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Under the Hood: A Look at Advantage Versus Bonus to Hit

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Bedrockbrendan:
BY RICK MOSCATELLO

Dungeons and Dragons 5E has introduced a relatively new mechanic: “Advantage”. Before this edition, having some sort of advantage usually just meant a bonus to the roll, usually +2 or +4 in exceptional cases. But now we have Advantage, where you roll two dice and take the higher roll. Let’s compare Advantage to the more common bonuses, +2 or +4 to hit:

Column 1: Unmodified die roll needed to hit (we’re going to focus on combat here, so a 1 always misses, and a ‘natural’ 20 always succeeds).

Column 2: Chance of succeeding with unmodified roll (i.e., the chance of rolling the needed number, or higher).

Column 3: Chance of succeeding with advantage.

Column 4: Chance of succeeding with +2.

Column 5: Chance of succeeding with a +4.

.cus td{border:1px solid #cccccc; overflow:hidden; word-break:normal;}123*45295%99.8%95%95%390%99%95%95%485%98%95%95%580%96%90%95%6**75%94%85%95%770%91%80%90%865%88%75%85%960%84%70%80%1055%80%65%75%1150%75%60%70%1245%70%55%65%1340%64%50%60%1435%58%45%55%1530%51%40%50%1625%44%35%45%1720%36%30%40%1815%28%25%35%1910%19%20%30%20***5%9.75%5%5%


[SIZE="2]*= Rounded to the nearest whole percent, except in cases where such rounding might cause confusion.
**=note that this is an edge case where the +4 to hit is superior than Advantage, due to the “a roll of 1 is always a miss” giving no benefit to the bonus on lower rolls. If a 1 could hit, the bonus would be useful if you needed to roll lower than 6, and this little edge case would disappear amongst all the previous 100% chances of hitting.
***= here I’m assuming a natural 20 is needed to hit; if not, the chances for bonuses are 15% and 25%, respectively.[/SIZE]
     
Looking at the chart, it’s clear that Advantage is very similar to a +4 to hit, with the differences in this case being small until you get to the extremes.
     
In more recent editions of D&D, if a player is in such a terrible situation in combat that he needs to roll over a 20 to hit (against, apparently, a creature with an armor class well above 30), the rules allow for it: a “natural 20” (a 20 is rolled on the die, without modifiers) is automatically a hit.
     
In Advanced Dungeons and Dragons (published 1977) there was a big difference between “need a natural 20 to hit” and “needing a 21 to hit”. In the latter case, a player couldn’t hit if he rolled, say, a 19, and had a +2 bonus. Instead, he would need to roll a natural 20, and then also have at least a +1 modifier. It was thus possible for some creatures to literally be un-hittable in combat. This was more of a theoretical thing—once characters passed around 5th level, only AD&D’s Will o’ Wisp had an armor class low enough that this was likely, and this creature very seldom appeared (it didn’t really live in dungeons, and was in no way related to dragons, after all).
     
Ultimately, study and comparison of bonuses and Advantage is just theory-craft. You’re always going to want Advantage, you’re always going to want bonuses to hit, you’re always going to take both if you get the chance. The only thing shown here is that Advantage is always better than +2 to hit, and that if you get a choice, you’ll often take Advantage over +4 to hit, unless you need a 6, 16, 17, 18, or 19, but not a natural 20. I don’t see this choice coming up anywhere in the 5E rules, but, hey, people read articles online to find those edge case advantages, right? I’ll let the interested reader make the comparison to +3 to hit.

Spinachcat:
Thank you BB for this great analysis!!!

I am not 5e fan, but its great to see the math of the concept.

Bedrockbrendan:

--- Quote from: Spinachcat;778513 ---Thank you BB for this great analysis!!!

I am not 5e fan, but its great to see the math of the concept.
--- End quote ---


I just want to clarify. This is not a piece I wrote. It was written by Rick Moscatello who submitted the the article to us. Because only mods can post in the article sub forum, we will be the posters, but each article has an Author tag with the name of the writer.

Thanks for the feedback though. There will be more articles coming during the week.

The Butcher:

--- Quote from: BedrockBrendan;778529 ---I just want to clarify. This is not a piece I wrote. It was written by Rick Moscatello who submitted the the article to us. Because only mods can post in the article sub forum, we will be the posters, but each article has an Author tag with the name of the writer.

Thanks for the feedback though. There will be more articles coming during the week.
--- End quote ---

Who's Rick Moscatello? Is he a poster here?

A little "About The Author" might make for a neat addition.

I'm working on that article, BTW.

Bedrockbrendan:

--- Quote from: The Butcher;778539 ---Who's Rick Moscatello? Is he a poster here?
--- End quote ---

I can only provide whatever information the author sends with the article. In this case, the author's name.


--- Quote ---A little "About The Author" might make for a neat addition.

I'm working on that article, BTW.
--- End quote ---

I like About the Author as something to end the article with. I will see about adding this in for future articles.

We are trying to reduce confusion with the writer names and looking into possibilities. For now, what I can do is put the name of the author in the post itself so it is clearly visible. I will go back and edit all the existing articles so they appear this way.

Looking forward to your article!

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