Just for the sake of completeness, I'm going to take Chris' profession guide link and reduce it to ore amounts. That'll at least give you the "minimum" amount.
Absolute Minimum
The technical absolute minimum is 0 ore, as you'd just buy all the bars/gems you need from the auction house and you'd never deal with ore at all.
Minimim w/ Mining
This answer will include the minimum figured assuming you only mine for bars and dust and that all gems come from the auction house.
- 160 Copper Ore
- 60 Tin Ore
- 140 Mithril Ore
- 15 Truesilver Ore
- 50 Thorium Bar
- 200 Adamantite Ore
- 10 Titanium Ore
Minimum w/ Mining & Prospecting
This answer assumes that you'd obtain each gem from the common ore most likely to drop it via prospecting based on figures on Wowhead. However, I also assumed no gems dropped during mining, which means these values won't be the absolute minimum.
- 160 Copper Ore
- 310 Tin Ore
- add 150 more for Horde characters
- add 200 more if you'd rather not farm/buy Small Illustrious Pearls
- 125 Iron Ore
- 215 Mithril Ore
- 15 Truesilver Ore
- 250 Thorium Ore
- add 50 more if you'd rather not farm/buy Powerful Mojos
- 200 Fel Iron Ore or Adamantite Ore
- add 75 more if you'd rather not farm/buy Black Diamonds
- 220 Adamantite Ore
- 350 Cobalt Ore
- 25 Saronite Ore
- 10 Titanium Ore
- 3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)
Quick Average: Mining & Prospecting
For the purposes of this answer, I assume that everything you do will skill you a point in Jewelcrafting, but I incorporate the average percentage drop of gems from the ore that is most likely to drop that gem.
For obsidium ore, the figure is the same as the minimum. Assuming each gem has an equal chance to drop, you'll be obtaining the gems in equal numbers. Since you need 3 of each of them for the transmutes, the percentage that you'll get a gem you need is 100% until you've gotten enough of that gem for all the transmutes you'd need.
- 160 Copper Ore
- 755 Tin Ore
- add 400 more for Horde characters
- add 535 more if you'd rather not farm/buy Small Illustrious Pearls
- 420 Iron Ore
- 390 Mithril Ore
- 15 Truesilver Ore
- 1155 Thorium Ore
- add 170 more if you'd rather not farm/buy Powerful Mojos
- 1180 Fel Iron Ore or Adamantite Ore
- add 445 more if you'd rather not farm/buy Black Diamonds
- 310 Adamantite Ore
- 1400 Cobalt Ore
- 140 Saronite Ore
- 10 Titanium Ore
- 3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)
Quick 90th Percentile
With the absence of data points from actual instances or simulations, I cheated on this one. My calculation for the 90th percentile was (([AVG]-[MIN])+[AVG]*.9)+[BAR], where
- AVG - Average ore needed to prospect gems based on drop rate
- MIN - Minimum ore needed to prospect gems
- BAR - Ore needed for bars
It's not perfect, and it also assumes that you always skill when crafting things with jewelcrafting. The same caveat applies to Obsidium in this answer as it does in the quick average.
- 160 Copper Ore
- 1120 Tin Ore
- add 610 more for Horde characters
- add 815 more if you'd rather not farm/buy Small Illustrious Pearls
- 670 Iron Ore
- 540 Mithril Ore
- 15 Truesilver Ore
- 1950 Thorium Ore
- add 550 more if you'd rather not farm/buy Powerful Mojos
- 2245 Fel Iron Ore or Adamantite Ore
- add 765 more if you'd rather not farm/buy Black Diamonds
- 385 Adamantite Ore
- 2310 Cobalt Ore
- 240 Saronite Ore
- 10 Titanium Ore
- 3205 Obsidium Ore (500 + 2700 from Shadowspirit Diamond and Fire Prism transmutes)
True Average & 90th Percentile
It quickly gets too complicated for me to want to bother attempting this in a completely legitimate fashion. One would have to make sure they had enough base inventory to accomplish both feats which results in a trickle-back effect where you have to go back and make older stuff again at times. That's best left for either a simulation program or someone with free time and a burning desire to snag your bounty. :)
For anyone interested in doing that, good luck. Also, so it doesn't get missed, Raven Dreamer posted the skill up formula he found for the percent chance you will skill up on a yellow or green recipe as a comment to the original question:
[chance of gaining skill point] = (grey skill - current skill) / (grey skill - yellow skill)
"Grey skill" and "yellow skill" are the numbers at which the recipe turns grey or yellow respectively.
I am sorry to say but the only way you can gain reputation with Earthen Ring after completing the quests from Vashj'ir, Deepholm, the Twilight Highlands and Thrall quest line from 4.2 is with championing by wearing there tabard and doing dungeons.
Sources: wowpedia.org, wowhead and tentonhammer
Best Answer
I decided to test the potion for myself, and while it does work I feel like that it has a greatly reduced drop rate in this area. Testing else where I would get 1 loot every 5 enemies slain, but in this specific location it was 20-25.
But yes, the potion will work, but not frequently.