Chances on ability checks don't seem to add up

Question

I'm going through the Dungeon Master's Guide, and I see that DCs should be based on the "average person". What I'm having a hard time with is that if someone has a +5 modifier to their History checks (quite knowledgable), and the task is "hard" (DC 20), then they still only have a 1/4th chance of success.

It seems to me the chances don't quite add up.

Do I have this correct? How can I (or should I?) express that a person who doesn't know History has no chance of passing a History check, but a historian should probably have a better than 1/4th chance.

I am a player now, but wish to be a DM in the future.

I guess my bigger issue is the difference between an average person and someone who is well-trained. Someone with a 0 in Arcana has a 25% chance of success against a "medium" (DC 15) task. Where as someone well trained in magic (+5 modifier to Arcana checks) has only a 50% chance. That seems quite out of whack to me.

Answer 1

Firstly, a check with a DC of 20 is a really hard check to complete. To use real world history, asking who shot President John F. Kennedy (or allegedly shot) would be a DC of about 10. Asking what kind of rifle and ammo he used would be a DC of 20.

Secondly, the numbers aren't as bad as you imply. Bardic inspiration and the guidance spell can help give a bonus to the history check (providing you have the right party members). These are available at level 1. Once you reach level 3 the party may have access to the enhance ability spell which can give advantage on the saving throw.

Thirdly, a bonus of +5 to the roll would be typical for a very low level character. Once the character has leveled up a bit that number will improve. For example, a level 13 wizard would expect to have a +5 intelligence modifier and would have a +5 proficiency bonus. Assuming they are proficient in history, the odds of them knowing some obscure piece of information a 50% chance at least.

Fourthly, the sage background allows a character to know where they might be able to track down a piece of information.

Finally, if such information is important to the party then there should be an option for them to find it out. Point them in a the direction of a sage or a library and has them perform some minor quest to obtain it.

Answer 2

Any character can attempt to pass an ability check

But nobody is guaranteed a success or a failure. It is useful to recall that an ability check only is attempted when the DM calls for a check because "something is going on" and there is a need to determine "what happens next" as a result of a character trying to do something.

Ability Checks
An ability check tests a character’s or monster’s innate talent and training in an effort to overcome a challenge. The DM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.

That part up there will be important to remember when you are a DM.

For every ability check, the DM decides which of the six abilities is relevant to the task at hand and the difficulty of the task, represented by a Difficulty Class. The more difficult a task, the higher its DC. The Typical Difficulty Classes table shows the most common DCs.

What proficiency and expertise offer is a higher chance to succeed on any given check.

There may be an occasion that a DM will assign a very high DC (like 25) and if someone wants to try it alone, the DM can advise them that it's too hard for them. But see below (the section on skew the odds in the character's favor) on how you can make success more possible by using Help, Guidance, Advantage, or Bardic Inspiration to put the odds more in the character's favor.

Do I have this correct? How can I (or should I?) express that a person who doesn't know History has no chance of passing a history check

Since you aren't a DM you don't have to, but since you want to be one let's walk through this ahead of time.

1. There is no gating of "you can't even try" as implied in your question.

   It's not a matter of not knowing, or knowing, history: it's a matter of how much history a given character knows or remembers. @Alan Mills' answer gives a nice example that I'll not repeat here. History is an Intelligence ability check (PHB, Chapter 7, Using Ability Scores; read the whole thing). According to Chapter 7,

   Intelligence, measuring reasoning and memory

   We see in the Chapter 1, description of abilities ...

   Intelligence Measures: Mental acuity, information recall, analytical skill (Basic Rules, p. 10)

   What is being measured is the chance that a character recalls or knows something.

How do I make sense of this as a new player?

Since you say that you are new to D&D in your comment, you don't have any real points of comparison to base your intuitive grasp upon.

@KorvinStarmast im brand new to DnD I know jack about other editions...

What you are running into is an expectations mismatch between the game and your experiences with life, and what terms mean in normal conversation. That's fine. The ability / skill system for this edition of the game has puzzled plenty of us who have been with the game for a few editions. There are a lot of questions about skills and abilities on this Q&A site, and on forums/discussion sites for this game. In a nutshell, it is a matter of comparative difficulty, not absolute difficulty.

Being proficient in History does not make a character a Historian

All it makes the character is better at history checks than another character who isn't proficient.

Having expertise in history would be closer to "being a historian"

Even though that's still an awkward mapping of real life meanings to game mechanics meanings, let's look at what expertise does since it doubles a proficiency score.

• Expertise is a Rogue class feature, but the doubling of a proficiency bonus crops up in a number of other places in the game via other features.

Let's apply this idea to your +5 bonus to History checks example. That bonus does not exist in a vacuum. Someone had to choose to assign points to Intelligence to get that score as a beginning character.

At first level, this character is already out of the ordinary. They need a 16 Intelligence (+3 to Int based checks) and Proficiency in History to get that +5.

A commoner has an intelligence of 10 (+0 bonus to the roll), and an average player character has an intelligence of about 12 (+1 bonus to the roll) if you roll up your character using the 4d6-keep-the-best-3-dice, method. (Chapter 1, p. 9)

Without proficiency that 16 Intelligence character has a +3 to History checks. With proficiency the character has a +5. With expertise the proficiency bonus is doubled, so History checks are made with +7. That's closer to "expert/historian".

Let's raise that character to level 5 and thus have a proficiency bonus of +3. (see the table on Tiers of Play, PHB p. 17, Basic Rules p. 12). +3 for Int, +3 for Proficiency, +3 for expertise (double proficiency) and now you have a +9 ... versus the commoner with a +0 and the average adventurer who has a +1. The commoner doesn't know no history, he just doesn't remember a lot of history.

By the way, the percentages that have you so concerned ... don't actually matter. Each roll of the dice is its own instance, and the d20 system is kind of swingy that way. If you have +9 and roll a 2, you still fail that DC 15 check. A given roll of the dice doesn't care what the odds are. Also, a DC of 15 means "roll equal too or greater than 15."

You have your probabilities slightly skewed: the probability of rolling 15 or more on a d20 is 30%, not 25%. ~@kviiri in a comment

How important is this history check?

In Chapter 7, the rule is that unless success or failure is significant, it isn't necessary to roll. The DM just narrates the outcome. This is true with any ability check.

• Here's the "Prepare you to be a DM" piece: you don't even have to roll if knowing or not knowing something doesn't make a significant impact on a player character decision or situation.

Skew the odds in the character's favor by using class features

1. Find ways to get advantage on the roll for the ability check. That boosts your odds of success from about a +3 to a +5. If you look in Chapter 7, you find that getting Help from a fellow character gives your character advantage.
   Working Together

   Sometimes two or more characters team up to attempt a task. The character who’s leading the effort—or the one with the highest ability modifier—can make an ability check with advantage, reflecting the help provided by the other characters (Basic Rules, p. 62)

2. Have your party cleric (or druid) cast guidance (a cantrip) on the character. That adds from 1 to 4 to the roll.

3. Ask the bard for bardic inspiration; that adds 1 to 6 to the roll at first level.

   And now we see how a commoner with an Int of 10 can have a good chance to make that DC 15 roll (using averages): +4 from Advantage if they get help, +2.5 from guidance, and +3.5 from a bard's inspiration. That's a +10 on a d20. They have a slightly better chance to recall that historical factoid than the 5th level character whose expertise gave them +9. The commoner's Target Number is 5, and the "expert's" target number is 6. (TN meaning "that number or higher and I pass the check).

The second half of this answer by @NeilSlater is a fine explanation of how to make the ability check, and the contest rules that are in Chapter 7, work when you are a DM.

Answer 3

It's not as bad as it sounds!

A 1 in 4 chance of succeeding does seem like low odds of success for an expert in the field, but keep in mind that your character will grow!

So, your character has a +5 to history checks! That's actually pretty easy to get, even at level 1. Just start with 16 or 17 points in INT (easy with point buy or standard allocation, not unusual when rolling for stats), and start with proficiency in History.

A 16 or 17 will give you a +3 modifier to related skills and abilities. Your proficiency will give you an additional modifier equal to your proficiency bonus, which is +2 for a level 1 character. And that gives your +5 bonus! Yeah, this does still give you a 1/4 (25%) chance of success on a DC 20 check, but let's compare that to a more "average" history modifier.

A stat of 10 or 11 is often considered to be represent of a perfectly average trait, not remarkable for being either stronger or weaker than the normal human, so this is what the "average" individual would have. A 10 or 11 gives a +0 modifier, so no bonus there. Additionally, the average person is probably not a trained historian, so we can't add their proficiency bonus either.

The result is that the "average" history check would be 1d20+0, giving them a 1/20 chance (5%). Compare this to the level 1 character described above, and that character already has five times the success rate of the typical individual!

Don't forget that your character will get better at it!

As your character levels up, they will get better at what they do. Classes typically get the option to improve their stats or take a feat at 4th, 8th, 12th, 16th, and 19th levels, and these improvements can affect your skill checks! So let's take that same character, but at level 4.

Let's assume that your character has reached level 4, and you decide to put both points into INT (not uncommon if your character's a wizard). Their INT stat has now gone from a 16 (+3 mod) to an 18 (+4 mod)! Consequently, they now only need a 14 to succeed on the DC 20 history check! That is, they now have a 3/10 (30%) chance to succeed!

Let's put that same character at level 5!

At level 5, a character's proficiency bonus increases from +2 to +3. Keep in mind, this is character total level, not class level, so multiclassing does not affect this!

Assuming your character put those two points into INT earlier, they now have a +7 modifier to their history check! That's +4 INT modifier and the +3 proficiency bonus! You now have a 35% chance of success!

This of course will only get better as you level up. Assuming you put two more points in INT somewhere along the way and level high enough, you can maximize your chance of success by level 17! At that point, you can easily have 20 INT (+5 modifier even without proficiency) and will have a +6 proficiency bonus, giving you a +11 total modifier to history checks! That is, you now have a 55% chance to succeed on a DC20 check!

But we haven't even looked at other factors!

Level and proficiency aside, there are other ways to improve your chances! For example, Bardic Inspiration allows a bard to give you an additional die to add to any one ability check, attack roll, or save roll you make within the next ten minutes! I don't want to do the math right now, but suffice to say that a minimum bonus of one and an average bonus of 3.5 (at lower bard levels) improves an individual check's success rate more than the static +1 bonus from leveling up once.

There are other ways to improve your chances too, such as finding a way to give your character advantage on your roll! This will let you roll two D20s for the skill check and let you use the higher one, getting rid of the lower one! This is somewhere in the neighborhood of a +5 modifier as far as success odds go, although that varies a lot based on how far off your chances were to begin with. There are situations where one is significantly more beneficial than the other, but that's a very contextual thing and is probably off topic.

TLDR: It's easy to improve those odds, and your character will naturally do so as they level up

Answer 4

Yes, you have this correct

In comparison to the previous editions, 5e has its "bounded accuracy", that means bonuses you get from levels are not so big as they used to be. In terms of combat, this is intentional.

In terms of ability checks, as the DM, you are free to choose. The system does not decide, how competent the characters are — it's up to you to decide. See DMG page 236 "The Role of Dice":

Dice are neutral arbiters. They can determine the outcome of an action without assigning any motivation to the DM and without playing favorites. The extent to which you use them is entirely up to you

Some DMs rely on die rolls for almost everything.

One approach is to use dice as rarely as possible. Some DMs use them only during combat, and determine success or failure as they like in other situations.

Let's take your example:

Someone with a 0 in Arcana has a 25% chance of success against a "medium(dc15)" task. Where as someone well trained in magic (+5 arcana) has only a 50% chance.

How can I express that a person who doesn't know History has no chance of passing a history check

If you want to say, that an average person with zero Arcana knowledge can't know this with this huge 25% chance; on the other hand, a well-trained person should probably know the same thing for sure, you are free to do so. As the DM, you don't have to ask players for ability checks for everything they do. Just declare what do you think would be reasonable.