The disadvantage of being tall in rock climbing seems to be driven by higher weight

Previously, we observed that being tall is a disadvantage for male rock climbers. One argument which is often made is that this is due to the fact that taller climber also carry more weight than smaller ones.

Let us investigate this matter. We want to try to shed new light on two related questions here:

1. Is body height negatively related to climbing performance, even if you are (relatively) slim? 
2. Is the fact that taller climbers tend to climb worse due to their higher weight?

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).

We will use a technique which is called non-parametric regression, 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).

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.

These restrictions leave us with a sample of 9,775 male and 897 female climbers.

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

     

and for female climbers (the visualization is smoother due to the smaller sample size):

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.

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.

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):

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). 

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.

Summarizing, our results show that

1. Being heavier seems to go hand in hand with lower rock climbing performance (on average).
2. Being taller is a disadvantage if the relative weight (measured by the body mass index) is taken into account.
3. But this might be simple driven due to the fact that taller climber are on average heavier (in absolute terms)
4. Height does not seem to be much of a handicap anymore once we take absolute weight into account. 

What is the share of climbers who can send 8a or 9a?

In our previous post, 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).

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).

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:

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.

What 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).

The following graph shows the French grade distribution of all ascents:

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.

Here the same plot truncated below 7a and with percentages of ascents (7a and higher).

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?

 

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

Today, we want to investigate the correlation between height and individual climbing performance.  

We start with male rock climbers and will look at female climbers in a subsequent post. We focus here only on climbers between 155 cm and 200 cm (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 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.

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. 

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 included.

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.   

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 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 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.  

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.  

In a following post, we will focus on female climbers. 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.

PS: I just noticed that s similar analysis for US climbers with the same results have been published by Chris Ring in Rock and Ice.

 

Underlying Data

The data of this blog is taken from the popular rock climbing news website and database
8a.nu.

8a.nu 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).

The data from the website has been published by David Cohen via Kaggle.

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

• onsight, flash or redpoint ascents,
• without repeats,
• exclude ascents without a score by the respective climber 
• and routes graded between 6a and 9c+. 

We have excluded a few top ascents by unknown individuals (e.g. a 9b+ ascent by user Paolo Antoniotti). 

This leaves us with ca 2.7 million ascents which cover the time period up to 2017.