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jt512
Jul 26, 2005, 5:40 AM
Post #126 of 174
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In reply to: In reply to: In reply to: Just from a statistical viewpoint.... How does one go about "number crunching" averages on the YDS grades? Is there a mathematical formula? My take on it would be, when it comes to the 10 and up grades, it goes like this: 10a = 10.00 10b = 10.25 10c = 10.50 10d = 10.75 11a = 11.00 and so on. But I got nothing for 9+ (as it should be) this is the method i am using. logarithms just aren't my bag, and i guess i just didn't give it as much thought as jt512 (not sure i even can).
Good lord, another serious answer, but a much simpler one: The problem here is that, for instance, the "distance" in difficulty between, say between 5.8 and 5.9 cannot be expected to be equal to the distance between 5.10 and 5.11. For that matter, the distance between 5.10a and 5.10b is probably not the same as that between 5.11a and 5.11b. So, how can you compute an average (mean) difficulty rating for the sample of respondents. Well, you can't, unless you go through some complicated calibration process, like that which I outlined (which, obviously, is impractal). The practical solution (serious, now, I swear) is to compute the median rating, rather than the mean.
-Jay
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climbinginchico
Jul 26, 2005, 5:44 AM
Post #127 of 174
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In reply to: In reply to: In reply to: In reply to: Just from a statistical viewpoint.... How does one go about "number crunching" averages on the YDS grades? Is there a mathematical formula? My take on it would be, when it comes to the 10 and up grades, it goes like this: 10a = 10.00 10b = 10.25 10c = 10.50 10d = 10.75 11a = 11.00 and so on. But I got nothing for 9+ (as it should be) this is the method i am using. logarithms just aren't my bag, and i guess i just didn't give it as much thought as jt512 (not sure i even can). Good lord, another serious answer, but a much simpler one: The problem here is that, for instance, the "distance" in difficulty between, say between 5.8 and 5.9 cannot be expected to be equal to the distance between 5.10 and 5.11. For that matter, the distance between 5.10a and 5.10b is probably not the same as that between 5.11a and 5.11b. So, how can you compute an average (mean) difficulty rating for the sample of respondents. Well, you can't, unless you go through some complicated calibration process, like that which I outlined (which, obviously, is impractal). The practical solution (serious, now, I swear) is to compute the median rating, rather than the mean. -Jay
My brain hurts now.
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jt512
Jul 26, 2005, 5:45 AM
Post #128 of 174
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In reply to: Oh my goodness, what have I started? :shock: In reply to: For ratings less than or equal to 5.9, a three number grade difference seems to be equal to a four letter grade difference (for grades greater than or equal to 5.10). Is this about right? I'm just so used to Aussie grades.... at least with them the stats would be fairly straight forward....
Honest answer? The simplicity of the scale is an illusion. You have no simple way of knowing whether the distance between two number grades at one end of the scale is equivalent to the distance between two number grades at the other end of the scale. Chances are that the scale is approximately exponential.
-Jay
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annak
Jul 26, 2005, 5:47 AM
Post #129 of 174
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In reply to: In reply to: In reply to: In reply to: Just from a statistical viewpoint.... How does one go about "number crunching" averages on the YDS grades? Is there a mathematical formula? Oh, god, beware: post-Long-Island-Iced-Tea-but-nonetheless-almost-serious answer to follow. First of all, discard the "5" prefix. For grades 5.10 and above, use .00, .25 .50, and .75 for a, b, c, and d, respectively. Thus, 5.11c becomes 11.50, for instance. For ratings less than or equal to 5.9, a three number grade difference seems to be equal to a four letter grade difference (for grades greater than or equal to 5.10). If one wants to make the scale objective, one way to do so is to transform a rating such that the percentage of climbers in the poplulation who can climb the particular rating is proportional to the rating. In that case, the ratings, after transforming as above, should be further transformed by taking the logarithm. Well, you asked. Edit: What is sad is that I've actually given serious thought to this question in the past. -Jay This explanation definitely involves statistical viewpoint! Don't get me started: In reply to: [T]he problem of producing any sort of objective difficulty scale for routes becomes a statistical one, requiring some sort of averaging of the opinions of a panel of climbers. Indeed, a method for producing such an objective difficulty scale has been developed, but surprisingly, has not yet seen universal acceptance. Form a post of mine on rec.climbing: In reply to: Good idea to use a logistic model of the odds of success, conditioned on the rating of the climb. Since the probability of success at a given rating depends on the climber's level of skill, incorporating terms for skill level and the interaction between skill level and rating generalizes the model. I suggest on-sight level be the skill variable, since redpointing doesn't translate well to trad climbing. Sticking with the logistic model, but standardizing the notation and adding the skill variable: Let: i = 1 to n index n climbers j = 0 to m index m YDS ratings Yij = 1 if the attempt by the ith climber on the jth rated route is a success, or 0 if it is a failure. X1i = the climber's on-sight level at the time of the attempt X2j = the route's rating, rescaled in some sensible way P(Yij) = probability of success of Yij logit(Yij) = log-odds of Y(ij) Then: P(Yij)/[1-P(Yij)] = exp(a + b1*X1i + b2*X2j + b3*Xli*X2j) logit(Y) = a + b1*X1i + b2*X2j + b3*X1i*X2j I'm pretty sure that this is the system that Randy Vogel plans to use in the new Josh guide. It should put a virtual end to arguments about grades. What we climbers will still have to talk about is beyond me.
It's like grading "on the curve" -- I refuse to accept it -- ratings/grades must reflect the reality! On a different note -- I really like your X2j parameter -- gives one some flexibility, doesn't it?
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climbinginchico
Jul 26, 2005, 5:48 AM
Post #130 of 174
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Part of the problem with Jay is that if I killfiled him to save my brain the pain of his technical posts, I would miss out on all the great burns he nails people with. Damn you!
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kachoong
Jul 26, 2005, 5:53 AM
Post #131 of 174
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In reply to: Part of the problem with Jay is that if I killfiled him to save my brain the pain of his technical posts, I would miss out on all the great burns he nails people with. Damn you!
....never mind.... just assume that nothing is perfect and the universe exists in all places at once at the world is a geoid shape and that squirrels really do eat peanut butter... and your brain will adjust with time.... things just seem to fall into place... especially if you push them hard enough....
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jt512
Jul 26, 2005, 6:04 AM
Post #132 of 174
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In reply to: It's like grading "on the curve" -- I refuse to accept it -- ratings/grades must reflect the reality!
But making the ratings statistical, ie population based, is the only way to make them objective. How else could you possibly define a unit of difficulty, except by relating it to the proportion of climbers in a population who can succeed on routes given that rating. I mean, what makes a 5.15a a 5.15a rather than a 5.14d, other than fewer people can do the route. And, for a rating scale to make much sense at all there ought to be a common distance between points on the scale. That is, the differnce in difficulty between a 5.14c and a 5.14d should be the same as that between a 5.14d and a 5.15a; otherwise, the scale is pretty silly. So, how do you define that interval? It seems to me that the most sensible way is to make the rating proportional to some simple function of the proportion of climbers who can succeed at that rating. One such function, which happens to have nice properties for statistical analysis, is the log-odds (ie, logistic) function.
In reply to: On a different note -- I really like your X2j parameter -- gives one some flexibility, doesn't it?
You're the second person to make a comment like that. It's my fault -- I should have stated it better in the first place. All I meant was to trnsform the YDS rating to a real number scale, so it can be worked with algebraically; for instance, 5.11b --> 11.25, etc.
-Jay
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bvb
Jul 26, 2005, 6:19 AM
Post #133 of 174
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sprayfest. cool.
age: 48
height: 6' 2"
weight: 165
hardest sport: 5.12d (never really tried -- hate sport)
hardest trad: 5.13c (luv cracks)
hardest bolder: v9 confirmed, unrepeated shit prolly harder, so you can all SUKIT
ape index: +2
of course, this was all back in the '70's and 80's, you fucking n00bs.
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annak
Jul 26, 2005, 6:27 AM
Post #134 of 174
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In reply to: In reply to: It's like grading "on the curve" -- I refuse to accept it -- ratings/grades must reflect the reality! But making the ratings statistical, ie population based, is the only way to make them objective. How else could you possibly define a unit of difficulty, except by relating it to the proportion of climbers in a population who can succeed on routes given that rating. I mean, what makes a 5.15a a 5.15a rather than a 5.14d, other than fewer people can do the route. And, for a rating scale to make much sense at all there ought to be a common distance between points on the scale. That is, the differnce in difficulty between a 5.14c and a 5.14d should be the same as that between a 5.14d and a 5.15a; otherwise, the scale is pretty silly. So, how do you define that interval? It seems to me that the most sensible way is to make the rating proportional to some simple function of the proportion of climbers who can succeed at that rating. One such function, which happens to have nice properties for statistical analysis, is the log-odds (ie, logistic) function. -Jay
Well, since the formula includes the climbers' onsight level, one might hope that after enough samplig the consistency will be reached. In that respect your proposal is different from "the curve". Otherwise, the population based approach is meaningless -- e.g., next time I go to my home town, I can setup a 5.4 route that exceptionally small fraction of the local population will be able to climb -- ;). And I doubt that any of the LA 5.12 climbers will go there for climbing vacation to ensure adequate rating -- ;).
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stzzo
Jul 26, 2005, 6:30 AM
Post #135 of 174
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Registered: Feb 4, 2005
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In reply to: In reply to: In reply to: Just from a statistical viewpoint.... How does one go about "number crunching" averages on the YDS grades? Is there a mathematical formula? My take on it would be, when it comes to the 10 and up grades, it goes like this: 10a = 10.00 10b = 10.25 10c = 10.50 10d = 10.75 11a = 11.00 and so on. But I got nothing for 9+ (as it should be) Yeah, I understand.... but that means 5.9 to 5.10 is the same difference as 5.10 to 5.11 numerically..... when infact the difficulty isn't the same change.... if you know what I mean... :?
For example, first apply this conversion to the grades:
5.9 => 9
10a => 10
10b => 11
10c => 12
10d => 13
11a => 14
11b => 15
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5.15 => 30
Then, take the average, and apply the conversion in reverse. So an average of 14.5 would result in being midway between 11a and 11b. Maybe someone mentioned this already, but it would be cool to know the mode and standard deviation as well.
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stzzo
Jul 26, 2005, 6:36 AM
Post #136 of 174
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In reply to: In reply to: In reply to: Just from a statistical viewpoint.... How does one go about "number crunching" averages on the YDS grades? Is there a mathematical formula? My take on it would be, when it comes to the 10 and up grades, it goes like this: 10a = 10.00 10b = 10.25 10c = 10.50 10d = 10.75 11a = 11.00 and so on. But I got nothing for 9+ (as it should be) Yeah, I understand.... but that means 5.9 to 5.10 is the same difference as 5.10 to 5.11 numerically..... when infact the difficulty isn't the same change.... if you know what I mean... :?
For example, first apply this conversion to the grades:
5.9 => 9
10a => 10
10b => 11
10c => 12
10d => 13
11a => 14
11b => 15
.
.
.
5.15 => 30
Then, take the average, and apply the conversion in reverse. So an average of 14.5 would result in being midway between 11a and 11b. Maybe someone mentioned this already, but it would be cool to know the mode and standard deviation as well.
I'd give mine if you were still accepting guys' info.
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iclimbtoo
Jul 26, 2005, 6:52 AM
Post #137 of 174
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In reply to: Oh, god, beware: post-Long-Island-Iced-Tea-but-nonetheless-almost-serious answer to follow. -Jay
I'd be curious to know exactly how many, and the accurate content of alcohol in your bloodstream seen through a mathamatical formula.
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davidorchard
Jul 26, 2005, 12:46 PM
Post #138 of 174
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In reply to: ...it would be cool to know the mode and standard deviation as well. I'd give mine if you were still accepting guys' info.
i was going to do the mode and standard deviation, but it got late. I will try to get those down later.
go ahead and post your stats if you want, i am still putting them in the spread sheet, but they don't really change the numbers anymore except on the female side.
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jt512
Jul 26, 2005, 4:12 PM
Post #139 of 174
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In reply to: In reply to: ...it would be cool to know the mode and standard deviation as well. I'd give mine if you were still accepting guys' info. i was going to do the mode and standard deviation, but it got late. I will try to get those down later. go ahead and post your stats if you want, i am still putting them in the spread sheet, but they don't really change the numbers anymore except on the female side.
If you put them on a spread sheet, would you be willing to email me a copy. I'd like to look at the relationships between height, weight, ape index, and climbing levels.
-Jay
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gandolf
Jul 26, 2005, 4:27 PM
Post #140 of 174
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gender: M
age: 44
height: 6'0"
weight: 195
hardest sport: 11
hardest trad: 10D
hardest boulder: V1
ape index: 3"
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jt512
Jul 26, 2005, 4:33 PM
Post #141 of 174
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In reply to: If each letter grade represents one unit in difficulty, wouldn't it be more accurate to give the grades new numbers that are one unit apart (convert to an integer scale), take the average, then reverse the conversion?
No. It wouldn't matter if you called the distance between two letter grades 1.0 or .25. Either way, you have the same two problems. First, how does the difference in difficulty between number grades below 5.10 relate to the difference in difficulty between two letter grades at or above 5.10a. Second, what makes you think that the difference in difficulty between two letter grades, say 5.10a and 5.10b, is the same as the difference in difficulty between, say 5.12a and 5.12b? How do you objectively define a unit of difficulty anyway? I contend that the only way to do so is to use the percentage of the climbing population (or a function thereof) who can climb the route.
-Jay
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schveety
Jul 26, 2005, 4:40 PM
Post #142 of 174
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Sex: Female
Age: 23
Height: 5'5''
Weight: 120
Average trad: Follow up to 5.10, lead up to 5.8
Average sport: Don't climb sport
Bouldering: V3
Ape Index: -3"
I don't know who has an arm span longer than their height, you freaks.
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mischief8
Jul 26, 2005, 4:56 PM
Post #143 of 174
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Posts: 416
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Sex: F
Height: 5' 4"
Weight: 125 lbs
Trad: 5.10something
Sport: 5.11 c/d
Boulder: Don't know
Ape Index: -4"
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jt512
Jul 26, 2005, 5:02 PM
Post #144 of 174
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In reply to: In reply to: In reply to: It's like grading "on the curve" -- I refuse to accept it -- ratings/grades must reflect the reality! But making the ratings statistical, ie population based, is the only way to make them objective. How else could you possibly define a unit of difficulty, except by relating it to the proportion of climbers in a population who can succeed on routes given that rating. I mean, what makes a 5.15a a 5.15a rather than a 5.14d, other than fewer people can do the route. And, for a rating scale to make much sense at all there ought to be a common distance between points on the scale. That is, the differnce in difficulty between a 5.14c and a 5.14d should be the same as that between a 5.14d and a 5.15a; otherwise, the scale is pretty silly. So, how do you define that interval? It seems to me that the most sensible way is to make the rating proportional to some simple function of the proportion of climbers who can succeed at that rating. One such function, which happens to have nice properties for statistical analysis, is the log-odds (ie, logistic) function. -Jay Well, since the formula includes the climbers' onsight level, one might hope that after enough samplig the consistency will be reached. In that respect your proposal is different from "the curve". Otherwise, the population based approach is meaningless -- e.g., next time I go to my home town, I can setup a 5.4 route that exceptionally small fraction of the local population will be able to climb -- ;). And I doubt that any of the LA 5.12 climbers will go there for climbing vacation to ensure adequate rating -- ;).
For a population-based method to be valid, the sample (of climbers) has to be a representative sample of the population. If your local climbers suck (compared to the general population), then using them as the sample would lead to misleading results.
Terms for the climber's skill level and the interaction between skill level and route rating are only needed if you want a model that can be used to make valid prediction's about a climber's probability of success on a route of a particular rating; clearly, that is a function of both his skill level and the rating. But if all you want to do is to relate YDS ratings to objective, understandable difficulty levels, a simpler model should suffice. A simple logistic model logit(Yij) = a + bXi, where Xi is the rating of the ith route, and Yij = 1 if the jth climber was successful on the ith route, or 0 otherwise, would probably fit such data well.
-Jay
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skinnyclimber
Jul 26, 2005, 5:14 PM
Post #145 of 174
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In reply to: I am only accepting female stats from this point on.( come on ladies). Thanks for you responses so far. Averages # of Females in data: 17 age: 27.4 yr height: 5' 4.9" weight: 126lbs hardest sport: 5.10d hardest trad: 5.8+ hardest boulder: V2 ape index: 0.7" # of Males in data: 72 (including me) age: 27 yr height: 5' 10.8" weight: 164lbs hardest sport: 5.11b hardest trad: 5.9+ hardest boulder: V5 ape index: 1.5" PS. I apologize for omitting ice climbing, I will try to include it for the next time I do this (next year maybe). Thank you also for the other categories that I can add (like 'years climbed', that would have been a nice one).
As I suspected, the average female climber is totally hot, and can climb too!
Hello ladies. :D
Skinny
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renohandjams
Jul 26, 2005, 5:26 PM
Post #146 of 174
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I just realized that your data entry process sucks. Why didn't you just make a poll with all of the variables you wanted and then have the poll add it up for you? I just realized that someone has had to go through every page and add in each new variable, very inefficient and time consuming. Work smarter not harder.
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stonefoxgirl
Jul 26, 2005, 5:38 PM
Post #147 of 174
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Posts: 595
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gender: female
age: 28
height: 5'8"
weight: 135
hardest sport: 5.10d
hardest trad: 5.7
hardest boulder: V4
ape index: 0.0"
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sidepull
Jul 26, 2005, 5:41 PM
Post #148 of 174
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I think Jay brings ups some interesting concerns regarding difficulty. I think it would be a right tailed distribution and concur that you'd need to use some form of conversion (although not necessarily logistic).
Also, I know this is self-report data so you're going to have desirable response bias. For instance, everyone wants to have a high ape index whether they have one or not. I was involved in a statistics test where we looked at ape index and found that, on average, it doesn't exist. From that experience I'm really suspicious of people self reporting their measurements as opposed to having someone else measure. For instance, 8a.nu did a site poll and found that their members "claim" to have something like an average 6 inch ape index - BS!!! At least the results provided here are much more conservative. I guess I'm just urging people to look at the results with a grain of salt. For example, do all the "real" people you climb with actually climb V5 or just the internet climbers?
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screamer
Jul 26, 2005, 6:06 PM
Post #149 of 174
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I agree with renohandjams. Make some multifaceted poll.....What is the average climber? Once a month, weekend warrior, etc...Are we talking people who think climbing is a hobby or a lifestyle? Am i average if i climb on the weekends an occasional midweek half day or full day, some week or longer road trips thrown in to mix things up, obsess about it when i'm not climbing..Get emotional about sending/not sending..Oh yeah drinking lots of beer...
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ikefromla
Jul 26, 2005, 6:10 PM
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In reply to: do all the "real" people you climb with actually climb V5 or just the internet climbers? |
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