Reference: http://www.dragonsfoot.org/forums/viewtopic.php?f=1&t=9556&p=152931&hilit=+strength#p152931
Following is a pretty detailed analysis of a wide variety of creatures and the damage they do by the MM and by Weapon + Str. You will find that nearly every creature does an equivalent amount of damage whichever way you roll it. For weapon type, I used the favored racial weapon (if given) or the one in the picture of the creature (for giants).
The exceptions are Cloud Giants and Storm Giants which both do too little damage when you use the weapon technique. This could be due to using standard weapons damage values, instead of giving them "bigger" weapons which do, say, 1-12 damage
Bugbears do a bit less than they should if you use the MM values; they should probably roll the reccomended MM 2d4 then score a bonus point of damage to set them apart from Gnolls which are a bit weaker but also roll 2d4.
All of the demihumans are dead on except for elves, who score a bit of extra damage using the MM values. This could simply be to abstract out the addition of "leveller" 2nd and 3rd level elves who should do more damage, but its kind of a pain to have to detail the entire band if you're just doing a random encounter. It could also be a typo.
In conclusion I think it is safe to say that whether you use the MM values or the Weapon + STR technique, you'll get very equivalent results in any case.
GIANTKIND
Hill Giant
Average Strength: 19
MM: 2d8 for an average of 9
Club & STR: 1d6 + 7 for an average of 10.5
Stone Giant
Average Strength: 20
MM: 3d6 for an average of 10.5
Club & STR: 1d6 + 8 for an average of 11.5
Frost Giant
Average Strength: 21
MM: 4d6 for an average of 14
Battle Axe & STR: 1d8 + 9 for an average of 13.5
Fire Giant
Average Strength: 22
MM: 5d6 for an average of 17.5
Two Handed Sword & STR: 1d10 + 10 for an average of 15.5
Cloud Giant
Average Strength: 23
MM: 6d6 for an average of 20.5
Big Weapon & STR: 1d10 + 11 for an average of 16.5
Storm Giant
Average Strength: 24
MM: 7d6 for an average of 24
Big Weapon & STR: 1d10 + 12 for an average of 17.5
RANDOM HUMANOIDS
Kobold
Average Strength: 9
MM: 1d4 for an average of 2.5
Club & STR: 1d6 - 1 for an average of 2.5
Goblin
Average Strength: 10
MM: 1d6 for an average of 3.5
Spear & STR: 1d6 + 0 for an average of 3.5
Orcs
Average Strength: 12
MM: 1d8 for an average of 4.5
Polearm & STR: 2d4 + 0 for an average of 5
Hobgoblin
Average Strength: 15
MM: 1d8 for an average of 4.5
Polearm & STR: 1d10 + 0 for an average of 5.5
Gnolls
Average Strength: 16
MM: 2d4 for an average of 5
Club & STR: 1d6 + 1 for an average of 4.5
Bugbears
Average Strength: 17
MM: 2d4 for an average of 5
Sword & STR: 1d8 + 2 for an average of 6.5
Ogres
Average Strength: 18
MM: 1d10 for an average of 5.5
Spear & STR: 1d6 + 2 for an average of 5.5
DEMIHUMANS
Gnomes
Average Strength: 10
MM: 1d6 for an average of 3.5
Club & STR: 1d6 + 0 for an average of 3.5
Dwarves
Average Strength: 14
MM: 1d8 for an average of 4.5
Hand Axe & STR: 1d6 + 1 for an average of 4.5
Elves
Average Strength: 12
MM: 1d10 for an average of 5.5
Spear & STR: 1d6 + 0 for an average of 3.5
Halflings
Average Strength: 8
MM: 1d6 for an average of 3.5
Spear & STR: 1d6 + 0 for an average of 3.5
Three Dimensions
20 hours ago
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