There are a lot of people talking about the D&D Next open playtest, and one of the subjects I hear about a lot is the way Advantage/Disadvantage are currently working. The general opinion I’ve heard is that it is overpowered when compared to the +2/-2 bonus we’re used to from previous editions of D&D. My gut reaction to hearing that something is overpowered isn’t to jump into the mob and swing my nerf-bat around, it’s to look at as much data as I can and figure out if I agree or not. So that’s what I’m going to do!
Disclaimer: I am not a professional statistician, though I do a lot of analysis and number-crunching for my day job and both of these things are something I somehow enjoy doing. If you are a professional statistician, or love statistics, please leave a comment here and let me know if you agree/disagree with what I’m presenting! I’m open to the possibility that I’m working on false assumptions about math/statistics or that I’ve made a mistake somewhere in my processes. For most of my calculations I used math from the excellent site Anydice.com.
If you’re not familiar with what I’m talking about for the open playtest rules on Advantage / Disadvantage, they involve rolling 2d20 and taking the highest or lowest (respectively) of what you roll. My instant, gut reaction to this rule was “Ugh, more dice to roll? No thank you!” However, when you combine it with the idea that Wizards of the Coast is trying to reduce the number inflation in D&D and that these new rules keep the numbers rolled between 1 and 20 but change the odds of success or failure in interesting ways then I was thoroughly convinced.
Just to get some basic statistics out of the way, if you’re rolling a single d20 then your odds of rolling any one number are 5%. Therefore, in D&D you are trying to roll equal to or higher than a target number so your chances for rolling a 10 or higher are 55% and your chances for rolling a 15 or higher are 30%. Basic, I know, but I just have to lay down the framework. I find the 2d20 (highest/lowest) rule very interesting because it increases your odds of rolling a 20 (highest) or a 1 (lowest) from 5% to 9.75%. For further comparison, with 2d20 (highest) you have a 51% chance or rolling a 15+ and an 79.75% chance of rolling a 10+. You might be tempted to compare it to a single d20 roll, but what this really needs to be compared to is a flat +2 bonus that Combat Advantage gives in 4th Edition.
The crucial difference between the highest/lowest of two dice and a flat bonus is that with a flat +2 bonus your range of rolls goes from 1-20 to 3-22. With a +2 bonus your odds of rolling a 20+ go up to 15%, which is a decent amount higher than the 9.75% from Advantage. Just one step up, to a target roll of 19+, and a +2 bonus is at 20% while the Advantage rule is only slightly lower at 19% (9.75% chances of a 20, 9.25% chances of a 19). Here is a full comparison (with better option highlighted in green):
As you can see, unless your target number is between 1-3 and 19-20, then 2d20 provides up to a 15% better chance of success (at a target of 11+). If you take the numbers and compare them to an array of flat bonuses (+2, +3, +4, and +5) you get the following results:
What you can see from this data is that it would take a +5 flat bonus to a d20 roll to make it universally better than Advantage, and even then if your target is a 11+ the odds of success are exactly the same (75% for both). However, before I take these results and decide that I agree that Advantage is overpowered, let’s look at what is happening on the edges of the scale. Let’s say you’re facing a monster that is heavily armored and has an Armor Class of 19. With Advantage I have a 19% chance of hitting and with a +2 bonus I have a 20% chance, not much of a difference there. Even though Advantage is better than a +4 bonus on targets between 7 and 15, with a +4 bonus you would have a 30% chance of hitting an AC 19. What I’m starting to really like about the idea of Advantage/Disadvantage is that it preserves the highest numbers of 19 and 20 as difficult results to achieve while still keeping numbers in the 1-3 range as possible (though unlikely) results.
The next crucial consideration for whether or not the Advantage rules are overpowered (or unbalanced, take your pick) is to look at Disadvantage (2d20 and take the lowest roll) and how it compares to taking a -2 penalty on a roll:
What we see here is that it is actually better to have a -2 penalty on a roll when your target is between 4-18. That’s not too surprising considering we’re dealing with the same math, but what this means is that when taken as a complete rules package, Advantage and Disadvantage may actually balance each other out in addition to the other benefits of keeping the 1-20 range in tact and the dynamic changing of odds across the possible results. It also avoids the issue of having a 15% chance of rolling a 1 (much higher than any other roll due to the -2 penalty).
To put it another way, if your target to beat with your roll is between 7 and 15, you would actually be better off taking a -4 penalty than taking Disadvantage on the roll (even with the 25% chance of rolling a 1 that the -4 penalty causes). This is a very important consideration for us to keep in mind as we discuss, playtest, and provide feedback on these rules for D&D Next. In discussing this topic with a few of my players, something else that I am starting to like about the idea of rolling a second d20 is that when you already have one or more modifiers applying to your roll, it can be a lot easier to just roll extra dice than it is to remember a handful of different conditional modifiers. The more I think about it, the more I’m starting to really like what the Advantage/Disadvantage rules are doing with the math of D&D.Photo Credit: MegaBee
Special thanks to Joshx0rfz for helping me out with this post.