I have accumulated enough data to be convinced that the following simple formula gives an accurate value M for any attribute maximum:
where the coefficients L, A, and Q are tabulated below. (There lie the complexity.)
Level coefficient
The level coefficient L is to be computed from the item level ℓ as follows:
So the coefficient L is 1 for a level 1 item, and grows by 179/69 per level until reaching 180 for a level 70 item; then it grows by 15 per level reaching 255 for a level 75 item; finally it grows by 13 per level reaching 281 for a level 77 item.
Attribute coefficient
The attribute coefficient A is as follows:
(The Weapon attribute for the Shied is the Block Rating. For the other weapons, the attributes are the Min and Max Damage.)
Quality coefficient
The quality coefficient Q is equal to 1 for the General attributes. For the Weapon and Base Armor attributes, it depends on the quality of the item as follows:
Example
The maximum Base Armor for a Level 51 Rare Leather Cap is
PS This result builds heavily on the findings of many, including Nhat, Shilien, Jose Sarmento and MarkHark, also on contributions by many to the collection of data.
PPS You can use the spreadsheet "Quality Control" from my Dropbox to evaluate your items.
M = L × A × Q 
where the coefficients L, A, and Q are tabulated below. (There lie the complexity.)
Level coefficient
The level coefficient L is to be computed from the item level ℓ as follows:
Range of ℓ  Value of L 
1—70  ( 179 × ℓ  110 ) / 69 
71—75  15 × ℓ  870 
76—77  13 × ℓ  720 
So the coefficient L is 1 for a level 1 item, and grows by 179/69 per level until reaching 180 for a level 70 item; then it grows by 15 per level reaching 255 for a level 75 item; finally it grows by 13 per level reaching 281 for a level 77 item.
Attribute coefficient
The attribute coefficient A is as follows:



(The Weapon attribute for the Shied is the Block Rating. For the other weapons, the attributes are the Min and Max Damage.)
Quality coefficient
The quality coefficient Q is equal to 1 for the General attributes. For the Weapon and Base Armor attributes, it depends on the quality of the item as follows:
Quality  Value of Q 
Common  10 × 0.115 = 1.150 
Uncommon  12 × 0.115 = 1.380 
Rare  13 × 0.115 = 1.495 
Epic  14 × 0.115 = 1.610 
Legendary  15 × 0.115 = 1.725 
Example
The maximum Base Armor for a Level 51 Rare Leather Cap is
(179×51110)/69 × 1.5 × 1.495 = 293.1175 
PS This result builds heavily on the findings of many, including Nhat, Shilien, Jose Sarmento and MarkHark, also on contributions by many to the collection of data.
PPS You can use the spreadsheet "Quality Control" from my Dropbox to evaluate your items.
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