STR:ATT Ratio Formula (Warriors)?

The next best estimator (still ignoring weapon type) is to add DEX/3 to your STR; so you get

( STR+DEX/3 ) / ATK

Specific weapons and skills affect the relative amounts. And if you're nearer to dexless, you can more readily ignore it.

ex. I have 821 str, 98 dex, 186 atk on my Paladin
(821+98/3) / 186 = 4.59

 Spoiler

To get the exact number to divide dex by instead of 3, take
(0.5+0.5*0.9*mastery)*(0.6*slash+0.4*stab)

Where
slash = 3.0, 4.0, 4.4, 4.6, 4.8, 5.0
^ spear, 1h sword, 1h axe/bw, 2h sword, 2h axe/bw, polearm
stab = 3.0, 3.2, 3.4, 4.0, 4.6, 5.0
^ polearm, 1h axe/bw, 2h axe/bw, 1h sword, 2h sword, spear

Or, for a skill that only slashes, or only stabs, you just have *(slash) or *(stab) for the appropriate weapon. Or in the case of Brandish, (0.5*slash + 0.5*stab).

Dividing dex by 3 is equivalent to mastery of 60% and a stab/slash of 3.9 average (which fits 1h and Spear best)

Going back to my Paladin example, you see:
First estimate: 4.41
Above estimate: 4.59
Exact: 4.58
As you can see the first estimate's not bad, and the above estimate is actually quite close.