4 minutes ago, Spacesong said:So your +3 to hit and dmg is coming from being level 3, then?
His STR is 17 (+2). So +2 (STR) +1 (specialization) = +3 total with the long axe.
With a hand axe, his ATK/DMG bonus is +2. Thown, it would be +0/+2, though I'm not sure, whether STR bonus to thrown weapons for damage (only) is a AD&D thing or OSE or B/X also?).
Does this help?
Example:
So Reigenleif has +0 STR and +1 DEX. Let's consider her taking specialization in spear as an example.
Melee: ATK would be +0 (STR) + 1 (spec.) = +1. +1 DMG ditto.
Thrown: ATK would be +1 (DEX) + 1 (spec.) = +2 ATK. DMG would be +0 STR + 1 (spec.) = +1
Or, you could specialize with the broadsword, or not specialize at all and take another weapon proficiency. You have x4 (or x3 with specialization).