I guess that is one way to think about it...but I personally find this way of thinking a little bit confusing. Not saying technically wrong, but it might be. And not to get all Bayesian on us here, but these are the priors and not the true probability.
Probability theory get's quite counterintuitive after all...and the whole draw system is also very a Game Theoretical prospect. Especially for units with few tags. Changes in weather or just luck may cause drastic swings in the success from year to year, causing delayed reactions by applicants in the subsequent years. Some larger units have stable statistics and predictable odds...others are more dynamic. And people are emotionally attached to certain units. All these things drive irrational and unpredictable behavior.
The draw is analogy to a line for Black Friday sales. All that matters is your place in line (random) and the number of people in front of you that came for the same thing you did. It's impossible to predict the former, and difficult to predict the latter. If you happen to be lucky and be first in line, go straight for the good deal on the big ticket item rather than the good deal on extension cords. (One year my wife waited in line for hours for a pre-lit Christmas tree that apparently no one wanted...she could have gone in and bought one at noon). If you're at the back of the line, but behind a bunch of irrational pre-lit tree shoppers, you might still get that iPad.
TopRut demonstrated that many (if not most) applicants do not apply "rationally" (their order is messed up). If the percentages are as high as they suggest, it is conceivable that you could draw a better unit than would otherwise be expected thanks to foolish applicants. It's not so simple as looking at the total number of applicants in each unit to determine your odds. You can really only get a good feel for your first choice chances based on the number of available tags and trends of first choice applicants. Those who apply for your top choice unit as their 2-3 choice, may have done so irrationally by choosing a less competitive first choice and effectively removed themselves from the unit's pool of applicants. They may be ahead of you in line but went straight for the tree.
And then there is Game Theory...you throw in things like the NM Premium Statewide Tag...and that changes things. 1100+ people applied for ELK-1-700 last year (the first year offered). Interestingly, 226 applied for it as their THIRD choice...there's ONE TAG. Entirely irrational! Anyway, it's conceivable that one of those silly fools put it as their 2 or 3 choice and still could draw it! The foolish hunter may have been 100th in line but if he put other high demand units ahead and they sold out because the 99 rational applicants ahead of him chose those hunts rather than "wasting" an application on the Premium Statewide. This isn't how it worked out in 2018...but who's to say it couldn't happen in the future?
Now, maybe some people are like me and say "1100 people for one tag? that's a waste of a choice!" As a result, maybe less people apply this year. Or, maybe people think "only 1100 applied? and a lot of dummies applied as a 3rd choice? maybe I should apply for my first choice" And as a result, MORE people apply for the one tag. I have NO ability to predict this behavior. Yet, it has the potential to improve the odds of drawing in a trickle down fashion if many people apply for a single tag using one of their three choices.
If EVERY applicant (besides you) behaved rationally, it would be safer to assume the chance of drawing a second choice Unit X Archery is 0%...but we know that's not the case. And even if it were the case, as illustrated by the Premium Statewide hypothetical, you could still have a chance at drawing the Unit X Archery tag on second choice if everyone in front of you chose Unit Y muzzleloader...however unlikely that is. But of course that is the question...is it impossible (i.e. 0%)?
So it's hard to predict how these things could turn out. But, it's safe to say that you cannot get any better odds than your worst draw odds. So, in that sense, I agree with BlueRidge...in another sense, it's hard to say exactly what that worst probability is...we must just use the priors (historical data) to inform our choices.
So I just follow some simple rules:
0) Only apply for hunts you would be happy to draw
1) Apply in order of lowest to greatest historical draw probability (highest to lowest value);
2) if that order doesn't align with your subjective desire (value) for the hunt, pick different hunts...seriously; and
3) if you really want to hunt, don't be picky on your third (worst) choice. (put the prelit tree on the shopping list)
4) Don't party app in units with few tags
Okay, now I'm just rambling...tis the season! Tags on the brain!