Now, unfortunately your system has to be used by actual humans, and humans kind of suck at arithmetic and risk assessment. The average human simply stalls out when asked to do repeated math functions - even if they are simple addition. And players will be straight up confused when their character doesn't live through something that they had a 90% chance of living through... even after attempting it ten times in a row. So with that in mind, here are some math don'ts:
- Don't use fractions. I once had this alternate save system where people added 2/5 or 3/5 to their saves each level so that good and bad save progressions would add up - it was mathematically kind of pretty but it was a complete cluster fuck. As Mister Cavern I had to redo everyone's save bonuses every level. People just couldn't wrap their heads around adding .4s to things at all. So I don't give a fuck how nice the math comes out adding some kind of fraction to things, just don't do it. Whole numbers only unless you want players to look at you like lost lambs every time they have to interact with the numbers.
- Always use linear addition. For various reasons it is sometimes necessary to have a big bonus at the beginning of a progression and then a more measured bonus after that. It may be tempting to add these bonuses in some kind of logarithmic fashion or to have bonuses add up to arbitrary values that are then cross referenced to a table or to add half of subsequent bonuses or whatever. Do not succumb to this temptation, because that kind of shit paralyzes people. Players have enough problems adding 4 and 3, the moment you ask them to add 5 and half of 4 they are drooling vegetables.
- Don't let numbers get too large. It is a fact of mathematics that numbers raised to an exponent have the same relation as numbers that are lowered by the same exponent. That you could have perfectly identical mathematical relationships between levels by constantly raising things to the same exponent. And that shit works just fine in a computer game. But humans lose track of numbers when they get big. Dong repeated subtraction from a 3 digit number is hard for people, and doing repeated subtraction from a 4 digit number might as well be pushing Sisyphus's rock. Sometime try watching a Mister Cavern deal with an epic level Solo against a group of PCs, it's hilarious, yet also faintly sad.
- The numbers have to start large enough that they can get smaller. Player characters can't really start in the AD&D "single hit die" crowd, because it is sometimes game mechanically relevant for there to be children or cats. Basically this means that a first level character who begins life with less than 10 hit points or so feels ridiculous in the face of potential hazards that are supposed to be substantially weaker than they are (like familiars or poisonous snakes).
- Numbers actually shouldn't diverge very much as levels continue to rise. This is not to say that an 8th level character has to take shit from a 4th level character, but that two 8th level rogues need to have fairly similar abilities with lock opening for an "8th level lock" to have much meaning.
- Numbers should be pretty tight at 1st level too. The entire RNG is only 20 points long, so the days of a Halfling Rogue getting +5 for Dex, +5 for Skill Training, +2 for Racial Bonus and +3 for Skill Focus at 1st level while a Dwarven Fighter gets a -1 Dex modifier to the same task really has to end. Any task that players within the same party are expected to all perform, need to be relatively tight in total bonus one to another.
- Any ability gained at any level needs to be competitive at the level they have it. Which in turn means that abilities need to either go obsolete or stay numerically competitive in a predictable fashion.
- And finally, characters need to be different one from another. Despite the fact that them diverging much is what makes the game fall apart and the math stop "just working" - it is precisely the existence of the difference at all that makes one character feel different from another. Players seriously do want their characters to have a different Sneaking bonus than another character.
But there's another thing about level appropriate challenges that is only tangentially about the math. People fucking hate it when you tell them that a Level 8 character should be climbing a DC 23 wall. They have no problem at all being told that an Ice Wall is DC 23 Wall and is appropriate for an 8th level character. The 4e difficulty system would have offended people even if it had provided usable DCs, simply because the presentation of those DCs was offensive. Difficulties need to be task oriented rather than level oriented or no tasks you compete will ever feel at all meaningful.
-Username17