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Some of my players wanted to create characters with ability scores higher than 20 as 1st level PCs. I cannot do that as I am running an adventure path which is made for characters with average stats. How can I explain to them the balance of the ability score system?

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We currently have no idea what drives your players to act this way. Is it because they want to be powerful? Is it because they do not understand the rules? Is it another reason? Are you talking about point buy or rolled? No game works without rules, and these are the rules here. That is how it is. If they don't want these rules, they should go play a different game. That's it. –  kravaros Jan 5 at 21:02
@kravaros They are all new players. They don't understand the rules. –  Randumbness Jan 5 at 21:36
Would "Some of my players don't seem to understand why they can't buy starting ability scores higher than 18 (pre-racial), what do I tell them?" be an on-point re-wording of your question? Just to know if I understood the question. –  Zachiel Jan 5 at 23:02
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Explain that the balance is intended to provide the maximum amount of entertainment. Stats too low can be amusing and an empathetic DM can always work with that. If stats are boosted above 20 to start, the unfair advantage it provides would probably make the adventure dull/boring due to lack of investment into the character. I like to use extremes in explanations (although that has its own faults) to show how bad it could be. If your first level character had God like stats, nothing is challanging so there is very little incentive to do much...unless they would like 20th level stats and fight first level enemies. For further ammunition, explain that every encounter, monster, and trap is based off of an average stat system. When you mess with the stats you mess with the balance.

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Classically speaking, Dungeons and Dragons considered scores between 3 and 18 to be the bounds of human achievement. This was based on how, back in the day, we actually rolled for each of these abilities (3d6, which generates a bell curve between 3 and 18 with the top of the curve happening at 10). You couldn't have a higher STR than 18 because d6es don't have 7 pip sides. Now, it should be noted that even by AD&D there were modifications to this being made (if you got an 18 STR you also rolled a d100 and added that, so a guy with an 18/95 was stronger than a guy with 18/12) but that's how it started.

The lines have been blurred a bit but that same basic idea holds. Human PCs can't have STR higher than 18 because there are no humans that strong. An 18 STR human represents the strongest of the strong, at least among normal people. That's not saying that a human PC can't have some magical artifact that supernaturally increases their strength, or that they can't improve it over time (both old skool DnD and Pathfinder kind of hand-wave that) but they can't start with those scores because they don't get to start out as gods.

Another angle: back in the days of 1E, dwarves got if memory serves a +1 to their CON, allowing them to achieve a 19. If you were to allow a human PC to buy/roll their way to 19, you'd have diluted much of the advantage that dwarves have starting out over humans. It's not (just) that dwarves don't have to spend as many points to get there, it's that dwarves are physically hardier than humans and as such the best of the best dwarves would be uniformly hardier than the best of the best humans. Those upper bounds simply were not available to humans.

Again, this has been diluted a bit by subsequent editions but if you're looking to house rule this back into place, there is a long line of tradition and tested gameplay on your side.

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In Pathfinder humans get +2 to any one stat of their choice; so with a good roll or points buying humans can easily have a 20 stat. –  Rob Jan 6 at 11:07
Dwarves get a +2 to Con and Wis. The standard for Pathfinder is a +2 to one thing, or a +2 to two things and -2 to another. –  Jonathan Hobbs Jan 6 at 13:34
I made a small alteration to my text to make it about how 1E operated rather than how current Pathfinder operates (because you are correct, with the RAW you can absolutely create a human with a 20 CON). –  NotVonKaiser Jan 7 at 3:56
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It's honestly really difficult not to want at least one stat at a higher level but if you want to enforce the limit, you make them use a stat buying character creation method, and lower the normal point threshold. It can seem kind of cruel but you can tell them that if they want that 18+ stat, they're going to hurt for it. If telling them outright that this world doesn't require the same dynamic level of power, it seems the only way as much as I hate to limit players in their chargen.

Edit: Given the new information that the players are all new to the system, they may not realize what the scale is actually supposed to be and are getting lost in the ability modifiers over the ability scores themselves. They also probably don't have a firm grasp on zero = normal, not lacking. Perhaps if you explain to them some common probability charts for 3d6 and show why it's statistically rare to achieve the beloved 18 (1/216 chance with 3d6, or a 1.62% with 4d6k3), let alone the 20 if you have the right race and for any RAW starting character shouldn't be starting above this.

Completely aside my official answer above as a personal opinion, D&D might not be the right system for this sort of setting as it relies heavily (in my experience) on needing those numbers if you want characters to advance at a respectable rate.

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This doesn't help at all with explaining to them why they can't get attributes over 20 off the bat. Someone asking for higher stats can also ask for higher stat points, and it's not like this addresses the question they have around stats in the first place. –  Jonathan Hobbs Jan 6 at 4:25
I've never really known players who want stronger characters to be satisfied with any answer. They always strive to get that one golden idea they have in their heads, thus giving a forced constraint as a solution –  CatLord Jan 6 at 4:45
An answer that talks about how they won't accept an explanation and how to deal with that would be better. It remains the case that switching the system underneath them won't deal with their concerns about wanting higher scores, especially when they can just ask for higher point buy - and offering a lower point threshold sounds like it would dig a deeper hole for the DM if the players open a book to read about this point buy system and find that the DM's cheating them out of points. This is really not addressing the situation the asker is facing in a constructive way. –  Jonathan Hobbs Jan 6 at 4:55
The book says the number can fluctuate either way, but focuses more on increasing it. As far as changing systems, I find the D&D stat system counter intuitive since 3e and further. Other systems are a little easier to have "average" stats with the normal build without "cheating" as you say. Plus in other systems, the individual skills get better chances to shine and less heaping advancement. –  CatLord Jan 6 at 5:09
So? Consider that the asker is not asking how to enforce the limit, just asking how to explain to their players what's going on. The point I'm making is: this is providing the solution to some other problem, and at best evading this one entirely. –  Jonathan Hobbs Jan 6 at 5:11
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