On the Dungeon World+ Discord, Gojson asked how he could roll up a DW character, rather than just allocating the preset stats.

I suggested he do it old school, rolling 3d6 down the line for each attribute. That may work for you as well, and—if you’re playing a hack that drops ability scores (3-18), as most DW hacks do—then just use the modifiers:

3d6Modifier
3-3
4-5-2
6-8-1
9-120
13-15+1
16-17+2
18+3

The table I listed is from Dungeon World, but you could certainly come up with your own table for house rules.

One community member wanted to know why the ranges were irregular. I pointed out that they were symmetrical:

distribution of die rolls 3-18 on a bell curve

But the ranges aren’t necessarily intuitive. There are some arbitrary decisions. I pointed out that I might have made 17 or 18 (< 2% chance) a +3, rather than just 18 being a +3.

Jeremy Strandberg responded

IIRC, they chose the ranges they did in order to:

1) throttle how long it took for PCs to get a +3 modifier

2) to match the modifier ranges of one of the earlier D&D editions (B/X, I think?).

Which sent me scurrying for my editions of early D&D. I couldn’t find my physical copy but I had bought the PDF of Holmes Basic (the first Basic D&D, though it was just called Dungeons & Dragons at the time). It was a hodgepodge, without any standard modifiers based on scores, so it definitely wasn’t the source. For instance:

Constitution18add 3 to each hit die
 17add 2 to each hit die
 15-16add 1 to each hit die
 7-14no bonus
 6 or lesssubtract 1 from each hit die but never less than 1
Dexterity13 or morefire any missile +1
 9-12no bonus
 8 or lessfire any missile -1

Jeremy said, “This prompted me to go looking, and this is the thread I was remembering in which the current stat array was proposed and adopted: Very small tweaks on stat scores.”

Like Holmes Basic, Moldvay Basic also varied by stat, but for STR, CON, and WIS it worked out to: 

3d6 DW3d6 Moldvay
STR, CON, WIS
Modifier
33-3
4-54-5-2
6-86-8-1
9-129-120
13-1513-15+1
16-1716-17+2
1818+3

As a match for Dungeon World, that may have been the ultimate inspiration. 

In Moldvay, for DEX, it usually worked out like that, except for initiative adjustment.

STR, CON, WIS, DEX (usually)DEX (initiative), CHAINTModifier
3  -3
4-53 -2
6-84-83-8*-1
9-129-129-120
13-1513-1713-15+1
16-171816-17+2
18 18+3
* INT: 3-8 had three levels of difficulties with language: 3=“Has trouble with speaking, cannot read or write”, 4=“Cannot read or write Common”, 6-8=“Can write simple Common words.”

But note that 5e, while keeping the consistency across attributes of earlier editions, opted for more granularity.

Ability Scores and Modifiers
1−5
2–3−4
4–5−3
6–7−2
8–9−1
10–11+0
12–13+1
14–15+2
16–17+3
18–19+4
20–21+5
22–23+6
24–25+7
26–27+8
28–29+9
30+10

See also: Attributes/Stats for Characters in Old School RPGs.

Photo credit: You can purchase the attribute buttons from WeegonzaBazaar on Etsy.