Say you've got a 15 stat, giving you a stat modifier of +2.5 (effectively +2).
Then you've got a Favoured Class alternate option that gives you "+1/2 to " (which you've taken once).Would your bonus on this check be +2 (2 + 0.5, round down) or +3 (2.5 + 0.5)?
There are no half stat modifiers. Both 14 and 15 grant a +2 bonus.
The favored class options that give a +1/2 bonus are worthless unless you take them at least twice.
As far as I understand, with Rules As Written, your bonus would be +2, because I have never seen anything that lets you stack fractions like this. However, it would be a perfectly reasonable house rule to allow the fractions to stack, since if you were really rolling 0.5d40 instead of 1d20, then the fractions would both make differences, and would automatically stack.
Similarly, I'd like to see fractional Base Attack Bonuses and fractional Base Saving Throw Bonuses stack (right now, wirh Rules As Written, only the whole numbers stack, meaning that -- for instance -- Oracle 1/Sorcerer 1 has a Base Attack Bonus +0 instead of +1 with a remainder of +1/4 that could be stacked with another fraction).
An interesting related question: how do multiple fractions stack together.
For example, a Magus gets 1/2 level + Int in arcane pool points. A Tiefling Magus's Favored Class Bonus adds +1/4th of a point to their arcane pool. How many points does a level 3 Magus with 10 Int have?
.5*3=1.5, round down to one, plus .25*3=.75, round down to zero, equals one?
Or .5*3+.25*3=2.25, round down to two?
Fractions are always rounded down before you add them to other modifiers.
Many of these alternate class rewards add only 1/2, 1/3, 1/4, or 1/6 to a roll (rather than 1) each time the reward is selected, or add 1/2, 1/3, 1/4, or 1/6 to a class ability (such as adding to a bloodrager's number of bloodrages per day or a swashbuckler's total number of panache points). When applying such a benefit to a die roll or class ability, always round down (minimum 0). You may thus need to select such an option several times before the benefit applies.
Rounding: Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.
Unchained supposedly has Fractional rules. I know they cover Saving throw Fractionals but they may also cover stats too. Definitely sounds like a book worth grabbing.
This does sound good. Now I have gotten more curious: Does the messageboards dice roller support any fractions (that you could use with fractional bonuses)?
Oh well, it was worth a shot.