How exactly do fractional BAB/saves work?

[vollmond]

I see references all over the place to using fractional BAB and saves (including a PbP game I'm applying to), but despite extensive Googling, I cannot seem to find out how exactly it works. Would be good to see explanations for both regular and gestalt, though I don't have an immediate need for gestalt.

[Reluctance]

Look at how saves and BAB go up at predictable rates. It's easy to turn +1 every 3 levels into +1/3 per level, which stacks more easily when multiclassing comes into play.

[Endarire]

Fractional BAB
Each class grants a certain amount of BAB each level. At level 5, a full BAB class grants 5, a 3/4 BAB class grants 3 (technically 3.75), and a 1/2 BAB class grants 2 (technically 2.5).

If you go Rogue1/Wizard1/Cleric1, then by the PHB rules, your BAB is 0. With fractional BAB rules, your BAB is 0.75 + 0.5 + 0.5, or 1.75 which rounds down to 1.

[Andraste]

It's so you BAB and saves have fractions in them so they add up if you take levels in different classes that would otherwise not get you more in them.

Your BAB increases each level by this
Good: +1
Medium: +3/4
Poor: +1/2

Normally, if you take 1 level each in two classes with poor BAB, you wouldn't get anything, but this way you get +1 because it adds up.

Saves work similarly
Good: +1/2
Poor: +1/3

If you have good saves in something on the very first level you take, you get +2 to that.