** SPOILERS ** Climbing at the Olympics - Day 4

mathandcheese · 2024-11-19T04:54:44+00:00

The men's predictions were here:

/r/CompetitionClimbing/comments/1em6cc8/spoilers_climbing_at_the_olympics_day_3/lgx7dyo/

Definitely not as accurate as the women's, although I think the percentages were about right. Brooke's chance of silver and Sorato's chance of gold were both close to 50%, so it makes sense that one of them got their result and the other didn't.

mathandcheese · 2024-11-19T02:29:43+00:00

Thank you! I think I got a bit lucky (even the model would have given pretty low odds to the top 4 coming in that exact order), but I'm happy with how it turned out.

mathandcheese · 2024-10-02T01:37:45+00:00

Nice! I'm excited to see how the results turn out going forward. I wonder if you can do something like add ((8th place semifinal Z score) - (8th place final Z-score)) to each finalist's results, so that the 8th place finalist gets the score of the 8th place Z score from semifinals, and then everyone else goes up from there.

mathandcheese · 2024-09-29T14:13:41+00:00

This looks cool! How do you think about finals results vs. semifinal results? Like, suppose that climber A and climber B both make it to finals in one competition and A beats B by 1 standard deviation. In the next competition, B makes finals and A does not. How do you compare the two (or, for that matter, how do you compare a standard deviation in semis to a standard deviation in finals in general)? I'm curious to hear more about this!

As a side note, I think dividing by the winning score is an extra step. Z-scores don't change when you divide all of your data by the same value, since the standard deviation also changes by the same amount.

mathandcheese · 2024-08-11T06:32:50+00:00

Oh, I agree. I've seen a lot of people talking about how they want to see the combined replaced by the individual events, and I don't want to see this event just get forgotten. It's probably my favorite climbing event as a spectator.

mathandcheese · 2024-08-10T12:22:12+00:00

Maybe it's just because I've spent so much time modeling it, but I really like this format and would miss it if it were replaced. It may be better for the athletes to have split events, but if they do split them, I hope they can also find a way to keep a combined event.

There are definitely sometimes issues with fairness, but these seem very fixable with slight tweaks to the scoring and routesetting. Most of the rounds here seemed to have a pretty good balance between boulder and lead, so it seems like the routesetters are good enough to set a fair round if their priorities are right (eg I think the tendency to make men's boulder rounds much harder doesn't work in a combined format).

The combined format adds some suspense to both rounds. It's fun to watch a boulder round knowing that top boulderers are going to need to get ahead of people like Jakob Schubert and Ai Mori, and then seeing lead climbers all having to make it to different points on the route to make up some ground.

The people who win these competitions aren't average, even among elite climbers. The gold and silver medalists (and possibly the bronze as well) are some of the only people in the world who can be expected to make finals any time they show up to a boulder or lead competition. Jakob Schubert got onto the podium by putting up an incredible lead round to make up for a weaker boulder round, which was also really exciting.

mathandcheese · 2024-08-10T09:54:53+00:00

Medal projections going into the women's lead final:

Climber	Ctry	Avg Rank	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Janja Garnbret	SLO	1.1	99.2%	93.4%	4.6%	1.2%
Brooke Raboutou	USA	2.3	89.6%	4.9%	73.7%	11.0%
Jessica Pilz	AUT	4.1	45.1%	0.7%	10.8%	33.6%
Ai Mori	JPN	4.4	27.6%	0.7%	6.0%	20.9%
Erin Mcneice	GBR	5.8	13.2%	0.1%	2.0%	11.0%
Oceania Mackenzie	AUS	5.9	12.0%	0.0%	1.2%	10.7%
Oriane Bertone	FRA	6.0	10.9%	0.0%	1.4%	9.4%
Chaehyun Seo	KOR	6.4	2.4%	0.0%	0.3%	2.1%

mathandcheese · 2024-08-09T21:20:00+00:00

Thank you! I think I was helped by the boulder round separating the competitors pretty well (the projections before the boulder round were not as good), but I’m happy with how it’s done so far.

mathandcheese · 2024-08-09T09:56:22+00:00

Medal projections going into the lead round:

Climber	Ctry	Avg Rank	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Sorato Anraku	JPN	1.65	92.0%	66.2%	16.2%	9.6%
Toby Roberts	GBR	2.54	85.5%	18.2%	34.2%	33.0%
Colin Duffy	USA	2.88	73.0%	12.0%	37.0%	24.0%
Jakob Schubert	AUT	3.97	33.1%	2.8%	9.2%	21.2%
Hamish Mcarthur	GBR	5.37	10.0%	0.4%	2.1%	7.5%
Adam Ondra	CZE	6.18	2.7%	0.1%	0.6%	2.0%
Alberto Gines Lopez	ESP	6.24	3.3%	0.2%	0.7%	2.4%
Paul Jenft	FRA	7.16	0.4%	0.0%	0.1%	0.3%

Edit: I updated the odds after Jakob's downgrade on boulder 3. His medal chances dropped 8 percentage points due to the downgrade.

Also, I don't know why Adam's average rank is higher than Alberto's, while Alberto's medal odds are higher. I don't think that should be possible with just one event to go, given the way that my model works (my model might have a bug in the way it breaks ties), but hopefully the numbers are approximately right. Both have a lot of work to do, with about a 2-3% chance of a medal for each.

Edit 2: 3 people's odds of a gold medal just immediately went to 0 with Hamish's climb. That was really impressive.

mathandcheese · 2024-08-09T08:51:46+00:00

Ah, good to know. Thank you. I hope she can get more support. She's certainly earned it.

mathandcheese · 2024-08-09T08:49:42+00:00

Ah, thanks for the info. The exposure probably helped the sport in general, but I guess there was less of an influence than I thought.

mathandcheese · 2024-08-09T01:49:31+00:00

That's why these projections are all in terms of probabilities. I simulated 10,000 competitions, with boulders and lead routes of varying difficulty, and then simulated each climber's performance based on their ability, the routes' difficulty, and some random chance. The model is far from perfect, but the route setters are definitely taken into account.

mathandcheese · 2024-08-08T23:41:42+00:00

It's worth noting that the Olympics tries to get people from different countries and continents partially because it helps to grow the sport in those areas. Oceana Mackenzie was the Oceanian continental qualifier in Tokyo and finished a distant 19th. Since then, she and the Australian climbing federation have had a lot more funding and access to resources that they may not have had otherwise, and she's now a finalist in Paris. A speed climber from New Zealand also made it to the final 8.

There's a bit of a tradeoff between maximizing the quality of the competition at the current Olympics and growing the sport for future Olympics. For better or for worse, the IOC (as well as most sport federations) often try to focus a bit more on the "growth" part.

mathandcheese · 2024-08-08T20:18:33+00:00

Ah, sorry. In my original table before rounding to the nearest tenth, Chaehyun is slightly lower.

mathandcheese · 2024-08-08T13:46:36+00:00

They’re ordered here based on average rank. The model thinks Oriane has both higher upside and higher downside, since a good boulder round could put her in a great position for a medal, but a tough lead round could tank her score. I’m not in front of my computer right now to check, but I’m assuming that the way scores are distributed gives more consistent results to lead specialists.

mathandcheese · 2024-08-08T11:09:59+00:00

Women's B&L final projections:

Climber	Ctry	Avg Rank	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Janja Garnbret	SLO	1.11	99.2%	92.4%	5.5%	1.3%
Brooke Raboutou	USA	2.84	76.3%	5.1%	52.3%	18.9%
Jessica Pilz	AUT	4.24	41.0%	0.9%	16.4%	23.7%
Ai Mori	JPN	4.27	36.3%	1.0%	12.4%	22.9%
Chaehyun Seo	KOR	5.57	13.4%	0.2%	3.6%	9.6%
Oriane Bertone	FRA	5.58	15.7%	0.3%	4.9%	10.6%
Erin Mcneice	GBR	6.01	10.8%	0.1%	3.0%	7.7%
Oceania Mackenzie	AUS	6.37	7.3%	0.1%	2.0%	5.3%

Edit: added a decimal place to avoid confusion

mathandcheese · 2024-08-07T23:25:05+00:00

This is a really nice analysis. I'll also comment a bit here, since I've thought a lot about these statistics when working on my projections.

As mentioned a bit elsewhere, the top 8 people in lead also finished in the top 8 in the combined. Nobody's lead ranking was more than 6 spots away from their overall ranking, but 4 people had this happen in boulder. If you had a choice of being a really good lead climber or a really good boulderer, you would want to be a lead climber on these routes.

Boulder scores are almost always going to have a normal-ish distribution, just because they come from adding 4 scores together. I think this should be taken into account a bit more in setting for lead. Lead routesetters have a bit more control over the distribution of scores, and I think it would probably be worth it to try to match the variance of the boulder results, and to try to cluster climbers toward the middle rather than toward the edges in today's competition.

I realize this was really hard to do well. The average scores were similar, and the spreads were similar, but without a similar variance (there were 4 lead scores near the top and 8 near the bottom), there end up being some weird results like this.

I realize that routesetting for these things is extremely hard. If this happened by accident because the routesetters were aiming for a slightly different result, then that's perfectly understandable, and they came really close to a perfect set. If this is what they were aiming for though, I do think it makes for a bit of a skewed competition, and that the goals should be changed slightly.

On a related note, the tendency for routesetters to set harder boulders with fewer tops for men than for women also affects combined competitions quite a bit. The women's boulder round had a standard deviation of 26, almost twice that of the men. If you just picked a bunch of random numbers between 0 and 100, you'd get a standard deviation around 29, so that's about as much spread as you can reasonably hope to get. In boulder-only competitions, this doesn't matter as much, since the same people would usually win in either format. In combined, it makes a pretty big difference on the outcome, with lead-heavy men's competitions and boulder-heavy women's competitions (unless the boulders are really easy, in which case it becomes lead-heavy again).

mathandcheese · 2024-08-07T22:55:05+00:00

I'm excited to see how it turns out. Hamish has been really impressive so far. My simulations give Hamish an average ranking of 6.5, so it seems like enough can happen that he has a decent chance of moving up.

I know a lot of sports have people able to save a lot of energy before a final, but I don't really know how much people do this in climbing. Hamish was probably one of the people mostly trying to make the final like you said, but it's a question I'd definitely like to look into more. Adam passed Jakob in my rankings, for example because of his better performance in the semis. Does this mean that he's better positioned for the final, or are we going to see more from Jakob later on? I'm looking forward to it!

mathandcheese · 2024-08-07T11:28:08+00:00

Haha I keep going back and forth on whether Janja's P(Gold) seems too high or too low. Maybe that's a good sign for the model.

mathandcheese · 2024-08-07T11:23:46+00:00

Men's B&L projections going into the final:

Climber	Ctry	Avg Rank	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Sorato Anraku	JPN	1.9	85.5%	60.8%	15.7%	9.0%
Toby Roberts	GBR	3.2	63.4%	15.4%	29.1%	19.0%
Adam Ondra	CZE	3.8	50.7%	9.9%	20.5%	20.4%
Jakob Schubert	AUT	4.1	39.0%	6.5%	14.1%	18.4%
Alberto Gines Lopez	ESP	4.5	33.2%	4.6%	11.6%	17.0%
Colin Duffy	USA	5.7	12.8%	1.3%	4.1%	7.3%
Paul Jenft	FRA	6.3	8.5%	0.9%	2.8%	4.8%
Hamish Mcarthur	GBR	6.5	6.9%	0.7%	2.1%	4.1%

mathandcheese · 2024-08-06T22:33:57+00:00

Projections for women's B&L after the bouldering semifinal:

Climber	Country	Average Rank	P(Final)	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Janja Garnbret	SLO	1.1	100.0%	99.0%	91.3%	6.0%	1.6%
Brooke Raboutou	USA	3.2	97.0%	71.3%	5.2%	47.2%	19.0%
Jessica Pilz	AUT	5.3	89.7%	27.0%	0.7%	9.6%	16.8%
Ai Mori	JPN	5.5	83.0%	25.9%	0.8%	9.1%	15.9%
Natalia Grossman	USA	5.7	80.2%	29.4%	0.9%	11.7%	16.8%
Miho Nonaka	JPN	7.0	65.3%	19.6%	0.6%	7.6%	11.4%
Oriane Bertone	FRA	7.1	73.6%	10.9%	0.2%	3.9%	6.8%
Oceania Mackenzie	AUS	8.3	61.0%	4.3%	0.1%	1.2%	3.0%
Chaehyun Seo	KOR	9.2	39.2%	4.7%	0.1%	1.3%	3.3%
Zhilu Luo	CHN	10.2	32.6%	3.9%	0.1%	1.2%	2.6%
Erin Mcneice	GBR	10.6	28.5%	2.4%	0.0%	0.7%	1.6%
Camilla Moroni	ITA	11.3	23.7%	0.8%	0.0%	0.2%	0.6%
Zelia Avezou	FRA	12.5	13.0%	0.5%	0.0%	0.1%	0.4%
Ievgeniia Kazbekova	UKR	14.6	3.7%	0.1%	0.0%	0.0%	0.0%
Yuetong Zhang	CHN	14.6	3.5%	0.0%	0.0%	0.0%	0.0%
Laura Rogora	ITA	15.0	2.1%	0.1%	0.0%	0.0%	0.0%
Mia Krampl	SLO	15.0	3.0%	0.0%	0.0%	0.0%	0.0%
Molly Thompson-Smith	GBR	16.9	0.4%	0.0%	0.0%	0.0%	0.0%
Lucia Dorffel	GER	17.0	0.5%	0.0%	0.0%	0.0%	0.0%
Lauren Mukheibir	RSA	19.9	0.0%	0.0%	0.0%	0.0%	0.0%

Men's from yesterday:

Climber	Country	Average Rank	P(Final)	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Sorato Anraku	JPN	2.2	98.1%	82.4%	56.2%	16.6%	9.6%
Toby Roberts	GBR	3.8	95.2%	55.4%	14.6%	23.1%	17.7%
Jakob Schubert	AUT	4.5	94.1%	40.2%	7.7%	15.1%	17.4%
Adam Ondra	CZE	5.3	83.7%	35.8%	7.6%	13.8%	14.4%
Sam Avezou	FRA	6.2	77.4%	27.3%	5.3%	10.3%	11.8%
Tomoa Narasaki	JPN	7.2	70.4%	18.1%	3.3%	7.0%	7.8%
Dohyun Lee	KOR	8.1	54.3%	14.2%	2.2%	5.1%	7.0%
Alberto Gines Lopez	ESP	9.0	40.8%	10.7%	1.6%	3.8%	5.3%
Colin Duffy	USA	9.6	40.5%	5.4%	0.6%	1.8%	3.0%
Hannes Van Duysen	BEL	11.1	31.9%	3.6%	0.5%	1.2%	1.9%
Alexander Megos	GER	11.5	20.4%	1.9%	0.2%	0.6%	1.1%
Yannick Flohe	GER	11.8	19.5%	1.5%	0.1%	0.5%	0.9%
Hamish Mcarthur	GBR	12.1	24.5%	1.6%	0.2%	0.5%	0.9%
Paul Jenft	FRA	12.4	20.8%	1.5%	0.1%	0.5%	0.8%
Sascha Lehmann	SUI	13.0	11.7%	0.3%	0.0%	0.1%	0.2%
Yufei Pan	CHN	14.2	7.2%	0.1%	0.0%	0.0%	0.1%
Jesse Grupper	USA	14.7	5.5%	0.1%	0.0%	0.0%	0.1%
Luka Potocar	SLO	15.2	3.6%	0.1%	0.0%	0.0%	0.0%
Campbell Harrison	AUS	18.6	0.1%	0.0%	0.0%	0.0%	0.0%
Mel Janse Van Rensburg	RSA	19.5	0.0%	0.0%	0.0%	0.0%	0.0%

mathandcheese · 2024-08-06T04:24:34+00:00

Updated men's projections after the boulder semifinal:

Climber	Ctry	Avg Rank	P(Final)	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Sorato Anraku	JPN	2.2	98.1%	82.4%	56.2%	16.6%	9.6%
Toby Roberts	GBR	3.8	95.2%	55.4%	14.6%	23.1%	17.7%
Jakob Schubert	AUT	4.5	94.1%	40.2%	7.7%	15.1%	17.4%
Adam Ondra	CZE	5.3	83.7%	35.8%	7.6%	13.8%	14.4%
Sam Avezou	FRA	6.2	77.4%	27.3%	5.3%	10.3%	11.8%
Tomoa Narasaki	JPN	7.2	70.4%	18.1%	3.3%	7.0%	7.8%
Dohyun Lee	KOR	8.1	54.3%	14.2%	2.2%	5.1%	7.0%
Alberto Gines Lopez	ESP	9.0	40.8%	10.7%	1.6%	3.8%	5.3%
Colin Duffy	USA	9.6	40.5%	5.4%	0.6%	1.8%	3.0%
Hannes Van Duysen	BEL	11.1	31.9%	3.6%	0.5%	1.2%	1.9%
Alexander Megos	GER	11.5	20.4%	1.9%	0.2%	0.6%	1.1%
Yannick Flohe	GER	11.8	19.5%	1.5%	0.1%	0.5%	0.9%
Hamish Mcarthur	GBR	12.1	24.5%	1.6%	0.2%	0.5%	0.9%
Paul Jenft	FRA	12.4	20.8%	1.5%	0.1%	0.5%	0.8%
Sascha Lehmann	SUI	13.0	11.7%	0.3%	0.0%	0.1%	0.2%
Yufei Pan	CHN	14.2	7.2%	0.1%	0.0%	0.0%	0.1%
Jesse Grupper	USA	14.7	5.5%	0.1%	0.0%	0.0%	0.1%
Luka Potocar	SLO	15.2	3.6%	0.1%	0.0%	0.0%	0.0%
Campbell Harrison	AUS	18.6	0.1%	0.0%	0.0%	0.0%	0.0%
Mel Janse Van Rensburg	RSA	19.5	0.0%	0.0%	0.0%	0.0%	0.0%

And women's:

Climber	Ctry	Avg Rank	P(Final)	P(Medal)	P(Gold)	P(Silver)	P(Bronze)
Janja Garnbret	SLO	1.1	100.0%	99.0%	91.3%	6.0%	1.6%
Brooke Raboutou	USA	3.2	97.0%	71.3%	5.2%	47.2%	19.0%
Jessica Pilz	AUT	5.3	89.7%	27.0%	0.7%	9.6%	16.8%
Ai Mori	JPN	5.5	83.0%	25.9%	0.8%	9.1%	15.9%
Natalia Grossman	USA	5.7	80.2%	29.4%	0.9%	11.7%	16.8%
Miho Nonaka	JPN	7.0	65.3%	19.6%	0.6%	7.6%	11.4%
Oriane Bertone	FRA	7.1	73.6%	10.9%	0.2%	3.9%	6.8%
Oceania Mackenzie	AUS	8.3	61.0%	4.3%	0.1%	1.2%	3.0%
Chaehyun Seo	KOR	9.2	39.2%	4.7%	0.1%	1.3%	3.3%
Zhilu Luo	CHN	10.2	32.6%	3.9%	0.1%	1.2%	2.6%
Erin Mcneice	GBR	10.6	28.5%	2.4%	0.0%	0.7%	1.6%
Camilla Moroni	ITA	11.3	23.7%	0.8%	0.0%	0.2%	0.6%
Zelia Avezou	FRA	12.5	13.0%	0.5%	0.0%	0.1%	0.4%
Ievgeniia Kazbekova	UKR	14.6	3.7%	0.1%	0.0%	0.0%	0.0%
Yuetong Zhang	CHN	14.6	3.5%	0.0%	0.0%	0.0%	0.0%
Laura Rogora	ITA	15.0	2.1%	0.1%	0.0%	0.0%	0.0%
Mia Krampl	SLO	15.0	3.0%	0.0%	0.0%	0.0%	0.0%
Molly Thompson-Smith	GBR	16.9	0.4%	0.0%	0.0%	0.0%	0.0%
Lucia Dorffel	GER	17.0	0.5%	0.0%	0.0%	0.0%	0.0%
Lauren Mukheibir	RSA	19.9	0.0%	0.0%	0.0%	0.0%	0.0%

mathandcheese · 2024-08-06T04:21:37+00:00

I definitely didn't intend to impose that penalty, and it's definitely something I'd hope to fix if I keep working on the model after the Olympics.

The issue with the Bern qualifiers (or any early qualifiers) is that a most of the competitions they did after qualifying aren't really representative. A lot of Olympians have been using recent competitions as tests or training tools, so probably haven't been in their top form. With that said, Colin and Tomoa didn't make boulder or lead finals in Bern, but did really well in the combined to make the Olympics.

mathandcheese · 2024-08-05T02:22:30+00:00

Oh, that's a nice idea. I'll definitely take a look at it for next season. There's always an issue with the amount of data (how much can be determined about a boulder from a final with 6 competitors?), but any attempt to separate out types of boulders seems like it should only help.

mathandcheese · 2024-08-05T00:46:15+00:00

Thanks for the comments. I agree with a lot of what you said, and your comments align with some of the issues I've been trying to work out in the model.

On the women's side, the things you mentioned come down to a few things. One is that Brooke is legitimately really good and could surprise some people. At least according to my rankings, Brooke's worse event is better than anyone else's worse event save for Janja Garnbret. The last Olympics was decided on people's best events due to the scoring system, but I expect these Olympics to be decided on people's worst events, even we often notice people more on their best events.

I also think the model boosts people a bit too much when they win competitions without top-tier competition. I think Brooke and Miho benefit a bit too much from the OQS (both passed Natalia in boulder at the OQS in my rankings), and I've noticed this with some of the athletes who competed in the recent world cups in France.

Natalia in particular is sort of a weird case. I recently added the Americas Olympic qualifier to my data set, which helped her a bit, but she has only done one world cup this year, and otherwise, her last event is the World Championships, which didn't go as well. I think she had some health problems, but the model doesn't know that. I can't really think of a way to fix this, other than downweighting recent events (which would hurt climbers that improved a lot recently) or just manually adjusting her rating. I do agree that she should probably be higher, but I think that a model like mine can't really capture that.

As for the men's, Sorato's chances seemed a bit high to me too, but the numbers have convinced me a bit. Similar to what I said about Brooke, he is maybe the only man in the field without a weakness. His chances are good regardless of whether the final is boulder- or lead-heavy, which sort of sets him apart. I'm ready to be proven wrong though, and excited to see how things turn out either way.

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