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Statistical RAFOgraphy


Shaggai

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 I didn't think it had been fully confirmed, but perhaps I missed something. I'll correct that.

 

Recall that Shallan recognized Amaram's Shardblade and when she and Kaladin were in the chasms (I think?) she mentioned something about her brother being killed and Kaladin made the connection (I believe, don't have the book to check right now; she definitely recognized the Shardblade though).

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Recall that Shallan recognized Amaram's Shardblade and when she and Kaladin were in the chasms (I think?) she mentioned something about her brother being killed and Kaladin made the connection (I believe, don't have the book to check right now; she definitely recognized the Shardblade though).

True. I've edited the document with the information.
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  • 3 months later...

So I finally finished compiling the information for this. Using a sample size of 20 answered RAFO questions, and 30 answered non-RAFO questions (all of them about the Cosmere, compiled from Theoryland and some from the WoB thread), the statistics were:

75% of RAFO'd questions are answered "Yes" and 60% of total questions are answered "Yes". Therefore, the probability of any given RAFO being "Yes" is - without other information - between 75% and 60%.

This can get more complicated, of course. For example, take "the biggest RAFO": Has Hoid been to Braize? Since Brandon has stated that all questions regarding Hoid's life pre-Elantris will be RAFO'd, the probability gets more complex. I'm going to analyze this, so if you just want the probability you can skip to the end.

 

Since we don't have all the information, we need to use Bayesian probability, a branch of probability made for situations where you don't already know the probability and there are gaps in your knowledge. For what I consider to be an intuitive explanation of the math behind this, go here. It's all about ratios and, to some degree, stories.

 

We start with the prior probability (basically, how likely we would rate it before we ask the question) of Hoid having been to Braize. Since Hoid gets just about everywhere, I'll say that it's 75%, because 75% is easy to work with. If you disagree with any of my estimated figures, I can redo this with the ones you choose.

Now, we add in the information that the question was RAFO'd, that all questions about Hoid pre-Elantris get RAFO'd, and that 75% of RAFO's have the answer "yes". When we're done estimating the resulting probability, we'll multiply it all by the prior probability to get the final probability. You can also add each piece of information to the prior probability one at a time, but this time I'm going to do all of the information at once and then adjust for the prior probability.

I'll assume that Hoid's life pre-Elantris was equally long as his life post-Elantris up to now, because the numbers are easier that way. Again, you can challenge my estimates, and I'll redo this. Anyway, if Hoid hasn't been to Braize, there's a 100% chance of this being RAFO'd. If he has, however, there's a 50% chance of it being pre-Elantris, which would be RAFO'd. If it was after Elantris, though, the RAFO statistics kick in. That means that there's a 75% chance of it being RAFO'd. Since that's 75% of the remaining 50%, we add it to the 50% to get 87.5%. Now, the probability of it being "yes" is 87.5 to 100, or 87.5 out of 187.5. When we simplify that, we get 7/15. If we ignored the prior probability, we would say that the probability of it being yes is 7 out of 15 and the probability of it being no is 8 out of 15. But we're not going to ignore the most important piece of information.

Now, we multiply by the prior probability (75%), by multiplying the "yes" probability by three and the "no" probability by one. That leaves us with a probability of 21 to 8, or 21 out of 29. As a percent, that's about 72%. And now we know the probability that Hoid has been to Braize, which is "between 72% and 60%" (not just 72%, because I could be wrong about the probabilities. If you make that sort of estimate, it's always "between the estimate and the default").

 

tl;dr: Approximately 72% chance that Hoid's been to Braize. Statistical RAFOgraphy works!

 

Edit: Fixed some math.

Edited by Shaggai
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