Ummm...actually, the number is
very important, unless you're planning a WC.
The first number is your current BB rating; the decimal is important too. Your BB goes up by:
1 for every DoW w/CB
4 for ever DoW w/o a CB
2 for every noncore province you seize in an offensive war
1 for every noncore you seize in a defensive war
3 for every different-religion (major differences) nation you force-annex
6 for every similar-religion (inter-Christian) you force-annex
1 for every province-worth of territory you diplo-annex
? for every province you seize as a result of a turbo-annex (I think this amount changed recently, and I don't know to what)
1 for dishonoring an alliance (?)
And sometimes an event will raise your BB too.
Your BB will gradually go down, dependant on your DIP rating (with any modifiers). Your DIP rating will also affect the second number, which represents your BB max. Once you pass this max, you are in danger of triggering BB wars, if you are playing on one of the higher difficulty levels. In case you don't know, this means that everyone and their mother will DoW you constantly until that number goes back down.
Another thing (and this is why the decimal is especially important), is that if your BB exceeds 50% of your maximum, your stability costs will skyrocket. So if you have a BB max that's an odd number, it's nice to know if you're above or below .5. Also, if your BB is at 50% of max or higher, the AI is more likely to attack you, but certainly not as likely as if you exceed 100%.
Finally, the greater your BB, the more other nations dislike you, and your relations will suffer for it.
P.S. n00b
EDIT: Silly me, I forgot the EUII Wiki. It explains everything:
http://dhost.info/arsud/mediawiki-1.4rc1/index.php/Badboy
Except for one thing.
According to the Wiki, you will suffer 2BB if you DoW w/o a CB a country you have good relations with, but 4BB if you DoW w/o a CB a country you don't have so good relations with. What's up with that?
Wiki said:
You gain BB largely as a function of warfare: declaring wars, and taking provinces in peace deals, though there are some exceptions. Here is the short version:
BB Action
-- ------
1 Declaration of War (w/ casus belli)
2 DoW (w/o CB) relations +100 or more
4 DoW (w/o CB) relations less than +100
0 Gain a core province in any war
1 Gain a non-core province in a defensive war
2 Gain a non-core province in an offensive war
3 Force annex a country of different religion
6 Force annex a country of the same religion