Post by zur on Sept 8, 2018 16:54:17 GMT -5
TL;DR Q&A List:
* Rolling with one or more "Preferred" stats rolls a percentile d100, compares it to the minimum and maximum values a stat can be, then generates the stat, resulting in a more even random distribution.
* Rolling with zero preferred stats rolls the "Raw" dice for a given racial stat, resulting in a bell curve of possible outcomes
, which includes the possibility of rolling really low.
* These calculations ignore Racial and Class modifiers (+2 for Warrior, etc.) as they come after the pertinent generation code. Your attributes will be higher/lower depending on what you select in character generation. They also ignore the "Reroll" command, for simplicity's sake.
* The "Stat Label" is unique for every class AND every attribute. You cannot compare a Human wisdom's "Very Good" with a Human strength's "Very Good", nor can you compare those with an Elf Wisdom's "Very Good".
* The only way to get "AI" or "Poor" stats is to roll "Exceptional" or "Below Average" on a given stat and have your Race or Class affect it.
* For any given attribute score, the chance of getting a maximum roll is always a flat ( 1.00%) when using "Preferred" stats, or is dependent on the dice when using "Raw" stats
** Human STR/AGI/END uses 3d4+7, giving a ( 1.56%) of a max value roll. Elven Wisdom uses 4d7+5, giving a (~0.04%) chance of a max value roll.
* When rolling a Human, unless you are specifically going for maximum rolls on STR, END, AGI, and ignore/dump WIS, you have a better chance of getting higher attributes where you want them by using the "Preferred" system.
* When rolling a Human, you will, on average (Between ~6%-11% of the time), have better stat rolls by not prioritizing anything, but you lose the ability to control where those rolls go.
* There is no difference between prioritizing "STR AGI END WIS" and "STR AGI END"
While creating your character, you eventually reach the point where you decide how many attributes to prioritize, and in which order. While pouring through the codebase, I stumbled upon the code that generates your stats. As it turns out, the "Prioritization" uses a completely different method to generate your Stats.
roll_abilities_raw generates the numbers via a traditional method of "Dice" rolling, whereas roll_abilities_preferred uses an interesting, if somewhat convoluted, system to factor in the ability to prioritize any or all statistics. Before continuing, I ask you dear reader.. If you're rolling a half-giant known for their strength, but prioritize wisdom, do you end up with an incredibly weak, but very wise variant?
For actual values of racial rolls, I refer to this thread throughout this post: armageddonmud.boards.net/thread/447/code-details-megathread
If we presume gogogadget's "Stat Ranges By Race" to be accurate, it's obvious that we don't get 3d3+1 strength instead of wisdom. How do you factor in a half-giant's high strength roll and prioritize everything but?
You don't, unfortunately.
When one or more stats are prioritized, the game switches to a percentile d100 system. Each stat is temporarily represented by a percentile roll. If the sum of each stat (STR+END+AGI+WIS) is less than a static variable, AVERAGE_ATTRIBUTE_VALUE=28 * 4 == [112], the game 'silently' rerolls until "The sum of the rolls is at least average". Turns out "Average" in this context doesn't mean d100 average, it means in-game.
The above percentiles aren't arbitrary. If we only look at everything between poor and AI, we're essentially looking at a 1-7 scale. 4/7 = 57.1%, defining the upper limit of the 4th item of the scale, "good".
Anything below this scale is "Poor", while everything above this scale is "Absolutely Incredible."
We still require an actual number to go along with this temporary percentile. The method "float convert_attribute_percent_to_range(int roll, int minRange, int maxRange)" defines this conversion as:
The game feeds the result of convert_attribute_percent_to_range() into an int[] array, where it's used for various game functions.
For example's sake, lets prioritize WIS END AGI STR, and roll 97, 44, 29, and 10, respectively. Their sum, 180, is greater than 112, so this is a "valid" roll. This translates to:
STR - Below Average (10)
AGI - Above Average (29)
WIS - Exceptional (97)
END - Good (44)
At this point, we 'need' to know what race we are so that we can aquire minRange and maxRange. For a human, gogogadget's post shows the following:
We then apply convert_attribute_percent_to_range()..
The game then throws this number into the array, trunciating the decimal as it converts from a float to an int.
There's no doubt that this is an effective way to translate the system over, but the fact remains that we as players have this choice in front of us which system to use to roll our stats. Which is better, a xd4+n system that denies choice, or a d100 system that allows it, and also allows an average of 28 or more per skill? Knowing the minimum the system will allow us for "Preferred" will allow us to extrapolate a necessary "Raw" roll to emulate the same results.
A bit of math tells us the chance of rolling 3d4 and getting at least 5 is 93.75%. Rolling 4d4 and getting at least 7 has a chance of 94.14%. Therefore, the chances of rolling at least "Average" in regards to roll_abilities_raw is:
(.9375 * .9375 * .9414 * .9375) == 77.56%
. The odds of rolling above this "Average" are slightly lower, but this figure is relatively accurate
The chances of rolling greater than (28*4=112) on 4d100 is 93.79%.
The following are a few tables displaying the probability of rolling a given attribute:
We can culminate the above and ask, "What is the chance I'll roll N or above using either system for a given stat, when rolling a Human?"
So, what does this mean?
When Generating a Human:
* Using the "Raw" system, you have a marginally better chance at getting maximum scores in all four abilities (1481 / 100 Billion) than if you use the "Preferred" system (1000 / 100 Billion)
* Using the "Raw" system, you have a much greater ( 68.76%) chance of getting between "Above Average" and "Very Good"(Inclusive) with STR/AGI/END , as compared to the "Preferred" system ( 44.00%)
** For WIS, "Raw" chance of the above is ( 72.67%) compared to "Preferred" chance of ( 41.00%)
* Using the "Raw" System, the chance of getting "Extremely Good" or above STR/AGI/END is ( 15.63%). Using the "Preferred system, this chance is ( 23.00%), with a noticeable weight (22 in 23) towards anything not the maximum.
** For WIS, "Raw" chance of the above is ( 13.67%), compared to "Preferred" chance of ( 26.00%), with noticeable weight (25 in 26) of not achieving maximum value.
* Conversely, the chance of getting "Average" or below STR/AGI/END using the "Raw" system is ( 15.63%), while the "Preferred" system has a chance of ( 33.00%).
** For WIS, "Raw" chance of the above is ( 13.67%), compared to "Preffered" chance of ( 33.00%)
Lets put this into a practical example. I'm rolling a Human and I want STR and END to be "Very Good" or better. What system do I use?
Raw:
STR: ( 31.26%) of "Very Good" or better
END: ( 31.26%) of "Very Good" or better
== ( 9.77%) of both being "Very Good" or better.
Preferred:
"Very good" = 58 or better on d100.
* Chance of rolling >= 58 at least twice out of 4d100 = ( 57.59%)
You should use the Preferred system, preferring STR and END. You likely will not roll maximum, but you do have a (+47.82%) of getting what you want over rolling "Raw"
What if I want "Extremely Good" or better STR and END?
Raw:
STR: ( 15.63%) of "Extremely Good" or better
END: ( 15.63%) of "Extremely Good" or better
== ( 2.44%) of both being "Extremely Good" or better
Preferred:
"Extremely good" = 72 or better on d100
* Chance of rolling >= 72 at least twice out of 4d100 = ( 33.07%)
You should still use the Preferred system, prioritizing STR and END. You have a (+ 30.63%) of getting what you want over rolling "Raw"
What if I want "Exceptional" or better STR and END?
Raw:
STR: ( 6.25%) of "Exceptional"
END: ( 6.25%) of "Exceptional"
== ( 0.39%) of both being "Exceptional
Preferred:
"Exceptional" = 86 or better on d100
* Chance of rolling >= 86 at least twice out of 4d100 = ( 10.95%)
No surprise, Preferred system gets what you want with a (+10.56%) over raw.
What if I want Maximum (19) STR and END?
Raw:
STR: ( 1.56
%) of rolling 19
END: ( 1.56
%) of rolling 19
== ( 0.02%) of rolling both 19's.
Preferred:
Roll of 19 = 100 on d100
Chance of rolling 100 at least twice out of 4d100 = ( 0.06%)
Though the margins progressively shrink, "Preffered" system is still your way to go with a (+0.04%) chance over rolling Raw
Continuing the above pattern, but prioritizing three stats:
* The chance of rolling "Very good" or better prioritizing STR, END, AGI is ( 21.55%), compared to "Raw" chance of ( 3.05%)
* "Extremely Good" Prioritizing STR, END, AGI is ( 7.62%) compared to "Raw" chance of (0.38%)
* "Exceptional" prioritizing STR, END, AGI is ( 1.20%) compared to "Raw" chance of ( 0.02%)
* Maximum rolls prioritizing STR, END, AGI is ( 0.0001%) compared to "Raw" chance of (0.0003796%)
In short, the ability to put a high roll where you want it is very powerful, statistics wise, even if it makes it far more difficult to actually achieve a maximum roll.
* Rolling with one or more "Preferred" stats rolls a percentile d100, compares it to the minimum and maximum values a stat can be, then generates the stat, resulting in a more even random distribution.
* Rolling with zero preferred stats rolls the "Raw" dice for a given racial stat, resulting in a bell curve of possible outcomes
, which includes the possibility of rolling really low.
* These calculations ignore Racial and Class modifiers (+2 for Warrior, etc.) as they come after the pertinent generation code. Your attributes will be higher/lower depending on what you select in character generation. They also ignore the "Reroll" command, for simplicity's sake.
* The "Stat Label" is unique for every class AND every attribute. You cannot compare a Human wisdom's "Very Good" with a Human strength's "Very Good", nor can you compare those with an Elf Wisdom's "Very Good".
* The only way to get "AI" or "Poor" stats is to roll "Exceptional" or "Below Average" on a given stat and have your Race or Class affect it.
* For any given attribute score, the chance of getting a maximum roll is always a flat ( 1.00%) when using "Preferred" stats, or is dependent on the dice when using "Raw" stats
** Human STR/AGI/END uses 3d4+7, giving a ( 1.56%) of a max value roll. Elven Wisdom uses 4d7+5, giving a (~0.04%) chance of a max value roll.
* When rolling a Human, unless you are specifically going for maximum rolls on STR, END, AGI, and ignore/dump WIS, you have a better chance of getting higher attributes where you want them by using the "Preferred" system.
* When rolling a Human, you will, on average (Between ~6%-11% of the time), have better stat rolls by not prioritizing anything, but you lose the ability to control where those rolls go.
* There is no difference between prioritizing "STR AGI END WIS" and "STR AGI END"
While creating your character, you eventually reach the point where you decide how many attributes to prioritize, and in which order. While pouring through the codebase, I stumbled upon the code that generates your stats. As it turns out, the "Prioritization" uses a completely different method to generate your Stats.
roll_abilities_raw generates the numbers via a traditional method of "Dice" rolling, whereas roll_abilities_preferred uses an interesting, if somewhat convoluted, system to factor in the ability to prioritize any or all statistics. Before continuing, I ask you dear reader.. If you're rolling a half-giant known for their strength, but prioritize wisdom, do you end up with an incredibly weak, but very wise variant?
For actual values of racial rolls, I refer to this thread throughout this post: armageddonmud.boards.net/thread/447/code-details-megathread
If we presume gogogadget's "Stat Ranges By Race" to be accurate, it's obvious that we don't get 3d3+1 strength instead of wisdom. How do you factor in a half-giant's high strength roll and prioritize everything but?
You don't, unfortunately.
When one or more stats are prioritized, the game switches to a percentile d100 system. Each stat is temporarily represented by a percentile roll. If the sum of each stat (STR+END+AGI+WIS) is less than a static variable, AVERAGE_ATTRIBUTE_VALUE=28 * 4 == [112], the game 'silently' rerolls until "The sum of the rolls is at least average". Turns out "Average" in this context doesn't mean d100 average, it means in-game.
const char * const how_good_stat[] = {
"poor", /* < 0% */
"below average", /* 0% - 14% */
"average", /* 15% - 28% */
"above average", /* 29% - 42% */
"good", /* 43% - 57% */
"very good", /* 58% - 71% */
"extremely good", /* 72% - 85% */
"exceptional", /* 86% - 100% */
"absolutely incredible" /* > 100% */
};
The above percentiles aren't arbitrary. If we only look at everything between poor and AI, we're essentially looking at a 1-7 scale. 4/7 = 57.1%, defining the upper limit of the 4th item of the scale, "good".
Anything below this scale is "Poor", while everything above this scale is "Absolutely Incredible."
We still require an actual number to go along with this temporary percentile. The method "float convert_attribute_percent_to_range(int roll, int minRange, int maxRange)" defines this conversion as:
maxRange - minRange = deltaRange
(deltaRange * attributeRoll / 100) + minRange = ActualAttributeScore
The game feeds the result of convert_attribute_percent_to_range() into an int[] array, where it's used for various game functions.
For example's sake, lets prioritize WIS END AGI STR, and roll 97, 44, 29, and 10, respectively. Their sum, 180, is greater than 112, so this is a "valid" roll. This translates to:
STR - Below Average (10)
AGI - Above Average (29)
WIS - Exceptional (97)
END - Good (44)
At this point, we 'need' to know what race we are so that we can aquire minRange and maxRange. For a human, gogogadget's post shows the following:
Human:
Stat Dice Ranges DeltaRange
STR: 3d4+7 (10-19) 19-10 == 9
AGI: 3d4+7 (10-19) 19-10 == 9
WIS: 4d4+4 (8-20) 20-8 == 12
END: 3d4+7 (10-19) 19-10 == 9
We then apply convert_attribute_percent_to_range()..
float ActualAttributeScore
STR: ((9 * 10) / 100) + 10 == 10.9
AGI: ((9 * 29) / 100) + 10 == 12.61
WIS: ((12 * 97) / 100) + 8 == 19.64
END: ((9 * 44) / 100) + 10 == 13.96
The game then throws this number into the array, trunciating the decimal as it converts from a float to an int.
Str = 10
Agi = 12
Wis = 19
End = 13
There's no doubt that this is an effective way to translate the system over, but the fact remains that we as players have this choice in front of us which system to use to roll our stats. Which is better, a xd4+n system that denies choice, or a d100 system that allows it, and also allows an average of 28 or more per skill? Knowing the minimum the system will allow us for "Preferred" will allow us to extrapolate a necessary "Raw" roll to emulate the same results.
Human:
Stat Preferred Raw
STR: 29% "Above Average" == 12 3d4 >= 5, 5+7 == 12
AGI: 28% "Average" == 12 3d4 >= 5, 5+7 == 12
WIS: 29% "Above Average" == 11 4d4 >= 7, 7+4 == 11
END: 28% "Average" == 12 3d4 >= 5, 5+7 == 12
// Note that, while STR and AGI have similiar RAW roles, their
"Label" differs due to the 1%. This is largely ignorable, as the "Stat" command uses a different formula to acquire it (elaborated on in Footnotes, below)A bit of math tells us the chance of rolling 3d4 and getting at least 5 is 93.75%. Rolling 4d4 and getting at least 7 has a chance of 94.14%. Therefore, the chances of rolling at least "Average" in regards to roll_abilities_raw is:
(.9375 * .9375 * .9414 * .9375) == 77.56%
. The odds of rolling above this "Average" are slightly lower, but this figure is relatively accurate
The chances of rolling greater than (28*4=112) on 4d100 is 93.79%.
The following are a few tables displaying the probability of rolling a given attribute:
Human:
STR, END, AGI (3d4+7, 10-19)
(10+N=Stat) d100 Roll Result Preferred Odds(%) Raw roll result Raw Odds(%) Visual Label
9: 100 1 3d4+7 = 19 1.56 Exceptional
8: 89-99 11 3d4+7 = 18 4.69 Exceptional
7: 78-88 11 3d4+7 = 17 9.38 Extremely Good
6: 67-77 11 3d4+7 = 16 15.63 Very Good
5: 56-66 11 3d4+7 = 15 18.75 Good
4: 45-55 11 3d4+7 = 14 18.75 Good
3: 34-44 11 3d4+7 = 13 15.63 Above Average
2: 23-33 11 3d4+7 = 12 9.38 Average
1: 12-22 11 3d4+7 = 11 4.69 Below Average
0: 1-11 11 3d4+7 = 10 1.56 Below AverageHuman:
WIS (4d4+4, 8-20)
(8+N=Stat) d100 Roll Result Preferred Odds(%) Raw roll result Raw Odds(%) Visual Label
12: 100 1 4d4+4 = 20 0.39 Exceptional
11: 92-99 8 4d4+4 = 19 1.56 Exceptional
10: 84-91 8 4d4+4 = 18 3.91 Extremely Good
9: 75-83 9 4d4+4 = 17 7.81 Extremely Good
8: 67-74 8 4d4+4 = 16 12.11 Very Good
7: 59-66 8 4d4+4 = 15 15.63 Very Good
6: 50-58 9 4d4+4 = 14 17.19 Good
5: 42-49 8 4d4+4 = 13 15.63 Above Average
4: 34-41 8 4d4+4 = 12 12.11 Above Average
3: 25-33 9 4d4+4 = 11 7.81 Average
2: 17-24 8 4d4+4 = 10 3.91 Average
1: 9-16 8 4d4+4 = 9 1.56 Below Average
0: 1-8 8 4d4+4 = 8 0.39 Below AverageWe can culminate the above and ask, "What is the chance I'll roll N or above using either system for a given stat, when rolling a Human?"
Chance of rolling N Human STR/END/AGI or above(%):
N Raw Preferred Visual Label
19 1.56 1 Exceptional
18 6.25 12. Exceptional
17 15.63 23. Extremely Good
16 31.25 34. Very Good
15 50. 45. Good
14 68.75 56. Good
13 84.38 67. Above Average
12 93.75 78. Average
11 98.44 89. Below Average
10 100. 100. Below AverageChance of rolling N Human WIS or above(%):
N Raw Preferred Visual Label
20 0.39 1. Exceptional
19 1.95 9. Exceptional
18 5.86 17. Extremely Good
17 13.67 26. Extremely Good
16 25.78 34. Very Good
15 41.41 42. Very Good
14 58.59 51. Good
13 74.22 59. Above Average
12 86.33 67. Above Average
11 94.14 76. Average
10 98.05 84. Average
9 99.61 92. Below Average
8 100. 100. Below Average
So, what does this mean?
When Generating a Human:
* Using the "Raw" system, you have a marginally better chance at getting maximum scores in all four abilities (1481 / 100 Billion) than if you use the "Preferred" system (1000 / 100 Billion)
* Using the "Raw" system, you have a much greater ( 68.76%) chance of getting between "Above Average" and "Very Good"(Inclusive) with STR/AGI/END , as compared to the "Preferred" system ( 44.00%)
** For WIS, "Raw" chance of the above is ( 72.67%) compared to "Preferred" chance of ( 41.00%)
* Using the "Raw" System, the chance of getting "Extremely Good" or above STR/AGI/END is ( 15.63%). Using the "Preferred system, this chance is ( 23.00%), with a noticeable weight (22 in 23) towards anything not the maximum.
** For WIS, "Raw" chance of the above is ( 13.67%), compared to "Preferred" chance of ( 26.00%), with noticeable weight (25 in 26) of not achieving maximum value.
* Conversely, the chance of getting "Average" or below STR/AGI/END using the "Raw" system is ( 15.63%), while the "Preferred" system has a chance of ( 33.00%).
** For WIS, "Raw" chance of the above is ( 13.67%), compared to "Preffered" chance of ( 33.00%)
Lets put this into a practical example. I'm rolling a Human and I want STR and END to be "Very Good" or better. What system do I use?
Raw:
STR: ( 31.26%) of "Very Good" or better
END: ( 31.26%) of "Very Good" or better
== ( 9.77%) of both being "Very Good" or better.
Preferred:
"Very good" = 58 or better on d100.
* Chance of rolling >= 58 at least twice out of 4d100 = ( 57.59%)
You should use the Preferred system, preferring STR and END. You likely will not roll maximum, but you do have a (+47.82%) of getting what you want over rolling "Raw"
What if I want "Extremely Good" or better STR and END?
Raw:
STR: ( 15.63%) of "Extremely Good" or better
END: ( 15.63%) of "Extremely Good" or better
== ( 2.44%) of both being "Extremely Good" or better
Preferred:
"Extremely good" = 72 or better on d100
* Chance of rolling >= 72 at least twice out of 4d100 = ( 33.07%)
You should still use the Preferred system, prioritizing STR and END. You have a (+ 30.63%) of getting what you want over rolling "Raw"
What if I want "Exceptional" or better STR and END?
Raw:
STR: ( 6.25%) of "Exceptional"
END: ( 6.25%) of "Exceptional"
== ( 0.39%) of both being "Exceptional
Preferred:
"Exceptional" = 86 or better on d100
* Chance of rolling >= 86 at least twice out of 4d100 = ( 10.95%)
No surprise, Preferred system gets what you want with a (+10.56%) over raw.
What if I want Maximum (19) STR and END?
Raw:
STR: ( 1.56
%) of rolling 19
END: ( 1.56
%) of rolling 19
== ( 0.02%) of rolling both 19's.
Preferred:
Roll of 19 = 100 on d100
Chance of rolling 100 at least twice out of 4d100 = ( 0.06%)
Though the margins progressively shrink, "Preffered" system is still your way to go with a (+0.04%) chance over rolling Raw
Continuing the above pattern, but prioritizing three stats:
* The chance of rolling "Very good" or better prioritizing STR, END, AGI is ( 21.55%), compared to "Raw" chance of ( 3.05%)
* "Extremely Good" Prioritizing STR, END, AGI is ( 7.62%) compared to "Raw" chance of (0.38%)
* "Exceptional" prioritizing STR, END, AGI is ( 1.20%) compared to "Raw" chance of ( 0.02%)
* Maximum rolls prioritizing STR, END, AGI is ( 0.0001%) compared to "Raw" chance of (0.0003796%)
In short, the ability to put a high roll where you want it is very powerful, statistics wise, even if it makes it far more difficult to actually achieve a maximum roll.
