O O O It's Magic (More Wombat Love)

[Neri]

No: HPFGUIDX 159363

> Talisman:
> <huge snip>
> Once again we are left to prod the bloody entrails of exam results, 
> hoping some patterns congeal, so that we can conjure our clues from 
> the stinking carnage.
> 
> But, as we will see, the mysteries of Ms Rowling's "quite 
> complicated" marking system, run deep.
> 

Neri:
I think there's a simple explanation to the mystery. Since the 
questions in many cases don't have definite answers in canon, JKR 
takes it into account. She doesn't necessarily have answers that are 
wrong and answers that are right. Instead she has answers that are 
more right than others.

So for example, taking question 3: what's the most dangerous – 
dementors, inferi, hags, vampires or werewolves. JKR doesn't give 
(say) "inferi" 10 points and 0 for any other answer. Instead, inferi 
get 10, dementors get 9, werewolves get 6, hags get 3 and vampires 
get 1.

If most of the questions are graded this way then it is possible to 
get "Outstanding" with many different variations, as long as they're 
good enough. In addition we don't know what was JKR's benchmark for 
getting an O.

Now, I haven't actually tried to formulate this problem in algebraic 
terms <shudder> but a simple algebraic law says that in order to 
solve for n unknowns you need at least n equations. This means that 
if we have something like 18 questions times 5 answers per question = 
90 unknowns (the grade for each answer) then you'll need *at least* 
90 different O-grade sets of answers to discover these unknowns 
(throw in the benchmark for O as one additional unknown). That's 
assuming you know how to solve a system of 90 equations with 90 
unknowns. Don't look at *me*


But in general, I'd say the way you've been going about it isn't 
unreasonable. If you gather as many different O-grade sets of answers 
as you can find, and grade each answer by its popularity, the results 
should probably be pretty close to JKR's original grading. Not 
identical necessarily, but generally close. For example, your 
popularity pole might find that inferi are slightly more dangerous 
than demenetors while JKR originally graded inferi slightly less 
dangerous, but it would still mean that she probably graded inferi 
and dementors very close.  

Hope this helps,  

Neri