Acid Test
I'll compare the half-ogre to the half-orc, since they're similar in racial benefits (strong, dumb, can see in the dark).
1st lvl half-ogre fighter vs half-orc 4th lvl fighter
Base stats are 10. Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Weapon Specialization, Exotic Weapon Proficiency, and 2 other feats.
HP: 11 vs 23
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +6
Damage (melee): 2d6+3 (avg 10) vs 1d10+3 (avg 8.5)
Attack (range): +0 vs +4
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +4/+1/+1
Other: 10 ft reach, immunity to some enchantments vs 3 feats, ability increase, +1 initiative
A +3 level adjustment is too much. The half-ogre is very deficient in HP and loses out in attack bonuses. Its damage is impressive and its natural reach improves its melee capabilities beyond what the numbers indicate, but those HP...
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1st lvl half-ogre fighter vs half-orc 3rd lvl fighter
Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Exotic Weapon Proficiency, and 2 other feats.
HP: 11 vs 19
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +5
Damage (melee): 2d6+3 (avg 10) vs 1d10+1 (avg 6.5)
Attack (range): +0 vs +3
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +3/+1/+1
Other: 10 ft reach, immunity to some enchantments vs 2 feats, +1 initiative
A +2 level adjustment looks good. The half-ogre is less deficient in HP, and the gap will narrow with time because of the CON bonus. Its damage is impressive, and its natural reach improves its melee capabilities beyond what the numbers indicate.
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1st lvl half-ogre fighter vs half-orc 2nd lvl fighter
Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Exotic Weapon Proficiency, and 1 other feat.
HP: 11 vs 14
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +4
Damage (melee): 2d6+3 (avg 10) vs 1d10+1 (avg 6.5)
Attack (range): +0 vs +2
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +3/+0/+0
Other: 10 ft reach, immunity to some enchantments vs 1 feat, +1 initiative
Too strong at +1 level adjustment. HP are on par. Saves are on par. The half-ogre hits more often in melee, does 50% more damage than the half-orc, and has reach. The half-ogre doesn't hit as well with ranged attacks but again does 50% more damage than the half-orc. I'd say all that is worth more than a single feat.
I'll compare the half-ogre to the half-orc, since they're similar in racial benefits (strong, dumb, can see in the dark).
1st lvl half-ogre fighter vs half-orc 4th lvl fighter
Base stats are 10. Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Weapon Specialization, Exotic Weapon Proficiency, and 2 other feats.
HP: 11 vs 23
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +6
Damage (melee): 2d6+3 (avg 10) vs 1d10+3 (avg 8.5)
Attack (range): +0 vs +4
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +4/+1/+1
Other: 10 ft reach, immunity to some enchantments vs 3 feats, ability increase, +1 initiative
A +3 level adjustment is too much. The half-ogre is very deficient in HP and loses out in attack bonuses. Its damage is impressive and its natural reach improves its melee capabilities beyond what the numbers indicate, but those HP...
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1st lvl half-ogre fighter vs half-orc 3rd lvl fighter
Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Exotic Weapon Proficiency, and 2 other feats.
HP: 11 vs 19
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +5
Damage (melee): 2d6+3 (avg 10) vs 1d10+1 (avg 6.5)
Attack (range): +0 vs +3
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +3/+1/+1
Other: 10 ft reach, immunity to some enchantments vs 2 feats, +1 initiative
A +2 level adjustment looks good. The half-ogre is less deficient in HP, and the gap will narrow with time because of the CON bonus. Its damage is impressive, and its natural reach improves its melee capabilities beyond what the numbers indicate.
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1st lvl half-ogre fighter vs half-orc 2nd lvl fighter
Half-ogre has Weapon Focus and 1 other feat. Half-orc has Weapon Focus, Exotic Weapon Proficiency, and 1 other feat.
HP: 11 vs 14
AC: half-ogre AC will be 2 pts higher
Attack (melee): +5 vs +4
Damage (melee): 2d6+3 (avg 10) vs 1d10+1 (avg 6.5)
Attack (range): +0 vs +2
Damage (range): 2d6 (avg 7) vs 1d8 (avg 4.5)
Saves: +3/-1/+0 vs +3/+0/+0
Other: 10 ft reach, immunity to some enchantments vs 1 feat, +1 initiative
Too strong at +1 level adjustment. HP are on par. Saves are on par. The half-ogre hits more often in melee, does 50% more damage than the half-orc, and has reach. The half-ogre doesn't hit as well with ranged attacks but again does 50% more damage than the half-orc. I'd say all that is worth more than a single feat.