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. 

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. 

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. It's the same science that invented the stickclip and the participation trophy....... ;) 

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

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

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. 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. 

t.farrell wrote: 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? However, frankly, not only does this not matter at allIt does matterto 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 bellshaped 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 noone climbs. 

Data sources: 

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. 

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, noone really knows how many active climbers there are. 

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

Tradgic Yogurt wrote: 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. 

As the owner and setter in a gym, I can tell you that we started out with a basic bell and then adjusted and continue to adjust the curve weekly based on member feedback and experience. 