Over the past few days we've been posting thoroughly on the subject of channeler strength and how it follows the bell curve. I thought I'd address some of the misconceptions surrounding this issue once and for all.

1. RJ's own system
a. RJ says that strength follows a bell curve

June 2010

Luckers: Is strength in the power evenly distributed? Would on a scale of one to one hundred the most channelers be on the 50 mark?

Maria : Jim described a bell curve, with most channelers in the middle.

It is important to see that she only answered the first question. Strength is evenly distributed on a bell curve. She never mentioned any system from 1 to 100.

b. RJ follows a 21 level system

June 1995 : RJ said on channeler strength that he knew the rough strength of every channeler in the books, imposed on a 21-level system.

October 1996 : RJ confirms he uses a 21-graded scale.

c. RJ does not have a system from 1 to 100

October 1996 : RJ says he does not use 'a real scale' for OP stuff.

December 2005 : "For Sheep the Evicted, who has heard that I assigned various numerical strengths in the OP to Rand, Ishamael and others based on a scale of 100, no I did not. I have said that in my notes I have such a scale that I used to keep track of everyone, but its main use is for the lesser characters, in particular Aes Sedai, so that I can check on who should defer to whom, who should only listen a little more attentively to whom, and so forth."

Conclusions and extrapolations

While there is no doubt that RJ says that strength in the Power follows a bell curve, there is debate over the nature of this curve. RJ says on many occasions that no linear scale exists from 1 to 100, but rather that he has a scale from 1 to 21. Conversely, we can say that the bell curve follows these strength levels, and that most channelers are centered in the region of level 10, and not in the region of 50 out of 100.

The difference in the two theories is vast. One school believes that most channelers have 50% of maximum power, and thus are about half as strong as those with full power i.e. Rand, the Forsaken. This is wrong, and will be shown later.

The second school believes that most channelers peak at a certain strength i.e. strength level 10 out of 21. The difference however is that the respective strengths of the channelers can vary widely, and that the difference between the levels is not linear. This is the most likely scale that RJ followed. For instance we can see that Morgase can access the Source only 1 in 1000 times, and yet one level up Sorilea is a functional yet weak channeler. Linear? Unlikely, but this is merely one example.

Let us take a real world example. Let us take the speed of the cars on the freeway. They peak somewhere in the middle at say 100kph, with the majority of cars travelling between 80 and 120kph. There are then very few cars that go faster and slower, and perhaps one car going 5kph and some going extremely fast. Is it logical then to state that if most cars peak at 100kph that the fastest car is going 200kph? It makes no sense. There will be cars that go 250 and 300 and even 350 but they are exceedingly rare.

It is the same with channeling. While a strength undoubtedly exists where channelers peak in strength, there is no reason to believe that the strongest channelers are twice this strength. One merely needs to move more and more standard deviations away from the curve to find the higher numbers. Some posters find it unlikely that high strength channelers could be so many standard deviations removed from the mean, but its completely possible for the following reasons...

1. Morgase is literally thousands of times weaker than a normally functional channeler. By definition she is even less than 1% as strong as the average channeler and already several standard deviations to the left of the curve. If someone could access the Source 1 in 100 times, they would be ten times stronger than Morgase.

2. TPoD (New Alliances)- The girl was stronger in the One Power than she [Graendal] herself! Even in her own Age, that had been uncommon among men, and very rare indeed among women. This statement by Graendal reinforces that extremely rare strength is possible. Graendal is a woman of rare strength and we know that Someryn as a Wise One has never found a woman close to her in strength (ACoS - Patterns within Patterns). This already implies that most women don't come close to Someryn's strength among the Aiel. Graendal exceeds even her, then to top it off we have Cyndane who is more powerful and finally Lanfear. With this in mind, its easy to see that outliers in strength do exist that are far from the peak in strength.

Consider the rarity of the following channelers...

1 SD - 1 in 3 channelers
2 SD - 1 in 22 channelers
3 SD - 1 in 370 channelers
4 SD - 1 in 16 000 channelers
5 SD - 1 in 1.7 million channelers

Its completely possible that the highest level channelers sit 5 SD away from the mean, especially in light of Graendal's statement. While Graendal could be at 4 SD, Cyndane could be at 5 and Lanfear even at 6 SD.

2. Disproving that most channelers peak at around 50 out of 100

This is easy, you merely need to look at the series. I'll write another theory this week that shows that most channelers peak at x and that the highest strength levels are at approximately 3x.

1. Egwene/Aviendha and Rand

We know that Egwene is stronger than Amys and Melaine combined...

TFOH (Among the Wise Ones) - You are Aes Sedai, and strong enough in the Power to overwhelm Amys and Melaine together

We know that Amys is either as strong as Moiraine or a little weaker - there are two quotes that seem to oppose one another (LoC - like lightning and rain, ACoS - unseen eyes). Melaine is also in this region, but probably a level down with Faolain/Theodrin.

We also know that this huge strength gap is confirmed by Amys herself. TSR(Sharp Lessons) - I cannot shield you any longer. You are far stronger than I. In the One Power you are. You very nearly battered down my shield.

Therefore Egwene > Amys + Melaine (normally this would be enough to disprove the theory of these other posters, but I shall go on).

Moiraine says that Egwene and Aviendha could perhaps overwhelm one of the Forsaken if they work together. TFOH (News comes from Cairhien) - but what if who is with Rahvin is Semirhage, or Graendal? Or Lanfear? These two might overwhelm, one such, but could you face her and Rahvin together alone?

Of course this has been taken to mean that Egwene and Aviendha have so much strength combined that they can overpower the Forsaken and their knowledge. This is false.

TFOH (Prologue) - ... you are stronger than Aviendha and me together.

Thanks Egwene... which offers conclusive proof that Rand > Egwene + Aviendha. Not only that, but we know now that Egwene > Amys + Melaine.

We also know that Aviendha's strength is not nearly as weak we are expected to believe in other posts. TPoD (To Keep the Bargain) implies that Aviendha's strength is the same as Elayne's as that she requires more of hers to Travel. We also know that as early as TDR (The Bite of Thorns), that Elayne is stronger than any of the Black Ajah, of whom Liandrin is the strongest.

Therefore, in what inverted universe are we to believe that most channelers peak at 50 and that Rand is at 100?

This proves that...
- Rand > Aviendha + Egwene at that point
- Egwene > Amys + Melaine at that point
i.e. Rand > Aviendha + Amys + Melaine (which ties in nicely with Egwene's later statement that she would probably not be able to best one of the Forsaken even linked with the two strongest women in Salidar - ACoS - a pair of silverpike)

2. Flinn and Friends

WH (With the Choedan Kal) - abruptly the old man stopped and thrust out his hand straight forward toward Demandred, and Demandred found himself frantically fending off a net of saidin that struck his warding much harder than it should have, as hard as his own spinning would...

As hard as his own spinning would. We know from this quote that the circle of three i.e. Flinn, Corele and Sarene wove as powerfully as Demandred himself would have.

Flinn is a reasonably strong Asha'aman. We know that he exceeds Gedwyn and Rochaid (TPoD - Gathering Clouds) who are full Asha'aman who together think that they can do as good a job as Rand could against an army. Sarene and Corele appear to be average Aes Sedai.

We know from Elayne that linking allows you access to almost all of your strength, but we also know that linking, and especially mixed linking, provides other benefits.

Thus we see that Demandred = Flinn + Corele + Sarene, easily disproving that two average channelers equal Forsaken strength in combination.

3. Summary

These are two good examples of how the confirmed strength of channelers disproves that peak strength is at 50 out 100. There are many other examples, but they have possible confounders such as Talents, shielding, combat tactics etc. In the above examples we have confirmed channeler strength at those stages of the series proving that the peak strength is way below 50.

This does not disprove the bell curve, which peaks in the vicinity of level 10. It merely disproves that someone at level 10 is half as strong as someone on level 20/21.