Given the discussion Sidious’s Androl/Pevara thread has generated on the Bell Curve, I feel it is necessary to once again raise this issue as a separate topic of discussion. (I know, I know, the forum is overly clogged up with new threads, but I'm daring to post another one anyway.) Smiley face.

In any case, for those who aren’t aware, this thread is based on RJ’s statement that channeler strength in WoT can be represented by a Bell Curve distribution. For those unfamiliar with statistics, a Bell Curve is a perfectly normal distribution, peaking at the average and petering off to either side in a perfectly symmetrical manner.

A Bell Curve by definition means that the distance from the weakest to the strongest channeler is intersected at exactly the 50% mark by the mean (the average channeler). Any skewing of the distribution would mean that the term “Bell Curve” cannot be applied to the distribution. Instead, it would then be either a positively or negatively skewed distribution. But not a Bell Curve.

So the basic rule is that the average channeler has to be exactly half as strong as the strongest channeler. Or to put it differently, a channeler x standard deviations away from the mean on the weak side, must be exactly as far from the mean as a channeler x standard deviations away on the strong side.
RJ has also said that 62.5% of channelers are strong enough to become Aes Sedai. This means that Daigian – who is the weakest possible Aes Sedai – lies exactly on this margin. And it then means that 12.5% of all female channelers lie between Daigian and the average strength woman.

Since it has been strongly suggested that Lanfear is the strongest possible woman, we therefore know that 12.5% of all female channelers lie between Daigian and the channeler who has 50% of Lanfear’s strength.
By applying this logic, the key issue then is to determine – based on the evidence in the books – which channeler lies closest to 50% of Lanfear’s strength – in order to determine how strong all modern Aes Sedai are compared to the Forsaken.
We do know that:

Siuan was previously as strong as Moiraine. We are further told that “even if Siuan was healed to half her former strength, most Aes Sedai would still be stronger than her. This means that Siuan is now less than half her former strength. Yet she is still slightly stronger than Daigian.

A reasonable estimate is that Siuan is therefore about one third as strong as her former strength. We also know that she is not far above Daigian at this stage.

It is therefore very reasonable to suggest that the weakest Aes Sedai is around one third as strong as Moiraine and Siuan’s former strength. The question then is, was Moiraine’s previous strength above or below the average strength female (who has 50% of Lanfear’s strength).

So the question can be broken down to: Can two channelers of Moiraine’s strength match a Forsaken strength channeler?
This has been a topic of some discussion, especially because there are posters who fervently want Moiraine – and by extension all modern Aes Sedai - to be stronger than they actually are.

There are numerous pieces of evidence showing that it is impossible for Moiraine to be half as strong as Lanfear. Without providing an exhaustive list, here are a few examples:


Where has she felt the strength of a Foresaken at this point? What she actually said was:



Note that she's talking of overwhelming them, in the first place. Here's the definition of overwhelm:

Verb:
Bury or drown beneath a huge mass.
Defeat completely.

This does not mean "equal".

In the second place, Moiraine says "might". That's because she really doesn't know. We know that memories from the Rings are fragmented. Based on this statement, the strength of Lanfear is not something Moiraine remembered with accuracy.

Either way, Egwene, close to her full potential, and Aviendha, far from hers, can indeed overwhelm a Graendal or a Lanfear. No one denies that. Its far from proof Moiraine is less than 50% Lanfear's strength.

Because clearly, Aviendha knows more that RJ? You keep forgetting these characters are fallible! Even in your outdated list, Amys sits at strength 30, Melaine at 20-25, and Egwene at 50, correct? No matter how much of her strength she had gained at that point, Egwene cannot be stronger than both these women, in both our scales. Want further proof of that? Here's a quote from Elza on Cadsuane's strength:



If Cadsuane needs an angreal to draw more than Elza and Merise, her base strength is clearly less than their added strength. Cadsuane is marginally weaker than Egwene (at her full potential), and Merise is pegged at about equal to Amys. The real zinger though is that Elza is far weaker than Melaine. If Egwene is stronger than Amys and Melaine combined, Cadsuane has to be stronger than Merise and Elza together.

I leave it to you to decide who is more correct... an Aes Sedai who must constantly weight strength and does so in real time, versus a fresh Wise Ones apprentice who has no real experience weighing strength, and is doing so from her memory of the strength of two of her mentors.


Sorry, no dice.

That is not what Egwene says at all:


She's saying she's not sure that linked with two women definitely stronger together than Aviendha in tFoH, she may not be able to stop a male Foresaken. This sharply contradicts Moiraine's statement that she and Aviendha might "overwhelm" a Lanfear or a Graendal. Egwene is clearly wrong here, given the success of the circles during the Cleansing. And she clearly has no issues later setting a trap which would bring her in direct confrontation with Mesaana.


Of course that was needed. These channelers don't have anywhere near the knowledge and skill of the Foresaken.


Yes he does. The mistake you're making is assuming that Flinn was utilizing the mixed circle perfectly at his first try at one.

Huh? He's far from the most powerful after Taim. In KoD, when Rand needed the strongest Asha'man to face Semirhage, he picked Narishma and Sandomere, not Flinn. We have no clue where Flinn is placed. He may be as strong as Corele for all we know.

And the steady descent into absolute madness seems complete.

Explain this, please:


If an Asha'man and two Aes Sedai can only just match Demandred's weavings, how the heck can one Asha'man and one Aes Sedai overmatch Rand's weaving? Unless the Asha'man have gotten better with mixed circles over time, and Flinn was far from as good as he could be in WH... In fact, Demandred's doubts on whether both the women with Flinn were Aes Sedai only confirm this. He can't credit with certainty that one man in a circle with two women would just match Demandred's strength.

About the one paragraph in this pile of codswallop I can agree with.

Except no, one Foresaken isn't as strong as 4 or five modern AS. Liandrin tells her cronies that three of them can outmatch Moghedien. This is three fairly weak AS against the weakest Foresaken. Then we have two sisters weaker than Liandrin giving Nynaeve a tough challenge. The idea that a Foresaken is as strong as 4 average AS, let along 5, is laughable in the extreme.

Yeah, no. You're just building castles in the air. First of all, the quote of paramount importance is RJ's statement on bell curves. And to your point that he didn't understand the meaning of a bell curve:



Even his assistant knew the implications of the bell curve. RJ was a physicist by training, and DomA reports that Brandon has actually seen graphs in the notes where RJ has drawn the bell curve. You're shoving your head deep in the sand and ignoring the one irrefutable fact in this debate. Everything must be interpreted in the light of this fact. That's the long and the short of it. And the inescapable conclusion is that a few Aes Sedai levels are above the 50% mark, Moiraine's especially so.