If you have a leftover tag or a 0 PP draw I would plan on getting out there at least a day or 2 early to scout. Points in Wyoming buy you land access for all intensive purposes, not bigger antelope or some other advantage.
My hunting partner and I put together a pretty successful hunt on a leftover tag last year, but we were there a full day early and scouted or hunted every moment for 3 straight days sunrise to sunset and we walked around 25 miles during those 3 days. The cool thing was even with a lot of hunting pressure we were constantly seeing antelope in the distance or going from one stalk to another.
We had a lot of luck either on small chunks of public land or small fingers coming off of bigger chunks of public land or in areas that were essentially land locked to vehicles.
I know there are conflicting opinions, but I would say hunt the opener and be camped near where you plan to hunt. I'm not sure I saw a single truck or hunter before an hour after sunrise because a lot of people don't put much effort into antelope hunting.
I would put in for a good area to build preference points with a special permit and if you don't draw that buy a leftover tag at the normal price in July. Putting a tag that is normally a left over as a 2nd/3rd draw on a special tag application is throwing away $200.
You probably want to ignore the drawing statistics prior to 2014, there were huge quota cuts this year and a lot of people were pushed out of traditional drawn areas to leftover tag units.