What's worse, -2 or disadvantage?

Question

So, I'm building a system that adds an extra level of flavor, with some minor mechanics as an optional side system for a 5e campaign. The basic function is, you collect points, then collect a deficit. Once you get enough points again, that deficit is escalated.

So for example, one effect causes creatures making a perception check (based on smell), gain advantage. The escalated version is they no longer need a roll - they can pick up your trail easily, and are able to track you.

One mechanic I'm not sure about however is the comparison between a hard deficit, vs disadvantage. I.e. -2 to a roll, vs disadvantage on a roll.

So, are these comparable, and if so, which is worse?

Answer 1

TL;DR Disadvantage is more impactful.

In this article the equivalent bonuses of advantage and disadvantage were calculated:

https://theangrygm.com/probability-for-gamers/

(The article is very long, the relevant information pertaining to this question is explained below.)

The tables show that disadvantage can be equivalent to a penalty of -5 , if the number actually needed on the die is around ten. It is a lot less impactful if the number needed is very high or very low. On average (as evident from the tables) it is more than -2.

More detailed: Disadvantage decreases the chance of succeeding a check of a given DC. The percentage decrease depends on the number necessary on the d20. If the number is close to 1 or 20, the decrease is close to zero. If the number is around ten, the effect is maximal. Since every 5% chance are equal to one point on the d20 (1/20), the percentage decrease can be used to calculate an equivalent modifier.

Additionally, the monster building rules in the DMG suggest considering advantage or disadvantage to be worth +/- 4 as modifier.

Answer 2

They're different

Advantage/Disadvantage don't really compare well to bonuses and penalties, though the system wants you to use the former instead of the latter, mostly, and so it makes sense that one might presuppose that they must be similar.

The most important distinctions are:

• Advantage and disadvantage don't stack, so juggling and hopping on one foot while wearing full plate, for example, doesn't make you any worse at stealth than just doing any of those alone while trying to move quietly. A penalty, on the other hand, stacks with other penalties and so sneaking while affected by a bane spell and a negative temple of the gods spell would be worse than sneaking while subjected to either alone.
• Because Advantage and Disadvantage don't stack, and because there are myriad sources for both, including that the GM is supposed to award advantage or disadvantage rather than bonuses or penalties for situational ad-hoc modifiers, it's a pretty safe bet the players should always have a source of advantage for anything that they particularly care about, have time to plan for, or both. This means that additional sources of advantage are not very valuable. Disadvantage is a little less common, so a feature that confers that is a little better than one that confers Advantage, since it's less likely to overlap with pre-existing abilities.
• Because Advantage and Disadvantage involve more rolls, they impact the probability of criticals, which bonuses and penalties do not do. If you are concerned about an opponent hitting you and they only hit on a 20, making them roll twice reduces their chance of success twentyfold. A penalty would, contrarywise, have not effect. Similarly, if you want to critical, it's extra rolls you need, not to get a bonus.
• Because Advantage and Disadvantage change only the weighting of the distribution of rolls and not its set of possible values, they cannot change what tasks you are theoretically capable of accomplishing. This is particularly important because neither state matters for rolls where there is no significant consequence for failure-- you will still succeed eventually, after approximately 400 tries if you need a roll of '20'. Bonuses and penalties don't really change the shape of the distribution of a roll much, but they do make you capable of succeeding at things that would be impossible otherwise, or incapable of succeeding at a task you otherwise would not have trouble with.
• Because the effects of Advantage/Disadvantage are non-linear, they function very differently from bonuses on checks with more than 2 possible results. For example, failing a disarm attempt on a trap by less than 5 often does not trigger the trap, while failing it by 5 or more will cause the trap to trigger. For checks like these, which often have extreme consequences for a high-margin failure, PCs will often not attempt the task without very high odds of success. Usually, this means that disadvantage only matters if the player achieved those high odds by acquiring advantage. Typically needing numbers at the margins of the d20 roll, both advantage and disadvantage are less valuable than bonuses here. Alternatively, on checks with many results but no serious consequences for failure like most History checks, advantage makes it quite likely, typically, that an adventurer knows at least most basic knowledge about a topic while a bonus means an adventurer is comparatively somewhat more likely to hit a very high DC.

Answer 3

It depends

If a -2 or disadvantage is worse will depend entirely on what the scenario is. For starters, is it a skill check/saving throw or is it an attack? A 20 on an attack roll is always a hit because of it being a critical, but this is not true for other checks.

So some examples:

I am attacking Bob the Knight and I need a 20 to hit.

Here, disadvantage is clearly worse, because my chance of rolling a 20 will go down, while a -2 to hit would make zero difference, I already needed a 20 anyway.

I am attacking Bob the Mage and I need a 2 to hit.

With a -2 I would need a 4 to hit. With disadvantage, I would need to not roll 1 on two dice. The chance that I roll a 1-3 on a dice is 3/20 = 15% chance. The chance that I roll a 1 on two die is 39/400 = 9.75% (see here for an explanation). In this case, it is better to have disadvantage because the chance to fail is less with disadvantage than with a -2 on the roll.

I am picking a very difficult lock and I need a 20 to succeed.

This is different from the attack scenario, because in this case, a 20 is not a guaranteed success. The moment I get -2 on my dice roll, I can no longer succeed at all! (Unless you're using a commonly used houserule that skill checks can also crit and always succeed, but this is not actually RAW.)

In this case, disadvantage would obviously be vastly superior, a chance of rolling 20 on both die is clearly higher than the chance to roll 22 on a single 20-sided dice.

In general, disadvantage tends to be worth around -5 is the common 'shorthand' for how bad disadvantage is, but it clearly depends on the circumstances. In some cases, even a -1 will make a roll completely impossible.

There are even compiled tables that compare this sort of problem, using a roll you need to hit (the DC) to how much of a penalty that roughly equals to:

DC 2 = Disadvantage = -0.95 to hit

DC 5 = Disadvantage = -3.2 to hit

DC 10 = Disadvantage = -4.95 to hit

DC 11, Disadvantage = -5 to hit

DC 12, Disadvantage = -4.95 to hit

DC 13, Disadvantage = -4.8 to hit

DC 14, Disadvantage = -4.55 to hit

DC 15, Disadvantage = -4.2 to hit

DC 16, Disadvantage = -3.75 to hit

DC 17, Disadvantage = -3.2 to hit

DC 18, Disadvantage = -2.55 to hit

DC 19, Disadvantage = -1.8 to hit

DC 20, Disadvantage = -0.95 to hit

TL;DR: In general, disadvantage is worse than -2 to hit, but there are edge cases.