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Estarriol
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Posted - 2004.07.30 20:07:00 -
[61]
 Originally by: TornSoul
1 : You dont get Gaussian distribution when using 2 dices (you get triangular distribution)
Try throwing the dice a whole bunch of times, say at least 100, and plot the sum.
Sum the totals with one and two dice, respectively, if you don't believe what the outcome will look like.
Estarriol
P. S.: And get that cough checked out.
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Estarriol
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Posted - 2004.07.30 20:07:00 -
[62]
Originally by: TornSoul
1 : You dont get Gaussian distribution when using 2 dices (you get triangular distribution)
Try throwing the dice a whole bunch of times, say at least 100, and plot the sum.
Sum the totals with one and two dice, respectively, if you don't believe what the outcome will look like.
Estarriol
P. S.: And get that cough checked out.
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TornSoul
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Posted - 2004.07.31 01:18:00 -
[63]
OK I think I finally know what you are on about
This : Uniform Sum Distribution - Yes?
We are talking about two different measurements all together.
You wording here
Originally by: Estarriol
No, the total damage over a given time is expected to be Mean * #.
However, the actual total damage will be distributed in a Gaussian around this expected value.
It's like throwing a pair of dice.... you expect to get a 7, but obviously you have a fairly good chance of getting something besides 7... otherwise no one would play those games.
made me think we were talking about the same thing (distribution of the value of single values/events)
But I guess you just used a bad analogy?
Uniform Sum Distribution and distribution of single values/shots are two different measurements.
I dont quite understand what your point is.... (assuming I guessed correctly what it is you mean - else I'm totally lost...)
Care to clarify?
 BIG Lottery
[u |
TornSoul
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Posted - 2004.07.31 01:18:00 -
[64]
OK I think I finally know what you are on about
This : Uniform Sum Distribution - Yes?
We are talking about two different measurements all together.
You wording here
Originally by: Estarriol
No, the total damage over a given time is expected to be Mean * #.
However, the actual total damage will be distributed in a Gaussian around this expected value.
It's like throwing a pair of dice.... you expect to get a 7, but obviously you have a fairly good chance of getting something besides 7... otherwise no one would play those games.
made me think we were talking about the same thing (distribution of the value of single values/events)
But I guess you just used a bad analogy?
Uniform Sum Distribution and distribution of single values/shots are two different measurements.
I dont quite understand what your point is.... (assuming I guessed correctly what it is you mean - else I'm totally lost...)
Care to clarify?
BIG Lottery
[u |
Estarriol
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Posted - 2004.07.31 05:34:00 -
[65]
Quote:
made me think we were talking about the same thing (distribution of the value of single values/events)
But I guess you just used a bad analogy
Care to clarify?
*Sigh.*
Ok let me see if I get this straight.
Your assertion is that individual hits seem to have a roughly uniform distribution of damage. However, you believe that it should be Gaussian.
I don't know where you get the idea that the damage from a single hit should be Gaussian.
The Gaussian (normal) distribution arises naturally from the sum of many identical events. When you sum the total from many individual hits, whether they be normal or uniform or anything else, you will find that the result begins to approaches a continuous normal distribution. Perhaps the ubiquity of this distribution in natural processes is what led you to believe that the individual event should be normally distributed as well.
Your initial assertion that the total damage is mean dmg. * no. of hits was incorrect, since that is only the expectation value. The actual damage from trials will not be a point mass, but will be distributed somewhere between 0 and maximum possible damage.
Rolling one die will be a (discrete) uniform distribution, not a point mass at the mean (3.5).
The sum of two dice will give a stairstepped distribution, looking somewhat like a triangle but not exactly. It will peak at 7 but has probabilities of other sums as well.
If you continue increasing the number of dice, you will see that the sum of the individual events (die rolls, uniform distribution) will look more and more like a normal distribution.
Perhaps you felt that this analogy was a bad one, but I believe it exactly describes the process in the game, since eve has discrete outcomes (levels of damage) and discrete events (hits) summed over time.
Please forgive the fact that the analogy was not more clearly explained at the outset. My own education is in mathematics, so I had simply assumed that you knew these facts about basic probability and would immediately understand what I was getting at.
Estarriol
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Estarriol
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Posted - 2004.07.31 05:34:00 -
[66]
Quote:
made me think we were talking about the same thing (distribution of the value of single values/events)
But I guess you just used a bad analogy
Care to clarify?
*Sigh.*
Ok let me see if I get this straight.
Your assertion is that individual hits seem to have a roughly uniform distribution of damage. However, you believe that it should be Gaussian.
I don't know where you get the idea that the damage from a single hit should be Gaussian.
The Gaussian (normal) distribution arises naturally from the sum of many identical events. When you sum the total from many individual hits, whether they be normal or uniform or anything else, you will find that the result begins to approaches a continuous normal distribution. Perhaps the ubiquity of this distribution in natural processes is what led you to believe that the individual event should be normally distributed as well.
Your initial assertion that the total damage is mean dmg. * no. of hits was incorrect, since that is only the expectation value. The actual damage from trials will not be a point mass, but will be distributed somewhere between 0 and maximum possible damage.
Rolling one die will be a (discrete) uniform distribution, not a point mass at the mean (3.5).
The sum of two dice will give a stairstepped distribution, looking somewhat like a triangle but not exactly. It will peak at 7 but has probabilities of other sums as well.
If you continue increasing the number of dice, you will see that the sum of the individual events (die rolls, uniform distribution) will look more and more like a normal distribution.
Perhaps you felt that this analogy was a bad one, but I believe it exactly describes the process in the game, since eve has discrete outcomes (levels of damage) and discrete events (hits) summed over time.
Please forgive the fact that the analogy was not more clearly explained at the outset. My own education is in mathematics, so I had simply assumed that you knew these facts about basic probability and would immediately understand what I was getting at.
Estarriol
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Venril
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Posted - 2004.07.31 06:48:00 -
[67]
Originally by: Iece Quaan
Kinda sucks when it takes an obsessed statistician to get you guys to listen to us.
/me agree's
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Venril
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Posted - 2004.07.31 06:48:00 -
[68]
Originally by: Iece Quaan
Kinda sucks when it takes an obsessed statistician to get you guys to listen to us.
/me agree's
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ProphetGuru
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Posted - 2004.07.31 07:41:00 -
[69]
I'm so confused.
Evolution..... Just when you thought you were winning.
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ProphetGuru
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Posted - 2004.07.31 07:41:00 -
[70]
I'm so confused.
Evolution..... Just when you thought you were winning.
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Joshua Calvert
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Posted - 2004.07.31 08:52:00 -
[71]
I'm with you ProphetGuru.
This looks like a bad case of trying to add apples and pears and coming up with oranges.
I think.
LEEEEERRRRRRRRRRROOOOOOOOOYYYYYYYYYYYYYYY! |
Joshua Calvert
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Posted - 2004.07.31 08:52:00 -
[72]
I'm with you ProphetGuru.
This looks like a bad case of trying to add apples and pears and coming up with oranges.
I think.
LEEEEERRRRRRRRRRROOOOOOOOOYYYYYYYYYYYYYYY! |
TornSoul
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Posted - 2004.07.31 13:51:00 -
[73]
Edited by: TornSoul on 31/07/2004 15:13:29
(Changed my mind - Posting here instead)
Instead of picking at each statement you made (some I agree with and others not) let me explain where I'm comming from, and why I find it reasonable that the damage of individual shots (and *not* their sum - I still have no idea why you bring that into it all...) should be Gaussian distributed
You earlier mentioned that
Quote:
There is no reason to believe that the amount of damage that a shell inflicts on a target, once it has been determined to hit at all, follows any such distribution.
On the surface I agree with that, but the next question then is *what does* determine the amount of damage done?
CCP has introduced 'wrecking' shots - Shots that give higher than 'normal' (however we define that) damage.
At the same time theyve made sure that this is a 'rare' occurance.
By doing that they are saying that "The probability of 'high' damage is less than the probability of 'low' damage"
And this furthermore reflects how we 'normally' expect damage to happen in games : The really good (lots of damage) hits are rarer (less likely to happen) than hits with lower damage - and the 'medium' hits, have a 'medium' (somewhere in between) chance of happening.
The common analogy to this is the dart board (with 10 in the center, and 1 on the outer ring).
It's harder to hit the 10, than the 5 and so forth.
I'm sure you will agree that the probability of getting X points (in a single shot) has a Gaussian distribution?
So to answer
Quote:
I don't know where you get the idea that the damage from a single hit should be Gaussian
My reasoning for using Gaussion distribution, rather then the now used uniform distribution, is a simple extension of the above "higher damage = less chance of happening".
On a more 'subjective' level, I also believe that using this 'damage model' (Gaussian) for guns furthermore gives players a better 'feel' for what to 'expect' from the gun - Which gameplay wise is a bonus IMO.
As it is now, the damage is 'all over the place' for any single shot, because of the used uniform distribution - Each (possible) 'amount of damage' beeing equally likely to happen (at the same range)
--------------
In your first post you state that
Quote:
If the damage for each individual shot follows a uniform distribution, then you must know that the total damage over any given time will still come to resemble a Gaussian (bell) curve.
I now know what you meant by that (and you are correct)
And my question remains - What has that got to do with the above?
Regardless of what distribution (uniform or Gausssan) is used for the damage of individual shots the distribution of 'total damage' will be Gaussian (a point you fail to mention btw)
So why bring this fact into it at all?
It cant be used as an argument for or against using uniform or Gaussion distribution for the individual shots.
I think that more than anything confused me at first - ie. that the fact you presented cant be used as an argument for either case....
--------------
Quote:
Please forgive the fact that the analogy was not more clearly explained at the outset. My own education is in mathematics, so I had simply assumed that you knew these facts about basic probability and would immediately understand what I was getting at.
Well good for you... and we needed to know that becuase?
Theres no need to be patronizing, by implying that your failure to make yourself understood by me, is in any way tied to my knowledge of probabilities (basic or not).
Maybe you just didnt state your case very well?
Which I in no way would connect to your ability to understand basic probability principles....
BIG Lottery
[u |
TornSoul
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Posted - 2004.07.31 13:51:00 -
[74]
Edited by: TornSoul on 31/07/2004 15:13:29
(Changed my mind - Posting here instead)
Instead of picking at each statement you made (some I agree with and others not) let me explain where I'm comming from, and why I find it reasonable that the damage of individual shots (and *not* their sum - I still have no idea why you bring that into it all...) should be Gaussian distributed
You earlier mentioned that
Quote:
There is no reason to believe that the amount of damage that a shell inflicts on a target, once it has been determined to hit at all, follows any such distribution.
On the surface I agree with that, but the next question then is *what does* determine the amount of damage done?
CCP has introduced 'wrecking' shots - Shots that give higher than 'normal' (however we define that) damage.
At the same time theyve made sure that this is a 'rare' occurance.
By doing that they are saying that "The probability of 'high' damage is less than the probability of 'low' damage"
And this furthermore reflects how we 'normally' expect damage to happen in games : The really good (lots of damage) hits are rarer (less likely to happen) than hits with lower damage - and the 'medium' hits, have a 'medium' (somewhere in between) chance of happening.
The common analogy to this is the dart board (with 10 in the center, and 1 on the outer ring).
It's harder to hit the 10, than the 5 and so forth.
I'm sure you will agree that the probability of getting X points (in a single shot) has a Gaussian distribution?
So to answer
Quote:
I don't know where you get the idea that the damage from a single hit should be Gaussian
My reasoning for using Gaussion distribution, rather then the now used uniform distribution, is a simple extension of the above "higher damage = less chance of happening".
On a more 'subjective' level, I also believe that using this 'damage model' (Gaussian) for guns furthermore gives players a better 'feel' for what to 'expect' from the gun - Which gameplay wise is a bonus IMO.
As it is now, the damage is 'all over the place' for any single shot, because of the used uniform distribution - Each (possible) 'amount of damage' beeing equally likely to happen (at the same range)
--------------
In your first post you state that
Quote:
If the damage for each individual shot follows a uniform distribution, then you must know that the total damage over any given time will still come to resemble a Gaussian (bell) curve.
I now know what you meant by that (and you are correct)
And my question remains - What has that got to do with the above?
Regardless of what distribution (uniform or Gausssan) is used for the damage of individual shots the distribution of 'total damage' will be Gaussian (a point you fail to mention btw)
So why bring this fact into it at all?
It cant be used as an argument for or against using uniform or Gaussion distribution for the individual shots.
I think that more than anything confused me at first - ie. that the fact you presented cant be used as an argument for either case....
--------------
Quote:
Please forgive the fact that the analogy was not more clearly explained at the outset. My own education is in mathematics, so I had simply assumed that you knew these facts about basic probability and would immediately understand what I was getting at.
Well good for you... and we needed to know that becuase?
Theres no need to be patronizing, by implying that your failure to make yourself understood by me, is in any way tied to my knowledge of probabilities (basic or not).
Maybe you just didnt state your case very well?
Which I in no way would connect to your ability to understand basic probability principles....
BIG Lottery
[u |
Estarriol
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Posted - 2004.07.31 16:03:00 -
[75]
Edited by: Estarriol on 31/07/2004 16:12:01
TornSoul,
I don't really know what to say in the forum at this point that will avoid sounding 'patronizing' but still get the point across.
I'd be more than happy to clear up any misunderstandings if you'd like to continue the discussion on irc. Just join #eve-evo and ask for me.
Estarriol
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Estarriol
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Posted - 2004.07.31 16:03:00 -
[76]
Edited by: Estarriol on 31/07/2004 16:12:01
TornSoul,
I don't really know what to say in the forum at this point that will avoid sounding 'patronizing' but still get the point across.
I'd be more than happy to clear up any misunderstandings if you'd like to continue the discussion on irc. Just join #eve-evo and ask for me.
Estarriol
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TornSoul
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Posted - 2004.07.31 16:34:00 -
[77]
I might just do that - As I've gotten curious as to why you've brought up the issue of 'Uniform Sum Distribution'.
I still dont see the relevance - But wouldnt mind beeing convinced otherwise.
BIG Lottery
[u |
TornSoul
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Posted - 2004.07.31 16:34:00 -
[78]
I might just do that - As I've gotten curious as to why you've brought up the issue of 'Uniform Sum Distribution'.
I still dont see the relevance - But wouldnt mind beeing convinced otherwise.
BIG Lottery
[u |
Azure Skyclad
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Posted - 2004.07.31 22:00:00 -
[79]
What i *think* Tornsoul is saying is:
If you go to punch an idiot in the face, you have just as much chance of hitting him in the foot as you do hitting him on the end of his schnozzer...or miss (as it currently stands)
This is silly (unless you trip over)
What it should be is:
If i go to punch an idiot in the face, then hitting him in the shoulder or in his teeth is entirely possible but hitting him in his foot is just bloody stupid.......or miss.
I think
I *could* be wrong
La Maison de tous Les Plaisirs
Star Fraction
http://www.voodoorockers.co.uk/ |
Azure Skyclad
|
Posted - 2004.07.31 22:00:00 -
[80]
What i *think* Tornsoul is saying is:
If you go to punch an idiot in the face, you have just as much chance of hitting him in the foot as you do hitting him on the end of his schnozzer...or miss (as it currently stands)
This is silly (unless you trip over)
What it should be is:
If i go to punch an idiot in the face, then hitting him in the shoulder or in his teeth is entirely possible but hitting him in his foot is just bloody stupid.......or miss.
I think
I *could* be wrong
La Maison de tous Les Plaisirs
Star Fraction
http://www.voodoorockers.co.uk/ |
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TornSoul
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Posted - 2004.08.01 01:30:00 -
[81]
Spot on 
BIG Lottery
[u |
TornSoul
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Posted - 2004.08.01 01:30:00 -
[82]
Spot on
BIG Lottery
[u |
DarK
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Posted - 2004.08.01 03:49:00 -
[83]
And the mind boggles.
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DarK
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Posted - 2004.08.01 03:49:00 -
[84]
And the mind boggles.
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JP Beauregard
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Posted - 2004.08.01 04:51:00 -
[85]
Edited by: JP Beauregard on 01/08/2004 14:26:18
Originally by: Azure Skyclad
What i *think* Tornsoul is saying is:
If you go to punch an idiot in the face, you have just as much chance of hitting him in the foot as you do hitting him on the end of his schnozzer...or miss (as it currently stands)
This is silly (unless you trip over)
What it should be is:
If i go to punch an idiot in the face, then hitting him in the shoulder or in his teeth is entirely possible but hitting him in his foot is just bloody stupid.......or miss.
I think
I *could* be wrong
Nope, I think it's more along the lines of:
If you hit an idiot in the mouth, you are now equally likely to take out any number of teeth, equally likely to break his nose in any number of places or equally likely to cause blindness in either eye or both. You may also give him a consussion or miss.
And that is a bad thing. Because we want to make sure we take out his front teeth more often than his molars, break the nose ONCE in the middle where it really hurts or give him the proverbial ONE black eye without any lasting blindness. All other things might and should occur, including the concussion and the miss but we need to be able to count on that.
Man, I hate analogies... Can we keep this abstract? Kinda protects the thread from wanton argument 
JP Beauregard
=== The Pilkington Guides to EVE === |
JP Beauregard
|
Posted - 2004.08.01 04:51:00 -
[86]
Edited by: JP Beauregard on 01/08/2004 14:26:18
Originally by: Azure Skyclad
What i *think* Tornsoul is saying is:
If you go to punch an idiot in the face, you have just as much chance of hitting him in the foot as you do hitting him on the end of his schnozzer...or miss (as it currently stands)
This is silly (unless you trip over)
What it should be is:
If i go to punch an idiot in the face, then hitting him in the shoulder or in his teeth is entirely possible but hitting him in his foot is just bloody stupid.......or miss.
I think
I *could* be wrong
Nope, I think it's more along the lines of:
If you hit an idiot in the mouth, you are now equally likely to take out any number of teeth, equally likely to break his nose in any number of places or equally likely to cause blindness in either eye or both. You may also give him a consussion or miss.
And that is a bad thing. Because we want to make sure we take out his front teeth more often than his molars, break the nose ONCE in the middle where it really hurts or give him the proverbial ONE black eye without any lasting blindness. All other things might and should occur, including the concussion and the miss but we need to be able to count on that.
Man, I hate analogies... Can we keep this abstract? Kinda protects the thread from wanton argument
JP Beauregard
=== The Pilkington Guides to EVE === |
Meridius
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Posted - 2004.08.01 09:45:00 -
[87]
I'm with Josh
Good work though, i think
________________________________________________________
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Meridius
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Posted - 2004.08.01 09:45:00 -
[88]
I'm with Josh
Good work though, i think
________________________________________________________
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Azure Skyclad
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Posted - 2004.08.01 11:16:00 -
[89]
Mr Beauregard.
I was going to say something. However, in the spirit of this:
Originally by: JP Beauregard
Man, I hate analogies... Can we keep this abstract? Kinda protects the thread from wanton argument
I'll keep my gob shut
La Maison de tous Les Plaisirs
Star Fraction
http://www.voodoorockers.co.uk/ |
Azure Skyclad
|
Posted - 2004.08.01 11:16:00 -
[90]
Mr Beauregard.
I was going to say something. However, in the spirit of this:
Originally by: JP Beauregard
Man, I hate analogies... Can we keep this abstract? Kinda protects the thread from wanton argument
I'll keep my gob shut
La Maison de tous Les Plaisirs
Star Fraction
http://www.voodoorockers.co.uk/ |
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