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A fractional solution without fractions:
Don't list class BAB and saves at all. List ranks in Combat, Fort, Ref, and Will. For every 3 ranks you have in Combat, your BAB increases by +1. For every 3 ranks you have in a saving throw, your save bonus increases by +1. Determine class progressions for ranks in Combat and saves accordingly.
Boy do I feel stupid. That's a neat way to sidestep the problem.
It also opens the door for new mechanisms that are very level sensitive to be based off the raw 'Combat' number - i.e. a flashy weapon trick with a DC of 30 being easy for a 10th level fighter (combat=30) but impossible at 3rd level (combat=9 + 20 on dice).

Freesword |
Edit: I think Freesword brought this up before I did in this thread...don't want to look like I'm stealing anyone's ideas.
Glad to see you warming to the idea, but while I may be the first to have mentioned it in this thread, I can't take credit for being the source. Quandary introduced this concept to me months ago in another discussion. I just pass it along because in my opinion it is the best way I have seen for dealing with multi-class BAB and Save stacking.
It may not be quite as mathematically precise as the fractional formula, but it comes real close and is easier on the math-phobic.

Slime |

Just use the current base reference table for Good and Poor save and stack the proper level, good first, bad after:
In class descritptions, save some room and indicate
Ex.:
Fighter, Fort.: GOOD, Ref.: POOR, Will: POOR
Monk, Fort.: GOOD, Ref.: GOOD, Will: GOOD
Add the good levels and check the chart and add the bad levels and do the final total. No fraction and no piling of +2's.
So a Fighter 4/Monk 2 has 6 levels of Good saves in Fort., 2 levels of good saves and 4 levels of Poor saves in Will and Reflex.
Check the progression Chart and you get Fort.: +5, Will and Reflex :+4 (from +3 (good colum, level 2) and +1 (poor colum level 4)).
A better progression than the Fort: +7, Will and Reflex:+ 4 you would currently get from that multi-class compared to the +5 on all tree that Full class Monk (who should have the better saves) gets at 6th level.
No fractionnal Math, no dependence on BAB, no piling of +2's, no new mechanics, less page taken in class description chart.