Hope it's okay, I'm gonna throw in my 2 cents on the draw odds discussion.
In the last 27 years of applying, I've been blessed to have drawn three sheep tags (1988 bighorn in Colorado, 2001 in desert in Nevada, 2009 bighorn in Wyoming). One of my sons also drew a Wyoming sheep tag in 2007 and another son drew an Arizona desert sheep tag in 2008. We took quality rams on all of the hunts.
When it comes to drawing odds for sheep...I am a FIRM believer you have to work the odds while still applying for quality units.
For my example I am going to talk about a guy who applies in 9 states for sheep tags (OR, ID, WY, AZ, NM, MT, CO, NV, UT). When applying in several states, even a TINY difference in draw odds gives you HUGE leverage. So here it goes....
Scenario 1: You apply for the very best tag in every state, and have say a 0.25% chance to draw on average. In 9 states that is a 2.25% chance to draw. On average it would take 44 years to draw. You could possibly never hunt sheep even though you spent a lifetime applying.
Scenario 2: You apply in units that have a 0.50% chance to draw on average. In 9 states that is a 4.5% chance to draw. On average it would take 22 years to draw, so you would likely hunt sheep once and possibly twice in your lifetime.
Scenario 3: You apply in units that have a 1.0% chance to draw on average. In 9 states that is a 9% chance to draw. On average it would take 11 years to draw, so this guy would likely hunt sheep 3 time and possibly 4 times in a lifetime.
This year I'm applying in 7 states for quality sheep units and estimate my draw odds at just under 9%, or about 1 in 11 odds to draw a sheep tag. Not too shabby...I'll take those odds.