To add onto some of the other answers in here: it’s pretty much impossible to increase the chance that your bags will be one of the first on the carousel, because there are multiple times where bag order effectively gets randomized:

1. The order at which passengers arrive at the airport is random, so you might be among the first, in the middle of the pack, or among the last.
2. there are often multiple check-in counters, so your bag tends to get mixed up among other bags for your flight and other flights.
3. Once the bag enters the luggage maze beneath the airport, there are a number of things that could happen to it and other bags that change the order in which bags are handled:
   • security checks;
   • problems with reading the label;
   • your bag somehow getting lost in the maze;
   • technical or human errors;
4. The bags then end up on carts and get pulled to the airplane. The order in which these bags end up on the carts is also random, and airport employees often are under a lot of pressure to get these bags loaded efficiently. To do this, they’re going to fit as many bags on a cart as possible, trying to squeeze them in and generally putting on the bags quite randomly.
5. At the plane itself, the bags again get unloaded randomly and loaded into the hold randomly. Same rules apply: they’re just going to put these bags in the most optimal way to save time, so randomly and tightly fitting.
6. Once the plane lands, the luggage gets unloaded. It might be through a different cargo door, and again the focus is on getting everything out of the hold and into the luggage maze as fast as possible.
7. The bag then gets unloaded onto the caroussel, again in a random fashion. It could even again go through another luggage sorting system, with the same isues as in point 3.

I haven’t flown in I think 7 years by now, but before that I tended to take 2 flights a year, more or less in some years. I think I’ve had 1 time in those 40 or so times I’ve flown that I had one of my 4 bags be among the first 5 or so bags to end up on the carousel, and the other 3 bags I checked in didn’t arrive until 10 or 15 minutes later. It’s effectively random.

Math II

This is basically @CactusCake’s answer, simplified. I think my intuition was the same as theirs: You often get counterintuitive things happening (see: the Birthday Problem, I won’t spoil the answer), so we must first get a general idea of “all things being equal, what is the chance?”.

But the answer titled “Math” gets bogged down in hard-to-justify specific details (“Take a Boeing 727!” — “Why?!”), that lead to ballpark numbers (seat occupancy percentages are competitive info, very selectively given out!), that then anyway don’t lead to a numerical or algebraic answer: So there was no reason for those numbers anyway (and the comments didn’t like them!).

So. Reformulation: Let’s assume we have done N different flights (single flights, not ends of connecting flights) where we’ve always checked 1 suitcase in, and the other passengers always checked in 99 other suitcases altogether. So, what is the probability after N flights that we’ve NEVER been first to unload?

Very simple, all these flights are independent occurrences (previous flight doesn’t influence next flight), so it’s the product of these N identical probabilities (see under: IID, Independent & Identically Distributed). And each flight we’ve got a 99% (or 99-out-of-a-100, or 0.99, whatever you prefer) probability of disappointment.

So the chance of unbroken disappointment is .99^N (using ^ for “power of”; this clearly goes to zero for large N) for N flights, … But the real question is, Would you have to be cursed particularly unlucky to be disappointed 100 times in a row??

• 1 flight: 0.99000000 or 0.990
• 2 flights: 0.98010000 or 0.980
• 3 flights: 0.97029900 or 0.970

So I think the OP thought along these lines, “(1- N/100) is a fair approximation, thus after N=100 flights the chance is basically zero”, which is just plain wrong (a linear approximation of a power; a nonsensical negative probability past 100; etc). But it’s that “tail” past the two most significant digits that grows surprisingly fast!

To save calculating and typing, skip steps by just doubling N so you have the square of the previous: N=2, 4, 8, 16, 32, 64; because A^(2N)= A^(N+N)=A^N * A^N = (A^N)^2. So you must double your flights to halve your chance of unbroken disappointment…

• 1 flight: .99000000
• 2 flights: .99000000 * .99000000 = .98010000
• 4 flights: .98010000 * .98010000 = .96059601
• 8 flights: .96059601 * .96059601 = .92274469
• 16 flights: .92274469 * .92274469 = .85145777
• 32 flights: .85145777 * .85145777 = .72498033
• 64 flights: .72498033 * .72498033 = .52559648
• 96 flights = (64 + 32) flights = .72498033 * .52559648 = .38104711 = about 38%

So if three friends each (independently!) take 100 flights each, you expect one of them to have never been first to unload.

Conclusion: You’re unlucky (you missed a 2-in-3 chance of at least once being first), but not particularly unlucky.

And you see the same double-flights-to-halve-chance principle holds for any number of suitcases that are checked in: You’re plotting points f(x) for x=N of a function f(x)=a^x with the parameter a close to (but less than) 1, so x going to infinity (basically for b suitcases on each flight, a=1-(1/b) = (b-1)/b — as said, always less than one, and we have large-ish b, say between 50 and 500?

[[Yes yes I know I’m seemingly horribly rounding in that table, repeatedly multiplying 8-digit-precision and keeping 8-digit-precision… But that was for ease of understanding! They were actually calculated with 20-digit precision, and .381 for N=96 is correct. For 100 flights, it’s a 0.36603234 or over-one-in-three chance.]]

So, further confounding factors: (1) Have you actually checked stuff in on all (or vast majority of) hundred flights? (2) Have you actually never been first? Because (2a) if yours appears first but you have poor positioning at luggage belt, you still won’t retrieve yours first; and first class/priority have best chance for good positioning, and (2b) on international flights if you don’t have “retina scan”/Privium/… fast checking, you may have arrived at the belt with the luggagge already there, exactly the time you were first, natch! Also, (3) practically each flight the first 5items on the belt are pushchairs and child car seats, as they were collected at the gate (after loading checked luggagge, so unloaded first); this may mislead your observations?

With that as a given, on the flights I take you have to pay to check in (always for ‘budget’ companies, the last 2–3years for more medium like BritishAirways in my case — the complimentary gin&tonic is a receding memory on shorter flights!!); so I check in only when I’m on a significant trip, say 10+days or 7days in a cold/wet destination; or sports/elegant dinners thus extra clothes. 5-day academic conference = handluggage only. “Significant trips” tends to be further, so larger plane, so 100+ checked in suitcases seems reasonable to me and the 1-in-3 chance (all else being equal) stands: Redo for 50 if you feel 100 suitcases is not justified.

So this is all a priori reasoning, with the other answers (economy = bottom of unloading priority; economy = checkin on intercontinental closes before business checkin; LIFO to an extent; maybe you have a habit of checking in early; … ) being strong factors on top.

A couple of problems with the premise of your question:

Is it possible that the baggage carousel has bags from other flights still going round? Also, you tend not to hang around once you have your bag. So you don’t really get to see whether your bag was one of the first off the plane or one of the last – it just shows up after what feels like a long time.

This could be a simple case of confirmation bias. You tend to notice when you think you have had to wait a long time at the baggage carousel, sigh and think “oh no, not again”. You perhaps tend to not notice when your wait at the baggage carousel is shorter than usual.

Math

In addition to the existing, quite valid answers provided regarding flyer status, ticket class, and loading/unloading methods used by the airlines to prioritize baggage handling, the problem you experience could simply be ascribed to randomness.

You say you’ve flown 100+ times, but how many times exactly in excess of 100 flights have you checked bags? Consider that the most passenger airliners have seats for around 200 – 500 passengers. If we assume most of them sell 90% of their seats and then 50% of those seats are associated with one or more checked bags (I’m just guessing numbers here but trying to stay conservative), then a small aircraft would still have about 45 passengers checking bags. A more averaged sized aircraft might have 100-200 passengers checking bags (and many more – almost every passenger – on any transcontinental flights), some of whom will check more than one bag.

If you exclusively took small planes, and baggage handling was purely random, then you might expect to see your bag be first out on the carousel about once in every 50 flights. But we’re pretty sure it’s not purely random. And it’s probably also safe to assume you’re not exclusively travelling on small aircraft. Maybe your bag’s turn to be first off just hasn’t come around yet. Or maybe it has and you just didn’t get to the carousel immediately when it happened. Or maybe your bags just have a hideous design that the baggage handlers don’t want to go near.

Your baggage is not guaranteed not to come first but the odds are stacked against you as described by answers you already got:

• First and Business class often get preferential treatment.
• Airline status gives early baggage privileges to those who have it.

There are other things that have an impact too:

• Baggage on short connections can get prioritized. Sometimes baggage makes it even when the passenger doesn’t! On Thai Airways, the last time I flew with less than 30 mins to connect, they added a label to mine saying Hot Connection. Even if not labelled, they probably know.
• Fragile baggage can get loaded and unloaded by a separate process. Usually loaded last and unloaded first. Sometimes they place it on the carousel at arrivals, sometimes next to it.

The main reasons on why the OP’s baggage never arrive one of the first fall under two broad categories – priority baggages and when you check your baggage.

Some baggage get prioritised when getting off the plane

Flight class matters

As the OP has pointed out in the question, the order for a baggage to be loaded on the luggage belt (or their equivalent) may depend on the flight class you are flying on. For example, American Airlines’s priority baggage delivery states the following eligibility:

This service applies only to:

First Class and Business Class customers

Virgin Atlantic’s introduction to Premium Economy states (emphasis mine):

Skip the queues

With dedicated check in and bag drop, we’ll fast track your airport experience. You’ll also enjoy priority boarding and, where possible, your bag will be one of the first off the plane when we arrive.

Frequent flyer status also matters

Also as @jcaron pointed out in the comments, it can also depend on one’s frequent flyer status. As an example, oneworld Emerald and Sapphire members gets priority baggage according to American Airlines and Cathay Pacific; Star Alliance Gold, and SkyPriority members also get priority baggage handling.

These benefits are usually offered regardless of which class one is flying in. So it is possible for someone travelling in economy to have their luggage delivered first on this basis, despite deplaning after the OP.

The time you check your bag can decide when it gets off

…but it is not a guarantee.

While a common school of thought says baggage operates on a LIFO (last in, first out) system, there is an old discussion on here that questions if it is actually always the case.

In some cases, some operators could use a FIFO (first in, first out) system. This can perhaps be achieved if e.g. the origin airport uses the right cargo door, and the destination airport uses the left cargo door (Boeing 787 do have cargo door on both sides, though I am nowhere near an aviation expert and this is pure speculation).

Lastly as @RoboKaren points out in a comment, "LIFO is confounded by the use of baggage carts or by cargo units." They make the ordering more random, and in this case the first class of reasons will then assume a higher precedence.

A footnote on flight class: It is unfortunate that the OP seemed to have rejected his own proposed reason due to a false premise – while it is true that an average non-economy passenger should arrive at the luggage belt prior to an average economy passenger, not all does so on a regular basis due to a variety of reasons.

As an anecdotal example, I have travelled on a non-economy class for a few times, and every time I got hold up slightly in the immigration queue (as I am subject to immigration control on where I am travelling), and arrived the luggage hall finding mine and a handful of priority luggages going round and hundreds of passengers from the same flight waiting, perhaps impatiently.

May it be because you come to airport well in advance and submit your luggage promptly?

After I have started coming to airports later and register for flight towards the end of this process, I have noticed that my bags come to conveyor belt much earlier than they used to!

This is a purely anecdotal evidence of course.