I've only recently started playing with a dedicated group, and I kept thinking that Advantage was about the equivalent to a +5 (and disadvantage equiv. to a -5 ) But I started getting very curious about it. What is it really?
The boring explanation:
Around this same time I was wondering about creating a "skill monkey" character and this would be very useful to know for it. So I simulated it (almost). I'm fairly comfortable with Excel and other spreadsheet applications. I created a roll table of d20 results. 1 - 20. Done. We'll call that Die1. Now I need to know about Die2. For each result of Die1 I need to have a Die2 result of 1-20. Okay, this means that I'm now analyzing results from 400 possible dice roll combinations.
For the Advantage, I need to look at the maximum between Die1 and Die2.
For Neither, I'll just look at Die 1 results.
For Disadvantage, I need to look at the minimum between Die1 and Die2.
More math
With this "bounded accuracy system" I decided to ignore the + and - modifiers. We can use algebra to say that rather than:
d20 roll + Mod >= DC
we can say that
d20 roll >= DC - Mod
The results:
When the DC-Mod is at 11, that's the greatest difference. 25% between having Advantage and Nothing. And a further 25% between having Nothing and being at Disadvantage.
With 5% equal to +/- 1, my initial assessment is showing to have some merit.
But then the other results start jumping out at me.
50% Success Rates
When Disadvantaged, you have a 49% chance of success at a DC-Mod of 7.
With Nothing, you have a 50% chance of success at DC-Mod of 11.
With Advantage, you have a 51% chance of success at DC-Mod of 15.
That shows that it's only a +/- 4 between the breakpoint of 50%.
Quite the Slope
Supporting the above discovery, we see that because of the breakpoint locations, we either slow down our failure rate or speed it up.
While advantaged, there is no real difference in our success rates, until DC-Mod > 15. And that stands to reason. If DC - Mod >20 (i.e. 21 or higher) it is almost impossible to achieve on just a d20 roll. Therefore we need to lose 51% success in just 6 steps of DC - Mod.
This is the opposite while disadvantaged. We lose 51% in the first 6 DC-Mod values. Beyond that, the remaining 49% success rate changes comparatively little amongst the remaining 14 DC-Mod values.
Averages
What does the above discoveries actually mean?
And this is what surprised me. Across all possible DC's the averages show that I "should" succeed:
Mathematically I bottom out at only a +/- 3 for being Advantage or Disadvantage.
But I must admit, having Advantage and seeing one of the die rolls show a 1, or being at disadvantage and seeing a 20, really makes this feel worse at those moments in time.
The boring explanation:
Around this same time I was wondering about creating a "skill monkey" character and this would be very useful to know for it. So I simulated it (almost). I'm fairly comfortable with Excel and other spreadsheet applications. I created a roll table of d20 results. 1 - 20. Done. We'll call that Die1. Now I need to know about Die2. For each result of Die1 I need to have a Die2 result of 1-20. Okay, this means that I'm now analyzing results from 400 possible dice roll combinations.
For the Advantage, I need to look at the maximum between Die1 and Die2.
For Neither, I'll just look at Die 1 results.
For Disadvantage, I need to look at the minimum between Die1 and Die2.
More math
With this "bounded accuracy system" I decided to ignore the + and - modifiers. We can use algebra to say that rather than:
d20 roll + Mod >= DC
we can say that
d20 roll >= DC - Mod
The results:
When the DC-Mod is at 11, that's the greatest difference. 25% between having Advantage and Nothing. And a further 25% between having Nothing and being at Disadvantage.
With 5% equal to +/- 1, my initial assessment is showing to have some merit.
But then the other results start jumping out at me.
50% Success Rates
When Disadvantaged, you have a 49% chance of success at a DC-Mod of 7.
With Nothing, you have a 50% chance of success at DC-Mod of 11.
With Advantage, you have a 51% chance of success at DC-Mod of 15.
That shows that it's only a +/- 4 between the breakpoint of 50%.
Quite the Slope
Supporting the above discovery, we see that because of the breakpoint locations, we either slow down our failure rate or speed it up.
While advantaged, there is no real difference in our success rates, until DC-Mod > 15. And that stands to reason. If DC - Mod >20 (i.e. 21 or higher) it is almost impossible to achieve on just a d20 roll. Therefore we need to lose 51% success in just 6 steps of DC - Mod.
This is the opposite while disadvantaged. We lose 51% in the first 6 DC-Mod values. Beyond that, the remaining 49% success rate changes comparatively little amongst the remaining 14 DC-Mod values.
Averages
What does the above discoveries actually mean?
- Having either Peaks out at a +/- value of 5 when the DC-Mod is at 11 needed for the die roll.
- The breakpoint (around 50% success rates on the die roll alone) shows a +/- of 4.
- One extreme or the other show either a substantial drop or virtually little.
And this is what surprised me. Across all possible DC's the averages show that I "should" succeed:
- 65% of the time while I have Advantage
- 50% of the time with neither (my baseline really)
- 35% of the time while at a Disadvantage
Mathematically I bottom out at only a +/- 3 for being Advantage or Disadvantage.
But I must admit, having Advantage and seeing one of the die rolls show a 1, or being at disadvantage and seeing a 20, really makes this feel worse at those moments in time.
