I have been working on a new idea for d20 checks to build diminishing returns into the core mechanic. Here is the result I’ve come up with:
Whenever you make a check, roll a d20 and add your modifier.
If the die result is between 1 and 5 (lower 25% of results), reroll with a -15 modifier. Repeat until the d20 result is a 6 or greater (the -15 modifiers are cumulative. 2 rerolls use a -30 modifier, etc.)
If the die result is between 16 and 20 (upper 25% of results), you may reroll with a cumulative +15 modifier.
This produces the following probability distribution:
For the purposes of the following discussion, “effective d20 result” means the final d20 roll plus any +/-15 modifiers.
For effective d20 results between 5 and 15, the probability distribution is the same as for a flat d20 (every +1 gives a +5% chance of success). Most of the game is balanced to fall within this zone. Above and below these numbers, the probability distribution flattens, providing diminishing returns for difficulties beyond this zone. Each +1 gives approximately a +1.25% chance of success (1/4 the effectiveness it would have in the primary zone). This flattens off even further in the tails, meaning that any modifier has some chance to succeed.
While this system adds a bit of extra complexity with the rerolling, it means that the game design no longer needs to worry about bounded accuracy. Here’s an example. Say most monsters the characters will face have an attack bonus of +5. A defensive character can work on increasing their AC up to 20 and will get the full benefit of that defense. Monsters only have a 25% chance to hit them. Say that same character decides to invest even more heavily in armor to boost their AC to 25. In the old system, this would make them unhittable (except on a 20), which means those last 5 AC points increased their survivability by 400%. Under this system, those last 5 AC points only reduce the monster’s to-hit chance from 25% to about 19%, a ~30% increase in survivability. This might not be worth the character investing resources into (although it does help a lot if a particularly accurate foe comes along).