A nice way of factoring in variable modifiers into a probability calculation is modeling them as dice. The more probable a modifier is, the more frequent it appears on the model die's faces.
With Dungeon World, the most consistent modifier is the stat modifier arising from the character's stats. In a bird's eye view of the system, we can assume that one of the six stats of the character will be affecting any roll at any moment, so a six-sided die can be chosen to pick our random stat for the purposes of probability calculation.
In this AnyDice program, I have created such a die (named
M for modifier) and mapped it into the standard range of stat modifiers assigned at character creation. There's 1/6 probability that your modifier will be a +2, 1/3 for +1, 1/3 for nothing and 1/6 for -1.
If we roll that die along with the usual 2d6, we get a bell curve distribution of 1 through 14. That output somewhat includes our answer but it's not clear enough. So I also made a function for sorting those results into the three categories of "clean hit", "hit with consequences" and "miss", represented as
So the final results are:
- 64.35% chance of a hit, broken down as…
- 23.15% chance of a clean hit (10+)
- 41.20% chance of a hit with consequences (7-9)
- 35.65% chance of a miss (6-)
There are other occasional modifiers coming into play through other moves, but they are so much dependent on a specific game context that they would be very hard to determine how often they would come up. I chose to ignore them, but it is always possible to add more modifier dice into such a calculation.