Origin of the "bell curve" for route setting

When learning how to set climbing routes in gyms, setters are often told to set route difficulties according to a "bell curve". An example of this is mentioned on this page.

What is the origin of this "bell curve"? Is there any science behind it, or is it just a dogma?

Statistics it is also the reason why tons of people go outside for the first time and can't climb harder than V1 or V2 when they are climbing V5 in their gym.

ViperScale . wrote: Statistics it is also the reason why tons of people go outside for the first time and can't climb harder than V1 or V2 when they are climbing V5 in their gym.

Tell us more.

I know what a bell curve is, and I know what the central limit theorem says about weak convergence to a Gaussian.  That says nothing about the distribution of climbers by grade (because a climber's grade is not a sum of independent random variables), and even if you did know the functional form of the distribution of climber grades, you still can't know the parameters of the distribution (e.g. mean and variance) without doing a measurement.

So I ask again: what science is there behind this notion?

What is the science behind creating your account today and coming to the MP forum with a question about routesetting?

Anon Anon wrote: I know what a bell curve is, and I know what the central limit theorem says about weak convergence to a Gaussian.  That says nothing about the distribution of climbers by grade (because a climber's grade is not a sum of independent random variables), and even if you did know the functional form of the distribution of climber grades, you still can't know the parameters of the distribution (e.g. mean and variance) without doing a measurement.

So I ask again: what science is there behind this notion?

It's the same science that invented the stick-clip and the participation trophy....... ;)

I'm not sure what you are asking...

Are you asking if it is true that climbing ability has a distribution like a bell curve? In that case, yes, that is likely true, for climbing skill as well as for a lot of other things, like an IQ. Anytime you have a large population, you will have a lot of attributes showing a normal distribution, aka bell curve.

Are you asking if it is true that the peak of the gym climber bell curve falls somewhere around V2-V4? I don't know where this number comes from, but anecdotal observation suggests that it is about right.

@Luke Bertelsen: I usually ask questions on stackexchange, but there is no SE for climbing, so I thought I'd give this a try.

@Lena chita: I'm asking if there is any science to back up the anecdotal observations you make.  I.e. has anybody actually done a study and compiled real statistics on climber grades?  (Also, climber grades are most definitely not a bell curve in the usual sense, i.e. Gaussian, if for no other reason than that there are no negative grades.  At a more sophisticated level, the high end of the distribution is likely described by some sort of power law, i.e. Pareto distribution.)

t.farrell wrote:Maybe you could ask MP for user data and fit your own distribution? Seems like you’re answering your own question. 

Use data from 8a.nu and likely get a very different distribution XD

ViperScale . wrote: Statistics it is also the reason why tons of people go outside for the first time and can't climb harder than V1 or V2 when they are climbing V5 in their gym.

No, that’s why YOU can’t harder than a V2 outdoors. 

Or just open a climbing gym with equal numbers of the various route difficulties and see which ones have the most customers on them. It´s that scientific.

A lot of people seem to think that I need to be convinced that the distribution of climbers looks in some vague way like a bell curve.  I don't.  I'm asking about what hard, quantitative data exists on the matter.  To reiterate once more, what I would like to know is: What science/statistics are available regarding the distribution of climber grades?

Thanks t.farrell for an honest answer and possibly helpful suggestion.

@Kyle Tarry

However, frankly, not only does this not matter at all

It does matter--to me!  That's why I'm asking the question.  It also matters to analytical route setters, because it helps you know what fraction of your routes you should devote to different grades.

I'm sorry if you find the mathematical language intimidating, but I don't think it detracts from the question.  I'm not looking for opinions, I'm looking for data.  I'm hoping at least one of the people who visits this thread will understand and be able to provide a link that is useful.  

I've been to a handful of gyms that allow people to vote on the grade  and they take the mean of those votes and assign it to the route. I've notice routes reflect the gym proximity to quality outdoor climbs as well. Where a 5.11b at a gym in Kansas maybe be completely different, difficulty wise, than a 5.11b at a gym in Colorado or Utah. 

Kyle and Jim already said most what I what I was going to say. It's pretty clear from the link you cited that the term "bell curve" is just being used to mean some sort of vaguely bell-shaped distribution. I imagine that most climbing gym managers have at least a rough idea about which grades get the most traffic, and they don't want to waste wall space or pay route setters to create a disproportionate number of routes that almost no-one climbs.

Here's a quote from Henri Poincaré that's somewhat relevant: "Everyone believes in the [Gaussian distribution]: the experimenters because they think it is a mathematical theorem, the mathematicians because they think it is an experimental fact".

Be the scientist!  As a general rule, if you're looking for the "science" behind something, you should take a few minutes to try to think through what it would take to design a scientific experiment to test whatever your hypothesis is.  It's a fun exercise and will help you understand the assumptions that need to be made for basically all research.  It seems to me that if this data existed, it would likely only be for one particular gym and you would have to assume that the results transfer to other gyms... which it almost certainly wouldn't because one gym might cater to kids' birthday parties while another might often hold serious competitions.

It is probably just generally accepted wisdom, which isn't science but often has truth embedded in it as well, especially in business.  It also seems fairly intuitive to me - the 5.8-5.10D routes are the most climbed at my gym by far.  5.5s and 5.6s get climbed by kids because they are too boring for most, and I can almost always get on anything 5.12 or above whenever I want.    

With only a little bit of thinking, one experiment could be that you set up a video camera in your gym from afar to capture how many people climb each route, and then watch the video on hyperspeed and plot the number of ascents of each route vs. the route's grade and graph it.  Or run a survey from the front desk asking climbers their most-climbed grade(s).  See if you get a bell curve from the results.  

Anon Anon wrote: What science/statistics are available regarding the distribution of climber grades?

None, really. At least not anything that's statistically sound. Anything that relies on voluntary reporting is going to be subject to all sorts of unknown biases. I imagine that there are a great many climbers like me that fumble their way up trad 5.9 and gym 5.11 and who would never bother to respond to such a questionnaire, assuming we even have reliable records of what we actually climb, which I certainly don't.

Even simpler questions are very difficult to answer. For example, no-one really knows how many active climbers there are.

t.farrell wrote:

There is no science. It’s an assumption about the distribution of climbers’ abilities. I’d speculate that it’s probably closer to lognormal, but as in your link, I have no data. The Normal distribution is generally used because of familiarity and a (supposed) tendency in nature to trend towards Normality (but as you likely know, objects in nature exhibit other trends as well).

Maybe you could ask MP for user data and fit your own distribution? Seems like you’re answering your own question. 

Well, by definition, if climbers can't be negative, that's not normal.

Tradgic Yogurt wrote:

Well, by definition, if climbers can't be negative, that's not normal.

BTW, that's really a bad joke, but it's also true. Anon Anon is not wrong, if a statistic cannot take on negative values, by definition in cannot be normally distributed. Aitchison's tome on lognormals has a good discussion about this.

Anon Anon wrote: When learning how to set climbing routes in gyms, setters are often told to set route difficulties according to a "bell curve". An example of this is mentioned on this page.

What is the origin of this "bell curve"? Is there any science behind it, or is it just a dogma?

As it happens UKC publish their tick-list stats and back in 2009 using something like 500,000 data points for sport climbing it was described as an almost perfect bell-curve with the median at 6a+.

One issue you may run into applying science to this is that the ratings themselves can be fairly ambiguous and contrived - they’re dependent on the route setter, locale, etc.  Due to this variability, it may be difficult to rigidly fit a distribution model to the data with much accuracy.  The model may be able to account for this variability, but I suspect that the grades are so contrived that it will be hard to narrow down to a specific distribution.

It will be more difficult than fitting a model about a more rigidly defined metric, such as “how high can you jump”.

Hamish Malin wrote: One issue you may run into applying science to this is that the ratings themselves can be fairly ambiguous and contrived - they’re dependent on the route setter, locale, etc.

There's another problem. North American ratings are discrete category labels, not numerical values. If you want to fit a continuous distribution like a normal or lognormal distribution then you first have to map each rating to a numerical value, and there are many possible ways to do that, all of them somewhat arbitrary and subjective. For example, if you map to the French system then the difference between 5.10a and 5.10c is about the same as the difference between 5.8 and 5.9, but if you map to the Australian system then it's about twice the difference. Any conclusions you draw about the resulting distribution are entirely dependent on an arbitrary choice of rating scale.