D&D 5E Why I Am Starting to Prefer 4d6 Drop the Lowest Over the Default Array.

[TheCosmicKid]

My observation, taking into account that point buy doesn't allow numbers outside of 8-15 if you translate the resulting numbers into point buy cost:
- Take the numbers as rolled, no restrictions, no reroll. Average 21 points
- Only allow numbers between 8 and 15. Average: 27 points
- Throw out numbers below 8, allow 18. Average: 34 points.
- Throw out numbers below 8, roll until you get at least 1 18. Average 40 points.

How did you value scores below 8 or higher than 15? Did you extrapolate from the 8-15 values or use some other method? (When I did this I used the 3E values because they go up to 18, and extrapolated backwards from 10.5 for values below 8.)

But the biggest problem I have with rolling dice for stats (unless you C.H.E.A.T.) is the wide disparity of results. In my test I grouped the results of 6 to represent a typical gaming group and compared the difference in point buy cost for each character. What I found was that in the majority of "tables" there was a significant difference in ability scores. Using point buy as a yard stick, most tables had a difference of 30 points or more. That's a huge variation, if not in outright combat ability, in options for what people can play and how much they can contribute to out of combat skills.

I know a few different methods of rolling but normalizing the results. @TwoSix already described one earlier in the thread. You can also (my preferred method) use a d6 to add or subtract 1 from random scores in the array until you hit a target value. Or, if you're all generating characters together, you can "draft" scores from a rolled pool so that everybody gets the same exposure to high and low scores.

(As an aside, a 30 point difference does seem anomalously large. That would imply somebody consistently has a point-buy value of at least 50, which is supposedly rare.)

 

[Oofta]

How did you value scores below 8 or higher than 15? Did you extrapolate from the 8-15 values or use some other method? (When I did this I used the 3E values because they go up to 18, and extrapolated backwards from 10.5 for values below 8.)


I know a few different methods of rolling but normalizing the results. @TwoSix already described one earlier in the thread. You can also (my preferred method) use a d6 to add or subtract 1 from random scores in the array until you hit a target value. Or, if you're all generating characters together, you can "draft" scores from a rolled pool so that everybody gets the same exposure to high and low scores.

(As an aside, a 30 point difference does seem anomalously large. That would imply somebody consistently has a point-buy value of at least 50, which is supposedly rare.)

I took a SWAG at what point buy should be which may have contributed to the point differential. I counted negative points for everything below 8. IIRC 7 was -1, 6, was -2 and so on. I didn't want to over-count low numbers.

For numbers above 15 I did +3 then +4 (so 15 is 9, 16 is 12, 17 is 16, 18 is 20). Depending on what assumptions you make you will get different results.

Obviously comparing point buy to die rolls is going to be a little iffy when you get numbers outside of the 8-15 range. If you throw out everything outside of 8-15 you get an average of around 27. Almost as if they had done the math themselves.

 

[TheCosmicKid]

For numbers above 15 I did +3 then +4 (so 15 is 9, 16 is 12, 17 is 16, 18 is 20). Depending on what assumptions you make you will get different results.

Yeah, but the results seem consistently to over(?)value the high numbers and pull the average up.

Obviously comparing point buy to die rolls is going to be a little iffy when you get numbers outside of the 8-15 range. If you throw out everything outside of 8-15 you get an average of around 27. Almost as if they had done the math themselves.

Almost. It's 26.25, so they're being a little bit generous. But of course, the rules for rolling don't say to throw out everything outside of 8-15 (and I think most players would be bummed if they did).

 

[MostlyDm]

We are doing this (which I stole from this board at some point) after the current campaign ends at 20th (we are close):

Everyone rolls ONE set of 4d6 drop lowest, then each set is written down on a sheet of paper. Players pick the stat array they want from the list, and players can even pick the same one. This way, either everyone is screwed equally, or everyone gets the god stats.

Nice!

I came into this thread to post my method again, like I always do, but it's already been posted.

Glad to see it's gotten out there. That's awesome!

The best times are when you have a couple interesting different ones, like one with extreme highs and lows and one that's all-around good.

 

[MostlyDm]

This yields significantly stronger characters, and is definitely not a balanced approach.

Sent from my C6603 using EN World mobile app

Obviously, the larger your party the higher the chance of an overpowered set.

I usually run small groups, 2-4 players, so it's never been a big deal. Most often I find the big complaint about rolling is inter-party inequity rather than general overpoweredness.

An easy solution if you have a big party is to use the same rules, but everyone is just rolling 3d6 rather than 4d6 drop lowest. I'm not going to crunch the numbers, but that's going to skew lower, so it should balance out okay.

 

[FormerlyHemlock]

I think maybe you need to look at that table again, and look at the examples of stats people have been using. How often do you see three stats of 16 or higher in that table? Or two stats higher than 16 but none lower than 10? There's only one out of all of them that has two stats above 16, and yet, when people always talk about their stat rolled PCs, they always seem to have at least two. That's my point. And it very well does merit accusations of fudging when 90% of the examples people use statistically should only be 5%.

Could you quote which stats you refer to which "people have been using"? You entered this thread in post #3 IMMEDIATELY griping about the statistical improbability of the OP's experiences, and that the OP is "either ignoring low rolls, or cheating".

OP mentions specific rolled arrays twice AFAICT:

(1) "you kind of want 4 stats 14 or higher or a 14 dex with medium armor or 15 strength in heavy armor"
(2) "our Bladedancer rolls 3 scores over 16"

(He also says "With point buy you can get 20 dex by level 6 or 8" and "A 20 strength is nice for a strength based fighter but 18 strength+ feat is a great option" but that has nothing to do with rolled stats since he's talking about point buy in one, and in the other he's just talking about 20 Strength, however you get it.)

In (1), there is no mention of "two stats higher than 16 but none lower than 10". There's no mention of a specific character at all, in fact, just a list of goals: either 14+, 14+, 14+, 14+; or [some other criterion I don't quite understand but which might be 14+, 14+, 14+, 15+ or perhaps 14+, 14+, 15+. Zardnaar would have to clarify.]

Of the rows on your spreadsheet, I see 7 rows which can achieve 14+, 14+, 14+, 14+ after racial modifiers: #1, #2, #3, #5, #6, #12, #15, just under half.

The Bladesinger is clearly exceptional, but nothing else in the OP is. When you posted in this thread saying, "So you're preferring 4d6 because you're ignoring the lower rolls and only taking the higher ones over an array? Big shocker there. I say ignoring, because almost all of your examples are dependent on statistically higher than normal rolls," what did you mean by "almost all your examples?" Did you mean "that one Bladesinger you mentioned in the fifth paragraph"?

For now, I just want you to look at the math and realize that there's a reason why "statistically you would have the majority of your PCs having stats be higher than array or point buy", and it has nothing to do with cheating. It's because of math.

I'll steal this table from http://anydice.com/articles/4d6-drop-lowest/ to illustrate:

Highest at least One Two Three
18 9.34% 0.38% 0.01%
17 30.07% 4.03% 0.34%
16 56.76% 17.85% 3.26%
15 79.40% 42.16% 14.13%
14 92.80% 69.01% 36.29%

One in thirty PCs will roll three 16s or higher. It's uncommon by the standard of "things that happen at the table", and such a PC will no doubt be memorable--but it isn't uncommon by the standards of "things that get talked about on the Internet."

I'll readily concede that some people do cheat or ignore low rolls. But the fact that your very first post in this thread, in response to the OP, was to accuse him of cheating or statistical hijinks... well, that wasn't supported by the text of the OP. Clearly you have a pet peeve, and you were responding primarily to your own bias (i.e. Bayesian prior) and not to the evidence in the post.

 

[FormerlyHemlock]

Sort of, but nothing official as a houserule. For example, if I tell any group of players (especially if I don't know them) to roll up PCs with 4d6, and if that generation isn't in front of everyone else, then I guarantee you that the stat sets from those PCs will be much higher than what is statistically possible. Largely because one of two things:

If the stat sets aren't what the player likes, he or she will reroll them until they get a set they like (how many of us kept clicking on the "reroll" button when creating video game PCs lol)
If a stat roll is really low, then the player will simply roll another set of dice. I.e. "I rolled a 16, 15, 12, 12, 11, and 6. I'll just roll one more time to get rid of that 6."

Statistically, the odds are good that if you roll 4d6, then you're going to have at least one low score. And yet, over 35 years of seeing PCs handed to me, it almost never happens.

So the whole point of what I was saying is that if you do those aforementioned things, then of course 4d6 is going to look better, because you're stacking the odds in it's favor by fudging the rules as written. That's all. Personally, I don't care if people fudge their dice rolls if the table is OK with it, but don't compare it to array or point buy as being superior when you do so, that's all.

Simple solution if you still want to create characters in advance: have the DM roll the stat arrays and IM them to the players. If you want to create the illusion of player choice, have the DM roll up six arrays, and the player (over IM) can roll or pick a number between 1 and 6, and he gets the corresponding array. Easy peasey.

 

[FormerlyHemlock]

I took a SWAG at what point buy should be which may have contributed to the point differential. I counted negative points for everything below 8. IIRC 7 was -1, 6, was -2 and so on. I didn't want to over-count low numbers.

For numbers above 15 I did +3 then +4 (so 15 is 9, 16 is 12, 17 is 16, 18 is 20). Depending on what assumptions you make you will get different results.

Obviously comparing point buy to die rolls is going to be a little iffy when you get numbers outside of the 8-15 range. If you throw out everything outside of 8-15 you get an average of around 27. Almost as if they had done the math themselves.

If anyone is curious, here is an implementation of OOFTA's algorithm as described above: https://repl.it/I9Sd/1 Just hit the Run button.

Average point buy total is approximately 31. Average span within a four-person party is approximately 22. That suggests that most parties are roughly in a range from 20ish up through 42ish, using OOFTA's valuation function:

| 3 -> -5
| 4 -> -4
| 5 -> -3
| 6 -> -2
| 7 -> -1
| 8 -> 0
| 9 -> 1
| 10 -> 2
| 11 -> 3
| 12 -> 4
| 13 -> 5
| 14 -> 7
| 15 -> 9
| 16 -> 12
| 17 -> 16
| 18 -> 20

 

[Bradley Hindman]

I'm not big on PCs playing Potatoes and letting the party down so to speak. Its not gonna end well if you have a melee based PC with 12 strength or dex for example.

While I fully recognize that this is a common viewpoint that it often goes along with the race to the ability cap (spend every ASI on the primary stat until 20 is reached), I have never understood the thinking. If my fighter has a 16 STR and yours has a 20 STR, there is a "measly" +2 difference between our attack bonus. Why do I say measly? A +2 difference means means that I miss 1 out every 10 melee attacks because of my 'inferiority'. In a typical gaming session, (5 rounds per combat, 4 combats per session) I might make 20 attacks total. My inferiority means I missed twice due to my low Strength. That's once every other combat. (Of course higher level fighters attack more often . . . ).

If you want to compare my hits with my superior friends hits, it will depend on AC. But, if I have even chances to hit with each attack, I hit 5 times for every six that my superior friend hits. Maybe I am just an optimist, but that just doesn't seem like that big of a deal.

 

[FrogReaver]

While I fully recognize that this is a common viewpoint that it often goes along with the race to the ability cap (spend every ASI on the primary stat until 20 is reached), I have never understood the thinking. If my fighter has a 16 STR and yours has a 20 STR, there is a "measly" +2 difference between our attack bonus. Why do I say measly? A +2 difference means means that I miss 1 out every 10 melee attacks because of my 'inferiority'. In a typical gaming session, (5 rounds per combat, 4 combats per session) I might make 20 attacks total. My inferiority means I missed twice due to my low Strength. That's once every other combat. (Of course higher level fighters attack more often . . . ).

If you want to compare my hits with my superior friends hits, it will depend on AC. But, if I have even chances to hit with each attack, I hit 5 times for every six that my superior friend hits. Maybe I am just an optimist, but that just doesn't seem like that big of a deal.

Just as Important as the attack bonus is the +2 damage you get from having 20 str vs 16 str. +2 damage is generally going to equate to 17% to 30% more damage all on it's own. The attack bonus will usually help 15% - 25%. On average that measly +2 bonus means about 40% more damage. Some of it through hitting more and some of it through hitting harder.