[RPG] subtle mathematical difference between increasing the target number and adding detrimental modifiers

dicestatisticssystem-agnostic

Modifying difficulty works in various ways within and between various roleplaying systems. But generally speaking, it seems added difficulty either modifies the target number (altering the check) or reduces the effectiveness of a roll (appending positive or negative modifiers, depending on how checks work).

Say you need to roll above 15. Let's say that in one situation, that difficulty bumps up to 17; in another situation, the target number is the same, but your roll has a −2 modifier. Superficially, the math looks like it would be the same: in either case, the roll becomes 2 more difficult.

I'm wondering whether there is actually a deeper, non-obvious difference between the two. Similar to how a 2d6 looks like a more complicated 1d12, but in reality, is made dramatically different by the rules of probability: the 1d12 gives a flat line of unweighted results while the 2d6 gives a curve naturally favoring middle values. Perhaps mathematics does similar witchcraft on these two styles of difficulty.

Best Answer

The basic math does not change, no. 1d20+5-2 >= 15 is the same as 1d20+5 >= 15+2, and 3d6+5-2 >= 15 and 3d6+5 >= 15+2 are equal as well, in case you're wondering about those pesky curves.

However, there are five basic ways the outcome can still be different in certain cases.

  • The first is if there are any rules or abilities that kick in on a modified roll result that's below (or above) a particular value. Angelo Fuchs gives the example of crits in CyberPunk when spending luck: the luck-modified roll, if greater than a certain threshold, explodes.
  • The second way is if there's a rule that is activated when the DC or target number is above or below a particular threshold, like D&D 3.x's rule forbidding certain skill checks on DCs greater than 10 without ranks in that skill.
  • The third, which I've never spotted in the wild, would be if there's a way to reduce or remove unfavorable DC modifiers as such; this seems unlikely, given the way DCs are usually based on inherent aspects of the task.
  • The fourth is if there are rules that allow penalties to rolls to be subsumed by an existing penalty of the same type or removed by an ability; e.g., D&D 3.x applies only the largest penalty by default and allows feats to remove penalties regardless of amount.
  • And the fifth, the odd one out, is if it only affects rolls and there's an ability or rule to forgo rolling, like D&D 3.x's take 10 rule.
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