UKC

the mathematics of sport climbing grade distribution?

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 jsmcfarland 07 Dec 2014
Hi there,

A while back I remember there was a two part post on a fairly well known blog where they did an analysis of some numbers from the 8a database about how hard sport climbing grades were relative to each other, e.g. a 8b climb ended up being 2.7 times harder than a 8a+ (based on relative numbers of people reporting climbing the respective grades) etc.

Leaving aside whether you agree with that or not, does anyone else remember this? I've lost it out my bookmarks and wanted to take another look at it but can't remember which blog/site it was Already checked all the major blogs I can think of and no luck. A few hours thinking up all sorts of combinations of google search terms didn't get me anywhere either.

Help?
In reply to jsmcfarland:
Interesting. With the UKC data I get 8b being only 1.35 times as difficult at 8a+ ( which seems more reasonable to me than 2.7 times as hard. Not that I'm in a position to judge the relative difficulty at this grade!)
Post edited at 06:29
 Si dH 07 Dec 2014
In reply to jsmcfarland:

There was a thread with some links that got resurrected briefly on ukb in the last week or so
 Offwidth 07 Dec 2014
In reply to Sally Bustyerface:

In reality the next grade up isnt that much harder it just feels that way for climbers at their limit.
 Robert Durran 07 Dec 2014
In reply to jsmcfarland:
> A while back I remember there was a two part post on a fairly well known blog where they did an analysis of some numbers from the 8a database about how hard sport climbing grades were relative to each other, e.g. a 8b climb ended up being 2.7 times harder than a 8a+ (based on relative numbers of people reporting climbing the respective grades) etc.

Sounds like pseudo mathematical bollocks to me. If half as many people can climb a route, it means just that; not that it is twice as hard (whatever that would mean anyway).
 remus Global Crag Moderator 07 Dec 2014
In reply to Robert Durran:

> Sounds like pseudo mathematical bollocks to me. If half as many people can climb a route, it means just that; not that it is twice as hard (whatever that would mean anyway).

I think it's called 'applied maths'
 climbwhenready 07 Dec 2014
In reply to jsmcfarland:

It's quite interesting, Diff has about half as many ticks as VDiff on UKC so must be about twice as hard
In reply to climbwhenready:

> It's quite interesting, Diff has about half as many ticks as VDiff on UKC so must be about twice as hard

Niiice!
In reply to climbwhenready:

> It's quite interesting, Diff has about half as many ticks as VDiff on UKC so must be about twice as hard

Never mind that - sports 4b is 4 times as hard as 8c according to UKC.
OP jsmcfarland 07 Dec 2014
In reply to Si dH:

Can you send me a link? I couldn't find it :s
In reply to jsmcfarland:

I think that thread might have been more about age and grade.
 Oujmik 08 Dec 2014
In reply to jsmcfarland:

What would be really interesting is to start with a 'gradeless' dataset, just climbers, routes and some metric of how hard each climber found each route (could be as simple as 0=not onsighted, 1=onsighted although obviously this would struggle with hard sport). Then some kind of Bayesian network could be used to simultaneously estimate the difficulty of every climb and the ability of every climber. Obviously there are loads of complications, but I believe some computer gaming leagues as well as possibly an elite chess league use this kind of ranking (although in these cases they only have the rate ability as the players compete with each other rather than with a route).
 daveagilesold 08 Dec 2014
In reply to jsmcfarland:

You're not the only person to have thought of this. Although you are right in saying that there has not been much written on it- if anything in blogs. There are a few authors that have tried to express the difference in terms of the physiological characteristics of the climbers, the following two references might be of interest, if academic journals are your thing:

Delignières, D., Famose, J. -P., Thépaut-Mathieu, C., & Fleurance, P. (1993). A psychophysical study of difficulty rating in rock climbing. International Journal of Sport Psychology, 24, 404-404.

Baláš, J., Panáčková, M., Strejcová, B., Martin, A. J., Cochrane, D. J., Kaláb, M., et al. (2014). The relationship between climbing ability and physiological responses to rock climbing. Scientific World Journal, 2014(678387), 1-6.

Its certainly not an easy question to answer. There are quiet a few questions that emerge, e.g. is it a purely psychological effect of the grade you can't climb always feeling harder (perhaps an obvious feeling?), resulting in a 'extended' gap between future grades and a 'compression' of the grades you can already climb; there will also be diminishing gains when you begin to reach your physical/ psychological potential- e.g. you will have to train harder, smarter for longer to make the next grade.

Keep your eyes peeled over the next couple of years. A world wide multi-centre study is in the works that will be looking at the relationship between technical, tactical, physical and psychological components of a climbers performance and how these relate to climbing grades. It almost certainly won't provide a definitive answer, but will be a good start.
OP jsmcfarland 09 Dec 2014
In reply to jsmcfarland:
Yaaay so I found the original blog post I was looking for that started the whole thread off, if anyone else is interested then here are the two posts:

http://philtraining.blogspot.co.uk/2014/06/ratings-difficulty-and-worlds-fi...
http://philtraining.blogspot.co.uk/2014/07/ratings-difficulty-appendix.html

next will be trying to work out a way to objectively quantify the hardness of trad and sport routes so I could compare the two.......surely that's impossible :P
Post edited at 05:43
In reply to jsmcfarland:

My guess is that if you drew a graph of increasing grade on the X axis and percentage of climbers achieving it on y you would get something looking like half a bell curve and if you counted sigmas away from x = 0 there would be a halfway reasonable correlation with French grade e.g. 68% of climbers would be within 1 sigma from x=0 (roughly 6b), 95% within two sigma (say 7b) and 99.7 percent within 3 sigma (say 8b) and pretty much nobody climbing 9b.
 Offwidth 09 Dec 2014
In reply to jsmcfarland:

In the blog he defines harder as the ratio of the number of people climbing the grade below to those climbing the grade. Yet the actual increase in physical difficulty will be very much less than that: if you limit out at a knob position of 10 on strength or stamina, turning it up to 11 often won't be possible. Also I'm sure climbers mainly work their best grade on a route that suits them and the range of available climbs to choose from limits out on the very top grades.
 steveriley 09 Dec 2014
In reply to jsmcfarland:

I can't help think your trying to time a race using a ruler, but I'm interested in the discussion
 dr evil 09 Dec 2014
In reply to jsmcfarland:


http://www.ukclimbing.com/forums/t.php?t=594543&v=1#x7844590

This is a related thread based on the UKC logbook database
 AdrianC 09 Dec 2014
In reply to jsmcfarland:

And while we're in the area, how does Benford's Law apply to grades?
In reply to AdrianC:

Damn you Adrian C - you have discovered my unpublished paper which reveals the cheaters in UKC logbooks!
OP jsmcfarland 10 Dec 2014
In reply to tom_in_edinburgh:

Thats kind of what I was thinking about.

Everything can be measured (whether the measurement chosen is the best 'fit' or not is not the point), and if it can be measured and there is a big enough sample size (ukc database seems good) then it can be analysed. I'm definitely no mathematician, people loose me as soon as they start talking about sigma etc so I will have to educate myself somehow.

I kind of like the thoughts in the other thread about if 1000 people can climb vs, but only 500 HVS then HVS is twice as hard as VS, though I guess the point is that HVS doesn't have to be twice as hard as VS for you not to climb it, just 0.0001% harder than your current limit.
 Michael Hood 10 Dec 2014
In reply to jsmcfarland: > I kind of like the thoughts in the other thread about if 1000 people can climb vs, but only 500 HVS then HVS is twice as hard as VS,

All that's really doing is defining "twice as hard" to mean half the number of people able to do it.

 Michael Gordon 10 Dec 2014
In reply to Michael Hood:

> > I kind of like the thoughts in the other thread about if 1000 people can climb vs, but only 500 HVS then HVS is twice as hard as VS,

> All that's really doing is defining "twice as hard" to mean half the number of people able to do it.

Exactly. It's just coming up with a phrase which describes the situation less accurately than it did before. One could just as well say that HVS is twice as cool as VS as half as many people can climb it. So what? It's entirely meaningless. Might as well just say half as many folk can climb it - at least that actually means something.
 Michael Hood 10 Dec 2014
In reply to Michael Gordon: I think "HVS is twice as cool as VS" is about as apposite as you can get, great phrase

Now we can have arguments about whether E1 is twice as cool as HVS, E2 twice as cool as E1 and whether there is a constant coolness ratio as we go up the grades, etc.
 jimtitt 10 Dec 2014
In reply to jsmcfarland:

> I kind of like the thoughts in the other thread about if 1000 people can climb vs, but only 500 HVS then HVS is twice as hard as VS, though I guess the point is that HVS doesn't have to be twice as hard as VS for you not to climb it, just 0.0001% harder than your current limit.

Or of course there are only a quarter the number of HVS´s compared to VS´s and we can all climb both, logically HVS is easier
 Michael Gordon 10 Dec 2014
In reply to Michael Hood:

Certainly more coolness is required as you go up the grades! So the harder stuff must be more cool.

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