The 'Mighty' bonus adds damage equal to the lowest of either your character's Strength bonus or the Mighty bonus itself. So if the Mighty bonus is +3, but your Strength bonus is +1, it adds +1 damage. If the Mighty bonus is +2 but your Strength bonus is +3, it adds +2 damage.

Strength ordinarily applies bonus damage to melee and thrown weapons, but not to ranged weapons like bows. Every two points of strength increases the bonus damage by 1 point. IE:
10-11 strength = +0 damage
12-13 strength = +1 damage
14-15 strength = +2 damage
16-17 strength = +3 damage
18-19 strength = +4 damage
etc.

The "mighty" property allows the bow to benefit from your strength score and deal extra damage, as a melee weapon would. However, it's capped at the mighty modifier. So mighty x3 only benefits up to +3 damage (16 strength). If your strength is higher than that, the excess is wasted.

Also, enhancement bonus on bows only adds to accuracy, not damage. You need magic arrows if you want a magic bonus on damage.

OK - thank you both. I wasn't aware that the enchantment bonus referred to the attack roll i.e. whether you hit or miss a target.

So, <copied and pasted from NWN 2 Wiki> "Ranged attack roll = 1d20 + base attack bonus + dexterity modifier + size modifier".

If the roll was 15
If my base attack modifier is 8 +1 enchantment
My dexterity is 17 (+3)
Size modifier - Is this whether the weapon is not displayed as a feat? Let's say -2 for the purposes of the example:

the calculation is: 15 roll + 8 attack mod +1 enchantment + 3 Dex bonus - 2 size mod = 25. If that's correct, what does this compare to in terms of the targets defense or is there no correlation between the two?

Then, if use a bow with a roll of 1D8 and have Might 3 would my damage be for example
1D8 roll = 5
Mighty roll = 2 (Dex mod is say, 3 as well)
Damage 5 + 2 = 7

Thanks again. I am looking on wiki but they provide formulas rather than examples and it's therefore difficult to follow the various factors in each calculation. If you know of a D&D 3.5 rules link that is clear and provides examples then please let me know, otherwise I'll spend the next month asking questions on here!

On most weapons, enhancement bonus benefits both attack and damage. Bows and arrows (and similar weapons such as crossbows or slings) are the exception to the rule; bows are attack only, arrows are damage only. Smaller creatures get a bonus to their accuracy, larger creatures take a penalty to their accuracy. Most of the races available to you (including elves) are "medium" sized and take neither a bonus nor penalty from size. Gnomes and Halflings receive a small bonus due to their small size. If the target has 25 or less AC, then you hit. If they have 26 or more AC then you miss.

Let's say you have Strenght +5 and bow with mighty +3 and it's a 1d8 bow while your arrows are +2.

the damage is 1d8+3+2
The base damage is rolled, mighty is not rolled, the arrow enhancement is not rolled,
But if there's an elemental damage, like frost arrow with 1d6 or 1-6, that's again a rolled extra for the damage.

Then, there's the critical range which for bow is usually 20, meaning you get a critical if you roll 20 on a d20.
And the critical multiplier, which is probably x3, meaning on a critical hit you do 3x the normal damage.

Actually, there's a little more to a critical hit. If you roll within the crit range of the weapon (a 20 in the case of a bow), then a second roll is made. If that second roll is good enough to hit the target, then the roll is confirmed as a critical. If not, then it's just a regular hit.

As for the multiplier, that's an indication of how many times damage is rolled (and the result is added together). The damage isn't rolled just once and then multiplied.

Also, to add a little more to this, variable damage (other than the base damage) and elemental damage isn't rolled multiple times on a critical hit. For instance, if your weapon (or arrow) has 1d6 fire damage (or 1d6 bonus piercing damage, etc), that 1d6 is only rolled once on a critical. So if most of the damage on your weapon is from elemental damage then you actually won't see critical hits doing that much more damage, since none of that elemental damage is increased on a crit. This even applies to fixed elemental or magic damage, like the flat damage bonus on adamantine weapons. However, damage from enhancement bonus and feats (such as weapon specialization and power attack) are multiplied.

Ah, the "confirm critical" I forgot,
the "what's included" in a critical calculation I never knew.

Thanks for the comprehensive explanations.

In the character screen under "main hand", where does the mighty appear. So for instance (and I'm making some numbers up for my benefit):

1) Composite Longbow + 1
2) Attack bonus +8/+2
3) Damage 1-8 +2

So is this accurate:
1) The weapon equipped + 1 attack role i.e. if I hit or not
2) In addition to the 1D20 attack roll but why the two numbers?
3) Roll of 1-8 for damage + 2 < Is this the mighty modifier?

I'll probably get there in the end!

Correct
Your character is high enough level that he gets 2 attacks. The second number is the AB of the second attack.
I'm actually not sure anymore if the Mighty damage is displayed there. This could be just the damage bonus from arrow enchantment. If it's not the arrow enchantment, then it's the Mighty bonus (or both combined). Someone else will know for certain.

#2) Why the two numbers? During a 6 second round, you will attack 2 times. One with +8, another with +2. For every base attack bonus of 6, you get another +1 for another attack.

+1
+2
+3
+4
+5
+6/+1
+7/+2
+8/+3
+9/+4
+10/+5
+11/+6/+1
+12/+7/+2
...

So for the last example, you will attack 3 times in 6 seconds. If your dex and size bonus and enhancement bonuses all added to +10, you would strike with +22/+17/+12
That is, 3 strikes. On d20+22, another d20+17 and another d20+12.

#3) I do believe the +2 is the mighty weapon factor. (but I don't know for certain)

1) correct; attack rolls determine whether you hit or miss.
2) you have a second attack, allowing you to strike more quickly. That said, those numbers don't look accurate. The character you described (17 dexterity, +1 bow, level 6-10) couldn't possibly have attack values that low.
3) yes, the +2 is from your mighty modifier. If your strength were higher, you could raise it to +3.

Note he said he was making up numbers. :)

Brilliant - thank you all. Watch this space for further NWN 2 enquiries! :)