The BaB (base attack bonus) is to be added to melee attack (BaB+str mod+feats like weapon focus); to ranged attacks (BaB+dex mod+feats like weapon focus); to CMB (BaB+str mod+size) and to CMD(BaB+str mod+dex mod+size+10).
For example, a level 1 fighter with a melee weapon focus feat,str +2 and dex+1 should sound like this:
BaB+1
melee attack bonus (BaB(1)+str mod(2)+weapon focus(1))=+4
ranged attack (BaB(1)+dex mod(1))=+2
CMB (BaB(1)+str mod(2)+size(0))=+3
CMD (BaB(1)+str mod(2)+dex mod(1)+size(0)+10)=14
base attack bonus is "static" for every level, so it won't change until you gain a new lvl in a class (and even then it doesn't always change).
The attack bonus is normally base attack bonus plus ability modifier that applies plus bonus from feats and similar.
It's to simplify combat, you just have to take that attack, add perhaps a circumstantial bonuses, or magic/spell bonuses, and it's good.
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I'm just wondering How to handle keeping track of attack bonus, more specifically, the "Attack Bonus" box for each weapon - should we just list the *total* attack bonus when using that weapon here? It seems logical to me. We're only just learning about CMB and CMD, and there's the Base Attack Bonus box above that, so it has kind of confused the issue a little for us.
Yes, each weapon should have it's own full bonus listed in the box beside that weapon.
The Base Attack Bonus box is strictly for the 'Attack Bonus' you gain from class level (which has various efects on it's own, like eventually giving you extra attacks, all of which are unaffected by things like strength or Weapon Focus).
For a melee attack for example, to streamline combat a little bit, instead of having the players check their BaB, add their strength mod and size mod, and add their weapon focus, is it feasible to list the total attack bonus in the "Attack Bonus" box for the weapon? The way we had always done it in the past with the beginner's box we only listed the actual bonus the weapon had, if any, not the total.
This is exactly what that box is for. Use it for it's intended purpose.
every weapon you have has its own box to reduce such calculations, it's got everything in it you need (including the magic +X bonus you might get if the weapon is magic).
Just roll a d20 and add that bonus.
Other boni that change from round to round can't really be included and have to be added on the spot, examples would be if the cleric casts "divine favor" on you. If you are worried about combat speed, ask the casters to pick other spells.
If however you normally get/take buffs like power attack, feel free to write that attack and damage under the weapon, just be sure to redo it when you loose that bonus.
You could also write both, like a paladin could write his normal attack, and in brackets the numbers if he smites, as it is quite common for him.