No point system, not sure on number of non residents applications but a few years ago I had the nonresident gun odds calculated at 1 in 627 for bull and 1 in 85 for cow. I'm sure that's changed by now. I know they've already drawn as I've gotten my first rejection notification of the year.
Found those numbers;
"At least 90 percent of elk permits are drawn for residents with up to 10 percent going to nonresidents. This year, 21,494 residents and 14,208 non-residents applied for an elk permit."