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 Rating. In this paper Dean estimates rock climber ratings and route difficulties using the “Whole-History Rating” based on data of the rock climbing site www.thecrag.com. The “Whole-History Rating” is a player rating which is an adaption of the Bradley - Terry model. I have to admit, I knew neither of them but I have worked with Elo ratings before (looking at soccer). In the past, I also wrote a paper looking at (changing) inequality of the allocation of player talentacross soccer clubs in German based on estimated player ratings (together with Roman Sittl). This is why I am delighted to see such approaches now being applied to rock climbing.

What is really nice is firstly that the topic is in my view extremely interesting, not only for research but for the sport itself. Secondly, the code seems to be fully available on GitHub. Thirdly, the estimated route difficulties are visually contrasted to the true (Australian) grades, as shown in the following figure further below from the paper. It looks quite reasonable (the large variance is perhaps a little bit irritating but that might just be a few very extreme observations for each grade). Fourthly, what is extremely interesting is the fact that www.thecrag.com dataset also seems to covers “No go’s” or unsuccessful climbing ascents (in contrast to the 8a.nu data). This is something I personally collect for my own ascents but I never have seen someone else collecting it. This really allows to estimate the player and route ratings soundly. Finally, the methodological description is short but seems solid (but I have not thought everything through as I would if I had to peer-review the article).

Some feedback for improvement the paper from my side would be the following: Firstly, the paper is extremely short (which is common in computer science as far as I know) but a little bit more information here and there would be helpful in my view (e.g. about the Australian Ewbank grade system in comparison to the French or US grade system or about the underlying dataset). Secondly and more importantly, I would love to see in the end some more climbing-related interpretation – perhaps even contrasting the route rating and the successful / unsuccessful player ratings attempting that route for a well-known Australian route. I say that because it would demonstrate that such an algorithm is not just interesting for research per se but might, for example, be used as supporting evidence in a grading dispute etc. Thirdly, a minor point, do one really needs climber's ability to vary on a weekly level since on average climbers performance seems to be rather constant after a few years?

But I only say that because I think the article is great and I would like to see more! Thanks Dean. 

In general, if you have any interesting rock climbing related research for me, please make me aware of it!  

 

Which bouldering and rock climbing destinations are most impacted by the coronavirus pandemic?

I am a bit reluctant to write about the coronavirus pandemic. There is on the one hand already a lot of information out there. On the other hand, we still miss crucial aspects of this novel virus (such as the number of unknown cases). And, I cannot really contribute anything important to this topic. It is however consuming a lot of attention and interferes for many of us with our favorite sport (due to widespread lockdowns and social distancing regulations). This is why it is after all very relevant for the bouldering and rock climbing community, and why I decided to take this topic up here. 

First and foremost, please, adhere to the local regulations considering climbing and movement. You not only jeopardize future free access to local crags but also actual lives if you still continue as usual (e.g. by spreading the virus to remote communities or stressing already strained emergency resources)!

As the title says, I want to take here a look which bouldering and rock climbing destinations are most impacted by the coronavirus pandemic? Where could climbing (hopefully soon) be safe again? 

You can find below a simple visualization which shows the most important bouldering and rock climbing destinations, on the x-axis ranked by number of ascents in the 8a.nu database (until 2017). On the y-axis, you can find the number of confirmed COVID-19 cases per 100.00 inhabitants according to Johns-Hopkins University Center for Systems Scienceand Engineering. This gives a rough picture about which climbing destinations are most impacted by the coronavirus.

The number of confirmed COVID-19 cases is only a very crude proxy for the severity of the local conditions. There are, for example, large differences in tests performed between countries, and more testing means one will detect more cases. My home country, Germany, performes alot of tests and has a high rate of infections but a comparable low death rate. This is likely because there many mild cases detected through widespread testing. Other countries are suspected to artificially keep down the number of confirmed cases, by various means. Notwithstanding all these flaws, there will be on average a close relationship between the actual conditions and the number of confirmed cases. To consider the large differences in population numbers, I here look at confirmed cases by 100.000 inhabitants.

As you can see, a large part of the countries famous for their climbing spots in Europe are severely affected. Italy and Spain have established near complete lockdowns. The situation is also tense in Central Europe and the USA. It (yet) seems to be better Eastern Europe, in Greece, Mexiko, Australia and New Zealand, and other countries in Asia or South America. This is might be due to limited testing. It is not meant as a travel recommendation (some of these health systems have been already strained prior to the pandemic). But it might show where climbing might sooner be possible again.   

How much harder is onsighting vs redpointing?

Every rock climber knows that a successful onsight is much harder than an ascent with perfect beta after rounds of projecting. An onsight means climbing a route successfully at the first attempt without prior information or rehearsal on the route. During an onsight, we might not know where the crux lies or how long the route actually is. In contrast, being able to learn about a route, to mentally accommodate to the hard sections, the rest points and footholds, allows us to reach our maximum performance during a redpoint ascent.

Most of us also have a good sense of the routes we typically can climb in a first attempt with or without prior knowledge or in a second or subsequent attempt. But it is much harder to guess how much more difficult, let’s say an onsight ascent is, compared to a successful redpoint ascent. We might know that Adam Ondra did Silence (9c or 5.15d), currently the world’s hardest route, after weeks of practicing specifically for that route. Adam was also the first to flash a route of the grade 9a+ or 5.15a (a flash means a successful ascent of a route in the first go with prior information, for example from other climbers), and he did three 9a or 5.14d onsight. Alex Megos, however,was the first to onsight a 9a or 5.14d, he climbed up to 9b+ (redpoint). Up to today, no one onsighted a route harder than 9a. But is the difference between 9b+ redpoint and 9a onsight an meaningful estimate of how much harder an onsight is? A first attempt without beta might be easier among lower-graded routes compared to the elite level. Here, we want to investigate this question in a quantitative way.

As in previous posts, we will therefore access the data of the website 8a.nu which provides climbers with the opportunity to save their climbs and view personal scorecards. A scorecard is simply an overview about routes achieved, the respective style and the grade among others. In this post, we look at the maximum onsight and the maximum redpoint grade of 8a.nu users who made their scorecard public. We focus here on climbers who climbed redpoint at least 6a or 5.10a or higher. The available dataset covers entries up to September 2017. This leaves us with almost 18,000 climbers.

How do the results look like? First, we take a look at the overall difference between the maximum (redpoint) performance and the maximum onsight performance. The following graph shows the distribution of maximum performance for each climber in our dataset by style. This kind of graph is called a violin graph. The wider the violin, the more climbers there are with a certain maximum redpoint or onsight performance. The average maximum performance by style is illustrated by the black point in the middle of the violin. The average maximum redpoint performance is slightly above 7b+ or 5.12c. This is partly due to the fact that we disregarded climbers who do not climb above 6a or 5.10b. Apart from that the average ability of active 8a.nu users is quite high. Climbers who do not climb very often don’t bother much about creating and maintaining a public scorecard. The corresponding maximum onsight performance is slightly above 7a or 5.11d. This indicates that the average onsight level is approximately three grades below the maximum performance.

Next, we want to investigate whether the results differ across the performance spectrum. For this purpose, we group all climbers together by their maximum (redpoint) performance on their scorecard. Now we look at the average maximum onsight performance within each group. 

How does this grouping work and how did we finally calculate the average onsight performance? Let us take those climbers who sent 9b+ or 5.15c as maximum (regardless of whether they are included in the 8a.nu data). These are Stefano Ghisolfi, Alexander Megos and Chris Sharma (Adam Ondra is not included in this list despite the fact that he did three 9b+ because of his 9c redpoint). Alexander Megos did an 9a onsight while Stefano Ghisolfi and Chris Sharma onsighted up to 8c at maximum, according to Wikipedia. The onsight average of this group is therefore slightly below 8c+.

The following graph shows how the redpoint-onsight performance gap across all grades. On the x-axis, we have plotted the maximum (redpoint) performance. The y-axis shows the maximum onsight performance. If climbers onsighted grades similar to their redpoint performance, we would see a straight 45 degree line (indicated in red). The onsight performance is as one would expect, lower than the maximum performance and this is why the blue points are below the red line. It is apparent that the difference is small for climbers with a relatively low maximum performance and it widens for higher able climbers. This indicates that an onsight becomes harder the harder you climb. The average onsight maximum is 2-3 grades lower for climbers who climb up to 7a or 5.11d redpoint but it increases to almost 4 grades for climbers with a maximum grade of 8a or 5.13b (and still widens further). Interestingly, the gap again seems to be a little lower for the few climbers who can climb 9b or 5.15b or higher.

We have not considered flash ascents in this post. The reason is that there is almost no difference between the maximum onsight and flash performance in the 8a.nu data. The highest flash grades are higher than the average onsight grades but the difference is very small (ca. ⅙ of the difference between one grade or between 7a and 7a+). Personally, we think this seems surprising since a good beta might indeed give you valuable information.

First Ascentionists Over Time (Female and Male)

I have always been interested in the history of rock climbing. Lately, I tried to collect data about male and female first ascentionists to visualize climbing progression over tine. However, it turned out difficult to find a lot of data (particularly for female climbers). An exception to the rule is this really nice site http://stara.emontana.cz/climbing-milestones-from-6a-to-9c/  from which I got a lot of information.

It would be great if someone could point me to further sources, and help me correcting the existing data! I find it particularly difficult to get information about, among others,

• first onsights and flashes (who was the first to onsight 8a or flash 8b+?)
• first successful female and male bouldering ascents
• early first female ascents (does anyone know who did the first female 7a?)
• 'first' second ascents (who did the second 8c in the world?)

For routes with disputed gradings, such as Chilam Balam first redpointed by Bernabè Fernandez in 2003, I took the majority grade by all repeaters (9a+/9b in that case).

Graphs below, data (including sources) is available here via Google Spreadsheet or via ClimbStat GitHub (here you can also find the R-code to create the individual graphs. They have been merged together externally to one GIF). Further below you can find an excerpt.

Year	Ascensionist	Route	Grade (YDS)	Grade (French)	Sex	Confirmed?
1979	Lynn Hill	Ophir Broke	5.12d	7c	female	Yes
1985	Catherine Destivelle	Fleur de Rocaille	5.12d/5.13a	7c+/8a	female	Yes
1986	Luisa Iovane	Comeback	5.13b	8a	female	Yes
1988	Catherine Destivelle	Chouca	5.13c	8a+	female	Yes
1988	Isabelle Patissier	Sortileges	5.13d	8b	female	Yes
1990	Lynn Hill	Masse Critique	5.14a	8b+	female	Yes
1998	Josune Bereziartu	Honky Tonky	5.14b	8c	female	Yes
2000	Josune Bereziartu	Honky Tonk Mix	5.14c	8c+	female	Yes
2002	Josune Bereziartu	Bain de Sang	5.14d	9a	female	Yes
2005	Josune Bereziartu	Bimbaluna	5.14d/5.15a	9a/9a+	female	Yes
2017	Margo Hayes	La Rambla Extension	5.15a	9a+	female	Yes
2017	Angela Eiter	La planta de shiva	5.15b	9b	female	Yes
1961	John Gill	Thimble	5.12a	7a+	male	Yes
1967	Greg Lowe	Macabre Roof	5.12c	7b+	male	Yes
1970	John Gosling	English Hanging Gardens	5.12b	7b	male	Yes
1975	Steve Wunsch	Psycho Roof	5.12d	7c	male	Yes
1977	Ray Jardine	The Phoenix	5.13a	7c+	male	Yes
1979	Tony Yaniro	Grand Illusion	5.13b	8a	male	Yes
1983	Jerry Moffatt	The Face	5.13c	8a+	male	Yes
1984	Wolfgang Güllich	Kanal im Rücken	5.13d	8b	male	Yes
1985	Wolfgang Güllich	Punks in the Gym	5.14a	8b+	male	Yes
1986	Antoine Le  Menestrel	La Ravage	5.14a/5.14b	8b+/8c	male	Yes
1987	Wolfgang Güllich	Wallstreet	5.14b	8c	male	Yes
1990	Ben Moon	Hubble	5.14c	8c+	male	Yes
1991	Wolfgang Güllich	Action Directe	5.14d	9a	male	Yes
1995	Fred Rouhling	Akira	5.15b	9b	male	No
1996	Alex Huber	Open Air	5.15a	9a+	male	Yes
2003	Bernabè Fernandez	Chilam Balam	5.15a/5.15b	9a+/9b	male	Yes
2012	Adam Ondra	Change	5.15c	9b+	male	No
2017	Adam Ondra	Silence	5.15d	9c	male	No

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.     

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?