tag:blogger.com,1999:blog-31791042666717556362024-03-19T04:38:06.209+01:00Climbstat - Data Analytics and Visualization for Rock Climbing and BoulderingData science, statistics and visualization of rock climbing and bouldering related aspects. E.g. what is the role of height and weight in climbing? How much harder is onsighting vs redpointing? Is machine learning relevant for rock climbing?Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-3179104266671755636.post-86193598186860768302020-11-01T19:52:00.004+01:002020-11-02T05:48:35.548+01:00Research article looking at climber ability and route difficulties by Dean Scarff<p class="MsoNormal">Dean Scarff made me kindly aware about his extremely
interesting arXiv article <i style="mso-bidi-font-style: normal;"><span style="mso-bidi-font-weight: bold;"><a href="https://arxiv.org/abs/2001.05388" target="_blank">Estimation of Climbing Route Difficulty usingWhole-History Rating</a>. </span></i><span style="mso-bidi-font-weight: bold;">In
this paper Dean estimates rock climber ratings and route difficulties using the
</span>“Whole-History Rating” based on data of the rock climbing site <a href="http://www.thecrag.com">www.thecrag.com</a>. <span style="mso-bidi-font-weight: bold;">The </span>“Whole-History Rating” is a player rating which is an adaption
of the <a href="https://en.wikipedia.org/wiki/Bradley%E2%80%93Terry_model" target="_blank">Bradley - Terry model</a>. I have to admit, I knew neither of them but I
have worked with <a href="https://en.wikipedia.org/wiki/Elo_rating_system" target="_blank">Elo ratings</a> before (looking at soccer). In the past, I also wrote
a <a href="http://ftp.zew.de/pub/zew-docs/dp/dp16058.pdf" target="_blank">paper looking at (changing) inequality of the allocation of player talentacross soccer clubs in German</a> based on estimated player ratings (together with
Roman Sittl). This is why I am delighted to see such approaches now being applied to rock
climbing. </p>
<p class="MsoNormal">What is really nice is firstly that the topic is in my view extremely interesting, not only for research but for the sport itself. Secondly, the code seems to be
fully <a href="https://github.com/p00ya/climbing_ratings" target="_blank">available on GitHub</a>. Thirdly, the estimated route difficulties are
visually contrasted to the true (Australian) grades, as shown in the following
figure further below from the paper. It looks quite reasonable (the large
variance is perhaps a little bit irritating but that might just be a few very extreme
observations for each grade). Fourthly, what is extremely interesting is the
fact that <a href="http://www.thecrag.com">www.thecrag.com</a> dataset also
seems to covers “No go’s” or unsuccessful climbing ascents (in contrast to the
<a href="http://8a.nu">8a.nu</a> data). This is something I personally collect for my own ascents but I
never have seen someone else collecting it. This really allows to estimate the player
and route ratings soundly. Finally, the methodological description is short but seems
solid (but I have not thought everything through as I would if I had to
peer-review the article).</p>
<p class="MsoNormal">Some feedback for improvement the paper from my side would be the
following: Firstly, the paper is extremely short (which is common in computer
science as far as I know) but a little bit more information here and there would be
helpful in my view (e.g. about the Australian
Ewbank grade system in comparison to the French or US grade system or about the underlying dataset). Secondly
and more importantly, I would love to see in the end some more climbing-related
interpretation – perhaps even contrasting the route rating and the successful /
unsuccessful player ratings attempting that route for a well-known Australian
route. I say that because it would demonstrate that such an algorithm is not
just interesting for research per se but might, for example, be used as supporting evidence in a
grading dispute etc. Thirdly, a minor point, do one really needs climber's ability to vary on a weekly level since on average climbers performance <a href="http://climbstat.blogspot.com/2019/09/how-many-years-does-it-take-to-climb-7a.html" target="_blank">seems to be rather constant after a few years</a>?<br /></p>
<p class="MsoNormal">But I only say that because I think the article is great and
I would like to see more! Thanks Dean. </p><p class="MsoNormal">In general, if you have any interesting rock
climbing related research for me, <b>please make me aware of it</b>! <span style="mso-spacerun: yes;"> </span></p><p class="MsoNormal"><span style="mso-spacerun: yes;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZpkyorq-lHiSP6ZsKNbaPkrJM6ub2Vv7JILGEuxhrrtasEiPhk1tegx5knyb7LraXhEZz5xvVlRHTY3dy58JE2G8zC4CW0HMkQ-ZOQHiGF3bfNHXd0ov9BfRb5KYW1-Rgty_z85xHeEk/s1152/routeratungs_dean.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="909" data-original-width="1152" height="316" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZpkyorq-lHiSP6ZsKNbaPkrJM6ub2Vv7JILGEuxhrrtasEiPhk1tegx5knyb7LraXhEZz5xvVlRHTY3dy58JE2G8zC4CW0HMkQ-ZOQHiGF3bfNHXd0ov9BfRb5KYW1-Rgty_z85xHeEk/w400-h316/routeratungs_dean.png" width="400" /></a></div><br /> <p></p>
Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com1tag:blogger.com,1999:blog-3179104266671755636.post-91894997412430705062020-04-05T14:21:00.000+02:002020-04-05T14:28:53.817+02:00Which bouldering and rock climbing destinations are most impacted by the coronavirus pandemic?<br />
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</div>
<div class="MsoNormal">
<span style="font-family: inherit;"><span lang="EN-US" style="color: black; line-height: 107%;">I am a bit reluctant</span> to write about
the coronavirus pandemic. There is on the one hand already a lot of information out there. On the other hand, we still miss crucial aspects of this novel
virus (such as the number of unknown cases). And, I cannot really
contribute anything important to this topic. It is however consuming a lot of
attention and interferes for many of us with our favorite sport (due to widespread lockdowns and social distancing regulations). This is why it is after all very relevant for the bouldering and rock climbing community, and why I decided to take this topic up here. </span></div>
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<span style="font-family: inherit;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: inherit;">First and foremost, please, <b>adhere to</b>
the <b>local regulations</b> considering climbing and movement. You not only
jeopardize future free access to local crags but also actual lives if you still continue as usual (e.g. by spreading
the virus to remote communities or stressing already strained emergency
resources)! <o:p></o:p></span></div>
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<span style="font-family: inherit;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: inherit;">As the title says, I want to take here a look w</span>hich bouldering and rock climbing destinations are most impacted by the coronavirus pandemic? Where could climbing (hopefully soon) be safe again? </div>
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<span style="font-family: inherit;"><br /></span></div>
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<span lang="EN-US" style="color: black; line-height: 107%;"><span style="font-family: inherit;">You can find below a simple visualization
which shows the most important bouldering and rock climbing destinations, on
the x-axis ranked by number of ascents in the <a href="http://8a.nu/" target="_blank">8a.nu</a> database (until 2017). On
the y-axis, you can find the number of confirmed COVID-19 cases per 100.00
inhabitants according to <a href="https://github.com/CSSEGISandData/COVID-19" target="_blank">Johns-Hopkins University Center for Systems Scienceand Engineering</a>. This gives a rough picture about which climbing destinations
are most impacted by the coronavirus. <o:p></o:p></span></span></div>
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<span lang="EN-US" style="color: black; line-height: 107%;"><span style="font-family: inherit;"><br /></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE1iWOJkFiXrtlI-kYCEHpcYxb561fZNKef8A3gtzNLCSXwkbKnfNMNtqmTsS82OhSnQglmV1kggkUJZkXaMLE8FL7kiIS-yoVud1QhTKND3s3CPRvJLvlIvWZkZuWO4FmecpaK-FkvVI/s1600/covid19_pop.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="1000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhE1iWOJkFiXrtlI-kYCEHpcYxb561fZNKef8A3gtzNLCSXwkbKnfNMNtqmTsS82OhSnQglmV1kggkUJZkXaMLE8FL7kiIS-yoVud1QhTKND3s3CPRvJLvlIvWZkZuWO4FmecpaK-FkvVI/s400/covid19_pop.png" width="400" /></a></div>
<span lang="EN-US" style="color: black; line-height: 107%;"><span style="font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVbh9gwX996QddLlWuwhb_5qhh4smVCNHVZtnLbp9BnOmRGTn4I8D_8Bggeqg6Nqkzhd6JnvhpA5_BQsE4ALoQQY9Ij80Mul8ZN25ZOfKp9BKvnbddJFfC1il30qKqQC4oqGfvHRKNNI0/s1600/covid19_pop.png" imageanchor="1"></a><br /></span></span></div>
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<span lang="EN-US" style="color: black; line-height: 107%;"><span style="font-family: inherit;"><br /></span></span></div>
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<span lang="EN-US" style="color: black; line-height: 107%;"><span style="font-family: inherit;">The number of confirmed COVID-19 cases is only
a very crude proxy for the severity of the local conditions. There are, for
example, large differences in <a href="https://ourworldindata.org/coronavirus#our-database-on-covid-19-testing-data" target="_blank">tests performed</a> between countries, and more
testing means one will detect more cases. My home country, Germany, <a href="https://www.washingtonpost.com/world/europe/germany-coronavirus-death-rate/2020/03/24/76ce18e4-6d05-11ea-a156-0048b62cdb51_story.html" target="_blank">performes alot of tests</a> and has a high rate of infections but a comparable low death rate.
This is likely because there many mild cases detected through widespread
testing. Other countries are suspected to artificially keep down the number of
confirmed cases, by various means. Notwithstanding all these flaws, there will
be on average a close relationship between the actual conditions and the number
of confirmed cases. To consider the large differences in population numbers, I
here look at confirmed cases by 100.000 inhabitants.</span></span></div>
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<div class="MsoNormal">
<span lang="EN-US" style="line-height: 107%;"><span style="font-family: inherit;">As you can see, a large part of the countries
famous for their climbing spots in Europe are severely affected. Italy and
Spain have established near complete lockdowns. The situation is also tense in
Central Europe and the USA. It (yet) seems to be better Eastern Europe, in
Greece, Mexiko, Australia and New Zealand, and other countries in Asia or South
America. This is might be due to limited testing. It is not meant as a travel
recommendation (some of these health systems have been already strained prior
to the pandemic). But it might show where climbing might sooner be possible
again. </span><span style="font-size: 13.5pt;"><o:p></o:p></span></span></div>
Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com1tag:blogger.com,1999:blog-3179104266671755636.post-66369720330553511402020-02-16T21:36:00.001+01:002020-02-19T06:39:37.944+01:00How much harder is onsighting vs redpointing?<div class="separator" style="clear: both; text-align: center;">
<a href="https://www.blogger.com/blogger.g?blogID=3179104266671755636" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a></div>
Every rock climber knows that a successful onsight is much harder than an ascent with perfect beta after rounds of projecting. An onsight means climbing a route successfully at the first attempt without prior information or rehearsal on the route. During an onsight, we might not know where the crux lies or how long the route actually is. In contrast, being able to learn about a route, to mentally accommodate to the hard sections, the rest points and footholds, allows us to reach our maximum performance during a redpoint ascent.<br />
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Most of us also have a good sense of the routes we typically can climb in a first attempt with or without prior knowledge or in a second or subsequent attempt. But it is much harder to guess how much more difficult, let’s say an onsight ascent is, compared to a successful redpoint ascent. We might know that Adam Ondra did Silence (9c or 5.15d), currently the world’s hardest route, after weeks of practicing specifically for that route. Adam was also the first to flash a route of the grade 9a+ or 5.15a (a flash means a successful ascent of a route in the first go with prior information, for example from other climbers), and he did three 9a or 5.14d onsight. Alex Megos, however,was the first to onsight a 9a or 5.14d, he climbed up to 9b+ (redpoint). Up to today, no one onsighted a route harder than 9a. But is the difference between 9b+ redpoint and 9a onsight an meaningful estimate of how much harder an onsight is? A first attempt without beta might be easier among lower-graded routes compared to the elite level. Here, we want to investigate this question in a quantitative way.<br />
<br />
As in previous posts, we will therefore access the data of the website 8a.nu which provides climbers with the opportunity to save their climbs and view personal scorecards. A scorecard is simply an overview about routes achieved, the respective style and the grade among others. In this post, we look at the maximum onsight and the maximum redpoint grade of 8a.nu users who made their scorecard public. We focus here on climbers who climbed redpoint at least 6a or 5.10a or higher. The available dataset covers entries up to September 2017. This leaves us with almost 18,000 climbers.<br />
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<a href="https://www.blogger.com/blogger.g?blogID=3179104266671755636" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>How do the results look like? First, we take a look at the overall difference between the maximum (redpoint) performance and the maximum onsight performance. The following graph shows the distribution of maximum performance for each climber in our dataset by style. This kind of graph is called a violin graph. The wider the violin, the more climbers there are with a certain maximum redpoint or onsight performance. The average maximum performance by style is illustrated by the black point in the middle of the violin. The average maximum redpoint performance is slightly above 7b+ or 5.12c. This is partly due to the fact that we disregarded climbers who do not climb above 6a or 5.10b. Apart from that the average ability of active 8a.nu users is quite high. Climbers who do not climb very often don’t bother much about creating and maintaining a public scorecard. The corresponding maximum onsight performance is slightly above 7a or 5.11d. This indicates that the average onsight level is approximately three grades below the maximum performance.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcZrYhcxbVAivOYaMHmRc4AsJdSuojkUZmqiOBB7niDmp49wU6kZ3MbBvYCVSuib39rq1xXX3Dpx5IFlpLa1_SK4VeI708tGGp0I9DsS629fthtE4e2RDJOuJWpWG6I7L_ShbKIy1hL64/s1600/article_OS_RP_difference_graph1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcZrYhcxbVAivOYaMHmRc4AsJdSuojkUZmqiOBB7niDmp49wU6kZ3MbBvYCVSuib39rq1xXX3Dpx5IFlpLa1_SK4VeI708tGGp0I9DsS629fthtE4e2RDJOuJWpWG6I7L_ShbKIy1hL64/s400/article_OS_RP_difference_graph1.png" width="400" /></a></div>
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Next, we want to investigate whether the results differ across the performance spectrum. For this purpose, we group all climbers together by their maximum (redpoint) performance on their scorecard. Now we look at the average maximum onsight performance within each group. <br />
<br />
How does this grouping work and how did we finally calculate the average onsight performance? Let us take those climbers who sent 9b+ or 5.15c as maximum (regardless of whether they are included in the 8a.nu data). These are Stefano Ghisolfi, Alexander Megos and Chris Sharma (Adam Ondra is not included in this list despite the fact that he did three 9b+ because of his 9c redpoint). Alexander Megos did an 9a onsight while Stefano Ghisolfi and Chris Sharma onsighted up to 8c at maximum, according to Wikipedia. The onsight average of this group is therefore slightly below 8c+.<br />
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The following graph shows how the redpoint-onsight performance gap across all grades. On the x-axis, we have plotted the maximum (redpoint) performance. The y-axis shows the maximum onsight performance. If climbers onsighted grades similar to their redpoint performance, we would see a straight 45 degree line (indicated in red). The onsight performance is as one would expect, lower than the maximum performance and this is why the blue points are below the red line. It is apparent that the difference is small for climbers with a relatively low maximum performance and it widens for higher able climbers. This indicates that an onsight becomes harder the harder you climb. The average onsight maximum is 2-3 grades lower for climbers who climb up to 7a or 5.11d redpoint but it increases to almost 4 grades for climbers with a maximum grade of 8a or 5.13b (and still widens further). Interestingly, the gap again seems to be a little lower for the few climbers who can climb 9b or 5.15b or higher.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiofraAdCUEeHDurF-6L2scc3DuqhgzipmrXok-UqvnWjvhXOeeKjMG36PNTHazt5-lpK68GVjD5OHX7ou4NK76WfEzbz4QmLjAWUnxVy14iQD2FzYWB9jC6xbQxyVhfdR9Y8rF2m1-Pvk/s1600/article_OS_RP_difference_graph2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiofraAdCUEeHDurF-6L2scc3DuqhgzipmrXok-UqvnWjvhXOeeKjMG36PNTHazt5-lpK68GVjD5OHX7ou4NK76WfEzbz4QmLjAWUnxVy14iQD2FzYWB9jC6xbQxyVhfdR9Y8rF2m1-Pvk/s400/article_OS_RP_difference_graph2.png" width="400" /></a></div>
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We have not considered flash ascents in this post. The reason is that there is almost no difference between the maximum onsight and flash performance in the 8a.nu data. The highest flash grades are higher than the average onsight grades but the difference is very small (ca. ⅙ of the difference between one grade or between 7a and 7a+). Personally, we think this seems surprising since a good beta might indeed give you valuable information.<br />
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<br />Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com6tag:blogger.com,1999:blog-3179104266671755636.post-18894683367146905482020-01-11T06:45:00.000+01:002020-01-18T19:28:33.568+01:00First Ascentionists Over Time (Female and Male)I have always been interested in the history of rock climbing. Lately, I tried to collect data about male and female first ascentionists to visualize climbing progression over tine. However, it turned out difficult to find a lot of data (particularly for female climbers). An exception to the rule is this really nice site <a href="http://stara.emontana.cz/climbing-milestones-from-6a-to-9c/">http://stara.emontana.cz/climbing-milestones-from-6a-to-9c/</a> from which I got a lot of information.<br />
<br />
It would be great if someone could point me to further sources, and help me correcting the existing data! I find it particularly difficult to get information about, among others,<br />
<br />
<ul>
<li>first onsights and flashes (who was the first to onsight 8a or flash 8b+?) </li>
<li>first successful female and male bouldering ascents</li>
<li>early first female ascents (does anyone know who did the first female 7a?)</li>
<li>'first' second ascents (who did the second 8c in the world?)</li>
</ul>
For routes with disputed gradings, such as <i>Chilam Balam </i>first redpointed by Bernabè Fernandez in 2003, I took the majority grade by all repeaters (<a href="https://www.hardclimbs.info/climbs/chilam-balam" target="_blank">9a+/9b in that case</a>).<br />
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Graphs below, data (including sources) is available <a href="https://docs.google.com/spreadsheets/d/1FhG8rPLJID0nYJDcB6D8O30S8QTnbh43cKxhECCp_KY/edit?usp=sharing" target="_blank">here via Google Spreadsheet</a> or via <a href="https://github.com/AJWarnke/climbstat" target="_blank">ClimbStat GitHub</a> (here you can also find the R-code to create the individual graphs. They have been merged together externally to one GIF). Further below you can find an excerpt.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz3p9Pv-9rhQCXcOrRAnBzeYwkspF1ZuiONWBe0jlamzddY_EEg1nJHMLvjW8XlvH9kQNbKAxfklTYQnAG2nU-WMPTXeDjOHiXwgo0cLwY2pY-eTCNMYwnQWKla0xg6qTFfpUXyHWuU4k/s1600/ascensionists_male.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="542" data-original-width="903" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz3p9Pv-9rhQCXcOrRAnBzeYwkspF1ZuiONWBe0jlamzddY_EEg1nJHMLvjW8XlvH9kQNbKAxfklTYQnAG2nU-WMPTXeDjOHiXwgo0cLwY2pY-eTCNMYwnQWKla0xg6qTFfpUXyHWuU4k/s400/ascensionists_male.gif" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOSIhT0AEBjXlD6YK-YU6C9XrGvZ4NIFdiM1Cue5NJFHw4JftDWPyjDGARKgFsIYknPWkXJQJSGQ7WOqJRENrssslCQCUcrkFmrhAyQnwvTSwPTxe_609YTQO0CcYXXM2Bg5P7VH17Lmg/s1600/ascensionists_over_time.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="1000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOSIhT0AEBjXlD6YK-YU6C9XrGvZ4NIFdiM1Cue5NJFHw4JftDWPyjDGARKgFsIYknPWkXJQJSGQ7WOqJRENrssslCQCUcrkFmrhAyQnwvTSwPTxe_609YTQO0CcYXXM2Bg5P7VH17Lmg/s400/ascensionists_over_time.png" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY-ifDeCWgQVXXRngqQ1hmTAIh3egQErOgM2Q3TpXhU94Mrx6BC6Z-COvDAGSoqti3KtdR3m5Kc2stKL_gw1QCEw-h3dOR9JML4tBAcybYZZNv4jBwKKfNl0cfhxOebLJwi9yAEc8poNs/s1600/ascensionists_female.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="1000" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY-ifDeCWgQVXXRngqQ1hmTAIh3egQErOgM2Q3TpXhU94Mrx6BC6Z-COvDAGSoqti3KtdR3m5Kc2stKL_gw1QCEw-h3dOR9JML4tBAcybYZZNv4jBwKKfNl0cfhxOebLJwi9yAEc8poNs/s400/ascensionists_female.gif" width="400" /></a></div>
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<table border="0" cellpadding="0" cellspacing="0" style="width: 586px;"><colgroup><col style="mso-width-alt: 1280; mso-width-source: userset; width: 26pt;" width="35"></col>
<col style="mso-width-alt: 5193; mso-width-source: userset; width: 107pt;" width="142"></col>
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<col style="mso-width-alt: 1792; mso-width-source: userset; width: 37pt;" width="49"></col>
<col style="mso-width-alt: 1865; mso-width-source: userset; width: 38pt;" width="51"></col>
<col style="mso-width-alt: 2596; mso-width-source: userset; width: 53pt;" width="71"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15.0pt; width: 26pt;" width="35">Year</td>
<td style="width: 107pt;" width="142">Ascensionist</td>
<td style="width: 120pt;" width="160">Route</td>
<td style="width: 59pt;" width="78">Grade (YDS)</td>
<td style="width: 37pt;" width="49">Grade (French)</td>
<td style="width: 38pt;" width="51">Sex</td>
<td style="width: 53pt;" width="71">Confirmed?</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1979</td>
<td> Lynn Hill</td>
<td>Ophir Broke</td>
<td>5.12d</td>
<td>7c</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1985 </td>
<td> Catherine Destivelle</td>
<td>Fleur de Rocaille</td>
<td>5.12d/5.13a</td>
<td>7c+/8a</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1986 </td>
<td>Luisa Iovane</td>
<td>Comeback</td>
<td>5.13b</td>
<td>8a</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1988 </td>
<td> Catherine Destivelle</td>
<td>Chouca</td>
<td>5.13c</td>
<td>8a+</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1988 </td>
<td> Isabelle Patissier</td>
<td>Sortileges</td>
<td>5.13d</td>
<td>8b</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1990 </td>
<td>Lynn Hill</td>
<td>Masse Critique</td>
<td>5.14a</td>
<td>8b+</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1998</td>
<td> Josune Bereziartu</td>
<td>Honky Tonky</td>
<td>5.14b</td>
<td>8c</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2000</td>
<td> Josune Bereziartu</td>
<td>Honky Tonk Mix</td>
<td>5.14c</td>
<td>8c+</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2002</td>
<td> Josune Bereziartu</td>
<td>Bain de Sang</td>
<td>5.14d</td>
<td>9a</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2005</td>
<td> Josune Bereziartu</td>
<td>Bimbaluna</td>
<td>5.14d/5.15a</td>
<td>9a/9a+</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2017 </td>
<td>Margo Hayes</td>
<td>La Rambla Extension</td>
<td>5.15a</td>
<td>9a+</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2017</td>
<td> Angela Eiter</td>
<td>La planta de shiva</td>
<td>5.15b</td>
<td>9b</td>
<td>female</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1961</td>
<td> John Gill</td>
<td>Thimble</td>
<td>5.12a</td>
<td>7a+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1967 </td>
<td> Greg Lowe</td>
<td>Macabre Roof</td>
<td>5.12c</td>
<td>7b+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1970</td>
<td> John Gosling</td>
<td>English Hanging Gardens</td>
<td>5.12b</td>
<td>7b</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1975</td>
<td> Steve Wunsch</td>
<td>Psycho Roof</td>
<td>5.12d</td>
<td>7c</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1977 </td>
<td>Ray Jardine</td>
<td>The Phoenix</td>
<td>5.13a</td>
<td>7c+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1979</td>
<td> Tony Yaniro</td>
<td>Grand Illusion</td>
<td>5.13b</td>
<td>8a</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1983</td>
<td> Jerry Moffatt</td>
<td>The Face</td>
<td>5.13c</td>
<td>8a+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1984</td>
<td> Wolfgang Güllich</td>
<td>Kanal im Rücken</td>
<td>5.13d</td>
<td>8b</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1985 </td>
<td>Wolfgang Güllich</td>
<td>Punks in the Gym</td>
<td>5.14a</td>
<td>8b+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1986</td>
<td> Antoine Le Menestrel</td>
<td>La Ravage</td>
<td>5.14a/5.14b</td>
<td>8b+/8c</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1987</td>
<td> Wolfgang Güllich</td>
<td>Wallstreet</td>
<td>5.14b</td>
<td>8c</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1990 </td>
<td>Ben Moon</td>
<td>Hubble</td>
<td>5.14c</td>
<td>8c+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1991</td>
<td> Wolfgang Güllich</td>
<td>Action Directe</td>
<td>5.14d</td>
<td>9a</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1995 </td>
<td>Fred Rouhling</td>
<td>Akira</td>
<td>5.15b</td>
<td>9b</td>
<td>male</td>
<td>No</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">1996</td>
<td> Alex Huber</td>
<td>Open Air</td>
<td>5.15a</td>
<td>9a+</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2003 </td>
<td>Bernabè Fernandez</td>
<td>Chilam Balam</td>
<td>5.15a/5.15b</td>
<td>9a+/9b</td>
<td>male</td>
<td>Yes</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2012</td>
<td> Adam Ondra</td>
<td>Change</td>
<td>5.15c</td>
<td>9b+</td>
<td>male</td>
<td>No</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td align="right" height="20" style="height: 15.0pt;">2017</td>
<td> Adam Ondra</td>
<td>Silence</td>
<td>5.15d</td>
<td>9c</td>
<td>male</td>
<td>No</td>
</tr>
</tbody></table>
Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com1Germany51.165691 10.45152600000005840.944362 -10.202770999999942 61.387020000000007 31.105823000000058tag:blogger.com,1999:blog-3179104266671755636.post-56168044585596804182019-10-12T18:59:00.001+02:002019-11-27T13:44:29.799+01:00Progressing like Adam Ondra or Stefano GhisolfiLast time, we have looked how averge climbers progress over time. Today, we want to look at individual performance trajectories of elite climbers such as Adam Ondra, Stefano Ghisolfi or Ramón Julian Puigblanque.<br />
<br />
To derive the progression over time (or over experience), we use a statistical technique which is called <a href="https://en.wikipedia.org/wiki/Multilevel_model" target="_blank">multilevel modelling</a>. This method can be viewed as a generalization of linear regression for (among others) datasets in which we follow individuals over time. A good introduction source is the book "<a href="http://www.stat.columbia.edu/~gelman/arm/" target="_blank">Data Analysis Using Regression and Multilevel/Hierarchical Models</a>" by <a href="https://statmodeling.stat.columbia.edu/" target="_blank">Andrew Gelman</a> and Jennifer Hill (multilevel models are also called hierarchical models). You can find some further information about this technique at the end of the blog post. <br />
<br />
The following graph shows the derived performance curves for some elite climbers. Adam Ondra (in red) started very young. His first ascents are recorded being just 8 years old. He continuously improved since then and in 2017, the last year recorded in our sample, he did the world's first 9c or 5.15d (<a href="https://en.wikipedia.org/wiki/Silence_(climb)" target="_blank"><i>Silence</i></a> in Flatanger). <span class="LabelBold10" id="ctl00_ContentPlaceholder_LabelUserName">Ramón Julian Puigblanque started much later in 1996 at the age of 14 or 15. We do not observe his first years but </span>in late 2000, he already climbed his first 8c+ (<i>El disbarat</i> in Montserrat). His experience profiles looks inversely U-shaped which is not uncommon for, among others, many <a href="http://arne-warnke.de/Publications/2012_Desjardins_Warnke.pdf" target="_blank">age-performance curves</a>.<br />
<br />
Next, we will look at three outstanding climbers who all started around the same age of being 11-12 years old. Jorge Diaz-Rullo, who did in 2019 (so far) three 9b (5.15b) and four 9a+ (5.15a), showed an extraordinary steep improvement until 2017. It will be certainly interesting to see his list of climbing achievements in a few years. Stefano Ghisolfi is almost a late bloomer among this group. His rise to excellence has notwithstanding been also incredible steep (who became the fourth climber in history to climb 5.15c or 9b+). Sèbastian Bouin recorded no ascents below 8c (5.14b). This makes it difficult to derive a progression curves and his profile is therefore more or less flat between 2011 and 2017. Piotr Schab started much younger (being around 7 years old) and progressed therefore at a lower pace. So far he however still seems to improve further. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgokZROC1PntojLEMqDdfxUUGUz6gcd4n_2uMEYgq4uWVojvQTyoIn48cEd0rSZjU9g7WnsGg9EjSyQmtZSpCDe3E9By-lYM3SrnZq1mM7yCspm4222CwcvXtomUxFDhWZkUi2PnKyrTnA/s1600/Growth_elites.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgokZROC1PntojLEMqDdfxUUGUz6gcd4n_2uMEYgq4uWVojvQTyoIn48cEd0rSZjU9g7WnsGg9EjSyQmtZSpCDe3E9By-lYM3SrnZq1mM7yCspm4222CwcvXtomUxFDhWZkUi2PnKyrTnA/s400/Growth_elites.png" width="400" /></a></div>
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Further profiles for Sachi Amma (starting age 12), Daniel Woods (6), Mathieu Bouyoud (13), David Graham (16), Domen Škofic (5), Jernej Kruder (7), Joe Kinder (16) and Daniel Jung (14) can be found below. We have included here only climbers who have registered via 8a.nu. This is why, for example, Chris Sharma or Alexander Megos, are not considered. Furthermore, some other well-known climbers are not included because they started well before 8a.nu was created (such as <span class="LabelBold10" id="ctl00_ContentPlaceholder_LabelUserName">Patxi Usobiaga, 1990) or others did not add their account until 2017 (Jonathan Siegrist).</span></div>
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You might wonder that these curves do not follow exactly the (top three)
true highest ascents. This is not surprising for two reasons. Firstly,
the curves are derived through a polynomial of the order of three,
meaning that all profiles are smoothed over time (or over experience).
Secondly, for the elite climbers the curves may seem sometimes slightly
biased downwards. This is actually a desired feature of multilevel
models which also allows to model climbers who we observe only for few
years. 'Extreme' observations are slightly <a href="https://en.wikipedia.org/wiki/Shrinkage_(statistics)" target="_blank">shrinked</a> to the overall
average. </div>
<br />
Some further information regarding multilevel models: Linear regression calculates one intercept and one set of
slope parameters for the entire sample. In multilevel models, each
individual has his or her own set of parameters. These are, however, not
calculated completely separately as it would be the case if one would
use one linear regression model for each climber in the whole dataset.
Multilevel methods have the advantage that we allow to model also
climbers who we observe only for a few years realistically. This is done
by adding some extra (distributional) assumptions. <br />
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Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com0tag:blogger.com,1999:blog-3179104266671755636.post-11619575600701606782019-09-29T22:07:00.003+02:002022-04-30T13:11:18.400+02:00How many years does it take to climb 7a or 5.11d?If you talk to beginners, you often hear how long does it take to climb 7a (5.12a)? In this post, we approach this question in a first out of a series of posts. We will look at average grade progression of rock climbers. The aim is to visualize individual improvement over time and to check whether the maximum performance tends to peak around a certain experience level.<br />
<br />
We are looking for this purpose again at the 8a.nu data, and start with male and female climbers who have started climbing between before turning 25 (we will look at the role of starting age for later climbing performance in a subsequent post). We consider only climbers who have logged at least three years and who enter their first ascent in the database within four years after starting climbing. These and a few other smaller restrictions leave us with 3225 climbers (2801 males and 424 females). In the following graph, you see on the x-axis experience in years (defined as current year minus starting year) and on the y-axis the performance. For each climber, we consider the highest three redpoint ascents by year. <br />
<br />
Each light blue line in the background depicts an individual experience-grade curve derived from a multilevel model (we will come to that also in a following post). It is obvious that the average climber in our sample climbs hard and starts strong. We have seen this already before, and it is not surprising because better climbers will be more inclined to save their ascents and to make their profile public. But it might well be the case that sometimes climbers rather state the age they started to train and climb seriously as starting age.<br />
<br />
We start here with a simple linear regression separately for male and female climbers in which we regress experience in cubic terms (experience, experience^2 and experience^3) on grades. The coefficient of determination (R^2) is around 0.21 for the joint regression including both males and females (with a separate intercept and separate slopes for both sexes). This shows that experience is an important factor (who would disagree?!) but far from being definitive. <br />
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<br />
We see that there is a steep improvement in the first three to four years which flattens subsequently. There does not seem to be much improvement (on average) any more beyond 6 years of experience. We have displayed only up to ten years of experience, but the results look similar if we extend that time period (the sample just gets smaller and smaller). There is no sign of an average performance decline for highly experienced climbers. <br />
<br />
Female and male experience-grade curves look very similar, with the female profile being parallelly shifted lower by two grades. Statistically, the slopes do not differ between males and females climbers.<br />
<br />
Coming back to the question in the title: How many years does it take to climb 7a or 5.11d? For males in the sample it seems just around 1.5 years and for females ca. 3 years. This shows that the 8a.nu dataset is likely not very representative for the average climber you will meet in a gym. The shape of the curves looks in my view however quite reasonable. <br />
<br />
In a following post, we will look at boulderer and compare the experience profiles between climbers and boulderer to see whether boulderer, for example, improve faster because experience might play a more decisive role in long endurance routes compared to short and obvious boulders. <br />
<br />
In the <a href="https://climbstat.blogspot.com/2019/10/improving-like-adam-ondra.html" target="_blank">next post</a>, we look at climbing profiles of elite climbers such as Adam Ondra. Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com6tag:blogger.com,1999:blog-3179104266671755636.post-9091671582156123572019-09-24T18:44:00.002+02:002019-10-13T14:25:31.817+02:00New Topic: Climbing Progression Over Time (how fast will you become better)In the next weeks, we will explore a new topic. We will statistically look how fast individuals typically improve in rock climbing and bouldering using multilevel models. For this purpose we will consider average (and exceptional) experience-grade profiles based on gender, starting age and starting grade. As a technique we will consider <a href="https://en.wikipedia.org/wiki/Multilevel_model" target="_blank">multilevel models</a> (and possibly same Bayesian models) which is well suited for tasks like this.<br />
<br />
I already excited to see whether individuals improve fast in bouldering than in rock climbing, or whether we can identify a limiting age before you have to start to become really good.<br />
<br />
Please let me know what you are interested in! Which (readily available) factors should be considered in your view for such an analysis?<br />
<br />
Part 1: <a href="https://climbstat.blogspot.com/2019/09/how-many-years-does-it-take-to-climb-7a.html">How many years does it take to climb 7a or 5.11d?</a><br />
Part 2: <a href="https://climbstat.blogspot.com/2019/10/improving-like-adam-ondra.html" target="_blank">Progressing like Adam Ondra or Stefano Ghisolfi</a><br />
Part 3: Progression differences between rock climbing and bouldering<br />
Part 4: The role of age. Is there a critical period to start before to become a professional climber? Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com7tag:blogger.com,1999:blog-3179104266671755636.post-52051198166684924702018-12-16T22:21:00.004+01:002022-05-03T08:19:59.534+02:00The disadvantage of being tall in rock climbing seems to be driven by higher weightPreviously, we observed that being tall is a <a href="http://climbstat.blogspot.com/2018/12/height-and-rock-climbing-performance.html" target="_blank">disadvantage for male rock climbers</a>. One argument which is often made is that this is due to the fact that taller climber also carry more weight than smaller ones.<br />
<br />
Let us investigate this matter. We want to try to shed new light on two related questions here:<br />
<ol>
<li>Is body height negatively related to climbing performance, even if you are (relatively) slim? </li>
<li>Is the fact that taller climbers tend to climb worse due to their higher weight?</li>
</ol>
To answer this question, we will look both at height and weight simultaneously. We will first look at relative weight, here measured with the body mass index (BMI). The BMI is calculated by dividing the weight by the square of the height. The division leads to a measure that is almost uncorrelated to height because all climbers can potentially have a low or high BMI regardless of whether they are tall or not (weight in contrast is highly correlated with height).<br />
<br />
We will use a technique which is called <a href="https://en.wikipedia.org/wiki/Nonparametric_regression" target="_blank">non-parametric regression</a>, which allows us to model or visualize also complex multidimensional relations without strong assumptions (in contrast to methods such as the linear regression approaches which require rather strong assumptions).<br />
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We will focus only on male climbers who are between 165 cm and 190 cm with a BMI between 18.5 and 25 (a range which is considered to cover normal weights) and female climbers between 150 cm and 180 cm with a BMI between 18.5 and 23. We make these assumptions to ensure that we have everywhere enough data available (non-parametric models make fewer assumptions, but they usually require larger datasets than let's say linear models; there are for example relatively few female climbers who have a BMI above 23). Furthermore, we consider only redpoint ascents 7a and higher.<br />
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These restrictions leave us with a sample of 9,775 male and 897 female climbers. <br />
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The following graph visualizes the relationship between height (in cm), weight (BMI) and maximum redpoint performance (7 corresponds here to 7a, 7.5. to 7b+ and 8 to 8a) for male rock climbers<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiblgVUNUbJOJnVPR_2s-H9lxE97xAJPGsfm8MggjYD-Nc7KUJn1r8ZixvcwuzpnLAfwbeMhHY_yy2y5eQI4fqOlghEkM5Ad9bTJ0k2YayqG1m-9N4p-7dmm-IiBN6HYp7jFE_M5URxZoU/s1600/height_bmi_males.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiblgVUNUbJOJnVPR_2s-H9lxE97xAJPGsfm8MggjYD-Nc7KUJn1r8ZixvcwuzpnLAfwbeMhHY_yy2y5eQI4fqOlghEkM5Ad9bTJ0k2YayqG1m-9N4p-7dmm-IiBN6HYp7jFE_M5URxZoU/s400/height_bmi_males.gif" width="400" /></a></div>
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and for female climbers (the visualization is smoother due to the smaller sample size):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj06WF-c56fkQ4yHK3ykBwlsZZzPpHjvrUaOZ2YaCqUy1Oqy_fDu7V2InMNLrM_Kzaxz-r_gusWHyemjlU5Zdzn_7lHTq5zCWtmr67IA4JvcwIdBnt3xYZ5VzNOUfLQtQDze3_EOhZFV68/s1600/height_bmi_females.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj06WF-c56fkQ4yHK3ykBwlsZZzPpHjvrUaOZ2YaCqUy1Oqy_fDu7V2InMNLrM_Kzaxz-r_gusWHyemjlU5Zdzn_7lHTq5zCWtmr67IA4JvcwIdBnt3xYZ5VzNOUfLQtQDze3_EOhZFV68/s400/height_bmi_females.gif" width="400" /></a></div>
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The results show a clear picture. Both being taller and being (relatively) more heavy is a disadvantage when it comes to performing in rock climbing. Particularly concerned are those who are tall but not thin. One should however again note that the relationship is not particularly strong: Climbers who are 15 cm taller climb on average less than one French (sub)grade lower than their smaller peers.<br />
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The visualization also shows that the relationship looks indeed quite linear. This indicates that the assumptions behind the linear regression approach seem to be fulfilled. A linear regression therefore (unsurprisingly) confirms these results. Height and relative weight (BMI) are both (significantly) negatively related to maximum redpoint performance. If we look at standardized measures, we see that the negative effect of being heavier seems to be somewhat stronger for (relative) weight than height.<br />
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Having answered the first question about relative weight, we will now give some insights about absolute weight. This question is harder to answer since there are, fortunately, no tall climbers with (very) low weight. Nor are there small climbers in our sample with a high absolute weight. The non-parametric methods we have used so far are not very well suited for such (sparse) data. Please take therefore the following results with a grain of salt. The nonparametric results for male rock climbers look as follows (the algorithm seems to not work for females correctly due to the lower sample size): <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZcIrffnXiFwNkDXv-eyOaLOGi-ZJuFKejEC9bGPW9lx-esk6BsLH7aUyc33Ziiv09AVkA6ycQdKfGbFJ1i_tJDA-OYl8_agOIhsp7ohbapSywUZMBxYYwsYnFwHuNxNVRpvJE8XemLfU/s1600/height_weight_males.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZcIrffnXiFwNkDXv-eyOaLOGi-ZJuFKejEC9bGPW9lx-esk6BsLH7aUyc33Ziiv09AVkA6ycQdKfGbFJ1i_tJDA-OYl8_agOIhsp7ohbapSywUZMBxYYwsYnFwHuNxNVRpvJE8XemLfU/s400/height_weight_males.gif" width="400" /></a></div>
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Height does not seem to be a big disadvantage anymore. The only exception seem to be climbers who are either very thin or comparable heavy. For the majority of climbers, we do not see a negative relationship with body height (or even a positive one for climbers weighting around 70 kg). <br />
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Results look in general again rather linear. Hence, we will again quickly have a look at linear regression methods. A simple regression indicates for both sexes that only absolute weight is negatively (and statistically significantly) related to climbing performance. The sign of height is positive in both cases, for male climbers even statistically significantly on the 10 percent level (the magnitude is however rather small). This might indicate that the negative height effect is simply due to the fact of higher absolute weight, even for thin (tall) climbers. <br />
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Summarizing, our results show that <br />
<ol>
<li>Being heavier seems to go hand in hand with lower rock climbing performance (on average).</li>
<li>Being taller is a disadvantage if the <u>relative</u> weight (measured by the body mass index) is taken into account.</li>
<li>But this might be simple driven due to the fact that taller climber are on average heavier (in absolute terms)</li>
<li>Height does not seem to be much of a handicap anymore once we take <u>absolute</u> weight into account. </li>
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<br />Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com2tag:blogger.com,1999:blog-3179104266671755636.post-55596303458485047622018-12-12T21:08:00.001+01:002022-05-03T08:17:31.045+02:00What is the share of climbers who can send 8a or 9a?<a href="http://climbstat.blogspot.com/2018/12/distribution-of-grades-in-8anu-data.html" target="_blank">In our previous post</a>, we have looked at the distribution of grades across almost 3 million rock climbing ascents in the 8a.nu data. Today, we will take a very similar approach and look at the highest climbing grade mastered by more than 30,000 rock climbers (both male and female).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoMM59ux2yfJx7WXBd5zfZv2bppfFngcrYA7tDqysQUSYZK_2v1_OXNOLVbKC-1XRycD97EXLk4h2zsSrXXnA83lHHX6KJ7nNF8fhy0deHIXy2scgg7ZkmkeNSoGufHIH3zjFom8zaR5A/s1600/distribution_max_grade.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoMM59ux2yfJx7WXBd5zfZv2bppfFngcrYA7tDqysQUSYZK_2v1_OXNOLVbKC-1XRycD97EXLk4h2zsSrXXnA83lHHX6KJ7nNF8fhy0deHIXy2scgg7ZkmkeNSoGufHIH3zjFom8zaR5A/s400/distribution_max_grade.png" width="400" /></a></div>
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The average peak grade is closely below 7b, and 8a is the mode grade (the most frequent individual maximum grade). In contrast to the distribution of all ascents, we do not see a clustering around 7a for the individual top performance. There are a similar number of 7a to 7c climbers. There are however much more climbers with an 8a limit than we would expect for a smooth distribution. Keeping this in mind, let us gauge how much more difficult is 9a compared to 8a and 7a: In the 8a.nu database, there are more than 4 times as many climbers who have achieved 7a compared to 8a, but there are almost 50 times as many climbers who sent 8a than 9a. Moreover, this is most likely a severe underestimation of the difficulty since I assume that elite climbers are over-represented at 8a.nu compared to other climbers (and top-level ascents which help you to receive publicity and sponsors are recorded more often).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitPbkIhXp7VO8jFG0Rp9A2UtlfUAvKiJGVakSD4uDHTb9IBitm5dCZQX2dyVDpjt5U82wryQXhLTVVKvXXzpTWNZ5ch8U88CUQOWZU8IsWaON80w_F8xXQZNkkWlr0qcs2DRl31D2xsh8/s1600/share_climbers.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitPbkIhXp7VO8jFG0Rp9A2UtlfUAvKiJGVakSD4uDHTb9IBitm5dCZQX2dyVDpjt5U82wryQXhLTVVKvXXzpTWNZ5ch8U88CUQOWZU8IsWaON80w_F8xXQZNkkWlr0qcs2DRl31D2xsh8/s400/share_climbers.png" width="400" /></a></div>
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Here, you can also see the distribution of the maximum grade achieved separately for male and female climbers only (85% of all registered climbers in the database are male). Let us start with female climbers:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQJlP90t4FmyWtaHJhKv-ddDRs46WX7QkRTp8EaoYrpu8FESZxWwM6RGld08f8PrWZWBlmRjniO4lrq6liv3s-oj7z8qDhtTKgeptiKFRaoW6pUZ4GQyRAVNg7PZ0L6SuSIJLvRE7BrcI/s1600/distribution_max_grade_women.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQJlP90t4FmyWtaHJhKv-ddDRs46WX7QkRTp8EaoYrpu8FESZxWwM6RGld08f8PrWZWBlmRjniO4lrq6liv3s-oj7z8qDhtTKgeptiKFRaoW6pUZ4GQyRAVNg7PZ0L6SuSIJLvRE7BrcI/s400/distribution_max_grade_women.png" width="400" /></a></div>
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For female climbers, the average top grade is close to 6c+ and 7a is the most frequently recorded top grade. Male climber's average grade is close to 7a+ and 8a is for them the mode grade. Interestingly, there are much more females who report 6a, 6b or 6c as peak grade compared to 6a+, 6b+ or 6c+ but we do not find this pattern for men.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtTH9BTRrp0WHg61RYWmpr7DljnanXrBok_GP9osRLZs4hS4ywixE6D3AO594o5JXEDIQn6JTBsAMauxIHOzmX_LeDoUmkWAk8mcFp1uyrAr_YdWzxBFGs8zQ_HzE4kF89INb3BljXZzI/s1600/distribution_max_grade_men.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtTH9BTRrp0WHg61RYWmpr7DljnanXrBok_GP9osRLZs4hS4ywixE6D3AO594o5JXEDIQn6JTBsAMauxIHOzmX_LeDoUmkWAk8mcFp1uyrAr_YdWzxBFGs8zQ_HzE4kF89INb3BljXZzI/s400/distribution_max_grade_men.png" width="400" /></a></div>
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<br />Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com0tag:blogger.com,1999:blog-3179104266671755636.post-36001133789753354422018-12-11T18:47:00.003+01:002022-05-03T08:12:32.272+02:00What is the average difficulty of a climbing route?In this post, we will take a look at rock climbing ascents recorded in the 8a.nu data (or to be more precise their grades). This post is about approximately 2.7 m ascents, often multiple ascents by one climber (we will look in a future post at the maximum climbing performance of climbers).<br />
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The following graph shows the French grade distribution of all ascents:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-L8WP3B0Gbhax42kwLDTUSYwn_KRdTPu3CVETueU24wffFSrcjaSlzFg6sXS1u-e4ARs3djuoz23GaJwXyOfLt5bF9aA_DC7VBakbzABzAQt9sjGZ5mRtOcHlVFGc-TkcHljm81kf24g/s1600/distribution_grades.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-L8WP3B0Gbhax42kwLDTUSYwn_KRdTPu3CVETueU24wffFSrcjaSlzFg6sXS1u-e4ARs3djuoz23GaJwXyOfLt5bF9aA_DC7VBakbzABzAQt9sjGZ5mRtOcHlVFGc-TkcHljm81kf24g/s400/distribution_grades.png" width="400" /></a></div>
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What is immediate obvious is that the distribution is not symmetric. First, there are few ascents below the French grade of 6a. We second find a remarkable uniform number of records between 6c and 6c+. The most number of entries is for 7a (or 5.11d) routes. Most 8a.nu user climber probably rather well and are reluctant to enter ascents below 7a in the database.<br />
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Here the same plot truncated below 7a and with percentages of ascents (7a and higher).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5YNbOZtSCD8rUvdaBmGYZgAEpkRK2au-r6CbqXs-aw7sTwf440cXBYJJJTzeh_xVor_3QuT9AM_Ws_JpO02WJtgO4Na2yuA3LHvcx1Jrp_TVrqsGNXSKlv-_zSyQTSJvjM8s15msxNBo/s1600/distribution_grades_7a_plus.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5YNbOZtSCD8rUvdaBmGYZgAEpkRK2au-r6CbqXs-aw7sTwf440cXBYJJJTzeh_xVor_3QuT9AM_Ws_JpO02WJtgO4Na2yuA3LHvcx1Jrp_TVrqsGNXSKlv-_zSyQTSJvjM8s15msxNBo/s400/distribution_grades_7a_plus.png" width="400" /></a></div>
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Interestingly, there are more French 8a routes recorded than 7c+, and a noticeable drop from 8a to 8a+. A possible explanation is that the French 8a grade could constitute a reference. Climbers might put more effort and try more 8a routes than either 7c+ or 8a+ (and perhaps are first ascenders more willing to grade a route 8a). This would also explain the large share of 7a routes compared to 7a+ (and perhaps 6c+). But perhaps there are other explanations I am not aware of? It is also worth mentioning that there is no spike at 9a, perhaps because of greater scrutiny?<br />
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Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com0tag:blogger.com,1999:blog-3179104266671755636.post-79713620622902277152018-12-09T08:13:00.002+01:002022-05-03T08:10:12.372+02:00The Disadvantage of Being Tall: Height and Rock Climbing Performance Part 1 (Men)<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">Today, we want to investigate the correlation between height and individual climbing performance. </span></time></span></time><br />
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">We start with male rock climbers and will look at female climbers in a subsequent post. We focus here only on climbers </span></time></span></time><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">between 155 cm and 200 cm (</span></time><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">5′ 1'' and 6' 7''). This allows us to analyze the climbing performance of almost 16,000 </span></time><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><span class="dataset-header-v2__meta-bullet"><span class="dataset-header-v2__meta-bullet"> male </span></span>climbers. </span></time><br />
<span class="dataset-header-v2__meta-bullet"></span><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"></time></span></time><br />
<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">First, we will have a look at the height distribution of these climbers:</span></time><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD_buzSCdzqfytFNtbBanhhh0a7o75YV4tgIHdaa-E92mORT4KyxAIjXpW6lr3WuKUfoJfivTHEPq0U2hgIZjaJVLx18kPs6HZ_fQjOdfyaIPS5tSkna16kIjnVacXXDwRJd_mvV4-Bwo/s1600/height_distribution_males.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD_buzSCdzqfytFNtbBanhhh0a7o75YV4tgIHdaa-E92mORT4KyxAIjXpW6lr3WuKUfoJfivTHEPq0U2hgIZjaJVLx18kPs6HZ_fQjOdfyaIPS5tSkna16kIjnVacXXDwRJd_mvV4-Bwo/s400/height_distribution_males.png" width="400" /></a></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">The average male climbers in our data is 178 cm, and 50% of the climbers are between 173 cm and 182 cm. There are only a handful climbers below 165 cm or above 195 cm.</span></time></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">Interestingly, a lot of climbers seem to round their height. More than 10% of the climbers give a height of 180 cm, but only 4% say they are 'just' 179 cm. This is the reason why certain bars stick out in the graph above. </span></time></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">We next look at the maximum performance by height. It should be remembered that the 8a.nu data is user based and therefore incomplete. Neither has Chris Sharma nor Alex Megos a scorecard. The available data also does not cover 2018. This is why, for example, Stefano Ghisolfi's recent 9b+ ascent of </span></time><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">Perfecto Mundo is not included.</span></time></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z">The following graph shows the maximum performance by height (in cm). Adam Ondra (185 cm) sticks obviously out, but there are high performing male smaller and taller climbers. Individuals 170 cm and 185 cm did redpoint French 9b, and climbers between 159 cm and 185 cm have redpointed 9a+. If one keeps in mind that 80% of the male climbers are between 170 cm and 187 cm, there does not seem to be an obvious pattern. Except perhaps for the lack of a tall climber, let's say above 190 cm, performing at the very top. <span class="dataset-header-v2__meta-bullet"><br /></span></time></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcfFqD8LE1QuYYHi_K7dXh3hnrFNYSRnXfHc1us8NTbUfpzU-P8BW4C0IwCBCAWyaNZXKpQXUafDEtPOk3ryuPTZrw-HFJNLHGK853Si4LXHpx-G4BBrs9XJ4DVnbvhyphenhyphenelpD1OaATtXRM/s1600/max_performance_by_height.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcfFqD8LE1QuYYHi_K7dXh3hnrFNYSRnXfHc1us8NTbUfpzU-P8BW4C0IwCBCAWyaNZXKpQXUafDEtPOk3ryuPTZrw-HFJNLHGK853Si4LXHpx-G4BBrs9XJ4DVnbvhyphenhyphenelpD1OaATtXRM/s400/max_performance_by_height.png" width="400" /></a></div>
<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z">We now relate the height to the performance using a regression approach. We fit a polynomial of height of the order of 3 (height, height squared and height cubed) using linear regression (the orange "Average" line). To see whether height makes a more or less a difference at the very top or for ordinary climbers, we further model the relationship at different points of the performance distribution (using <a href="https://en.wikipedia.org/wiki/Quantile_regression" target="_blank">quantile regression</a>). </time></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL0RNRH0kXC_wZfu3LSzPogW5nxqE-TephSQeb1xMe49WTNGEJCYUP1BDyhV9WRkeESkGKEZ2f1o12tpZOecm_iVJDv1TJnGyvmwS1TBAzouNa336jAQ934moNjwpZU4j0quv_fnYlBdw/s1600/height_regression.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="1000" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL0RNRH0kXC_wZfu3LSzPogW5nxqE-TephSQeb1xMe49WTNGEJCYUP1BDyhV9WRkeESkGKEZ2f1o12tpZOecm_iVJDv1TJnGyvmwS1TBAzouNa336jAQ934moNjwpZU4j0quv_fnYlBdw/s400/height_regression.png" width="400" /></a></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><br />The graphical results of our regression approach show that height indeed seems to matter. Height is (statistically significantly) negatively related to climbing performance for most climbers. The relationship seems to be linear for most of the performance, meaning that the taller you are, the worse your climbing performance on average.</span></time></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">How large is this relationship? The "Average" line suggests that a typical 165 cm tall 8a.nu climber climbs up to 7b while the taller counterpart measuring 195 cm 'only' achieves 7a. These difference seem large, but they are not if we consider the differences within different body sizes. Body height just explains a tiny 1% of the differences in climbing performance, according to this analysis. </span></time></div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">Interestingly, for ordinary climbers (who perhaps climb up to 7a) as well as for the elite, there may be a slight 'inverse U-shaped' relationship between climbing performance and height. Indicating that there is something like an optimal height for climbing. The best performing climbers seem to be around 170 cm for the ordinary climbers and perhaps even a bit smaller for the elite (although the sample size is of course much smaller). But again, height is only one of many factors playing a role here, and it does not seem to be a very important one. </span></time></div>
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In a following post, we will focus on female climbers. <a href="http://climbstat.blogspot.com/2018/12/height-and-rock-climbing-performance.html" target="_blank">We will also take a look at the role of weight, and whether there remains a negative effect of height if we take into account that taller climber are usually also heavier.</a> <br />
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PS: I just noticed that s similar analysis for US climbers with the same results have been published by <a href="https://rockandice.com/climbing-news/the-height-of-injustice-is-being-tall-an-advantage-in-your-climbing-career/" target="_blank">Chris Ring in Rock and Ice</a>. </div>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"> </span></time> </div>
Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com4tag:blogger.com,1999:blog-3179104266671755636.post-66676501859726155162018-12-07T14:38:00.002+01:002022-05-03T08:04:42.114+02:00Underlying Data The data of this blog is taken from the popular rock climbing news website and database<br />
<a href="https://www.8a.nu/" rel="nofollow" target="_blank">8a.nu</a>.<br />
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<a href="https://www.8a.nu/" rel="nofollow" target="_blank">8a.nu</a> allows climbers and boulderer to save their ascents and scores them according to the type (e.g. onsight, flash or redpoint) and the grade (based on French grades).<br />
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The data from the website has been published by David Cohen via Kaggle.<br />
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The data is still in the raw format which includes for example projects or toprope ascents which are usually not considered as 'proper' ascents. Furthermore, the database includes climbers who state unrealistic low or high heights or birth years. We have cleaned this dataset and focus only on<br />
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<a href="https://www.blogger.com/blogger.g?blogID=3179104266671755636" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="https://www.blogger.com/blogger.g?blogID=3179104266671755636" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="about:invalid#zClosurez" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="about:invalid#zClosurez" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a>
<li><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">onsight, flash or redpoint ascents,</span></time></li>
<li><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">without repeats,</span></time></li>
<li><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">exclude ascents without a score by the respective climber </span></time></li>
<li><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">and routes graded between 6a and 9c+. </span></time></li>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">We have excluded a few top ascents by unknown individuals (e.g. a 9b+ ascent by user Paolo Antoniotti). </span></time><br />
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet">This leaves us with ca 2.7 million ascents which cover the time period up to 2017. </span></time><br />
<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><br /></span></time><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"></time>
<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><span class="dataset-header-v2__meta-bullet"><time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"><br /></time></span></time>
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<time datetime="2018-03-22T15:44:54.513Z" title="2018-03-22T15:44:54.513Z"></time>Arne Jonas Warnkehttp://www.blogger.com/profile/17568523828168805793noreply@blogger.com0