Here are some numbers for people to chew on.
Chance to win loot (no coin): 30%
Chance to win loot (original roll and coin): 51%
So what if you're looking to win one specific piece of gear from a boss?
If you use your original roll and coin and if the boss has for your spec...
...one piece: 51%
...two pieces: 25.5%
...three pieces: 17%
...four pieces: 12.75%
So if you're trying to win a Sha-touched weapon and the boss has three possible items for your spec then even if you use your coin you only have a 17% chance to get the weapon.
Let's say I'm a Mistweaver monk and I want Jinya, Orb of the Waterspeaker [http://www.wowdb.com/items/86893-jinya-orb-of-the-waterspeaker] from Lei Shi but she's also got a monk tier shoulder token and a spirit belt that I don't want. How many attempts (weekly boss attempts and coin rolls combined) do I need to have a reasonable chance of getting that one specific item?
1 attempt: 10%
2 attempts: 19%
3 attempts: 27.1%
4 attempts: 34.39%
5 attempts: 40.95%
6 attempts: 46.86%
7 attempts: 52.17%
8 attempts: 56.95%
9 attempts: 61.13%
10 attempts: 65.13%
11 attempts: 68.62%
12 attempts: 71.76%
I stopped at 12 attempts because earlier in this thread I read that somebody used 11 coins in a single week for one boss (I don't remember which one and what they were looking for) and still didn't get anything. Assuming that boss had three items for his/her spec then this person fell on the bad side of a 70/30 split and has nothing to show for their work save for 342 gold. Less once you count repair bills.
Well hello there, gambler's fallacy!