In SD, privately owned Walk-In Areas & CREP land are more variable in terms of man-made (or cow-made) differences: haying/mowing, grazing, elimination from program enrollment altogether, etc. But by & large, they're the same year after year.
Federal & State land is VERY stable, except it may get grazed once every many years. The biggest weather variable is amount of water. And the biggest effect (especially lately) is either a) it's so wet you can't hunt it, or b) it's so wet it drowns out the cattails & they're no good in the winter. Walk-in & CREP land generally has less cattails so is affected less in this way. This year has been bad for drowned out cattails on WPA's. If I could pick anything to improve on State & Federal land, it'd be nesting cover. Unfortunately, it rarely changes & it's far from great, so it's nice to have some good private nesting cover nearby. That can change somewhat regularly.
So yes, as mentioned in comments above, the biggest factor is surrounding land. Both in terms of bird numbers & huntability. In SD, usually there are so many nearby private land options for pheasants to use, that they don't really NEED the public land at any given time. (not so in many places in other states) So number of birds using public land can vary quite a bit from year to year. In terms of hunting them, it's sometimes important to remember that they don't necessarily "live" on public land. You try to choose places to hunt, based on time of season & time of day, when the birds' best option is to "use" the public land, whether that be for roosting, loafing, feeding, avoiding bad weather, etc. Chances are, unless weather makes them hole up, they'll move around a lot in a day. But if I had to pick 1 variable adjacent to, or very near, public land that'll increase the odds of there being birds....it's corn. Yes, they eat beans & other things. But given a choice between easy corn & easy beans, they'll choose corn. Whether that corn is picked or standing is a whole nuther story.
In terms of raw bird numbers, if surrounding private land doesn't change much, neither does the number of birds....in the general vicinity. And this is usually the case. But the public land huntability can change a lot year to year.
Sorry, that's pretty disjointed, but I think I said my piece.