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Is a 91 Ability Roll Rare?

I have rolled quite a lot and never had a 90+ nor have I ever seen it on playthroughs! Does anyone know the percentage odds?

Screenshot: https://steamcommunity.com/sharedfiles/filedetails/?id=1763554764

Comments

  • OlvynChuruOlvynChuru Member Posts: 2,057
    It depends on the character you're making. Classes with high minimum stats (e.g. rangers) are more likely to roll high stats.

    Dainank
  • ThacoBellThacoBell Member Posts: 8,844
  • jmerryjmerry Member Posts: 71
    edited June 9
    For reference, the minimum stats for each standard race and class:
    Class      Str Dex Con Int Wis Cha
    Fighter      9   -   -   -   -   -
    Ranger      13  13  14   -  14   -
    Paladin     12   -   9   -  13  17
    Blackguard  12   -  14   -   -  14
    Cleric       -   -   -   -   9   -
    Druid        -   -   -   -  12  15
    Mage         -   -   -   9   -   -
    Abjurer      -   -   -   9  15   -
    Conjurer     -   -  15   9   -   -
    Diviner      -   -   -   9  16   -
    Enchanter    -   -   -   9   -  16
    Illusionist  -  16   -   9   -   -
    Invoker      -   -  16   9   -   -
    Necromancer  -   -   -   9  16   -
    Transmuter   -   -  15   9   -   -
    Thief        -   9   -   -   -   -
    Bard         -  12   -  13   -  15
    Sorceror     -   -   -   9   -   9
    Dragon Disc 10  14   -   -   -  15
    Monk         -   9   9   -   9   -
    Shaman       -   -  12   -  12   -
    
    Race       Str Dex Con Int Wis Cha
    Elf          -   7   6   8   -   8
    Half-Elf     -   6   6   4   -   -
    Dwarf        8   -  12   -   -   -
    Halfling     6   8  10   6   -   -
    Gnome        6   -   8   7   -   -
    Human        -   -   -   -   -   -
    Half-Orc     -   -   -   -   -   -
    
    Dash marks indicate that there's no minimum aside from the roll minimum of 3 plus or minus racial adjustments. All kits not mentioned here have the same stat requirements as their base class. Characters must meet the minimum stats for all of their races and classes; for example, a gnome cleric/thief needs 9 Wis, 9 Dex, 6 Str, 8 Con, and 7 Int.

    Rangers and Paladins will tend toward the highest rolls; Paladins are quite easy to roll over 90 for, with that 17 or 18 charisma skewing the odds. A human in one of the core four classes will tend to have the lowest rolls; getting suitable rolls for a character that plans to dual-class can take a while. With the race included, the highest possible minimums come for an Elf Ranger; such a character has minimum requirements in every stat, and needs 70 points of their roll just to meet them.

    [Edit note 6/9/19: I missed one. Dragon Disciple added to table, as it's very different from the base sorceror.]

    Post edited by jmerry on
    DainankMathsorcerer
  • MathsorcererMathsorcerer Member Posts: 2,607
    18d6 over at WolframAlpha--https://www.wolframalpha.com/input/?i=18d6

    expected value = 63, standard deviation = 7.246, so 91 is (91-63)/7.246 = 3.8642 standard deviations above the norm, which is at 99.99%, or about about 1 person in 1794.

    DainankRaduziel
  • DainankDainank Member Posts: 4
    edited June 7
    18d6 over at WolframAlpha--https://www.wolframalpha.com/input/?i=18d6

    expected value = 63, standard deviation = 7.246, so 91 is (91-63)/7.246 = 3.8642 standard deviations above the norm, which is at 99.99%, or about about 1 person in 1794.

    This is exactly what I wanted to know! Thank you!
    jmerry wrote: »
    For reference, the minimum stats for each standard race and class:
    Class      Str Dex Con Int Wis Cha
    Fighter      9   -   -   -   -   -
    Ranger      13  13  14   -  14   -
    Paladin     12   -   9   -  13  17
    Blackguard  12   -  14   -   -  14
    Cleric       -   -   -   -   9   -
    Druid        -   -   -   -  12  15
    Mage         -   -   -   9   -   -
    Abjurer      -   -   -   9  15   -
    Conjurer     -   -  15   9   -   -
    Diviner      -   -   -   9  16   -
    Enchanter    -   -   -   9   -  16
    Illusionist  -  16   -   9   -   -
    Invoker      -   -  16   9   -   -
    Necromancer  -   -   -   9  16   -
    Transmuter   -   -  15   9   -   -
    Thief        -   9   -   -   -   -
    Bard         -  12   -  13   -  15
    Sorceror     -   -   -   9   -   9
    Monk         -   9   9   -   9   -
    Shaman       -   -  12   -  12   -
    
    Race       Str Dex Con Int Wis Cha
    Elf          -   7   6   8   -   8
    Half-Elf     -   6   6   4   -   -
    Dwarf        8   -  12   -   -   -
    Halfling     6   8  10   6   -   -
    Gnome        6   -   8   7   -   -
    Human        -   -   -   -   -   -
    Half-Orc     -   -   -   -   -   -
    
    Dash marks indicate that there's no minimum aside from the roll minimum of 3 plus or minus racial adjustments. All kits not mentioned here have the same stat requirements as their base class. Characters must meet the minimum stats for all of their races and classes; for example, a gnome cleric/thief needs 9 Wis, 9 Dex, 6 Str, 8 Con, and 7 Int.

    Rangers and Paladins will tend toward the highest rolls; Paladins are quite easy to roll over 90 for, with that 17 or 18 charisma skewing the odds. A human in one of the core four classes will tend to have the lowest rolls; getting suitable rolls for a character that plans to dual-class can take a while. With the race included, the highest possible minimums come for an Elf Ranger; such a character has minimum requirements in every stat, and needs 70 points of their roll just to meet them.

    Thanks for all this data!

    StummvonBordwehrMathsorcerer
  • ChroniclerChronicler Member Posts: 774
    OlvynChuru wrote: »
    18d6 over at WolframAlpha--https://www.wolframalpha.com/input/?i=18d6

    expected value = 63, standard deviation = 7.246, so 91 is (91-63)/7.246 = 3.8642 standard deviations above the norm, which is at 99.99%, or about about 1 person in 1794.

    Actually the chance is higher than that, since the game automatically rerolls when the stat total is less than 75, and it takes minimum stats into account.

    Also, I don't think it rolls multiple D6 for every stat. I think it just rolls one die of appropriate size.

    If you use the D6 method it's rare that you even make it 75 minimum, let alone anything higher.

    Dainank
  • jmerryjmerry Member Posts: 71
    I'm pretty sure the method the game uses to roll stats is 3d6 for each stat, in order. Then racial modifiers are applied, and the roll is silently discarded if it doesn't meet race/class minimums or the 75 point minimum. It's a computer - it can afford to roll a lot.

    A brief experiment: roll an elf ranger, and look at the strength. Rolls that wouldn't reach 75 if strength was lowered to 13 are discarded. Taking 100 of these rolls, the results I got:
    Str Num Exp
    13  43  37.5
    14  25  26.8
    15  16  17.9
    16  12  10.7
    17   2   5.4
    18   2   1.8
    
    That "Exp" column is the expected number of rolls of that strength using the procedure I outlined. Other methods would lead to different, usually flatter, distributions. For example, the tabletop-popular 4d6 dropping the lowest would give a 13 27.2% of the time and a 14 25.3% of the time. That's already pretty implausible with the 43 rolls of 13 here; it would be 3.5 standard deviations above the mean, as opposed to only 1.1 with the 3d6 method.

    As a side note, how many rolls on average would it take to achieve the minimums for an elf ranger, ignoring the 75? Nearly a thousand; it's about a one in 976 chance. A human paladin is nearly as unlikely, at a one in 750 chance. A human or half-elf ranger goes up to a one in 567 chance; 14 Con is a lot easier to achieve without a penalty.

    Dainank
  • Grond0Grond0 Member, Moderator Posts: 5,013
    I agree with @jmerry - those sorts of tests (including on far larger sample sizes) have been done many times and there's no doubt at all that the game does roll 3d6 in arriving at stats.

    The minimum requirements for rolls do make a huge difference. I would expect rolling at least a 91 for a human fighter to take 10-15 minutes on average. Doing the same thing for a paladin though you would have to be pretty unlucky if you took more than a minute.

    Dainank
  • Grond0Grond0 Member, Moderator Posts: 5,013
    Thanks for that @jmerry - I'm sure lots of people will find that information useful in future.

    StummvonBordwehr
  • jmerryjmerry Member Posts: 71
    I've added a few lines to the tables in my posts here, as I missed a kit the first time around - Dragon Disciples have very different requirements than generic sorcerors. They're in about the same place as bards for the difficulty of rolling high scores. Oddly enough, while generic sorcerors are required to have 9 Int, DDs don't have an intelligence minimum at all; you can legally build a Dragon Disciple that can't read scrolls or use wands. It's unwise, but it's legal.

    ChroniclerStummvonBordwehrGrond0
  • MathsorcererMathsorcerer Member Posts: 2,607
    OlvynChuru wrote: »
    18d6 over at WolframAlpha--https://www.wolframalpha.com/input/?i=18d6

    expected value = 63, standard deviation = 7.246, so 91 is (91-63)/7.246 = 3.8642 standard deviations above the norm, which is at 99.99%, or about about 1 person in 1794.

    Actually the chance is higher than that, since the game automatically rerolls when the stat total is less than 75, and it takes minimum stats into account.

    Technically you are correct, but since I looked this up at work I wasn't going to get into that much detail about it.

    Eons ago, when we played pencil-and-paper with candles and quill pens, we had to roll our stats first and then choose a character class for which those stats would qualify. I doubt anyone has placed that sort of restriction on themselves since 1984, though, except for that one random DM who wants his game to be "old school".

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