D&D General Video on the math behind advantage (and Elven Accuracy)

[Charlaquin]

Just had this video pop up in my recommended feed and thought some folks here might appreciate it.



Summary: Mathematician works out the average result of an unmodified d20 roll with advantage (turns out its 13.833), then extrapolates to create a formula for doing the same for a die with any number of sides. Then does the same for roll 3 and take the best - functionally elven accuracy (for d20s it’s about 15.5). Then further extrapolates for taking the best of any number of rolls.

Interesting stuff, but I think we can all agree that the most valuable takeaway here is that the average result of rolling an infinity sided die with advantage is 2/3 (roughly 0.667).

 

[doctorbadwolf]

Man 13.8 is lower than you’d think reading folks talk about advantage being a big deal.

 

[CharlesWallace]

Just had this video pop up in my recommended feed and thought some folks here might appreciate it.



Summary: Mathematician works out the average result of an unmodified d20 roll with advantage (turns out its 13.833), then extrapolates to create a formula for doing the same for a die with any number of sides. Then does the same for roll 3 and take the best - functionally elven accuracy (for d20s it’s about 15.5). Then further extrapolates for taking the best of any number of rolls.

Interesting stuff, but I think we can all agree that the most valuable takeaway here is that the average result of rolling an infinity sided die with advantage is 2/3 (roughly 0.667).

Wow- he’s really charismatic! That was a great video. I lasted until hypercubes and then had to bail. I’m barely functional in a 3D world. Try as I might, I can’t grok 4D!

 

[Olaf the Stout]

I love Matt Parker. He's awesome.

 

[Rune]

I love Matt Parker. He's awesome.

His stand-up is pretty good, too. If you’re into spreadsheets.

 

[Blue]

I need to watch the video (but doubt I will clear half an hour to do so tonight), but don't get confused about what average means with a non-normalized distribution. Especially when your end-goal is just a boolean pass/fail for a threshold.

There's a 51% of rolling a 15 or higher. There's a 75% chance to roll a 10 or higher. Considering the rolls needed to hit, those are pretty impressive.

So if you normally have a 65% chance to hit (8+), you now have an 84% chance to hit. But if you applied GWM and now had a 40% chance to hit (13+), with advantage you have a 64% chance to hit. Basically offset the entire -5 penalty.

Chance to roll the target number or higher on a die.

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

 

[Charlaquin]

Man 13.8 is lower than you’d think reading folks talk about advantage being a big deal.

Well, that’s just the mean, which is far from the whole story. For example, this also demonstrates that 20 is the mode! (or for folks who don’t speak math, the most likely result). The overall impact of advantage depends on what number you need on the d20 to succeed, and it’s at its most impactful when you need a 10 or 11. That’s where it’s actually worth the “about +5” people often shorthand it to. The further your target number is above or below that, the less Advantage matters.

 

[Blue]

Well, that’s just the average result of an unmodified advantage d20 roll. How much of an impact advantage has depends on what number you need on the die to succeed.

This is very true, but with bounded accuracy the threshold of what you need to roll usually is closer to the middle that 1 or 20 - and that's where you have the biggest gains. 6-14 as your target numbers have bigger improvements than 1-5 or 15-20.

 

[Charlaquin]

I need to watch the video (but doubt I will clear half an hour to do so tonight), but don't get confused about what average means with a non-normalized distribution. Especially when your end-goal is just a boolean pass/fail for a threshold.

There's a 51% of rolling a 15 or higher. There's a 75% chance to roll a 10 or higher. Considering the rolls needed to hit, those are pretty impressive.

So if you normally have a 65% chance to hit (8+), you now have an 84% chance to hit. But if you applied GWM and now had a 40% chance to hit (13+), with advantage you have a 64% chance to hit. Basically offset the entire -5 penalty.

Chance to roll the target number or higher on a die.
View attachment 252477

AnyDice

AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.

anydice.com

Oh, yeah, absolutely. The mean is actually not all that useful to know in the context of D&D. Which is why the person who asked him the question did so in the first place - all the data they were actually able to find online was specifically about D&D, so it was all spreadsheets and graphs that show how various bonuses and target numbers are affected. But they just wanted to know what the mean was and couldn’t find it anywhere.

 

[Charlaquin]

This is very true, but with bounded accuracy the threshold of what you need to roll usually is closer to the middle that 1 or 20 - and that's where you have the biggest gains. 6-14 as your target numbers have bigger improvements than 1-5 or 15-20.

Yeah, I edited my post to clarify that.