As /u/eleventeenth_beatle and /u/drpinkcream noted, branch of service played a major role in theatre deployment. I'm going to just address the Army in this comment.

My understanding is that deployment was not done by draftee but by divisions, which were the primary independent units of the Army (see http://www.historyshotsinfoart.com/USArmy/backstory.cfm).

So the next question is, how were divisions assigned geographically, and how was a division's recruitment pool generated?

Per Maurice Matloff's "The 90-Division Gamble," (http://www.history.army.mil/books/70-7_15.htm), the manpower allotted to divisions had to be carefully regulated so that there wasn't too much of a drain on American industrial capability, and there was about a year's worth of training time for a given division before it was deemed combat-worthy. Furthermore, divisions didn't get all their troops at once - it was a piecemeal process as troops trickled in. (John Brown, Draftee Division, p. 16). The divisions pulled troops in from all over the country - for example, the 88th Division got one shipment largely from the Northeast, and then another from the Midwest and Southwest, dubbed 'Okies.' (Id., p. 17).

So you had divisions 'coming out the door' after a year after drawing troops from all over, and being assigned to one of four areas: Europe, North Africa, Pacific, or reserve within the US. (Matloff). The bulk of the Army's divisions were dedicated to Overlord, since the invasion had to be a massive punch a) to get through, b) to mollify the Soviets who were desperately calling for aid.

As another aspect to this, if geographic proximity to the theatre had no impact on deployment, did experience with the terrain? Like, would draftees from New Mexico be more likely to be deployed in North Africa because of experience with deserts?

EDIT: Reworded for clarity

Hello everyone,

Unfortunately, we have already had to remove a number of poor quality responses in this thread. In this thread, there have been a large number of incorrect, speculative, or otherwise disallowed comments, and as such, they were removed by the mod-team. Please, before you attempt answer the question, keep in mind our rules concerning in-depth and comprehensive responses. Answers that do not meet the standards we ask for will be removed.

Additionally, it is unfair to the OP to derail this thread with off topic conversation, so if anyone has further questions or concerns, I would ask that they be directed to modmail, or a META thread. Thank you!

I asked this before, but the thread never took off, so maybe I'll try and piggyback on this one:

What were the odds of getting conscripted in WW2, or the Vietnam war?

I mention those 2 instances as they seem to be the most prominent in the popular culture I'm exposed to, but I would assume it's happened in plenty of other times and places.

So if you were an eligible candidate in (insert war/country of choice), how likely were you to be drafted?

I checked the FAQ and didn't see anything similar based on some keyword searches of the page.