for you. I just wanted to help you look at some things now rather than later.

Thanks a lot. No you have not complicated things. I dont think i will succeed perfectly either, but the balance will be better analyzed than by GW at least. I am aware of those problems and I have a plan on how to deal with them.

Basically I will divide a units cost into 3 categorys, combat, shooting and magic. These thre categorys are clearly separated, and therefore motivate a price per category. Im just focusing on combat right now to narrow things down.

In a category there are seveal subcategorys, like charge and hold powers for combat. A unit is priced by the subcategory it performs best in. This might sound strange, but it is really the only way to stop things being unbalanced.

Think of it like this: If a unit behaves equally good in subcategory A, and B it clearly have a greater tactical value, being able to perform more tasks. If it is priced higher because of this tactical value it will mean it preform less good than equally priced special units, and therefore it will not be as good. It will instead lead to optimized armies, which is bad. Instead I will try and solve this by using the special and rare unit slots for units with better tactical values.

My points analysis will also very likely lead to non-fixed points values for equipment and abilities. This is ok by me, since it really is obvious that the effect is not the same in all situations.

I will also banish all fix-point unit upgrades that affect individual models. It is moronic. If an individual model gets better it's price sould increase. At least if you want to get rid of imbalances.

The biggest troubles is in the effects for things that cannot really be measured. Frenzy must charge. This wont get into the combat result equations. But for now i will just handle it by saying that i measure the power, not the tactical score

wilsongrahams
23-10-2009, 16:51
Well you seem to have it pretty much thought out already and with your explanation, it does make perfect sense to use a unit's best feature, as that is also what you would endeavour to do with it in the coming battle and so it's best feature is the only thing it will be doing tactically - nobody takes archers with the intention of getting them into combat - so they should be priced at how good they are at shooting.

When you say, altering the fixed prices for items, do you mean such as how a Lord and a Hero pay different points for a Spear and Great Weapon yet infantry all pay the same, whereas maybe they should pay different too?

Valaraukar
23-10-2009, 16:53
Not wishing to discourage you, but I feel there is still a lot more to make such a model work accurately. Here are just a few examples which appear to lie outside what you have mentioned thus far:

Have you considered for instance how unit size will effect the power of a unit and how you work that into a cost per model whilst retaining freedom of choice for the player.

Or psychology?

Or most difficult of all in my opinion the other units available to a particular army and how they can all interact on the gaming table.

Also for units and characters the interdependencies of different equipment combinations, such as the extra value a mount may give not only to a character but also the other equipment he is armed with. An example would be aldred's casket of sorcery which is much more valuable if highly mobile but still needs to be viable for a character on foot and the mount viable for a character without that item.

AFnord
23-10-2009, 21:11
While I gave a very simple example back in my first post with spider riders vs chaos knights, there are examples that will result in far more even results. If I have an idea what the probable result & probable deviation from that probable result is, I can plan ahead in a way that won't be possible if i simply go by my gut feeling. Yes, we all know that chaos knights>spider riders, but imagine the same charge vs common empire knights, suddenly you get into far more of a greyzone if it's worth it. What will the reward for my charge be? What are the odds that i will reap the reward? Should I hold back some of my forces if it fails? One die is very random, 10 is not. Anyone who knows anything about statistics will be able to tell you this. While you get freak occurances where all 10 will come up 6 (1,65*10^-6% of the times actually), this is really not worth planing for, as it's too unlikely, but what if it's a 1/4 chance? Should you plan for this eventuality? Is it worth it in this case?

Being able to calculate the odds will also dispel a lot of the psychological effect that some things has on you. Some things are simply scary to face, and you will find a lot of people, even good players, spending too much time and effort dealing with it, even tough it's not that dangerous. A classic example from 40k is anything that shoots large templates. These things are scary, so people will avoid them, even tough it sometimes is in your best interest to risk some units, and press the advance. But if you actually have an idea about how much it will kill, you will be more likely to make the right choice.

When your goal is winning (like in a tournament setting), being able to do simple math like this on the fly, in your head is important. Because more often than not, you will roll close to a statistical average, usually with a small deviation in some direction. You can calculate this deviation interval and decide how unlikely something will have to be for you to feel the need to plan for it. This works well when dealing with chemical processes, as these deviates from the average result, often far more than a large quantity of dice will, and yet people are prepared to use these products. The same way of thinking can easily be converted to the tabletop (after all, the math is incredibly easy). Most scenarios are, after all, not as obvious as chaos knights vs spider riders.

Malorian
23-10-2009, 21:16
Another thing people need to keep in mind is what you are risking if you lose.

Sure your knights should beat that block 70% of the time, but when happenes the other 30% of the time? What happens if you lose and break? What other units are put at risk?

Numbers are nice, but overall tactics are what win the day.

Emud
23-10-2009, 21:36
When you say, altering the fixed prices for items, do you mean such as how a Lord and a Hero pay different points for a Spear and Great Weapon yet infantry all pay the same, whereas maybe they should pay different too?

I mean units and characters should pay for performance. So most probably, different units pay different prices for the same equipment. Although I will leave characters for now, and just focus on base units.



Have you considered for instance how unit size will effect the power of a unit and how you work that into a cost per model whilst retaining freedom of choice for the player.

Or psychology?

Or most difficult of all in my opinion the other units available to a particular army and how they can all interact on the gaming table.


Unit size could be included several ways One way would be to add rankbonus depending on price difference. If unit A is half the price of unit B then unit A could have 1 rankbonus for the same total cost.

Psychology is maby not all that troublesome. Leadership tests is definatley doable by statistics. For fear and outnumbering the same reasoning as above could be used.

If you think hard about it there is often some approximation that can deal with the case. And as a very last resort there is the option to just use an extra "offset price" for special abilites and synergies. While it would be still very much open for debate, I still think It will be far more accurate using a mathematical model for pricing to determine the largest part of the price. Then add the extra "offset price" for things that cannot be calculated exactly.



Also for units and characters the interdependencies of different equipment combinations, such as the extra value a mount may give not only to a character but also the other equipment he is armed with. An example would be aldred's casket of sorcery which is much more valuable if highly mobile but still needs to be viable for a character on foot and the mount viable for a character without that item.

True. Thats why I will start with ordinary units first, since they are the base of the game.

I have thought about it though, and the short answer is that if the effect is variable depending on stats, then the price should be too if you want to avoid imbalances. There are really no way around it. There are several ways to correct this, I have not decided on what strategy to use.

Also, lets not forget that perfect balance will never happen. Small differences are ok, its when they grow out of proportion it becomes a problem. So characters and items might not need a total work over.

In chess, black has lower chances of winning, but very few would consider the game imbalanced.


Another thing people need to keep in mind is what you are risking if you lose.

Sure your knights should beat that block 70% of the time, but when happenes the other 30% of the time? What happens if you lose and break? What other units are put at risk?

Numbers are nice, but overall tactics are what win the day.

Exactly what I think too. This is why optimizing armies wont work if the game is balanced. There are just endless strategies and tactics .

Brothersir
23-10-2009, 22:08
...nobody takes archers with the intention of getting them into combat - so they should be priced at how good they are at shooting.

Most times true, but Orc Arrer Boyz are widely viewed as a combat unit that also happens to shoot. So I think it can't be ignored.

puppetmaster24
23-10-2009, 22:18
well being crap at quick maths i just make an educated guess. then i ignore it and charge my wolfs into the deamon prince :evilgrin:

Emud
23-10-2009, 22:24
Most times true, but Orc Arrer Boyz are widely viewed as a combat unit that also happens to shoot. So I think it can't be ignored.

What I meant was that combat, shoting and magic are separate categorys, so they should be priced independantley and their price added together.

For sub categorys, what is most efficient is what should determine price. It does not matter if the unit is better at charging than holding a charge for example. It is stil its combat value that is estimated.

catbarf
23-10-2009, 23:31
Of course statlines matter. I could charge your goblin unit with my swordmaster unit and I could roll all 1's and 2's to hit and the goblins get lucky and kill one guy and I flee. This outcome would be the same weather or not I have a detailed calculation list in front of me or not.

I know what the outcome "Should" be with or without calculations but ultimataly it comes down to dice rolling.

So is it random: absolutly
Do stat lines matter : absolutly

We're not doing calculations to figure out whether Swordmasters are likely to beat Goblins. We do calculations for all those situations where your common sense answer can be no more than a giant 'Maybe'. Dice are random, this is obvious. But dice trends can be predicted, and we can figure out not what will happen, but what should happen, and the degree of security in that statement.

The point is: probability works. You may not find it interesting, but it provides a whole new way of looking at the game and it's something that I and others find fun.

Brothersir
24-10-2009, 06:36
What I meant was that combat, shoting and magic are separate categorys, so they should be priced independantley and their price added together.

For sub categorys, what is most efficient is what should determine price. It does not matter if the unit is better at charging than holding a charge for example. It is stil its combat value that is estimated.

Yeah, we're on the same page. I was replying to another poster that was saying that an archer unit should be weighed by the fact that they will not be intended to get in combat, whereas I'm saying archer units not only could end up in combat and this should be reflected in the calculations, but that some "archer" units are not primarily used for their shooting.

What I'm saying actually supports your methods.

blissneso
24-10-2009, 16:14
you are to maths as pleasure is to knives