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.
