Is a 91 Ability Roll Rare?
Dainank
Member Posts: 6
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
Screenshot: https://steamcommunity.com/sharedfiles/filedetails/?id=1763554764
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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.]
[Edit note 4/16/20: Dwarven Defender, Shadowdancer, Dark Moon Monk, Sun Soul Monk added to table. All standard kits not mentioned have the same stat requirements as their base class.]
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!
Thanks for all this data!
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.
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: 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.
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.
[Edit note 6/9/19: Dragon Disciple added to table]
[Edit note 4/16/20: Dwarven Defender, Shadowdancer, Dark Moon Monk, Sun Soul Monk added to table.
So, when I said humans in the core four classes would tend to have the lowest rolls? I was wrong; dwarves and halflings get lower rolls, because their racial modifiers are net negative. And for extremely high roll totals, the Avenger druid subclass has the hardest time, with their -4 total modifier from the class.
The numbers here are mostly pretty insensitive to the minimum stat requirements of races and core classes. A half-elf fighter/mage/cleric has minimum scores in everything but charisma - and they only take around 10% fewer rolls to get a given total than a human fighter. The big differences come from classes with high stat requirements - rangers, paladins, druids, bards, and specialist mages. It's easier to roll a total of 90+ on a human paladin than it is to roll a total of 85+ on a dwarf fighter. The champion here for the highest stat totals is an elf ranger, the only race/class combination that takes less than 100,000 rolls for a score of 100+ on average.
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".