Data 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?

The Disadvantage of Being Tall: Height and Rock Climbing Performance Part 1 (Men)

We start with male rock climbers and will look at female climbers in a subsequent post. We focus here only on climbers between 155cm and 200cm (5′ 1'' and 6' 7''). This allows us to analyze the climbing performance of almost 16,000 male climbers. First, we will have a look at the height distribution of these climbers:

The average male climbers in our data is 178cm, and 50% of the climbers are between 173cm and 182cm. There are only a handful few climbers below 165cm or above 195cm.

Interestingly, a lot of climbers seem to round their height. More than 10% of the climbers give a height of 180cm but only 4% say they are 'just' 179cm. This is the reason why certain bars stick out in the graph above.

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 Perfecto Mundo is not inculded.

The following graph shows the maximum performance by height (in cm). Adam Ondra (185cm) sticks obviously out but there are high performing male smaller and taller climbers. Individuals 170cm and and 185cm did redpoint French 9b, and climbers between 159cm and 185cm have redpointed 9a+. If one keeps in mind that 80% of the male climbers are between 170cm and 187cm, there does not seem to be an obvious pattern. Except perhaps for the lack of tall climber, let's say above 190cm, performing at the very top.

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 least 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 quantile regression).

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.

How large is this relationship? The "Average" line suggests that the a typical 165cm tall 8a.nu climber climbs up to 7b while the taller counterpart measuring 195cm '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.

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 170cm for the ordinary climbers and perhaps even a little 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.

As I'm sure you're aware, the "maximum performance by height plot" is really misleading. Just by virtue of fewer people being taller, the good-climber tail of the distribution won't be as well sampled by tall people (same with short people). For any two independent variables that are centrally peaked, you'll get that shape with a peak in the middle like that. The quantile regression solves that problem, so you're conclusions are solid, but it's important to call the above issue out! The Rock and Ice article rests its case on this statistical mistake!

Hi Astro, thanks for your remark. You are of course completely right: we should expect that the performance for smaller and taller climbers is on average below the performance of the “average” climbers. What I just tried to say with the graph is the following: Compared to the presence of extreme good smaller climbers, it catches the eye that there are no corresponding tall climbers performing at the same level. Perhaps I should have made that clearer but as you rightly pointed out, the regression approach should be less prone to a possible statistical fallacy due to differences in the sample sizes.

Iminterested why you chose 165cm and 195cm? At least in terms of percentile of the general population, they are very different groups. Literally only 1% of males are 195cm or taller, whereas at 165cm you're looking a 5-8% or so ... I'd be interested of the strength of the correlation comparing 165cm to 186/187cm which is a better 'percentile' comparison.

Hi, thanks for your comment. I do not think that your figures apply to the younger cohorts anymore who are on average taller than the general population (and much higher represented among the climbing community). There are of of course additionally large differences in average height between countries. For the 8a.nu sample (rock climbers as well as boulderer), 5% are below 165cm and 5% are above 190cm, 10% are below 169cm and 10% are above 187cm. See also the first graph here in the post.

You mean comparing the performances of rock climbers being 165cm tall with those of 186/187cm of height?

As I'm sure you're aware, the "maximum performance by height plot" is really misleading. Just by virtue of fewer people being taller, the good-climber tail of the distribution won't be as well sampled by tall people (same with short people). For any two independent variables that are centrally peaked, you'll get that shape with a peak in the middle like that. The quantile regression solves that problem, so you're conclusions are solid, but it's important to call the above issue out! The Rock and Ice article rests its case on this statistical mistake!

ReplyDeleteHi Astro, thanks for your remark. You are of course completely right: we should expect that the performance for smaller and taller climbers is on average below the performance of the “average” climbers. What I just tried to say with the graph is the following: Compared to the presence of extreme good smaller climbers, it catches the eye that there are no corresponding tall climbers performing at the same level. Perhaps I should have made that clearer but as you rightly pointed out, the regression approach should be less prone to a possible statistical fallacy due to differences in the sample sizes.

DeleteIminterested why you chose 165cm and 195cm? At least in terms of percentile of the general population, they are very different groups. Literally only 1% of males are 195cm or taller, whereas at 165cm you're looking a 5-8% or so ... I'd be interested of the strength of the correlation comparing 165cm to 186/187cm which is a better 'percentile' comparison.

ReplyDeleteHi, thanks for your comment. I do not think that your figures apply to the younger cohorts anymore who are on average taller than the general population (and much higher represented among the climbing community). There are of of course additionally large differences in average height between countries. For the 8a.nu sample (rock climbers as well as boulderer), 5% are below 165cm and 5% are above 190cm, 10% are below 169cm and 10% are above 187cm. See also the first graph here in the post.

DeleteYou mean comparing the performances of rock climbers being 165cm tall with those of 186/187cm of height?