## Sunday, September 29, 2019

### How many years does it take to climb 7a or 5.11d?

If you talk to beginners, you often hear the question 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 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 lightblue 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). We do not observe for all climbers ascents for all experience levels. This is why there are fewer lines in the first year and among very experienced climbers. It is also apparent that the average climber in our sample is quite strong and starts strong. We have seen this already before, and it is not really 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 use as starting age the time where they started to train and climb seriously.

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 their is a steep improvement in the first three to four years which flattens subsequently. There does not seem to be much improvement (on average) anymore beyond 6 years of experience. We have displayed only up to ten years of experience but the results look similar if we extent 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.

1. I like this, but i think that using the 8a data here would be misleading. How many people do you know that start recording their climbs as soon as they start?

1. Yes, you are completely right. That is why I think that the level is definitely biased due to wrongly entered starting ages. I think, however, the general shape make sense. What do you think?

2. i think yes but there's not really a way of see the "clipped" portion of the graph on the lower end. Good post though, made me think for sure.

2. This is incredibly interesting. Whether or not the data is representative of accurate climbing experience, the curve clearly gives some insight. Anecdotally, I have about 1.5 years of climbing experience myself and redpoint 11a, but I would like to think I put a lot more effort into training than the "average" climber. Certainly those posting to 8a.nu right off the bat might have a performance bias, but that makes it all the more interesting. Put an average joe on a mission to climb 11d in 1.5 years with a performance mindset and/or good genetics, and it seems 100% plausible and supported by this. Keep these posts coming, I dig the blog!

Disclaimer: My knowledge of statistics is poop, just a humble engineering student.

1. Thank you. I appreciate your feedback very much, and it encourages me to continue!

3. This is really helpful work from a motivation standpoint. Trying hard month after month, it's nice to see what one can hope to achieve over time. The data smoothing and cohorts are nice here - Would you be wiling to share the treated data that you used to produce the visualization? I'd love to play around with it a bit!

### 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...