Formulas:How Stats Affect Bear AC
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From Alterreality on the WoW forums, comes a long (mathfilled) post about bear tanking, with this gem for trading off +AGI, +dodge, and +defense gear:
PreBurning Crusade Bear Form Armor
Ever wondered what was better between AGI, Dodge, or +DEF? Well here is an equivalency to help you decide! (Armor values are the increased IN BEAR FORM)
Stat  Armor Increase 

Agility (1)  12.5 Armor 
Dodge (1%)  250 Armor 
Defense (1)  33.3 Armor 
Burning Crusade Bear Form Armor
Reclaculated for BC stats (24k Bear armor, and 23% dodge). It's important to note that the formulas change with changes in Dodge and Armor
Stat  Armor Increase 

Agility (1)  34.18 Armor 
Dodge (1%)  466.52 Armor 
Dodge Rating (1)  24.4925 
Defense (1)  37.32 Armor 
Armor Stat Weights
If you are comparing armor while buying on the AH, you want to compare the armor specs, so here are the tradeoffs:
Stat  Base Armor Increase 

Agility (1)  2.7 
Dodge (1%)  54 
Def (1)  7.2 
where equals ('=') means 'roughly equivalent to' while tanking in bear (Thank you to Galliard for the idea to express in this manner)
Using a weighting system (like the one found on wow.allakhazam.com), weight should be applied as follows:
Stat  Weight 

Armor  1 
Dodge Rating  4.05 
Agility  5.70 
Def Rating  2.6 
To calculate an items full "Armor" value:
(AGI * 2) + (+Def * 33.3) + (Dodge * 250) + (Armor * Armor_Modifier) = Final Armor Value
 This is the emulated ARMOR VALUE something like the "tank point".
Agility, Enchantment and leather working is influenced by nether the "bear armor fact" nor thick hide talent; Armor from gear is influenced by both; The Mark of Wild is influenced by only thick hide talent
(Note that by "bear form" here, the poster clearly meant Dire Bear Form.)
Damage Mitigation Mechanics
Let's move into a more indepth discussion of just how these numbers work.
First we assume the mob we are facing is lvl 73. The armor vs reduction formula can be found at damage reduction. Let's repaste it here (Simplified for a 73 mob):
Reduction = (Armor / (Armor + 11960)) (NOTE: No need for a % value)
Dodge (and Miss) reduces total damage by:
Reduction = Dodge/100
However, Dodge and Armor reduction have multiplicative diminishing returns, meaning that the total reduction from both is:
Tot Reduction = (1  (Armor / (Armor + 11960)) * (1  Dodge/100)
Unfortunately, the fact that both Armor and Dodge are in this formula makes it mildly worthless. To counteract this we will look for the amount of Total Reduction we get out of 1 point of Armor or Dodge at any respective value of the other stat. In otherwords, we want to know how much increasing armor by 1 point when we have X% dodge would increase our Reduction. To do this we take the derivative in respects to both Dodge and Armor. In doing so we get:
Delta Reduction by Armor = 119.6(D  100)/(A + 11960)^2 Delta Reduction by Dodge = 119.6/(A + 11960) NOTE: A = Armor; D = Dodge
Note that the linear Reduction of Dodge removes Dodge from the Dodge reduction formula. Now we have the relative Deta increases of Armor and Dodge, across all ranges of Dodge and Armor. From this we can get a Armor vs Dodge ratio by dividing the two formulas. It looks like this:
Armor/Dodge Ratio = 119.6/(A + 11960) / 119.6(D  100)/(A + 11960)^2 = (A + 11960)/(D  100) NOTE: This curve is linear in respects to Armor, but exponential in respects to Dodge
Assuming the afore mentioned stats apply (24k Armor and 23 Dodge) then:
1 Dodge = 466.524 BEAR Armor
Once you have this number the rest of the conversions are easy. The only hich being that the AGI:Dodge ratio I used was very loosely based on rather inaccurate looking data I gathered myself.