Vitruviansquid

2017-06-23, 07:20 PM

Fun observation:

In a fight, an RPG character's power can be thought of at its most basic as the amount of change he can bring about. When I say "change," I generally mean the change from alive monsters to dead monsters.

So if you look at it that way, a character's power is equal to the character's ability to deal damage.

A character who can deal 10 damage is twice as powerful as a character who can deal 5 damage.

But that's only half of the puzzle, because we are not considering that as the character is trying to make changes, there are also NPC baddies who are trying to change them. When I say "change" here, I mean the change from an alive adventurer to a dead adventurer. So health also matters.

A character who has 100 hp is actually twice as powerful as a character who has 50 hp.

But now that we realize damage is actually a value to mean "change over time" and hp is actually a value to mean "amount of time to be changed" we realize that a character's power can be found with the formula:

Power = hp * damage

Basically, a character with 100hp and 10 damage is AS powerful as a character with 50hp and 20 damage which is AS powerful as a character with 200hp and 5 damage. You see that all three of them have the same power (which in this case would be 1000 power)

This also gives rise to the understanding of these hp and damage is only as good as how much of the other you have.

The character with 20 damage is dealing twice as much damage as the character with 10 in the above example, but only gets to apply that damage for half the time.

So if you look at the D&D fighter who generally improves in both defense and offense as he levels up, he is actually growing quadratically. That's why you don't have enemies who are way over or under levelled to fight your PCs' party. (Before anyone asks, since the fighter scales quadratically it does not make him equal to the wizard. The wizard actually does not scale quadratically and has even more extreme scaling.)

Another fun observation:

Many dice systems break down as differences between modifiers and target numbers get too large. Why is this?

Each addition to your chance of success gets more less valuable as your chance of success goes up.

If I had a 5% chance of succeeding something, adding another 5% doubles my likelihood of success. I now have 200% efficacy.

If I had a 50% chance of succeeding something, adding another 5% only adds a tenth to my likelihood of succeed, so it only brings me to 110% efficacy.

That is if I am rolling 1 die. If I roll more dice to add up the values, the bell curve that forms exacerbates this problem.

In any case, I wanted to start a thread about the underlying math of RPGs because I, and I know a number of others, on this forum are writing RPG systems.

What are virtues and what are follies in an RPG's math system?

What do RPGs do to mitigate those?

Which systems have you seen have really good underlying math?

In a fight, an RPG character's power can be thought of at its most basic as the amount of change he can bring about. When I say "change," I generally mean the change from alive monsters to dead monsters.

So if you look at it that way, a character's power is equal to the character's ability to deal damage.

A character who can deal 10 damage is twice as powerful as a character who can deal 5 damage.

But that's only half of the puzzle, because we are not considering that as the character is trying to make changes, there are also NPC baddies who are trying to change them. When I say "change" here, I mean the change from an alive adventurer to a dead adventurer. So health also matters.

A character who has 100 hp is actually twice as powerful as a character who has 50 hp.

But now that we realize damage is actually a value to mean "change over time" and hp is actually a value to mean "amount of time to be changed" we realize that a character's power can be found with the formula:

Power = hp * damage

Basically, a character with 100hp and 10 damage is AS powerful as a character with 50hp and 20 damage which is AS powerful as a character with 200hp and 5 damage. You see that all three of them have the same power (which in this case would be 1000 power)

This also gives rise to the understanding of these hp and damage is only as good as how much of the other you have.

The character with 20 damage is dealing twice as much damage as the character with 10 in the above example, but only gets to apply that damage for half the time.

So if you look at the D&D fighter who generally improves in both defense and offense as he levels up, he is actually growing quadratically. That's why you don't have enemies who are way over or under levelled to fight your PCs' party. (Before anyone asks, since the fighter scales quadratically it does not make him equal to the wizard. The wizard actually does not scale quadratically and has even more extreme scaling.)

Another fun observation:

Many dice systems break down as differences between modifiers and target numbers get too large. Why is this?

Each addition to your chance of success gets more less valuable as your chance of success goes up.

If I had a 5% chance of succeeding something, adding another 5% doubles my likelihood of success. I now have 200% efficacy.

If I had a 50% chance of succeeding something, adding another 5% only adds a tenth to my likelihood of succeed, so it only brings me to 110% efficacy.

That is if I am rolling 1 die. If I roll more dice to add up the values, the bell curve that forms exacerbates this problem.

In any case, I wanted to start a thread about the underlying math of RPGs because I, and I know a number of others, on this forum are writing RPG systems.

What are virtues and what are follies in an RPG's math system?

What do RPGs do to mitigate those?

Which systems have you seen have really good underlying math?