Most tabletop roleplaying game systems have the concept of rolling dice as a way of determining whether a player character in the game succeeds or fails when attempting a non-trivial task. A die roll doesn't itself have any meaning. A 20 on a 20-sided die is just a number, no better or worse than a 1, or a 6, or a 6 on a 6-sided die. It's up to the game to define what the number of success is, and many game systems leave it up to the Game Master to make that determination. I don't think forcing the Game Master to set target numbers (DC, or Difficulty Class, in D&D) is great game design, and in this blog post I introduce some alternative methods.
In D&D rules-style games, a difficulty class (DC) must be set by somebody, whether it's the Game Master or the author of a published adventure. Players roll die and add bonus numbers in an attempt to reach that number.
There's usually a table in a Game Mastery guide explaining reasonable settings. It's usually something like 5 for something easy, 10 for something requiring effort, 15 for something requiring specialized skill, and 20 for something highly improbable. But this leaves a lot open to subjectivity when you try to map actual tasks to that kind of chart. Is swimming easy? What about swimming all your gear on? Swimming with boots on? What about riding a horse? What about walking a tightrope? On the one hand, there's the argument that the people of your fantasy world would find some of those things commonplace, so maybe DC 5? On the other hand, a lot of these tasks in a game are performed under duress, so maybe DC 10 is better? Or maybe it should be DC 15 because the alternative, in many cases, is death, so you have to assume a player character is giving it their all.
As a Game Master, I don't know what a "reasonable" DC is for most actions. Given enough variables, I can usually find justification for anything to be DC 20. That doesn't make for a very fun game, though, so for the sake of moving the story forward, I can just as easily justify DC 5 for basically anything.
None of the other players at the game table have to make that kind of decision. Sure, every player has to make difficult choices, but it only directly affects their own character. Admittedly, a cleric choosing not to spend an action to heal someone can have an affect on another player's character, but it was the group's collective decisions that anyone requires healing in the first place. The Game Master has a lot of choices to make about the world, and that's the Game Master's role. But only the Game Master is in a position of receiving input from other players, and making a completely subjective decision on its merits. Only the Game Master is asked to produce an arbitrary constraint governing whether another player gets to do the thing they've declared they want to do.
This kind of modeling is, I think, partly why the modern Game Master is sometimes understood to be a different kind of player than everyone else at the table. In extreme (but not uncommon, in my experience) cases, the Game Master is seen as the master of ceremonies, the host, and main performer. The game belongs to the Game Master, and the players are just visiting.
That may work for some Game Masters and gaming groups, but it's not the kind of game I'm interested in. As a Game Master, I'm just another player. The only difference is that I manage monster stat sheets instead of character stat sheets, and I manage the world's backstory instead of a character's backstory. I don't invent numbers governing what it takes to hit somebody with a sword. Those numbers are mathematically derived, and they're written down on the stat sheets. And so should the numbers for succeeding at a skill-based task.
There are a few systems out there that have managed to transcend the requirements of setting a target number or difficulty class. They work like this:
For example, suppose you build a rogue in an imaginary RPG system. You envision your rogue as a thief, so you invest 10 points in the Lockpick skill, and just 5 points in acrobatics. During the game, your thief must walk across a makeshift tightrope into a tower chamber. Your Game Master tells you to roll to walk the tightrope, and you roll a 7. You needed 5 or less to succeed because you have 5 skill points in acrobatics, so that's a failure. The Game Master says the tightrope snaps. You manage to grab onto the rope and climb into the chamber, but the noise has alerted the guards. They're on their way.
In the chamber, you find a locked treasure chest. This is what you're here for. You have 10 points in Lockpick, so you need to roll 10 or less. You roll to pick the lock, and you roll a 7 again. Success! You pick the lock and climb the rope down the side of the tower before the guards even get into the room.
That's an exciting scenario with no arbitrary target numbers from the Game Master. The only time the Game Master intervened was to rescue the player character, and frankly the Game Master didn't have to do that. A different Game Master might have required a dice roll to determine whether the rogue was agile enough to grab onto the tightrope before falling to their death. It's an elegant way of deciding success, and it's a matter between just the player's choices and their dice.
For some great examples of this system, take a look at the Blue Planet and Imperium Maledictum games.
You can try threshold numbers in your Pathfinder or D&D game. In D&D 5e (or Tales of the Valiant, assuming you've migrated away from Wizards of the Coast), double the proficiency bonus and treat the total bonus to roll as the threshold number. In Pathfinder, just treat the bonus to roll as the threshold.
For example, a 1st level character in Tales of the Valiant might have +2 from an attribute (such as DEX or INT) and a +2 proficiency bonus on the character sheet. Double proficiency for a 6 (4+2) threshold, which is a 30% of success.
With no DC in any Wizards of the Coast adventure I've ever seen exceeding 25, characters end up with at least a 50% chance of success by level 10. That's assuming they've got some magic items that provide boosts. With the Help action and Guidance or Bless spell, the chances are actually a lot higher.
By 10th level using a threshold number, a Tales of the Valiant character with a 10 bonus has a threshold of 15 (65% chance of success). A bonus of +12 is a 17 threshold (85% chance of success).
Yes, the percentages get stupidly high. If it's too high for your style of game, then don't double the proficiency bonus when calculating thresholds (and also, you're not running Tales of the Valiant as written).
Whether you use threshold or target numbers, the fact of tabletop RPG is that success is the actual default setting. For an RPG to continue, the player characters have to ultimately succeed, or they tend to die. Or they fail and the world adjusts around them to create a new game plot. Either way, skill tests aren't actually deciding the outcome of the story, they're only deciding the way the story gets told.
Given that horrible truth, why not just use target numbers instead of thresholds? It's all about justification. When a published adventure specifies a DC or target number, there's no questioning it. But when a Game Master has to make one up, there are mental cycles that need to happen. You have to have the internal debate over what a sensible target is for a specific situation under specific circumstances. When a player succeeds, you might wonder if you set it too low, and when a character fails you wonder whether you set it too high.
A threshold number removes the mental processing and makes it a static measure of chance, as defined by the players during character creation. And that's what an RPG ought to be about: the player characters.