Hello, today I saw a post on reddit by u/noelyoh that calculated the probability of getting an Olympic medal in climbing given your score. This is complicated due to the method of calculating a climber's score. In the 2020 Tokyo Olympic games, climbing is separated into three events: speed climbing, lead climbing, and bouldering. 20 Athletes went to the games and their score is the product of their placement in each event. For example, if a climber finished 1st, 9th, and 12th, then that climbers score would be 1*9*12=108 points. Lowest score wins.
This is interesting, as it highly encourages people to NOT be well rounded. Instead, you will likely do better by focusing on your strengths. For example, if a climber wins 1st in an event, and comes in dead-last in the other two, his/her score will be 1*20*20=400 points. At the same time, a climber that finishes 10th in each event gets 10*10*10=1000 points. To get an idea of how this will work in podium finishes, I have generated a plot to recreate the results of u/noelyoh. My plot shows the probability of landing on the podium given a certain number of points. The line color represents which medal you are likely to earn. So the gold line is the probability of earning gold, and so on. The black line is the combined probability of getting any medal.
This was generated using code available on my github. Interestingly, my results differ from u/noelyoh's as the spread of points appears to be much wider. I will update this post after I have investigated things further.
Edit: I asked the original poster about his data, and he clarified that only 8 individuals would be competing in the finals. This would lead to a much narrower band for scores leading to podium finishes. I made these adjustments to my code. After this update, my data matched exactly with the data seen in the reddit thread. The result? Getting a score of 40 results in a 50% chance of making it onto the podium. Getting a score of 20 gives you a 99% chance. And getting a score of 4 gives you 100% at first place. Really interesting. I want to thank the original redditer for helping me on this. I have also replaced the graphic with the correct data.
--2021-08-05