For Instance... If you had to guess a number between 1 and 10. And you only had once chance, your chances of wining would be 10%. However if you got to choose 5 numbers, then each time you played under those particular rules you would have a 50% chance of success.
The method of calculation here is still assuming you will hit 1 number out of the 5 out of the 10. Crafting in this game is more like pulling 5 times...but only pulling 1 out of 10 (compounding)...and then replenishing the pool with the one you pulled out after each pull.
The probability is only increased in two ways:
(1) Once an affix has been selected, it will not roll for x number of rolls (i.e. you pull a ball out of the hat of 100 possibilities and don't put it back in before selecting the next one)
(2) You have more than one chance at each affix to roll on a piece of gear. (i.e. you want to pull a red ball and the pool has 50 out of 100 red balls in it).
In this case, we have a specific "perfect" combination of stats: Str, Vit, AR, Life%, Armor
On vit shoulders, only 1 of those affixes is guaranteed...and the others is a combination of affixes that get thrown back in to the affix pool every time (i.e. option 1 above).
The replenishment of the affix pool will always make each craft random. There is a 100% probability that you will pull 1 stat...and a 0 to 100% probability you will pull any of the other desired stats.
The chances of getting a good pair of shoulders is much much better than the standard 6 number lottery, only because we don't have 50 affixes to choose from. We are looking for the perfect set of affixes amongst 20-30 different possibilities.
Calculating how many crafts it will take to hit this "better-odds" lottery is still mathematically impossible. You can formulate a model that will display your range of craft count possibilities...but can not calculate when you will hit the desired target amongst that range.