Let's assume you want the most powerful start in the Labyrinth. You have your Gateclosers at the ready to destabilize your Gate, you have your people (who, sadly, are still below 18 in every potential)... but you want a Jonathan in your team.

In chapter 2, you see the process of inserting Adjustment milestones in progress, and the Labyrinth attempts Adj. I (+1), resulting in Jonathan (who had, at best a 16 in Focus) still not qualifying, and so, everyone in the "batch" got Adj. II (+1+2) which makes all six viable Professionals. And some of them even end with 20 score in some stats because their 17 got transformed into 20.

So... you don't want your best and brightest (because if any of them has 18, they get immediately deposited in the Plaza with their Profession), but close. And mixed in, you want the person who has the lowest potential possible, to get the bigger boost. Your objective? Get your main Professionals already qualified for Tier 2 "out of the gate". Everyone with 25 or the right pairs of 20. You're aiming for a +8 boost if possible, which means Adjustment IV (+10).

Where do you find that catalyst?

The first point is: the Labyrinth scores potential (meaning genetic potential). There's a scene in book 1 where the spontaneous abortions of Professionals is discussed, and the fact that there are actually 3 kids born IN the Labyrinth, because they had an 18 Potential before birth. What happens during pregnancy and accidents after birth do not count, it's the pure luck of genetics (incidentally, yes, children of Professionals have a slightly higher chance of being qualified than a random mundane, even if "return to the mean" happens).

There's also bits of the story you haven't seen that touch on the above. Jacques Deschanel, which you've seen being thrown in the Labyrinth in the flashback at Versailles, is a veteran of the Napoleonic Wars who got some crippling injury of the hand and got the light duty of doing guardsman at Versailles. All traces of that got erased as he regenerated from combat, and the Labyrinth pulled him back toward his potential, rather than what he'd got from life's hazards.

So, you have to find the person with extreme bad luck in the genetic lottery.

Now, potential is scored on a bell curve of 10-20, with 15 being the average. But the thing is, the standard deviation is low. It's below 1 point. If it was greater, then it would be relatively easy to find someone with 18+ in any of 10 scores.

If this was a tabletop variant of D&D, you'd be tempted to roll 2d6+8, which gives you a nice 10-20 score with a 15 average. But with 2d6+8, then you have a one in 6 chance of getting 18 in any particular score. And that's where math mucks it a lot for you: if you have 10 different scores, and 1/6 chance of being qualified in any of the scores... then 83% of the people in the UK would be Professionals.

(that's because you want your players to qualify. If every D&D session started with "okay, that's nine times you've tried to roll a class and failed, you're out", you'd be out of a GM job quickly)

Now, I'm not going to talk about the 1-to-1 mapping of what actually the Labyrinth measures and names Strength, Intelligence, or Focus. It is not a linear mapping of what we'd measure as strength in lbs lifted or something, or IQ test result, let alone the g-factor ("g", when you talk about intelligence, is "general intelligence", and cannot be measured directly - you can measure different aspects of intelligence that are all strongly correlated with "g", like IQ testing). It correlates with those (high Strength translates in high physical strength), but it is not actually those. Presence, for instance, is not charisma or something. It's your actual presence in the world (and it is the most supernatural of the stats, followed possibly by Wisdom who is the most abstract and probably detached from reality).

But the math behind the Labyrinth potentials is simple: it's a very tight bell curve bounded by 10 and 20, and the variation is 1 in 15 for every point.

That means that, if 15 is average Intelligence, only one person in 15 has 16 or higher. And of those, one in 15 has 17 or higher. One in 3375 has 18 and qualifies for Arcanist, one in 50625 has 19+ and will not need more than 2 Milestones for tier 2, and finally, one in 759,375 is a "natural 20".

That works both ways, by the way. To get someone with a 11 or worse score in Int, it's one person in 50k.

However... there are 10 scores. Any of them qualifies you. So, even if you have only a chance in 3375 to get 18+ in a specific score, you have a one chance in 337.9 to have at least one score at 18 among them. That's why finding Professional was arduous: you pick a gaggle of people, throw them through the Gate, and only one in 338 isn't coming out because he/she won. You can winnow by pre-selection for some visible characteristics - and that's what the new method of Potential Scanners lets you. Otherwise, you have the way it happens in the flashback in Versailles - you send the people from academics, and you probably have a better chance than average of finding a 18+ in INT among them. And they might still qualify for others.

So, let's go back to out quest for a Jonathan. If you aim for Adjustment II, you need someone that doesn't qualify after a single step, so you want to find someone who has 16 or less in every score. That's... easy. It's actually almost exactly 50%. One person in two in the UK is a "Jonathan" with nothing higher than 16.

Which also means there was an 98% chance that the group of six had at least one Jonathan, by the way. Giving them a single Adjustment step would be unrealistic.

So, Adjustment II is trivial to get. What about III?

To get Adjustment III, you need someone who doesn't qualify after getting a +3 boost, so someone who is BELOW 15. In every score.

And that's where the math flips. To qualify for something you need one in any of ten scores, it doesn't matter which. So, to disqualify, you need every ten scores below your limit.

So, what is the probably of someone having 14 (or less) in every single score? It's actually one in 15^10, because one person in 15 is 14 or less in a specific score. And you want ten of them.

The Triple-Jonathan happens only once in 576 billions. If you get very, very lucky - and you have enough Potentials Scanners to examine the entire world population - you may find one.

What about IV then? If III requires extreme luck, how much worse is IV?

III gave you +6. You need someone who still hasn't any Potential at 18 with +6, that means someone with 11 or 10. In every score. 11 in a single score is 1 in 15^4 (50625). 11 in every score is 1 in 50625^10.

It is one in over 10^47. Gajillions of gajillions. It is that worse. If there was one trilion persons born every second since the birth of the universe itself, you would still have less than one chance in a trillion to have found one for your experiment across all that time.

So, no. Get your Adjustment II, and be happy with it.

This article was prompted by the fact that you know someone is going to attempt it. The French are already trying to make it happen. But no. They get a II, and that's it.

There is, of course, a way to make that happen. You pick a team of masochists, almost all of them will end up with multiple 18 scores, they swap immediately professions, and voila; they get 25 without leaving the Plaza. But they pay it with a large XP penalty.

And then, they have to make their way to tier two. It still takes time, because they end up on some forsaken tier one zone, with no one to powerlevel them.

I mean, 18 years later, the Gardener and his wife team still hasn't made his way back to France or anywhere else.