UKC

Do trad grades follow a geometric sequence?

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 planetmarshall 07 Aug 2014
I noticed that the Trad grades distribution on the stats page (http://www.ukclimbing.com/logbook/graphs.html -> Climbs by grade ->Trad) follows an almost perfect geometric sequence from VS up to E7.

Brief explanation to non-mathematicians, a geometric sequence is such that each value is some multiple of the previous. Here it appears that half as many climbers climb HVS than VS, and half as many again climb E1 and so on.

Do people think that HVS is 'twice as hard' as VS, and E2 twice as hard as E1, and so on?
 Bob 07 Aug 2014
In reply to planetmarshall:

No!

Grades and difficulty are a continuum, as climbers we just assign names/numbers to particular points on that line. They aren't discrete steps and the boundary between any two grades is fuzzy at best.
In reply to Bob:
> Grades and difficulty are a continuum, as climbers we just assign names/numbers to particular points on that line. They aren't discrete steps and the boundary between any two grades is fuzzy at best.

Well, they clearly *are* discrete steps. While there obviously is a continuum of difficulty, it's equally true that there is some sense of an 'average' VS and an 'average' HVS, and the data seems to bear out the hypothesis that they follow a geometric pattern of difficulty.
Post edited at 09:25
 3 Names 07 Aug 2014
In reply to planetmarshall:

None of which prove your first point, which is of course nonsense.
 Coel Hellier 07 Aug 2014
In reply to planetmarshall:

This graph is part of my argument for HS not being a "proper" grade (merely a subdivision). If you subsume the sub-grades, leaving the "full" grades M, D, VD, S, VS, HVS, E1 ..., the you get a pretty good skewed Gaussian profile, which is more or less what you expect.

That does not mean that the grades are geometric. If the grade progressions are linear, wouldn't you still expect a Gaussian for population of the grades? This would give you an exponential high-end tail, which is what you see.
In reply to 3 Names:

> None of which prove your first point, which is of course nonsense.

I haven't made any points, only observations. It's not nonsense, since the data clearly does follow a geometric pattern. I think this is interesting since grades are an artificial construct, whereas patterns like this are more typical of natural phenomena.
 Michael Ryan 07 Aug 2014
In reply to planetmarshall:


> Do people think that HVS is 'twice as hard' as VS, and E2 twice as hard as E1, and so on?

Some do.

This one of the best theories..

How hard is "hard?" How much harder is one grade than another?


http://philtraining.blogspot.co.uk/2014/06/ratings-difficulty-and-worlds-fi...
Removed User 07 Aug 2014
In reply to Coel Hellier:

You're assuming a normal distribution of climbers over the grades when everyone knows UKC is mainly punters.
 John H Bull 07 Aug 2014
In reply to planetmarshall:
Need to control for the number of available routes, as opposed to ascents. If there are twice as many VS routes as HVS routes then you might want to distinguish between availability of routes versus how hard people climb.
Post edited at 09:43
In reply to Coel Hellier:

> This would give you an exponential high-end tail, which is what you see.

It's not exponential though. An exponential tail would decay much more rapidly. Instead you get a common ratio between the grades of about 0.4-0.6

As far as difficulty goes, yes that's purely subjective, I was just curious if it reflected the general opinion ( from climbers I've talked to ) that there's a 'jump' between the perceived difficulty of climbs at each grade.

 Quiddity 07 Aug 2014
In reply to planetmarshall:

> Do people think that HVS is 'twice as hard' as VS, and E2 twice as hard as E1, and so on?

What would it mean for route X to be objectively 'twice' as hard as route Y?

Making ratio comparisons doesn't make any conceptual sense when you apply it to ordinal scale data. It is like saying that a student who got a B did 'twice as well' as a student who got a D, or that a runner who came 10th in a race did 'twice as well' as a runner who came in 20th.
 fraserbarrett 07 Aug 2014
In reply to planetmarshall:

Interestingly if you add up all the climbs below VS the combined total fits too, just about.
In reply to Quiddity:

> What would it mean for route X to be objectively 'twice' as hard as route Y?

Well that's basically the question I'm asking. Does the objective data support the subjective notion of 'difficulty'? Personally I haven't felt that there's a geometric sense in the difficulty of climbs, but then I haven't climbed beyond HVS. Certainly I found the jump from S to VS pretty large, but it's now hard to say with any objectivity whether I feel VS to HVS is a similar leap, or one twice as large.

 1poundSOCKS 07 Aug 2014
In reply to Michael Ryan:

I think it's about time the UKC logbook started predicting when we'll achieve a next grade.
 PPP 07 Aug 2014
In reply to planetmarshall:

Someone who can climb E3, will climb lower grade to warm-up or can do more of them. You don't expect to climb all day the highest grade you can, but you can climb something easier more times a day.
 Bob 07 Aug 2014
In reply to planetmarshall:

The key word in that statement is "perceived". If you gave a route a grade of HVS.9, how much easier is it than a route graded E1.0? If grades were discrete as you claim then the difference would be the same as between HVS.5 & E1.5, i.e. the nominal average of the grade.

Since we are all different and have different strengths and weaknesses when you get close to the boundaries of a grade then some will find a route easy for the grade and others won't. Since grades are (mostly) a consensus then the boundaries are necessarily fuzzy rather than distinct. If you were drawing the grades as a graph then rather than a series of sharp edged steps you'd draw a set of quarter circles upper-left leading to lower-right quadrant as each grade merged in to the next.
 Quiddity 07 Aug 2014
In reply to planetmarshall:

> > What would it mean for route X to be objectively 'twice' as hard as route Y?

> Well that's basically the question I'm asking.

The question was rhetorical, I am saying it doesn't make any conceptual sense unless you are going to try to quantitatively define difficulty in a way that doesn't use an ordinal scale with arbitrary labels.

> Does the objective data support the subjective notion of 'difficulty'?

If you are asking, is an average HVS harder than an average VS, then the answer is yes by definition. If you are asking, are there discrete steps between different grades, then the answer is no, grades are arbitrarily chosen steps on a continuum.

What I think you are actually asking, is is there are common multiplier to scale from grade VS to HVS to E1 - what I am saying is the question as asked doesn't make conceptual sense, as this type of operation is meaningless unless you are dealing with a ratio scale with a true zero, like seconds or metres or kilograms.
 Stevie989 07 Aug 2014
In reply to planetmarshall:

There will be an Easy,middling and Hard banding within each grade.

The difference between a 'HARD' HVS and an 'EASY' E1 will not be so much at all. (then you have your technical grades)
 MaranaF 07 Aug 2014
In reply to Removed User:

> everyone knows UKC is mainly punters

How patronizing is that!
 1poundSOCKS 07 Aug 2014
In reply to Stevie989:

Although most people will find an soft touch E1 easier than a sandbag HVS.
 3 Names 07 Aug 2014
In reply to Quiddity:

Thats what I said?
 Quiddity 07 Aug 2014
In reply to 3 Names:

more or less
In reply to Quiddity:

> What I think you are actually asking, is is there are common multiplier to scale from grade VS to HVS to E1 - what I am saying is the question as asked doesn't make conceptual sense, as this type of operation is meaningless unless you are dealing with a ratio scale with a true zero, like seconds or metres or kilograms.

Not exactly, and I am familiar with SI units of Measurement and Wikipedia, thanks.

We're all aware that difficulty is subjective, and that we can't answer the question "Is climb X twice as hard as climb Y" in any kind of objective fashion ( unless we were to actually define 'twice as hard' as 'on average, twice as many climbers have climbed route Y' or 'There are twice as many routes at the grade of climb Y as there are at the grade of climb X' in the first place ). Nonetheless, the consensus of climbers seem to have arrived at a grading scale that has 'converged' on a geometric progression and I was wondering if this reflects how climbers, subjectively, feel about the difficulty of the grades.

 Quiddity 07 Aug 2014
In reply to planetmarshall:
Ok I see what you are saying, it is not the grades that you are suggesting follow a geometric sequence but the number of ascents at each successive grade.

The thing is it's difficult to see what that would mean in subjective terms. Something like, is doing four HVSs in some sense equivalent, perhaps in terms of subjective effort, to doing two E1s or a single E2? I certainly find it difficult to imagine what the subjective difficulty of something would be if told it was equivalent to doing two of something else - subjective effort is not really additive like that.

While I could see that this might be more applicable right at someone's limit (ie, a leader with PB of E1 might or might not find doing their first E2 approximately the same subjective difficulty as doing two routes at their PB level) it certainly wouldn't be the case for an E8 leader, for whom I suspect the increase in difficulty from HVS to E1 to E2 would be perceived as much more linear.

If you are after speculation I'd suggest that this subjective feeling (and probably the data) is an artefact of diminishing returns from individual improvement, (ie. the better you get, the more effort you have to put in for each incremental improvement) rather than being anything intrinsic to a particular grading system.
Post edited at 11:32
In reply to Quiddity:

> If you are after speculation I'd suggest that this subjective feeling (and probably the data) is an artefact of diminishing returns from individual improvement, (ie. the better you get, the more effort you have to put in for each incremental improvement) rather than being anything intrinsic to a particular grading system.

I suspect this is close to the mark. It reminds me of 'Benford's Law' that predicts the occurrence of certain digits in quantities that arise naturally such as heights, weights ( and, oddly, tax returns hence its use in fraud detection ). I thought it was interesting as although our grading system is artificial, over time the effect of the consensus of thousands of climbers have resulted in it following a similar pattern to a naturally occurring phenomenon.
 dr evil 07 Aug 2014
In reply to planetmarshall:
What an interesting observation, thanks! I see the sports grades don't follow quite as smoothly, maybe because each grade is a smaller step and therefore more subject to variation?

 David Coley 07 Aug 2014
In reply to planetmarshall:

Given that all rock grades are defined in terms of the fraction of climbers that can do a route, with the fraction and the boundaries undefined, it is very easy to answer the question as to whether a climb is twice as hard as another. If only half the number of climbers can climb it, it is twice as hard. Seems a very natural way of putting it to me.

 Jimbo C 07 Aug 2014
In reply to planetmarshall:

My first thought was 'that can't be right' as it is such a seemingly random set of data but then I looked at the graph and I have to agree that it is more or less a geometric distribution between VS and E7 like you say.

I don't feel that the next grade up is twice as hard. If I had to define what is twice as hard as VS for me I'd say somewhere between E1 and E2 but there is no way to numerically define something like that.

What the graph does show is that each step up in grade sees roughly half the amount of successes from UKC logbook users. If you imagined an average climber based on this data then they climb HVS half as often as VS even though it's less than twice as hard. This then suggests that the average climber prefers to climb within their comfort zone (I know I do).
In reply to MaranaF:

> (In reply to Hardonicus)
>
> [...]
>
> How patronizing is that!

Twice as patronising as...
Post edited at 13:55
In reply to David Coley:
> (In reply to planetmarshall)
>
> Given that all rock grades are defined in terms of the fraction of climbers that can do a route, with the fraction and the boundaries undefined, it is very easy to answer the question as to whether a climb is twice as hard as another. If only half the number of climbers can climb it, it is twice as hard. Seems a very natural way of putting it to me.

I don't buy it. You are excluding people with less ability/drive as you go up the grade.
Surely it is the grade you have to train 'twice as hard' to get to (another uncategorisable thing).
 Quiddity 07 Aug 2014
In reply to David Coley:
> Given that all rock grades are defined in terms of the fraction of climbers that can do a route, with the fraction and the boundaries undefined, it is very easy to answer the question as to whether a climb is twice as hard as another. If only half the number of climbers can climb it, it is twice as hard. Seems a very natural way of putting it to me.

Nice idea but it doesn't really work in my view.

Half of what climbers? 50% of climbers who attempt it? 50% of all climbers? Does that include climbers who exclusively climb on bolts or on an indoor wall? Or just that the route only has 50% of the total number of successful ascents (logged on UKC)? Pretty sure any of those would give you a different result.

Imagine, if you will, two routes which require radically different skill sets - route A is strenuous and physical, route B is technically easy but extremely bold - what if only 50% of those who can climb route A can climb route B, but only 50% of those who can climb route B can climb route A. Then you are in the strange situation where route A is twice as hard as route B which is twice as hard as route A...?

Before we all get too excited, I am pretty sure that ascents by grade, as reported on the stats page include dogged and dnf logbook entries as well.
Post edited at 15:07
 ralphio 07 Aug 2014
In reply to planetmarshall:

I'm confused
 Franco Cookson 07 Aug 2014
In reply to planetmarshall:


You also need to remember that at the point of real H10 all abstract concepts begin to melt, which renders any description of the scale incorrect.
 David Coley 07 Aug 2014
In reply to Quiddity:



> Imagine, if you will, two routes which require radically different skill sets - route A is strenuous and physical, route B is technically easy but extremely bold - what if only 50% of those who can climb route A can climb route B, but only 50% of those who can climb route B can climb route A. Then you are in the strange situation where route A is twice as hard as route B which is twice as hard as route A...?

I don't think it does. The solution to the puzzle is that it doesn't have to be the same people.

All rock grades work as follows, and this goes for HVS, 6a, F7a+, V5 etc. (Alpine and aid grades are different). You create an ordered list of routes ordered by the number of people who can climb them (or the action to which the grade applies fro Brit. Tech. grade) then stick some boundaries in the list so you can give different names to the each chunk.

This means that given 1000 climbers
1. if 500 can climb a route and 500 can climb another route they must have the same grade. It doesn't mean the same people have to be able to climb both routes.
2. If 700 people can climb route A and only 200 can 200 can climb route B. Then route B can't be given an easier grade than route A.

These are I think the only two things you can tell from rock grades.

Of course back in the real world, we don't do such tests, but rather use the "that felt like 5c" test. However I think it useful to keep returning to the basic definition in the back of your head when grading routes. We all know routes with grades like HVS 4b where the following logic has been applied:

We climb the route and conclude "felt like HVS" this might well be correct, then " It had poor rock and no gear, so must be 4b, because that is what HVS 4b means"

A better way would be to conclude it is HVS, if it is, then see if anyone who normally can't do 4b can follow it. I often find that the truth is more like HVS 4a. But this is so far from the norm we don't want to use such grades.

As an example with about 20 data points. I was climbing at Hartland quay last month with a climbing club. The routes are run out and graded HVS to E3, 5a to 6a. Although only a few of the club could lead the routes, I don't think anyone failed on top rope. This includes a lot of climbers who lead HS, have mainly climbed at the wall and fail to follow me up VS at Chudleigh without a tight rope. Now some of these didn't do the 6a, but they all did the 5b's fine. Madness.












cp123 07 Aug 2014
In reply to planetmarshall:

It is exponential decay if it does drop by 0.4-0.6 x no of ascents per grade.

e.g. radioactive decay where the population size drops by half after each half life step.
In reply to David Coley:

And another thing...
If a grade were twice as hard as the previous grade it would mean that each time you moved up a grade you were twice as good a climber as you'd previously been. An absurd notion.
You could start a season doing VS and finish at E3 (2x2x2x2= a 16 x improvment in climbing ability?)
In reply to DubyaJamesDubya:
> And another thing...

> If a grade were twice as hard as the previous grade it would mean that each time you moved up a grade you were twice as good a climber as you'd previously been. An absurd notion.

I don't think it's that absurd, if by 'moving up a grade' we mean being comfortable onsighting that grade. Also by using the term "twice as good a climber", again we become stuck in defining exactly what it means to be "twice as good". Are there twice as many VS leaders as HVS leaders? Could you not then say that HVS leaders are 'twice as good'?
Post edited at 16:26
In reply to planetmarshall:

But I can state that I move up the grades during a season and I don't become twice as good each time I step up a grade nor do I require twice the skill etc.
 Quiddity 07 Aug 2014
In reply to planetmarshall:

> Are there twice as many VS leaders as HVS leaders? Could you not then say that HVS leaders are 'twice as good'?

No. I pointed this out before. For much the same reason that 20 degrees Centigrade is not twice as hot as 10 degrees Centigrade.
 Michael Gordon 07 Aug 2014
In reply to planetmarshall:

You could indeed say an HVS is twice as difficult to climb as a VS, but it wouldn't mean anything as a statement. Basically you've spotted a trend but are trying to apply a phrase to describe it that doesn't really work.

It just doesn't make sense to say a climb is twice as difficult as another. Twice as difficult to whom? If the lower graded route is at your limit then the harder route will be infinitely more difficult. If both routes are about 10 grades below your limit then the difference between the two routes will be very marginal indeed.

Better to just say there's a definite step up in difficulty between VS and HVS, two steps for VS-E1, four steps for VS-E3 etc.
 David Coley 07 Aug 2014
In reply to DubyaJamesDubya:

> And another thing...

> If a grade were twice as hard as the previous grade it would mean that each time you moved up a grade you were twice as good a climber as you'd previously been. An absurd notion.

> You could start a season doing VS and finish at E3 (2x2x2x2= a 16 x improvment in climbing ability?)

When did I say "a grade were twice as hard as the PREVIOUS grade"?

I said: if half the number of climbers can climb a route then it is twice as hard.

That might be HS to E1 for all I know.

 David Coley 07 Aug 2014
In reply to Michael Gordon:

> It just doesn't make sense to say a climb is twice as difficult as another. Twice as difficult to whom?

I really think you can say this. To me a climb is twice as hard if half the number of people can climb it. Feels like a very natural way of thinking about it and fits in well with the basis of climbing grades.
 Michael Gordon 07 Aug 2014
In reply to David Coley:
> (In reply to DubyaJamesDubya)
>
> When did I say "a grade were twice as hard as the PREVIOUS grade"?
>
> I said: if half the number of climbers can climb a route then it is twice as hard.
>
> That might be HS to E1 for all I know.

According to the OP (going by UKC statistics) this is more or less the case for every grade difference from VS to E7.
 Michael Gordon 07 Aug 2014
In reply to David Coley:
If the only justification for using the phrase 'twice as hard' is that half as many people can climb it, why not just say 'half as many people can climb it' - this as least means something in itself (irrespective of how dubious the statistic is in the first place!).
Post edited at 20:28
 remus Global Crag Moderator 07 Aug 2014
In reply to David Coley:

Its a nice idea
> I really think you can say this. To me a climb is twice as hard if half the number of people can climb it. Feels like a very natural way of thinking about it and fits in well with the basis of climbing grades.

It's a nice idea, just a shame that it's completely separated from reality by the fact that it is a completely impractical test to apply.
 David Coley 07 Aug 2014
In reply to Michael Gordon:

> According to the OP (going by UKC statistics) this is more or less the case for every grade difference from VS to E7.

Michael, I thought the OP's stats were based on the number of routes climbed, not the max grade of the climber or the grade the climber might claim she/he claims as their grade.

The few people I people I know who have climbed E8 or above spend most of their time climbing E4 or below. I think I climb just the same number of V.Diffs in a year as I did when my max grade was V.Diff. No. Actually that's not true, I now climb far more V.Diffs per annum than I did then.
 David Coley 07 Aug 2014
In reply to remus:

> Its a nice idea

> It's a nice idea, just a shame that it's completely separated from reality by the fact that it is a completely impractical test to apply.

Such is life.
 David Coley 07 Aug 2014
In reply to Michael Gordon:

> If the only justification for using the phrase 'twice as hard' is that half as many people can climb it, why not just say 'half as many people can climb it' - this as least means something in itself (irrespective of how dubious the statistic is in the first place!).

Reasonable point.
But much harder to sell the story to the press!
 Michael Gordon 07 Aug 2014
In reply to David Coley:
> (In reply to Michael Gordon)
>
> [...]
>
> Michael, I thought the OP's stats were based on the number of routes climbed, not the max grade of the climber or the grade the climber might claim she/he claims as their grade.

Yes, certainly one of the latter would be a much better measure, for the very good reason you give below!

>
> The few people I people I know who have climbed E8 or above spend most of their time climbing E4 or below. I think I climb just the same number of V.Diffs in a year as I did when my max grade was V.Diff. No. Actually that's not true, I now climb far more V.Diffs per annum than I did then.

 Jimbo C 08 Aug 2014
In reply to planetmarshall:

People seem to be missing the point that climbers don't choose routes at their absolute limit all of the time. This renders the notion that HVS is twice as hard as VS meaningless since the graph is a record of all routes logged.

HVS's getting climbed half as often as VSs does not mean they are twice as hard, not that 'twice as hard' can be defined in the first place.
 Ander 08 Aug 2014
In reply to 3 Names:
> (In reply to planetmarshall)
>
> None of which prove your first point, which is of course nonsense.

Agreed. It's a continuum. Analogue, not digital.
 Ander 08 Aug 2014
In reply to Jimbo C:
> (In reply to planetmarshall)
>
> People seem to be missing the point that climbers don't choose routes at their absolute limit all of the time. This renders the notion that HVS is twice as hard as VS meaningless since the graph is a record of all routes logged.
>
> HVS's getting climbed half as often as VSs does not mean they are twice as hard, not that 'twice as hard' can be defined in the first place.

Agreed.

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