Cool Things You Could Do With Stats
Stats are kinda boring and weird. I don't always like how disconnected from the rest of the character they are. Roll under helps a lot with each point being meaningful, but I think there's more you could do. Here are some ideas.
High Stat Abilities for each Class
Each class gets a different ability depending on the highest stat of the character. An Intelligence High Fighter might get some kind of tactical advantage, like being able to interrupt an enemy attack with your own. A Charisma High Thief would be more like a con man. Maybe their ability is to have more contacts in the underworld. A Strength High Magic User could get a punch spell or perhaps the ability to cast spells in heavy armor. This also serves as a way to further differentiate demi human classes from the human ones. A Strength High Elf is more like the ones from the Silmarillion. A Dex High Dwarf tosses around Bilbo's plates without breaking a single one. That kind of thing.
Your Stats: Wizard, Thief, Fighter, and Cleric
This is sort of a reversal of the first idea. Rather than giving classes more independence from stats, this assumes each class is exactly one stat. You could add Druid I think with this too. With each point of a stat in a stat, you'd get an ability that goes with the class. It would be a game where every character is probably multi class but it makes a lot of sense doesn't it? Thieves in the OSR are a narrow group of people with skills specifically meant to navigate dungeons. In general media, thieves can be bruisers or master minds or con artists which means they overlap with other categories.
Each stat would be a menu of different feats/abilities and each time you level up, you can pick up another feat along with a point in a single stat.
This idea has a lot of legs and I expand on it in the next one:
Roll for Blades
I think you could put a lot of flavor into your stats. For this example, I was thinking about a Dishonored or Thief type of setting.
So maybe you'd have stats like Blades, Blood, Shadows, Masks, Eyes, and the like.
Then each stat says a lot:
Blades: Your skill is violence, in ending life skillfully. For each Blade, you've ended at least one human life. You remember each one. For each Blade, you may conceal a knife on your person that cannot be found no matter how much you are searched.
Then, for each Blade you have, you pick an ability from the Blades menu.
Perhaps something like...
Stalker: When you know your prey's name and have absolute intention to kill them, you may follow them utterly unnoticed by them.
I'm not going to flesh these out right now but I think these are neat.
Ruin
Instead of losing HP, gain Ruin. Ruin starts at 1 and increases every time you roll a natural 1 or after you roll Ruin. You roll Ruin whenever you would take damage. If you roll equal to or less than your Ruin, you die (hardcore) or take an injury. Maybe you can take Injuries equal to your Con modifier minimum 1 before the next time you fail your Ruin test, resulting in death.
Once again, not fully fleshing these ideas out but Ruin could also affect encounter checks. Maybe whoever is leading the way or holding the torch adds their Ruin to an encounter check/table. Maybe Ruin effects which characters get targeted by enemies in combat or you roll Ruin to see who a falling rock strikes.
Get Rid of Them
This might help. I've had a fun time just using Tags instead of stats and taking them into account for adjudicating the roll rather than having it me one to one. The actual roll is based on the likelihood of success. Add a modifier from -2 to +3 to 2d6. Make it a chance in six and roll a d6. To me, this makes it less about character sheets and more about player problem solving.
There are some notions for your perusal. I might flesh the Blades one out more later. Peace!


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