Progressing like Adam Ondra or Stefano Ghisolfi

Last time, we have looked how averge climbers progress over time. Today, we want to look at individual performance trajectories of elite climbers such as Adam Ondra, Stefano Ghisolfi or Ramón Julian Puigblanque.

To derive the progression over time (or over experience), we use a statistical technique which is called multilevel modelling. This method can be viewed as a generalization of linear regression for (among others) datasets in which we follow individuals over time. A good introduction source is the book "Data Analysis Using Regression and Multilevel/Hierarchical Models" by Andrew Gelman and Jennifer Hill (multilevel models are also called hierarchical models). You can find some further information about this technique at the end of the blog post.

The following graph shows the derived performance curves for some elite climbers. Adam Ondra (in red) started very young. His first ascents are recorded being just 8 years old. He continuously improved since then and in 2017, the last year recorded in our sample, he did the world's first 9c or 5.15d (Silence in Flatanger). Ramón Julian Puigblanque started much later in 1996 at the age of 14 or 15. We do not observe his first years but in late 2000, he already climbed his first 8c+ (El disbarat in Montserrat). His experience profiles looks inversely U-shaped which is not uncommon for, among others, many age-performance curves.

Next, we will look at three outstanding climbers who all started around the same age of being 11-12 years old. Jorge Diaz-Rullo, who did in 2019 (so far) three 9b (5.15b) and four 9a+ (5.15a), showed an extraordinary steep improvement until 2017. It will be certainly interesting to see his list of climbing achievements in a few years. Stefano Ghisolfi is almost a late bloomer among this group. His rise to excellence has notwithstanding been also incredible steep (who became the fourth climber in history to climb 5.15c or 9b+). Sèbastian Bouin recorded no ascents below 8c (5.14b). This makes it difficult to derive a progression curves and his profile is therefore more or less flat between 2011 and 2017. Piotr Schab started much younger (being around 7 years old) and progressed therefore at a lower pace. So far he however still seems to improve further.

Further profiles for Sachi Amma (starting age 12), Daniel Woods (6), Mathieu Bouyoud (13), David Graham (16), Domen Škofic (5), Jernej Kruder (7), Joe Kinder (16) and Daniel Jung (14) can be found below. We have included here only climbers who have registered via 8a.nu. This is why, for example, Chris Sharma or Alexander Megos, are not considered. Furthermore, some other well-known climbers are not included because they started well before 8a.nu was created (such as Patxi Usobiaga, 1990) or others did not add their account until 2017 (Jonathan Siegrist).

You might wonder that these curves do not follow exactly the (top three) true highest ascents. This is not surprising for two reasons. Firstly, the curves are derived through a polynomial of the order of three, meaning that all profiles are smoothed over time (or over experience). Secondly, for the elite climbers the curves may seem sometimes slightly biased downwards. This is actually a desired feature of multilevel models which also allows to model climbers who we observe only for few years. 'Extreme' observations are slightly shrinked to the overall average.

 
Some further information regarding multilevel models: Linear regression calculates one intercept and one set of slope parameters for the entire sample. In multilevel models, each individual has his or her own set of parameters. These are, however, not calculated completely separately as it would be the case if one would use one linear regression model for each climber in the whole dataset. Multilevel methods have the advantage that we allow to model also climbers who we observe only for a few years realistically. This is done by adding some extra (distributional) assumptions.

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.