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Copy file name to clipboardexpand all lines: manuscript/ClimbingGrades.aux
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\citation{coulom2008whole}
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\citation{scarff2020estimation}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces\relax\fontsize {9}{11}\selectfont\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@\abovedisplayshortskip\z@ plus2\p@\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@\def\leftmargin\leftmargini\parsep 4\p@ plus2\p@ minus\p@\topsep 8\p@ plus2\p@ minus4\p@\itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin\leftmargini\topsep 4\p@ plus2\p@ minus2\p@\parsep 2\p@ plus\p@ minus\p@\itemsep\parsep }\belowdisplayskip\abovedisplayskip The posterior estimate of the slope parameter ($d=e^m$) for each of the 20 analyses.}}{7}{figure.1}}
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\newlabel{final-plot}{{1}{7}{\small The posterior estimate of the slope parameter ($d=e^m$) for each of the 20 analyses}{figure.1}{}}
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\newlabel{final-plot@cref}{{[figure][1][]1}{7}}
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\newlabel{finalplot}{{1}{7}{\small The posterior estimate of the slope parameter ($d=e^m$) for each of the 20 analyses}{figure.1}{}}
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\newlabel{finalplot@cref}{{[figure][1][]1}{7}}
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\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Summary of Bayesian analyses performed}}{8}{table.2}}
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\newlabel{datatable}{{2}{8}{Summary of Bayesian analyses performed}{table.2}{}}
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\newlabel{datatable@cref}{{[table][2][]2}{8}}
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\citation{carpenter2017stan}
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\citation{oneill2002}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces\relax\fontsize {9}{11}\selectfont\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@\abovedisplayshortskip\z@ plus2\p@\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@\def\leftmargin\leftmargini\parsep 4\p@ plus2\p@ minus\p@\topsep 8\p@ plus2\p@ minus4\p@\itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin\leftmargini\topsep 4\p@ plus2\p@ minus2\p@\parsep 2\p@ plus\p@ minus\p@\itemsep\parsep }\belowdisplayskip\abovedisplayskip The posterior estimate of each Australian climber's grade ($n=100$) through time and the posterior distribution of the proportional increase in difficulty per grade increment $d = e^m$.}}{11}{figure.2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces\relax\fontsize {9}{11}\selectfont\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@\abovedisplayshortskip\z@ plus2\p@\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@\def\leftmargin\leftmargini\parsep 4\p@ plus2\p@ minus\p@\topsep 8\p@ plus2\p@ minus4\p@\itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin\leftmargini\topsep 4\p@ plus2\p@ minus2\p@\parsep 2\p@ plus\p@ minus\p@\itemsep\parsep }\belowdisplayskip\abovedisplayskip The posterior estimate of each New Zealand climber's grade through time and the posterior distribution of the proportional increase in difficulty per grade increment $d = e^m$.}}{11}{figure.3}}
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\newlabel{nz_ascents}{{3}{11}{\small The posterior estimate of each New Zealand climber's grade through time and the posterior distribution of the proportional increase in difficulty per grade increment $d = e^m$}{figure.3}{}}
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\newlabel{nz_ascents@cref}{{[figure][3][]3}{11}}
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\citation{portugal2011weber}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces\relax\fontsize {9}{11}\selectfont\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@\abovedisplayshortskip\z@ plus2\p@\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@\def\leftmargin\leftmargini\parsep 4\p@ plus2\p@ minus\p@\topsep 8\p@ plus2\p@ minus4\p@\itemsep 4\p@ plus2\p@ minus\p@ {\leftmargin\leftmargini\topsep 4\p@ plus2\p@ minus2\p@\parsep 2\p@ plus\p@ minus\p@\itemsep\parsep }\belowdisplayskip\abovedisplayskip The relationship between grade and the log of the number of successful sends for two styles of climbing (bouldering and sport climbing) in two countries, based on whole climbing community statistics on \url {http://thecrag.com}}}{12}{figure.4}}
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\newlabel{fig.oneill}{{4}{12}{\small The relationship between grade and the log of the number of successful sends for two styles of climbing (bouldering and sport climbing) in two countries, based on whole climbing community statistics on \url {http://thecrag.com}}{figure.4}{}}
Copy file name to clipboardexpand all lines: manuscript/ClimbingGrades.tex
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\section*{Methods}
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We analysed 20 datasets across three countries (New Zealand, Australia, Germany) with the largest sets of data available on The Crag (\url{http://thecrag.com}), a popular online climbing logbook. Our datasets feature four different grading systems (Ewbanks, French sport, UIAA, V-scale) and three styles of climbing (two types of route climbing: sport and trad; as well as bouldering). Table \ref{table1} summarises the datasets.
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We analysed 20 datasets across three countries (New Zealand, Australia, Germany) with the largest sets of data available on The Crag (\url{http://thecrag.com}), a popular online climbing logbook. Our datasets feature four different grading systems (Ewbanks, French sport, UIAA, V-scale) and three styles of climbing (two types of route climbing: sport and trad; as well as bouldering). Table \ref{datatable} summarises the datasets.
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\afterpage{%
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}
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We describe two analyses in more detail. The first highlighted analysis uses self-reported data on whole-history of ascents for 100 Australian climbers of differing abilities to estimate the fundamental slope parameter for the Ewbank climbing grade scale for sport climbing. We repeated this analysis using the same criteria for selection (see Supplementary material) for climbers in New Zealand, resulting in a data set of 89 climbers.
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We describe two analyses in more detail. The first highlighted analysis uses self-reported data on whole-history of ascents for 100 Australian climbers of differing abilities to estimate the fundamental slope parameter for the Ewbank climbing grade scale for sport climbing. We repeated this analysis using the same criteria for selection (see Supplementary Material) for climbers in New Zealand, resulting in an additional dataset of 89 climbers.
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The estimated slopes of all 20 analyses are presented in figure \ref{final-plot}.
\caption{\small The posterior estimate of the slope parameter ($d=e^m$) for each of the 20 analyses.}
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\label{final-plot}
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\label{finalplot}
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\end{figure}
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The estimated slopes of all 20 analyses are presented in Figure \ref{finalplot}.
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In the second set of analyses we use whole-community successful ascent data from New Zealand and Australia. Finally we analyse a small data set of curated link-up boulder problems to illustrate the limitations of grading climbs in parts without considering fatigue.
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\subsection*{Estimating the slope of difficulty for the Ewbank climbing grade scale}
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