| bbangerter |
BAB is the Base Attack Bonus. Only leveling up increases BAB.
High strength scores increase the chance of hitting with a melee attack. This isn't an increase to BAB (so doesn't allow you to, for example, qualify for feats that require a certain BAB), but it does increase your chance to hit. This applies to Eidolon's in the same manner high strength applies to any creature. So your final +to hit is BAB + Str Bonus + Any other bonuses from items, spells, etc.