None -
Zero percento - unless you want to do some dirt,
The photo is looking up a dirt from the paved highway near Stanley.

The Sawtooth National Recreation Area has all the beauty of Yellowstone/Grand Teton with about 1/10 the people. The little town of Stanley has basic services - motels, cafes, stores.

If were going east to west, I would start in Jackson no later than the day after Labor Day. You might have a light snow or two in Wyoming or Idaho. Also you should expect chilly nights. If you start on the Oregon coast, I wouldn't start much later than August 20th since that would put you in Jackson the second week of August.

I used to live in Jackson. You can expect the first frost around Labor Day and the first snow by mid September. It will be gone the day, but the second snow is usually bigger, etc.

The road through Lava Beds is extremely exposed - zero trees - and hot in summer. The road from Arco to Challis to Stanley is moderately exposed, with tree areas along waterways - esp. the Salmon River. The roads in Idaho have narrow to zero shoulders; however, the traffic is light. Still, you have to know how to ride these kinds of roads.

Best - J