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Sunday, September 29, 2019

How 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.

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. 

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.

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.




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.  

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.

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.  

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. 

In the next post, we look at climbing profiles of elite climbers such as Adam Ondra.     

Tuesday, September 24, 2019

New 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 multilevel models (and possibly same Bayesian models) which is well suited for tasks like this.

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.

Please let me know what you are interested in! Which (readily available) factors should be considered in your view for such an analysis?

Part 1: How many years does it take to climb 7a or 5.11d?
Part 2: Progressing like Adam Ondra or Stefano Ghisolfi
Part 3: Progression differences between rock climbing and bouldering
Part 4: The role of age. Is there a critical period to start before to become a professional climber?

Research article looking at climber ability and route difficulties by Dean Scarff

Dean Scarff made me kindly aware about his extremely interesting arXiv article Estimation of Climbing Route Difficulty usingWhole-History Ra...