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TornSoul
   |
Posted - 2004.07.29 13:58:00 -
[1]
Now for the next 'bad thing'..... (not quite as bad as the first - but still)
How damage - or to be excact, the average (or Mean) value of damage, decreases as the range to the target increases (above optimal range)
Remember that as long as the range to the target is below optimal, the average damage remains the same (namely 2 * MinDam)
Here is how it looks, with the mean values plotted.
In the 2nd graph the wrecking shots are removed from the datasets when calculating the Means - As can be seen they 'distort' the graph quite a lot, becuase they are 'artificially' raised to a very high value.
The way damage degrades with increased distance seems to fit the picture that was posted a while back by the Dev team.
A few notes though:
At optimal+falloff (56km) - The Mean should be half that at optimal.
The expected Mean is thus MinDam (according to a devblog) = 125.664.
The obvserved Means at 54 and 58 km are (94.911, 75.497).
Both are way lower than the expected Mean....
Now - Its all fine and dandy that the observed data nearly matches (although it seems to be quite abit lower) what we've been told is should - The problem is just it's actually wrong doing it like that.....
Damage degrade should look like this
The size (area) of your target decreases 4 times, each time you double your distance to the target - And thus it gets 4 times harder to hit it, as you double your distance (1/x^2).
At least... Thats how normal statistics work.... EVE has chosen a different approach for some reason...
One problem with the normal damage degrading curve is ofc that it never reaches zero - ever (but it gets close).
Due to the gameplay of EVE its more desirable to have a cleary defined boundary where you no longer can inflict damage.
But wait - Targetting range gives us this automatically!!!
Thats the natural 'cut off' point for the damage graph, problem solved (damage doesnt 'bottom out' at zero dam though)
Personal skills and type of ship/equipment will vary excactly where the 'cutoff' will be ofc - Making things even more 'individual'.
As Mean is decreased (lower average value) as range increases, SD (standard deviation) should be increased.
SD could be kept the same, but by increasing SD we get more and more 'random shots', simulation that our shots land all over the place as we get further and further away - Which would be what we would expect.
This is illustrated here
Instead of just decreasing Mean (by shifting the graph to the left) SD has been increased (making the graph 'wider') as well, insuring the shots are more 'spread out'.
That would be the prober way to do it IMO.
BIG Lottery
[u |
TornSoul
|
Posted - 2004.07.29 13:58:00 -
[2]
Sofar so good.
Now for the bad news...
Assume MinDam = 100 (for ease of math)
Then the range the damage can fall within is : 100 to 300 {+ a 600-wrecking shot)
The bad news is - It's equally likely to hit for 100 as it is to hit for 300 - or 200 or 250 or....
In other words : The game uses 'uniform distribution' for damage....
Thats the equivalent of just rolling a dice... Each value is equally likely to 'happen'.
The collected data looks like this (250 shots fired at each range)
It should be obvious that the data indicates a uniform distribution of damage.
Now why is this so bad?
Because it's unrealistic and 'wrong'!
Imagine yourself throwing darts at a bullseye target (consisting of concentric rings, numbered from 10 in the middle downto 1 for the outer ring - you get the picture..)
It should be obvious that the likelyhood of hitting a 10 is less than hitting a 6 which again is less than hitting a 1.
EVE's current model says the chance of hitting a 10 is the same as getting a 6 or a 1 or... Which is just *wrong* :/
The value of damage inflicted should ofc be 'normal distributed' - or 'bell curved' (due to the shape of the graph).
The hight of the curve (y-axis) indicates the chance of the damage type happening.
*Thats* how damage should be distributed.
The incredible thing is : It's an extremly easy thing to get right.
To 'convert' the normal (uniform distributed) computer randomize to a 'normal distributed' one, there exists an extremly simple algorithm, called the Polar algorithm (theres others).
Simply add this new normal distributed random function, and use it where damage is calculated, and thats that.
In general, using normal distribution makes it possible to 'tailor' the random values in a surpricing number of ways, it's a very powerfull 'tool'.
That was one bad thing : The uniform distribution of random values.
BIG Lottery
[u |
TornSoul
|
Posted - 2004.07.29 13:58:00 -
[3]
Sofar so good.
Now for the bad news...
Assume MinDam = 100 (for ease of math)
Then the range the damage can fall within is : 100 to 300 {+ a 600-wrecking shot)
The bad news is - It's equally likely to hit for 100 as it is to hit for 300 - or 200 or 250 or....
In other words : The game uses 'uniform distribution' for damage....
Thats the equivalent of just rolling a dice... Each value is equally likely to 'happen'.
The collected data looks like this (250 shots fired at each range)
It should be obvious that the data indicates a uniform distribution of damage.
Now why is this so bad?
Because it's unrealistic and 'wrong'!
Imagine yourself throwing darts at a bullseye target (consisting of concentric rings, numbered from 10 in the middle downto 1 for the outer ring - you get the picture..)
It should be obvious that the likelyhood of hitting a 10 is less than hitting a 6 which again is less than hitting a 1.
EVE's current model says the chance of hitting a 10 is the same as getting a 6 or a 1 or... Which is just *wrong* :/
The value of damage inflicted should ofc be 'normal distributed' - or 'bell curved' (due to the shape of the graph).
The hight of the curve (y-axis) indicates the chance of the damage type happening.
*Thats* how damage should be distributed.
The incredible thing is : It's an extremly easy thing to get right.
To 'convert' the normal (uniform distributed) computer randomize to a 'normal distributed' one, there exists an extremly simple algorithm, called the Polar algorithm (theres others).
Simply add this new normal distributed random function, and use it where damage is calculated, and thats that.
In general, using normal distribution makes it possible to 'tailor' the random values in a surpricing number of ways, it's a very powerfull 'tool'.
That was one bad thing : The uniform distribution of random values.
BIG Lottery
[u |
TornSoul
|
Posted - 2004.07.29 13:58:00 -
[4]
Test system : Entropy 1618 - 2004/07/22
Test equip : Apoc with Tach laser with L gamma crystals
Tach : 33km optimal, 23 falloff, 5.172 dam modifier
Gamma : 20 EM + 24 thermal = 44 total.
Both target(a SCC) and shooter was at rest (ie. no 'polution' from transversal speed)
Test data set : 250 shots at 9 different ranges (for a total of 2250 datapoints)
Test ranges :
4.5 km
15 km
30 km
(33km = optimal range)
36 km
45 km
54 km
(56 km = optimal + fallof)
58 km
65 km
75 km
(79 km = optimal + 2*fallof)
All formulas are deducted (reverse engineered) from the statistical data, and are believed to be true for all types of guns/ammo, although only tested with laser type gun.
--------------
There exists the following textual categories of 'hits' :
misses X completely (no damage)
barely misses X (no damage)
glances off X (no damage)
barely scratches X
lightly hits X
hits X
is well aimed at X
places an excellent hit on X
perfectly strikes X (wrecking damage)
A wrecking shot *always* inflict *excactly* the same ammount of damage (regardless of range!) - ie. it's a 'constant' - Very useful for further analysis!
By observing (and playing around with) the different ammo/gun numerical charateristics the following formula 'emerges':
Max damage (wrecking shot) = (sum of ammo damage) * dam modifier * 3 = 44 * 5.712 * 3 = 753.984
Observed damage of wrecking shots (in log) = 754 (which is 753.984 rounded)
Analysing the data it turns out that each textual category 'covers' a specific damage range.
Using MinDam (MinDam = wreck dam/6) as a 'standard meassure of unit' the following ranges exists
MinDam is the minimum damage it's possible to inflict - Anything 'lower' is a miss.
--- Zero damage ---
misses X completely (no damage)
barely misses X (no damage)
glances off X (no damage)
*** Damage intervals ***
MinDam * 1.00
- barely scratches X
MinDam * 1.25
- lightly hits X
MinDam * 1.50
- hits X
MinDam * 2.00
- is well aimed at X
MinDam * 2.50
- places an excellent hit on X
MinDam * 3.00
MinDam * 6 : perfectly strikes X (wrecking damage)
Wrecking damage is not a range as the other categories, but an excact value
All the observed data (shots) conforms to the above ranges.
The Mean of the damage when within optimal range should be : 2 * MinDam = 2 * (44 * 5.712)/2 = 251.328
The observed Mean values are (248.991, 253.456, 244.915) - Very close to the theoretical value (this co-oporating that the theory is correct).
Note that wrecking shots are discarded when calculating Means - as they are 'artificially' higher than they 'should be' and thus distorts the Mean.
Notes:
Note how the textual categories are not 'equal in width'.
'barely' and 'lightly' are (0.25 * MinDam) in width, while the rest are (0.50 * MinDam) in width.
This is a purely arbitrary choice, as the textual ranges could be set to anything one would like, as they have zero influence themself.
The actual damage, the number, is random (within a range) and the textual categories are simply 'mapped' onto that after the number is generated.
Wrecking damage is often erronously quoted as beeing a "tripple damage hit" - ie. 3 times as high as anything else possible.
This is actually wrong, it's 'only' a "double damage hit", ie. 2 times as high as anything else possible.
The "tripple damage hit"-'myth', probably stems from how the numerical value of a wrecking shot is calculated via the above formula : (sum of ammo damage) * dam modifier * 3 (note the '3' in the formula), or the simple fact it's 3 times higher than the average damage (Mean)
In the data the chance of a wrecking shot is 1.33% (30 out of 2250)
This seems a bit of an odd value...
A base value of 1% seems like an obvious choice, so maybe I have a skill raising it to 1.20% (27 hits) or 1.25% (28 hits))
The difference upto 1.33% could be explained by statistical variance.
I dont think statistical variance can explain the entire difference between base 1% (22.5 hits) value and the observed 1.33% (its possibly ofc - just very very unlikely)
In any case - This is a 'poor mans' way of 'simulating' those really really good hits.
Using normal distributed damage we'd get this automatically, without having to introduce a special value thats 'suddenly' alot better.
BIG Lottery
[u |
TornSoul
|
Posted - 2004.07.29 13:58:00 -
[5]
Now for the next 'bad thing'..... (not quite as bad as the first - but still)
How damage - or to be excact, the average (or Mean) value of damage, decreases as the range to the target increases (above optimal range)
Remember that as long as the range to the target is below optimal, the average damage remains the same (namely 2 * MinDam)
Here is how it looks, with the mean values plotted.
In the 2nd graph the wrecking shots are removed from the datasets when calculating the Means - As can be seen they 'distort' the graph quite a lot, becuase they are 'artificially' raised to a very high value.
The way damage degrades with increased distance seems to fit the picture that was posted a while back by the Dev team.
A few notes though:
At optimal+falloff (56km) - The Mean should be half that at optimal.
The expected Mean is thus MinDam (according to a devblog) = 125.664.
The obvserved Means at 54 and 58 km are (94.911, 75.497).
Both are way lower than the expected Mean....
Now - Its all fine and dandy that the observed data nearly matches (although it seems to be quite abit lower) what we've been told is should - The problem is just it's actually wrong doing it like that.....
Damage degrade should look like this
The size (area) of your target decreases 4 times, each time you double your distance to the target - And thus it gets 4 times harder to hit it, as you double your distance (1/x^2).
At least... Thats how normal statistics work.... EVE has chosen a different approach for some reason...
One problem with the normal damage degrading curve is ofc that it never reaches zero - ever (but it gets close).
Due to the gameplay of EVE its more desirable to have a cleary defined boundary where you no longer can inflict damage.
But wait - Targetting range gives us this automatically!!!
Thats the natural 'cut off' point for the damage graph, problem solved (damage doesnt 'bottom out' at zero dam though)
Personal skills and type of ship/equipment will vary excactly where the 'cutoff' will be ofc - Making things even more 'individual'.
As Mean is decreased (lower average value) as range increases, SD (standard deviation) should be increased.
SD could be kept the same, but by increasing SD we get more and more 'random shots', simulation that our shots land all over the place as we get further and further away - Which would be what we would expect.
This is illustrated here
Instead of just decreasing Mean (by shifting the graph to the left) SD has been increased (making the graph 'wider') as well, insuring the shots are more 'spread out'.
That would be the prober way to do it IMO.
BIG Lottery
[u |
TornSoul
|
Posted - 2004.07.29 13:58:00 -
[6]
Test system : Entropy 1618 - 2004/07/22
Test equip : Apoc with Tach laser with L gamma crystals
Tach : 33km optimal, 23 falloff, 5.172 dam modifier
Gamma : 20 EM + 24 thermal = 44 total.
Both target(a SCC) and shooter was at rest (ie. no 'polution' from transversal speed)
Test data set : 250 shots at 9 different ranges (for a total of 2250 datapoints)
Test ranges :
4.5 km
15 km
30 km
(33km = optimal range)
36 km
45 km
54 km
(56 km = optimal + fallof)
58 km
65 km
75 km
(79 km = optimal + 2*fallof)
All formulas are deducted (reverse engineered) from the statistical data, and are believed to be true for all types of guns/ammo, although only tested with laser type gun.
--------------
There exists the following textual categories of 'hits' :
misses X completely (no damage)
barely misses X (no damage)
glances off X (no damage)
barely scratches X
lightly hits X
hits X
is well aimed at X
places an excellent hit on X
perfectly strikes X (wrecking damage)
A wrecking shot *always* inflict *excactly* the same ammount of damage (regardless of range!) - ie. it's a 'constant' - Very useful for further analysis!
By observing (and playing around with) the different ammo/gun numerical charateristics the following formula 'emerges':
Max damage (wrecking shot) = (sum of ammo damage) * dam modifier * 3 = 44 * 5.712 * 3 = 753.984
Observed damage of wrecking shots (in log) = 754 (which is 753.984 rounded)
Analysing the data it turns out that each textual category 'covers' a specific damage range.
Using MinDam (MinDam = wreck dam/6) as a 'standard meassure of unit' the following ranges exists
MinDam is the minimum damage it's possible to inflict - Anything 'lower' is a miss.
--- Zero damage ---
misses X completely (no damage)
barely misses X (no damage)
glances off X (no damage)
*** Damage intervals ***
MinDam * 1.00
- barely scratches X
MinDam * 1.25
- lightly hits X
MinDam * 1.50
- hits X
MinDam * 2.00
- is well aimed at X
MinDam * 2.50
- places an excellent hit on X
MinDam * 3.00
MinDam * 6 : perfectly strikes X (wrecking damage)
Wrecking damage is not a range as the other categories, but an excact value
All the observed data (shots) conforms to the above ranges.
The Mean of the damage when within optimal range should be : 2 * MinDam = 2 * (44 * 5.712)/2 = 251.328
The observed Mean values are (248.991, 253.456, 244.915) - Very close to the theoretical value (this co-oporating that the theory is correct).
Note that wrecking shots are discarded when calculating Means - as they are 'artificially' higher than they 'should be' and thus distorts the Mean.
Notes:
Note how the textual categories are not 'equal in width'.
'barely' and 'lightly' are (0.25 * MinDam) in width, while the rest are (0.50 * MinDam) in width.
This is a purely arbitrary choice, as the textual ranges could be set to anything one would like, as they have zero influence themself.
The actual damage, the number, is random (within a range) and the textual categories are simply 'mapped' onto that after the number is generated.
Wrecking damage is often erronously quoted as beeing a "tripple damage hit" - ie. 3 times as high as anything else possible.
This is actually wrong, it's 'only' a "double damage hit", ie. 2 times as high as anything else possible.
The "tripple damage hit"-'myth', probably stems from how the numerical value of a wrecking shot is calculated via the above formula : (sum of ammo damage) * dam modifier * 3 (note the '3' in the formula), or the simple fact it's 3 times higher than the average damage (Mean)
In the data the chance of a wrecking shot is 1.33% (30 out of 2250)
This seems a bit of an odd value...
A base value of 1% seems like an obvious choice, so maybe I have a skill raising it to 1.20% (27 hits) or 1.25% (28 hits))
The difference upto 1.33% could be explained by statistical variance.
I dont think statistical variance can explain the entire difference between base 1% (22.5 hits) value and the observed 1.33% (its possibly ofc - just very very unlikely)
In any case - This is a 'poor mans' way of 'simulating' those really really good hits.
Using normal distributed damage we'd get this automatically, without having to introduce a special value thats 'suddenly' alot better.
BIG Lottery
[u |
Oveur
|
Posted - 2004.07.29 14:27:00 -
[7]
Damn that's a good report. Forwarding it to ppl inhouse.
_____________________________
I say hey sky, s'other say I won say, I pray to J I get the same ol' same ol. |
Oveur
|
Posted - 2004.07.29 14:27:00 -
[8]
Damn that's a good report. Forwarding it to ppl inhouse.
_____________________________
I say hey sky, s'other say I won say, I pray to J I get the same ol' same ol. |
CaptMorgan
|
Posted - 2004.07.29 14:30:00 -
[9]
Edited by: CaptMorgan on 29/07/2004 14:33:51
Friggin sweet man...good job
EDIT: of coarse my personal best shot, recorded in my sig, does not go with this report too well.
Rum.com
Hadean Drive Yards
Your Civilian Auto Cannon perfectly strikes Sansha's Servant Ship, wrecking for 987,547,415.3 damage. |
CaptMorgan
|
Posted - 2004.07.29 14:30:00 -
[10]
Edited by: CaptMorgan on 29/07/2004 14:33:51
Friggin sweet man...good job
EDIT: of coarse my personal best shot, recorded in my sig, does not go with this report too well.
Rum.com
Hadean Drive Yards
Your Civilian Auto Cannon perfectly strikes Sansha's Servant Ship, wrecking for 987,547,415.3 damage. |
Joshua Calvert
|
Posted - 2004.07.29 14:36:00 -
[11]
I wish I was smart.
LEEEEERRRRRRRRRRROOOOOOOOOYYYYYYYYYYYYYYY! |
Joshua Calvert
|
Posted - 2004.07.29 14:36:00 -
[12]
I wish I was smart.
LEEEEERRRRRRRRRRROOOOOOOOOYYYYYYYYYYYYYYY! |
Hellmar
|
Posted - 2004.07.29 14:39:00 -
[13]
|
Hellmar
|
Posted - 2004.07.29 14:39:00 -
[14]
|
jukriamrr
|
Posted - 2004.07.29 14:56:00 -
[15]
Good lord TornSoul ....
|
jukriamrr
|
Posted - 2004.07.29 14:56:00 -
[16]
Good lord TornSoul ....
|
Leitari
|
Posted - 2004.07.29 14:56:00 -
[17]
scrolling down that post took alooong time.... o.0 nice work.
Here, Only the silent survive.
|
Leitari
|
Posted - 2004.07.29 14:56:00 -
[18]
scrolling down that post took alooong time.... o.0 nice work.
Here, Only the silent survive.
|
Grim Vandal
|
Posted - 2004.07.29 14:57:00 -
[19]
 Originally by: Joshua Calvert
I wish I was smart.
ROFL you are most of the times!! 
and I love these graphs, really gj. At least I have something to think about now while im at work 
if this post is useless, feel free to delete it 
Greetings Grim |
Grim Vandal
|
Posted - 2004.07.29 14:57:00 -
[20]
Originally by: Joshua Calvert
I wish I was smart.
ROFL you are most of the times!!
and I love these graphs, really gj. At least I have something to think about now while im at work
if this post is useless, feel free to delete it
Greetings Grim |
Beseb
|
Posted - 2004.07.29 16:45:00 -
[21]
Edited by: Beseb on 29/07/2004 16:47:11
/emote watches Hellmar and Oveur run down the hall to TomBs cubicle and shout "HAHAHA, look at this, one of our players just totally showed you up"!
Good work Torn.
|
Beseb
|
Posted - 2004.07.29 16:45:00 -
[22]
Edited by: Beseb on 29/07/2004 16:47:11
/emote watches Hellmar and Oveur run down the hall to TomBs cubicle and shout "HAHAHA, look at this, one of our players just totally showed you up"!
Good work Torn.
|
Jedan
|
Posted - 2004.07.29 16:52:00 -
[23]
Edited by: Jedan on 29/07/2004 16:54:01
nice testing, I second the thoughts about damage distribution not based on a normal distribution.
however your thoughts on damage over range -->"Damage degrade should look like this" picture is exactly what it has been before the balance changes see Dev Blog. Unfortunately someone "cleaned" up the images. but the red line displayed there were like the degrade was from optimal to max.
Changed with this reason specified:
"Also, the precise behavior of falloff has been tweaked slightly. There is no longer a sharp drop-off as you go beyond your optimal range, but instead a smoother one that reaches 50% accuracy at Optimal + Falloff range."
|
Jedan
|
Posted - 2004.07.29 16:52:00 -
[24]
Edited by: Jedan on 29/07/2004 16:54:01
nice testing, I second the thoughts about damage distribution not based on a normal distribution.
however your thoughts on damage over range -->"Damage degrade should look like this" picture is exactly what it has been before the balance changes see Dev Blog. Unfortunately someone "cleaned" up the images. but the red line displayed there were like the degrade was from optimal to max.
Changed with this reason specified:
"Also, the precise behavior of falloff has been tweaked slightly. There is no longer a sharp drop-off as you go beyond your optimal range, but instead a smoother one that reaches 50% accuracy at Optimal + Falloff range."
|
Nuclear Baggins
|
Posted - 2004.07.29 17:09:00 -
[25]
Hmmm looks great if only i knew what it all means
|
Nuclear Baggins
|
Posted - 2004.07.29 17:09:00 -
[26]
Hmmm looks great if only i knew what it all means
|
Sinist
|
Posted - 2004.07.29 17:34:00 -
[27]
Edited by: Sinist on 29/07/2004 18:21:15
Edited by: Sinist on 29/07/2004 18:09:46
Edited by: Sinist on 29/07/2004 18:09:09
Ok well ill put my graph thing idea if I feel like it. Its nothing remarkable.
Basically would say you should have a 100% chance of a perfect strike at exactly optimal range. And a 25% to 75% chance of average damage halfway between your optimal and falloff. And then near misses for very low damage at your extreme falloff +optimal.
And the percentages would favor better damage near your optimal and the extreme opposite near your falloff range.
*shrug* nice job tho torn. but hoenstly iw ould of rather i never seen this thread. i was better off not knowing and let this type of stuff being handles by ccp
|
Sinist
|
Posted - 2004.07.29 17:34:00 -
[28]
Edited by: Sinist on 29/07/2004 18:21:15
Edited by: Sinist on 29/07/2004 18:09:46
Edited by: Sinist on 29/07/2004 18:09:09
Ok well ill put my graph thing idea if I feel like it. Its nothing remarkable.
Basically would say you should have a 100% chance of a perfect strike at exactly optimal range. And a 25% to 75% chance of average damage halfway between your optimal and falloff. And then near misses for very low damage at your extreme falloff +optimal.
And the percentages would favor better damage near your optimal and the extreme opposite near your falloff range.
*shrug* nice job tho torn. but hoenstly iw ould of rather i never seen this thread. i was better off not knowing and let this type of stuff being handles by ccp
|
DHU InMe
|
Posted - 2004.07.29 18:15:00 -
[29]
Originally by: Hellmar
Yea, some player have pinned out problem a lot !
Nice links (updated 20 Dec 04):
BP, bugs about them.
(\_/)
(O.o)
(> <) This is Bunny. Copy Bunny into your signature to help him on his way. |
DHU InMe
|
Posted - 2004.07.29 18:15:00 -
[30]
Originally by: Hellmar
Yea, some player have pinned out problem a lot !
Nice links (updated 20 Dec 04):
BP, bugs about them.
(\_/)
(O.o)
(> <) This is Bunny. Copy Bunny into your signature to help him on his way. |
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