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Sunday, December 16, 2018

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 a 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 165cm and 190cm with a BMI between 18.5 and 25 (a range which is considered to cover normal weights) and female climbers between 150cm and 180cm 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 15cm 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 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. 

3 comments:

  1. Any chance you’d be willing to make the data available? I’d love to play around, but I can’t find the data on 8a.nu. Thanks!

    ReplyDelete
  2. Thanks for sharing great post about outdoor adventure activities. Keep it post!
    Outdoor Adventure Activities

    ReplyDelete

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