"I assumed that fertility drugs caused the ovaries to release more than one egg." — This is true, but it's not a net loss because those "extra" eggs were specifically going to be killed otherwise. I'll offer a more detailed explanation here, because the science is fun, and schools absolutely do not bother to demystify this for us. ;)

So, basically, your body has a constant rotation of eggs in various stages of development at any given time. You're born with your eggs in "suspended animation," so to speak; they exist, but they're not "ready" for fertilization yet, and as various factors in your life cause damage to the egg cells, those cells get discarded. When you reach sexual maturity, your body starts producing hormones to bring the eggs from "suspended animation" into a state ready for fertilization. It takes a couple months to get an egg from this first step, though, to ovulation-worthy. So your body has a running rotation of eggs in the active maturation process all the time.

Some eggs are just too damaged to respond to the "let's get ready!" hormones that your body hits them with. Sometimes, there are other issues with a given egg. Your body tries to fix the eggs' problems when it can, but it can't always do so. (And the older you get, the harder it is for your body to fix them; this is why egg quality declines with age.)

So your body runs quality control on the eggs that it's actively working on at any given time, gradually disposing of the "lesser" eggs in development — constantly. Such that, by the time you get your period in any given month, there are usually just a handful of very likely contenders for your upcoming ovulation, and your body will spend the next couple days juicing those eggs up to see which one is the best.

Normally, a few days before ovulation, it chooses just ONE best egg (or potentially picks just one of those eggs at random) from that month's cohort, and it gets rid of the extras that almost made it to the finish line. As it goes full-force into jazzing up the one egg it likes the most, it stops investing in the rest from that month's candidates. (With later cohorts of eggs in lesser stages of active development at the same time.)

In other words, without fertility drugs, you "release" one egg — and your body kills the rest of the competitors from its cohort. So, you release one, and you also lose a bunch.

By contrast, fertility drugs like the ones used in egg freezing are designed to make your body release as many of the eggs from that cohort as possible, instead of releasing only one of them and killing the rest.

So a standard egg freezing protocol involves this:

1) You take a hormone to encourage your body to jazz up all the contenders in that month's cohort. They'll keep growing for a couple days, and your body would normally start to decide on a favorite. That's when...

2) You add another hormone to tell your body: "Keep this whole cohort! Don't play favorites! Keep investing in all these eggs!"

3) You eventually stop taking Hormone 1 because your body has gotten the memo and the eggs are mostly approaching readiness. You keep taking Hormone 2, though, so that your body doesn't start throwing any of those eggs away.

4) You take another hormone — the "trigger shot" — to tell your body: "The release date is approaching. Put the finishing touches on these eggs so they can be used. It's time for them to ship." And that basically tells your body to prepare to release all those eggs (from that cohort) for ovulation. Instead, your doctor extracts them with a syringe and freezes them for you. :)

So... yes, fertility drugs cause you to "release" more than one egg; they're stimulating your ovaries to give them extra help in developing the eggs. This makes your ovaries more likely to produce an ovulation-worthy egg every month than if they weren't getting this help. BUT the extra help for your ovaries also means you might end up with more than one ovulation-worthy eggs in a given month. This is why the risk of multiples is substantial if you have unprotected sex while on them. But what the drugs are really doing is making you "release" eggs that your body was otherwise going to neglect and let die.

Lastly — very important — just because an egg reaches full maturity and gets ovulated/extracted, this isn't a guarantee that the egg is good. Sadly, some eggs make it all the way to ovulation/retrieval day and still aren't able to be fertilized, to implant, to make it full-term, to create a healthy child, etc. And the chances of the eggs being good can diminish with various factors, like the person's age at the time of ovulation, or various health circumstances. This is why freezing is a huge gamble: your body will do what it can to help those eggs develop optimally, but there's no knowing if the eggs truly ARE optimal until you actually try to use them. Hence, many people do more than one freezing cycle.

I hope this helps demystify it all!