Consider the numbers:
Both skills:
There are 6 possible count/quality combinations for each BOD.
8% of BODs are larges, 92% are smalls.
For Smiths:
Half of BODs will be weapons BODs, Half will be armor BODs.
There are 25 distinct weapon small types, before multiplying by 6 for the count/quality combinations. These are always iron.
There are 24 distinct armor small types, before factoring in the 6 variants. ELEVEN of the 24 DO NOT have a corresponding Large BOD (meaning the normal non-combinables in the range from Bronze 20 to Agapite 15 count are the only ones worth keeping, and many mid-range exceptional (Shadow 20-count, Copper, Bronze, Gold 10 & 20, Agapite 10) can be considered junk as well). Armor BODs, depending on skill level, will be as little as 10% iron (120 skill), or as much as 50%/50% iron & colored (Smith below 110).
25 x 6 = 150 possible Weapon Smalls
11 x 6 x 9 = 594 possible non-combinable armor smalls
13 x 6 x 9 = 702 possible Large-combinable armor smalls
= 1446 possible smalls in the 92% of BODs.
The larges break down to
5 x 6 = 30 for weapons
3 x 6 x 9 = 162 for armor
= 192 Larges
1638 possible smith BODs total.
That's why getting smith BODs can take forever. Of course, by filling the weapons and non-combinables, turning them in one at a time, and getting an immediate replacement BOD, you can increase your chances immensely.
For Tailors (since someone is bound to ask and not check the Wilki sticky in the Data Chest subforum):
Tailor BODs are 1 in 3 chance to be exceptional (As opposed to 50%/50% for smith). Otherwise the 6 count/quality combinations are the same.
Unlike Smith BODs, who make an Armor vs. Weapon check, the choice of smalls is random between all 55 possible types for smalls, 14 types for larges.
All Tailor BODs will fit at least 1 large - THREE different larges if a footwear BOD - even before factoring in that you can put exceptional BODs into a normal LBOD, and colored smalls into a normal leather LBOD (or cloth BOD, for footwear)
If the type is a leather BOD (footwear), then it has a 70% chance to be colored leather. If if is colored leather, the chance for each color is: 60% spined; 30% horned; 10% barbed
Tailors then have a total of the following possible BODs (compare this to the numbers for smiths)
29 possible cloth smalls, times 6 for count/quality = 174 distinct cloth smalls.
26 possible Leather smalls, times 6 for count/quality, times 4 for leather type = 624 distinct leather smalls.
174+624 = 798 distinct smalls
9 of the 14 larges are cloth, times 6 = 54
5 of the 14 larges are leathers, times 6, times 4 = 120
174 possible larges
Total number of Tailor BODs possible: 972 (a little over half the smith amount, and a heck of a lot more common, and with the good rewards being much closer to the bottom end of the chart of rewards).