Using this table we can determine by direct calculation many probabilities. For example, the probability of rolling only 1-18 attribute (before racial modifiers) is 6 x 0.0162 x 0.9838 ^5 = 8.96%
The probability of rolling 1 - 17 or 18 is 6 x (0.0162+0.0417) x 0.9421 ^5 = 25.77%
And the probability of rolling 1 16 or 17 or 18 is 6 x (0.0162+0.0417+0.0725) x 0.8696 ^5 = 38.91%
and we could go on and on for thousands of specific results we wanted to check. But let's get down to the nugget ...
A recent point buy character I created is a Bard. I wanted him to have the best 'reasonable' Charisma I could get out of the gate, and a good Dexterity. I wanted him to have decent Constitution and good Wisdom. It wouldn't do for the 'face' of the party to run his charismatic mouth only to agree to do something stupid. Strength was going to be his dump stat so I was going to put a little, if there was anything left, into Intelligence. Knowing that for the starting charisma I was going to play a Half-Elf, the final point array was going to look like this: Chr 16 Wis 14 Dex 14 Int 12 Con 12 Str 10. Now we could discuss whether this is the best starting array, but let's just roll with this. Subtracting out the racial modifiers, we would need to 'roll' the following stats: Chr 14 Wis 13 Dex 13 Int 12 Con 12 Str 10.
Now for the money question … What is the chance of me rolling below this starting value?
I'm going to roll a 14 (or better) at least 1 - 0.6451^6 = 92.8% of the time.
I'm going to roll a 14 (or better) with two 13s (or better) at least (1 - 0.6451^6) x (1 - 0.5123^5) x (1 - 0.5123^4) = 83.35% of the time.
I'm going to roll a 14 (or better) with two 13s (or better) and two 12s (or better) at least (1 - 0.6451^6) x (1 - 0.5123^5) x (1 - 0.5123^4) x (1 - 0.3835^3) x (1 - 0.3835^2) = 67.08% of the time.
And I'm going to roll the full six stats as I required at least 0.6708 x (1 - 0.2693) = 49.02% of the time, but I could (and probably would roll higher on one or two of those rolls without reducing my chances of rolling these minimums).
Now 49% of the time sounds fair, right? Except ...
I bet OVER 99/100 DMs would not force you to keep a 7 or lower. And if you take just one of these values that could be a 7 or lower out of the mix and allow it to be rerolled, the probabilities start to climb, a lot! And as I keep saying, this is the probability of getting this set of stats or better. There is an extremely high probability of getting better than the 14 - 13 - 13 - 12 - 12 - 10 I set as my target without missing the other numbers in the array.
I'm not going to cloud the discussion of this calculation with my feelings of what I would do with this knowledge.
Interesting info provided with the D&D Beyond Data Update, scroll down to see preferred methods of ability score generation. https://www.dndbeyond.com/forums/d-d-beyond-general/news-announcements/59795-dev-update-3-12-2020 Effectively it can be argued that point buy edges out the competition just barely, as there's a near even split on Point Buy & the standard array (which is just one variation of a point bought set). Simultaneously, it's maybe 51 % vs Manual's 48+ % where I'd guess the majority of users are using a rolling method (I believe 4d6, drop the lowest, and repeat 6 times would be the standard). My suspicion based on other polls is that people like myself who prefer a non-standard point buy pool are very much in the minority. Definitely something for me to sit and think on. I imagine I might be asking the greater community it's thoughts on Feats allotted as bonuses per campaign (via Training / Alternate Quest Rewards, straight level bonuses, etc.) as well as how many feats folks feel a PC should have within their career. Obviously that would be another thread.
Devil's advocate here, but a lot of people theorycraft, myself included, and you can't really theorycraft with rolled stats. If I want to see how a build comes together and its not part of an actual game, I utilize point buy. But that character isn't going to actually get played.
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Another medical problem. Indefinite hiatus. Sorry, all.
Totally fair, I've created a few dozen "When I get to 20th level I wanna look just like *this* guy," not to mention all the ridiculously overpowered NPC's I create and then scale down dramatically into a more correct NPC sheet. Imagine trying to recreate Elminster of 3rd Edition in 5th. I'd argue it could be done, but he'd have 10 to 20 Epic Boons, 4 or 5 Custom Blessings, and every feat that related to just being a BAMF (a BAMF'ing BAMF no less).
Campaigns that I run usually use a modified point buy (35 points, can buy up to 16).
You an me, Houligan, lol. I use a modified home-brewed point buy pool as well, at 37 points, with the starting stat of 8 and the highest purchase of 17. Allows for a nice array like 17, 15, 14, 12, 10, and 8. If I dropped it down to 36, it would actually look a little cleaner, at 17, 15, 13, 13, 10, and 8. I just feel it's more balanced than the 27 point buy is, regardless of the chorus. I don't mean to say I just completely disregard other opinions of course, just that I'm a bit skeptical: and it's hard to let go of that.
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Using this table we can determine by direct calculation many probabilities. For example, the probability of rolling only 1-18 attribute (before racial modifiers) is 6 x 0.0162 x 0.9838 ^5 = 8.96%
The probability of rolling 1 - 17 or 18 is 6 x (0.0162+0.0417) x 0.9421 ^5 = 25.77%
And the probability of rolling 1 16 or 17 or 18 is 6 x (0.0162+0.0417+0.0725) x 0.8696 ^5 = 38.91%
and we could go on and on for thousands of specific results we wanted to check. But let's get down to the nugget ...
A recent point buy character I created is a Bard. I wanted him to have the best 'reasonable' Charisma I could get out of the gate, and a good Dexterity. I wanted him to have decent Constitution and good Wisdom. It wouldn't do for the 'face' of the party to run his charismatic mouth only to agree to do something stupid. Strength was going to be his dump stat so I was going to put a little, if there was anything left, into Intelligence. Knowing that for the starting charisma I was going to play a Half-Elf, the final point array was going to look like this: Chr 16 Wis 14 Dex 14 Int 12 Con 12 Str 10. Now we could discuss whether this is the best starting array, but let's just roll with this. Subtracting out the racial modifiers, we would need to 'roll' the following stats: Chr 14 Wis 13 Dex 13 Int 12 Con 12 Str 10.
Now for the money question … What is the chance of me rolling below this starting value?
I'm going to roll a 14 (or better) at least 1 - 0.6451^6 = 92.8% of the time.
I'm going to roll a 14 (or better) with two 13s (or better) at least (1 - 0.6451^6) x (1 - 0.5123^5) x (1 - 0.5123^4) = 83.35% of the time.
I'm going to roll a 14 (or better) with two 13s (or better) and two 12s (or better) at least (1 - 0.6451^6) x (1 - 0.5123^5) x (1 - 0.5123^4) x (1 - 0.3835^3) x (1 - 0.3835^2) = 67.08% of the time.
And I'm going to roll the full six stats as I required at least 0.6708 x (1 - 0.2693) = 49.02% of the time, but I could (and probably would roll higher on one or two of those rolls without reducing my chances of rolling these minimums).
Now 49% of the time sounds fair, right? Except ...
I bet OVER 99/100 DMs would not force you to keep a 7 or lower. And if you take just one of these values that could be a 7 or lower out of the mix and allow it to be rerolled, the probabilities start to climb, a lot! And as I keep saying, this is the probability of getting this set of stats or better. There is an extremely high probability of getting better than the 14 - 13 - 13 - 12 - 12 - 10 I set as my target without missing the other numbers in the array.
I'm not going to cloud the discussion of this calculation with my feelings of what I would do with this knowledge.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
Devil's advocate here, but a lot of people theorycraft, myself included, and you can't really theorycraft with rolled stats. If I want to see how a build comes together and its not part of an actual game, I utilize point buy. But that character isn't going to actually get played.
Another medical problem. Indefinite hiatus. Sorry, all.
Totally fair, I've created a few dozen "When I get to 20th level I wanna look just like *this* guy," not to mention all the ridiculously overpowered NPC's I create and then scale down dramatically into a more correct NPC sheet. Imagine trying to recreate Elminster of 3rd Edition in 5th. I'd argue it could be done, but he'd have 10 to 20 Epic Boons, 4 or 5 Custom Blessings, and every feat that related to just being a BAMF (a BAMF'ing BAMF no less).
Campaigns that I run usually use a modified point buy (35 points, can buy up to 16).
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You an me, Houligan, lol. I use a modified home-brewed point buy pool as well, at 37 points, with the starting stat of 8 and the highest purchase of 17. Allows for a nice array like 17, 15, 14, 12, 10, and 8. If I dropped it down to 36, it would actually look a little cleaner, at 17, 15, 13, 13, 10, and 8. I just feel it's more balanced than the 27 point buy is, regardless of the chorus. I don't mean to say I just completely disregard other opinions of course, just that I'm a bit skeptical: and it's hard to let go of that.