[r-t] Blue Line Difficulty

[Graham John]

On 9 March, 2005(!!) Peter King started a thread entitled "Method
Difficulty" saying:

> Can anyone think of an objective measure for method difficulty?
> I know it is a highly subjective issue, rather like music, but, like
> it or not, there are measures there (like crus, or little bell roll ups
> or counts of other preferred combinations). Are there sensible
> equivalents for difficulty. What I mean is difficulty in learning and
> ringing (rather than conducting or composing). I sort of have in
> mind that there must be some measure of the number of bits
> of information you need to store to ring the method. So plain
> bob you only have to remember to dodge when the treble leads.
> Whole chunks of Cambridge can be condensed by learning
> "places in 56" (or wherever), or front work. However, large
> amounts of Belfast it seems you have to learn explicitly almost
> on a blow by blow basis. So Belfast is harder than Cambridge
> is harder than plain, seems reasonable. However, is this simply
> because we tend to ring lots of cambridge type methods with
> the same kind of work repeated and if we rang more Belfast
> type methods we would get used to those bits of work. Or is
> there something intrinsic to certain types of work making them
> harder to lump together.

http://lists.ringingworld.co.uk/pipermail/ringing-theory_bellringers.org/2005-March/013417.html

Discussion went on to talk about MethodMaster's difficulty index and
perceived shortcomings.

A discussion last week on Facebook about the most difficult TD Royal method
starting me thinking about adding a difficulty index to Complib, and what
would make a good algorithm. I thought it would also be good if the concept
could be applied to compositions as well as plain courses of methods e.g.
what is the relatively difficulty of a peal of a single method vs Smith's
23, Chandler's 23, or 38 Spliced Surprise Maximus.

One thing I have done so far is to split the lines into unique pieces of
work, and this appears to be a useful starting point, as this and the order
they come in, are what you need to ring it. The basis I have used to split
the line into pieces of work is whenever there are three blows of hunting
forwards or backwards. For Cambridge Surprise Major, this gives 12 unique
pieces of work, namely:

1, 2: isolated dodge up/down
3,4: lead & dodge/dodge & lead
5,6: treble bob at front and back
7,8 dodge, lie double dodge and its reverse
9,10: places up/down
11: backwork starting and ending with a double dodge
12: frontwork

Because Cambridge extends very simply, it does not introduce any new work.
There are twelve unique pieces of work at every stage.

Here are the number of unique pieces of work for some other methods:
Plain B Major: 7
Oxford TB Major: 7
Kent TB Major: 8
Stedman Triples: 9
Derwent S Major: 10
Cambridge S Major: 12
Cornwall S Major: 13
Double Norwich CB Major: 14
Pudsey S Major: 14
Superlative S Major: 14
Cray S Major: 14
Yorkshire S Major: 16
Lincolnshire S Major: 18
Lessness S Major: 19
Bristol S Major: 22
Belfast S Major: 25
Shepperton S Major: 27
Glasgow S Major: 28
Bristol S Royal: 28
Bristol S Maximus: 30
Orion S Maximus: 36
Rigel S Maximus: 39

On its own, the count of unique pieces of work is already starting to rank
methods in rough order of difficulty, but is probably insufficient on its
own. However it does suggest that any refinement needs to be subtle. One
way to do this, is to score each of the unique pieces of work sum the
scores as a complexity index. The pieces of work are of varying lengths and
one would expect the score for an isolated dodge and Cambridge places to be
different. The question is how to derive a score (based upon a sequence of
bell positions) to best reflect the difficulty of learning that piece of
work.

I have tried a few things, but I'm not yet happy I've found a good
solution. Does anyone have any thoughts on the matter?

Graham
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