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Random character generation is great, especially random Attributes.
People think Random attributes will ruin your game because D&D has taught them that Attributes cannot be raised quickly. If one rolls a bad character, they'll have to play 'Jake, the pointless', forever after. This problem vanishes once people can raise their Attributes after play.
There are 7 races to choose from, and 9 classes. We also have some campaign-specific races from these splat-books.
Oh?! A drow paladin? Well it's up to you, but the racial Charisma penalty will give you problems, as so many of the paladin's abilities come from their Charisma.
Ignore where the book says to roll Attributes - we use a point-buy system here. I don't remember the rules, but you can just use this website to calculate how it works.
I don't exaggerate. This is what point-buy systems can look like to new people.
Even better-designed systems, such as WoD, bewilder new players, given the immense range of options, and even reading about 7 Vampire Clans will inevitably slow a night down, and demand too much homework from anyone new to the game.
By comparison, random attributes work like this:
You are very Strong, but have low Wits, and high Intelligence. What kind of character would make sense?
This could be anything. The dice ask you questions, rather than listing huge lists of options and demanding that you read and understand.
One classic anime stars Louis the Rune Solder - a mage who uses his fists to solve his problems. Notice that we couldn't make such a mage in any point-buy system. Any points spent on Strength would detract from Intelligence. Point-buy systems will inevitably have one optimal result, and anyone deviating from that result will feel the punishment of the system.
So technically Louis the punch-capable mage could exist, but the player must pay the price, and feel that penalty.
While the point-buy systems gravitates towards generic fighters and optimized rogues, random Attributes allow for an acrobatic elf-sorcerer, or a charismatic rune-caster, who seems a bit dim but can learn and grow quickly. When someone gets a high Intelligence and Strength, they might decide to create a soldier; so they end up with a solder who's surprisingly intelligent. When someone wants to create a thief, but finds they have low dexterity, yet good mental Attributes and Strength, they can cast the character as a muscular extortionist and savvy con-man, without imagining them as a pick-pocket.
Players often have a favourite race, and nothing will go wrong in letting them choose one. But I've always found that once someone receives a race and simply rolls with it, they get on fine, and always find some interesting interpretation of that culture.
Random races also cut down on reading. They don't need to read about elves, dwarves, gnomes, halflings, calibans, tieflings, half-orcs, and half-elves. They get a single answer, which leads them to a page or two in the main book.
Random Attributes work great, and mirror the choices made for us in life (at least as much as any RPG can mirror anything). However, players should always be allowed to purchase skills, or some equivalent. Random Skills could only make for a confusing character.
Conversely, when players select skills, this reinforces the interpretation of their character. They get to take their body-builder cleric and make the character work by deciding what they would have focussed on in life.
In my experience, players retain the sense of ownership over a character - the feeling of having designed it - by simply getting a couple of choices at the end.