class: left, middle, title-slide # An Examination of Sport Climbing
Competition Format and Scoring System ## Quang Nguyen ### Loyola University Chicago ### 2021 CMSAC Reproducible Research Competition ###
qntkhvn
@qntkhvn
qntkhvn.netlify.app --- # How it started vs. how it's going .pull-left[ <blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/qntkhvn?ref_src=twsrc%5Etfw">@qntkhvn</a> Yo. I have an idea for a quick paper. We could probably write it up as a note in like a week. It's about the scoring system in sport climbing. Any interest?</p>— Volume Tweeter (@StatsInTheWild) <a href="https://twitter.com/StatsInTheWild/status/1411033054890500096?ref_src=twsrc%5Etfw">July 2, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> ] .pull-right[ ![](data:image/png;base64,#https://c.tenor.com/rLAxEJdZyT4AAAAC/who-wouldve-thought-not-me.gif) ] --- # Background - Sport climbing made its debut at Tokyo 2020 - 3 disciplines: speed climbing, bouldering, lead climbing - Only 1 set of medals for each gender at the Olympics - Combined scoring system: multiplying 3 disciplines' ranks (best score = lowest score) - Example: `\(1\)`st in speed `\(\times\)` `\(5\)`th in bouldering `\(\times\)` `\(7\)`th in lead `\(=\)` total score of `\(35\)` - 2 rounds: qualification (20 climbers), final (top 8 from qualification) --- # The Concerns * Climber interviews with Climbing Magazine in 2016: > "I am NOT in support of the format that imposes that all climbers must compete in speed climbing. That is like asking a middle distance runner to compete in the sprint. Speed climbing is a sport within our sport." - Lynn Hill, former US Climber. > "Honestly, the people that will suffer the most are the ones that focus only on speed climbing. Those skills/abilities don’t transfer as well to the other disciplines." - Mike Doyle, US Climber. * Words and phrases: "bogus", "a bummer", "less than ideal", "not in support", "cheesy and unfair". --- # Goals * Are the climbers' concerns valid? * What are some properties and limitations of sport climbing's "triathlon" format and rank-product scoring? * Use statistical simulation and data analysis of past competitions to investigate. --- # Simulation Study * Assumptions: * Independent disciplines * Uniform ranks * Examine properties of the rank-product scoring system --- # Advancement Probabilities .pull-left[ Given that a climber wins any discipline... * For a qualifier, what is the probability of qualifying for final (finishing at 8 or better)? `\(99.48\%\)` * For a finalist, what is the probability of winning a medal (finishing in top 3)? `\(85.01\%\)` ] .pull-right[ <img src="data:image/png;base64,#climbing_cmsac_rrc_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" /> ] --- # Advancement Scores .pull-left[ * Average target scores * For qualifiers: `\(435\)` to make top `\(8\)` * For finalists: `\(10, 21, 34\)` to win gold, silver, bronze ] .pull-right[ <img src="data:image/png;base64,#climbing_cmsac_rrc_files/figure-html/unnamed-chunk-5-1.png" width="504" style="display: block; margin: auto;" /> ] --- # Rank Correlation - Correlations between the overall rank and the ranks of the individual disciplines (speed, bouldering, and lead) - Use Kendall's `\(\tau\)`, a nonparametric measure of ordinal association. - Data: Tokyo 2020 Women's Qualification
climber
overall
speed
bouldering
lead
Janja Garnbret
1
14
1
4
Seo Chae-hyun
2
17
5
1
Miho Nonaka
3
4
8
3
Akiyo Noguchi
4
9
3
6
Brooke Raboutou
5
12
2
8
--- .pull-left[ # Rank Correlation * **Lead** and **bouldering** ranks are more highly correlated with **overall** rank than **speed**. * Positive association between **lead** and **bouldering** ranks. * Negative relationships between both **lead** and **bouldering** ranks with **speed**. ] .pull-right[ <br> <img src="data:image/png;base64,#climbing_cmsac_rrc_files/figure-html/unnamed-chunk-9-1.png" width="504" style="display: block; margin: auto;" /> ] --- # Principal component analysis .pull-left[ - Find underlying correlations that exist among the climbing disciplines - Speed climbing time - Bouldering tops - Lead holds ] .pull-right[ - Data: Tokyo 2020 Women's Qualification
climber
speed_time
bould_tops
lead_holds
Janja Garnbret
9.44
4
30.0
Seo Chae-hyun
10.01
2
40.5
Miho Nonaka
7.55
1
30.5
Akiyo Noguchi
8.23
3
27.5
Brooke Raboutou
8.67
3
26.5
Jessica Pilz
8.51
1
33.5
Aleksandra Mirosław
6.97
0
12.0
] --- # Principal component analysis .pull-left[ * PC1: lead and bouldering * Positively correlated * PC2: only speed ] .pull-right[ <img src="data:image/png;base64,#https://raw.githubusercontent.com/qntkhvn/cmsac_rrc/main/paper/pca.png" style="display: block; margin: auto;" /> ] --- # Leave-one-climber-out analysis - What would happen to the overall rankings (in particular, order of medalists) if one climber got disqualified? <!-- - Independence of irrelevant alternatives (IIA) --> <!-- - After a winner is determined, if one of the losing candidates drops out and the votes are recounted, there should not be a change in the winner --> <!-- - We have evidence for a violation of the IIA property from real data. --> - This has a connection with the independence of irrelevant alternatives (IIA) - IIA: rank orderings should not change if a losing candidate is removed and the scores are re-calculated - There's evidence for a violation of the IIA property from real data. --- # Leave-one-climber-out analysis - Panel 5: If 5th-place climber (Krasovskaia) was excluded, climber with actual rank 4 (Meul) would move up to 2nd!!! <img src="data:image/png;base64,#climbing_cmsac_rrc_files/figure-html/unnamed-chunk-14-1.png" width="720" style="display: block; margin: auto;" /> --- # Discussion - The idea of a climbing triathlon gives speed climbers a huge disadvantage. - The independence of irrelevant alternatives is violated, which is an issue of rank-product scoring. - Solution: 1 set of medals for speed and 1 set of medals for bouldering and lead. - It is confirmed that at Paris 2024, there will be 2 sets of medals: - Lead and bouldering, combined - Speed-only event <!-- Finally... --> <!-- - **#deepthoughts**: There are still so many sports, like climbing, that have essentially been untouched in terms of analytics. --> --- # Future work - Simulations with correlation - More examinations on performance, instead of ranks - Package/database for climbing data --- # Acknowledgements .pull-left[ <img src="data:image/png;base64,#hannah.png" width="67%" style="display: block; margin: auto auto auto 0;" /> Hannah Butler <br>Colorado State University ] .pull-right[ ![](data:image/png;base64,#greg.gif) Gregory Matthews <br>Loyola University Chicago ] --- # Cheers! ####
[nminhquang.99@gmail.com](mailto:nminhquang.99@gmail.com) ####
[@qntkhvn](https://twitter.com/qntkhvn) ####
[github.com/qntkhvn/climbing](https://github.com/qntkhvn/cmsac_rrc) ####
[qntkhvn.netlify.app/blog](https://qntkhvn.netlify.app/blog) ####
[qntkhvn.netlify.app/projects/climbing_cmsac_rrc.html](https://qntkhvn.netlify.app/projects/climbing_cmsac_rrc.html) <!-- - Upcoming sports analytics conferences: [UCSAS](https://statds.org/events/ucsas2021) (Oct 9) and [CMSAC](http://stat.cmu.edu/cmsac/conference/2021) (Nov 6-7) --> #### Slides created via the `R` package [**`xaringan`**](https://github.com/yihui/xaringan). <!-- # Appendix --> <!-- * Data source: https://en.wikipedia.org/wiki/Sport_climbing_at_the_2020_Summer_Olympics_-_Women's_combined --> <!-- * Climbing magazine interviews: https://www.climbing.com/news/olympic-climbing-survey-15-pro-climbers-weigh-in --> <!-- * [Speed climbing](https://i.imgur.com/B1X29QZ.gif) --> <!-- * [Bouldering and lead climbing](https://youtu.be/aLKavMRf0do?t=29) -->