Ok this is by no means scientific, lots of assumptions, lets say hunters kill 20% of the bucks in NM each year, also we'll assume a 25% buck to doe ratio.
So 8500 bucks killed divided by .2 we get 42500 bucks state wide, so at 38,000 tags issued there is darn near a tag issued for every buck. Keep in mind a 20% buck to doe ratio would include this years crop of bucks and spikes, which probably make up about half of the overall buck population. You literally have 38k people chasing around 20k mature bucks.
If we take 42,000 bucks divide by .25 we get an overall population of 170k deer, of the 170,000 deer how many live on reservations, ranches, or town deer. My totally uneducated guess would be at least 100,000. So this leaves 70,000 deer on public land, 17,500 bucks if the population has a 25% buck to doe ratio. Of the 38k buck tags issued how many are for public land? I would say the majority, in fact I would doubt if 30k tags are allotted for public land. So you literally have 30,000 hunters chasing around 17,500 bucks. Of the 17,500 bucks probably half would be forked deer or better so <8000 forked bucks for 30k hunters, nice.
This is how you end up with 12 and 13% success ratios. Way to many tags. I get there are vast areas of New Mexico that don't have a mature buck. This is problematic, not just for hunting but the simple survival of the species. At least survival on public land. Kinda sad really.
Drought has had a huge effect on numbers, and no doubt numbers are down because of drought, but I promise some of the deer population numbers are also due to overhunting. Even if my numbers are off by 25% it still would indicate a huge problem of overhunting.
Who knows maybe it is by design. I know the vast majority on here would pay more for a tag. Probably would be willing to hunt every other year if they knew the opportunity was better. $50 - 60 bucks for a deer tag does not seem unreasonable to me.