February 10, 2010

Amateur Medal Prediction for 2010

If I was a journalist writing for a newspaper or sports magazine, I'd have to open this story like this: Canada will win 27 medals at the upcoming 2010 Winter Olympics.

The nice thing about that kind of prediction is that it's easy to encapsulate the result in a single sentence. The bad thing is that the single number '27' doesn't really tell the whole story.

Back in 2006, you'll recall, I took a different approach at predicting Canada's medal haul. I predicted that Canada would win 21±3 medals at the 2006 Winter Olympic Games in Torino. Canada ended up winning 24 medals, overshooting my predicted total but well within my assessment of the uncertainty.

I repeated the exercise for Beijing in 2008, but didn't publish my prediction since I was using the Canadian Olympic Committee's internal assessment of our athletes. The results were actually quite similar. My pre-games prediction was for 15.5±2.5 medals, and the final total was 18.

The "±" part of my predictions comes from the statistical approach. To predict the total number of medals, I first assign each Canadian entry a probability of winning a medal in their event. Through some fairly straightforward math, that leads to a probability distribution for all the possible medal totals for Canada. The only parameters you can fiddle with are the medal probabilities you assign to each Canadian entry up front.

I've done the same thing for the upcoming 2010 Winter Olympics. I put Canadian entries into one of five probability categories: "Lock" (90% chance); "Strong Possibility" (65% chance); "Possibility" (35% chance); "Outside Possibility" (10% chance); and "No Possibility" (0% chance). I should comment at this point that for 2010 I do not have access to any COC evaluation of the team — I'm back in my armchair for these games. My assessment comes from a few days of looking over World Cup and World Championship standings and results from 2010. So in detail, the probabilities are only as good as my abilities as an analytical winter sports fan, and its probable that I've missed some things. Past evidence also suggests that I tend to have a pessimistic bias against Canada's chances, so my probability assessments may be too low.

My probability assessments are presented in the table at the end of this post. The table identifies the day of each event, the sport, the event, and the athlete, with my medal category and the corresponding probability for that event. (I have left the "No Possibility" entries out of the table.) I have also included the predictions that three major media outlets have released in the last couple of weeks. The Associated Press (AP) and Sports Illustrated (SI) have predicted all the medal winners in every event, and the Canadian Press (CP) has predicted all the Canadian medals. The Associated Press and Sports Illustrated both predict 30 Canadian medals, and the Canadian Press predicts 37.

It is clear that my (independent) assessment of the medal probability lines up qualitatively with the three media predictions, although there are some quantitative differences. The Canadian Press, for example, predicts that every single one of the "Strong Possibilty" Canadian medalists will actually win a medal.

With the probability values above, I can calculate a probability distribution for the total number of medals Canada will have won after each day of competition, including the final total after Day 16. The results are shown in the figure below.

The left-hand plot in this figure shows my prediction (today) of how Canada's medal total will evolve over the 16 days of the Games, assuming all events go as scheduled. The image shows the probability distribution, and the green lines show the mean and standard deviation of the probability distribution. The right-hand plot shows the full probability distribution for the medal count at the end of the games.

If I had to encapsulate this picture with a single number, I would have to say … 27. But I don't have to do that, so let's put it this way: the most likely total number of medals for Canada, assuming that my characterization of individual probabilities is not biased in one direction or the other, is 27. The probability that Canada will win between 24 and 31 medals is about 75%. The probability that Canada will win 30 or more medals is about 24%.

One of the reasons to be especially interested in Canada's medal total this year is that the COC has a well-publicized goal for its athletes to win more medals in 2010 than those of any other National Olympic Committee. On the face of it, my prediction makes that unlikely; it will probably take at least 30 medals to finish atop the medal table, and I am putting that at three-to-one odds. But then again, I've got a history of getting that wrong.

I'll plan to update my prediction after each day of competition, and post thoughts about the Games here as well.

Day Sport Event Athlete Athlete Probability AP SI CP
1 Freestyle Ski Moguls - W Heil, Jennifer Lock 0.90 GOLD GOLD GOLD
6 Speed Skating - LT 1,000m - W Nesbitt, Christine Lock 0.90 GOLD GOLD GOLD
9 Speed Skating - LT 1,500m - W Nesbitt, Christine Lock 0.90 GOLD GOLD GOLD
13 Ice Hockey Ice Hockey - W Team Lock 0.90 GOLD GOLD GOLD
15 Speed Skating - LT Pursuit - W Groves, Klassen, Nesbitt, Schussler Lock 0.90 GOLD GOLD GOLD
1 Alpine Ski Downhill - M Osborne-Paradis, Manuel Strong 0.65 GOLD SILVER SILVER
1 Speed Skating - ST 1,500m - M Hamelin, Charles Strong 0.65 SILVER   BRONZE
2 Freestyle Ski Moguls - M Bilodeau, Alexandre Strong 0.65 GOLD   BRONZE
4 Snowboard Snowboardcross - W Ricker, Maëlle Strong 0.65 BRONZE GOLD GOLD
5 Speed Skating - ST 500m - W Roberge, Kalyna Strong 0.65 SILVER SILVER SILVER
7 Skeleton Skeleton - W Hollingsworth, Mellisa Strong 0.65 GOLD SILVER GOLD
8 Speed Skating - ST 1,000m - M Hamelin, Charles Strong 0.65   BRONZE SILVER
9 Speed Skating - LT 1,500m - W Groves, Kristina Strong 0.65 SILVER SILVER SILVER
9 Freestyle Ski Ski Cross - M Del Bosco, Christopher Strong 0.65 SILVER SILVER GOLD
10 Figure Skating Dance - Mixed Moir, Virtue Strong 0.65 BRONZE SILVER SILVER
11 Freestyle Ski Ski Cross - W McIvor, Ashleigh Strong 0.65 GOLD SILVER SILVER
12 Bobsleigh Two-Man - W Humphries (Pilot) Strong 0.65   BRONZE SILVER
12 Speed Skating - ST 3,000m Relay - W Gregg, Maltais, Roberge, St.Gelais, Vicent Strong 0.65 BRONZE BRONZE BRONZE
14 Curling Team - W Bartel, Bernard, McRorie, Moore, O'Connor Strong 0.65 GOLD GOLD BRONZE
14 Speed Skating - ST 5,000m Relay - M Bastille, Hamelin, Hamelin, Jean, Tremblay Strong 0.65 SILVER SILVER GOLD
14 Speed Skating - ST 500m - M Hamelin, Charles Strong 0.65 GOLD GOLD GOLD
15 Curling Team - M Enright, Hebert, Kennedy, Martin, Morris Strong 0.65 GOLD SILVER GOLD
15 Snowboard Parallel Giant Slalom - M Anderson, Jasey-Jay Strong 0.65 GOLD GOLD SILVER
16 Ice Hockey Ice Hockey - M Team Strong 0.65 SILVER GOLD SILVER
2 Freestyle Ski Moguls - M Marquis, Vincent Possibility 0.35      
2 Speed Skating - LT 3,000m - W Groves, Kristina Possibility 0.35   BRONZE BRONZE
3 Figure Skating Pairs - Mixed Davison, Dubé Possibility 0.35      
4 Snowboard Snowboardcross - W Maltais, Dominique Possibility 0.35 GOLD   SILVER
5 Alpine Ski Downhill - W Brydon, Emily Possibility 0.35     BRONZE
6 Figure Skating Singles - M Chan, Patrick Possibility 0.35 BRONZE SILVER BRONZE
7 Alpine Ski Super G - M Guay, Erik Possibility 0.35      
7 Skeleton Skeleton - M Montgomery, Jon Possibility 0.35 GOLD BRONZE SILVER
8 Speed Skating - LT 1,500m - M Morrison, Dennis Possibility 0.35 SILVER SILVER BRONZE
8 Speed Skating - ST 1,000m - M Hamelin, Francois Possibility 0.35      
9 Bobsleigh Two-Man - M Rush (Pilot) Possibility 0.35     BRONZE
11 Freestyle Ski Ski Cross - W Serwa, Kelsey Possibility 0.35   BRONZE BRONZE
12 Bobsleigh Two-Man - W Upperton (Pilot) Possibility 0.35 BRONZE    
12 Speed Skating - LT 5,000m - W Hughes, Clara Possibility 0.35     BRONZE
13 Figure Skating Singles - W Rochette, Joannie Possibility 0.35   BRONZE BRONZE
14 Speed Skating - ST 500m - M Tremblay, François-Louis Possibility 0.35 BRONZE   BRONZE
15 Snowboard Parallel Giant Slalom - M Lambert, Michael Possibility 0.35      
15 Speed Skating - LT Pursuit - M Giroux, Makowsky, Morrison, Parrot (Turgeon) Possibility 0.35 BRONZE BRONZE BRONZE
1 Alpine Ski Downhill - M Dixon, Robbie Outside 0.10      
1 Alpine Ski Downhill - M Guay, Erik Outside 0.10      
1 Freestyle Ski Moguls - W Richards, Kristi Outside 0.10      
1 Speed Skating - ST 1,500m - M Jean, Olivier Outside 0.10      
2 Alpine Ski Super Combined - W Brydon, Emily Outside 0.10      
2 Freestyle Ski Moguls - M Rousseau, Pierre-Alexandre Outside 0.10      
2 Speed Skating - LT 3,000m - W Hughes, Clara Outside 0.10      
3 Cross-Country Ski 15km Free - M Kershaw, Devon Outside 0.10      
3 Snowboard Snowboardcross - M Fagan, Rob Outside 0.10      
3 Speed Skating - LT 500m - M Gregg, Jamie Outside 0.10      
5 Alpine Ski Downhill - W Janyk, Britt Outside 0.10      
5 Cross-Country Ski Sprint (Classic) - W Crawford, Chandra Outside 0.10      
5 Cross-Country Ski Sprint (Classic) - W Renner, Sara Outside 0.10      
5 Snowboard Half Pipe - M Lamoureux, Justin Outside 0.10      
5 Speed Skating - LT 1,000m - M Morrison, Dennis Outside 0.10   BRONZE BRONZE
5 Speed Skating - ST 500m - W Gregg, Jessica Outside 0.10      
5 Speed Skating - ST 500m - W St.Gelais, Marianne Outside 0.10      
6 Snowboard Half Pipe - W Nicoll, Mercedes Outside 0.10      
6 Speed Skating - LT 1,000m - W Groves, Kristina Outside 0.10      
7 Alpine Ski Super G - M Dixon, Robbie Outside 0.10      
7 Alpine Ski Super G - M Osborne-Paradis, Manuel Outside 0.10      
7 Skeleton Skeleton - M Pain, Jeff Outside 0.10      
8 Alpine Ski Super G - W Janyk, Britt Outside 0.10      
8 Speed Skating - LT 1,500m - M Makowsky, Lucas Outside 0.10      
8 Speed Skating - ST 1,500m - W Maltais, Valérie Outside 0.10      
9 Freestyle Ski Ski Cross - M Duncan, David Outside 0.10      
9 Freestyle Ski Ski Cross - M Hayer, Stanley Outside 0.10      
9 Speed Skating - LT 1,500m - W Schussler, Brittany Outside 0.10      
10 Cross-Country Ski Team Sprint - W Gaiazova, Renner, Webster Outside 0.10      
11 Freestyle Ski Ski Cross - W Murray, Julia Outside 0.10      
12 Cross-Country Ski 4 x 10km Relay - M Goldsack, Jewett, McMurtry (??) Outside 0.10      
12 Speed Skating - LT 5,000m - W Groves, Kristina Outside 0.10 SILVER    
13 Freestyle Ski Aerials - M Omischl, Steve Outside 0.10      
13 Freestyle Ski Aerials - M Shouldice, Warren Outside 0.10      
14 Snowboard Parallel Giant Slalom - W Loo, Alexa Outside 0.10      
14 Speed Skating - ST 1,000m - W Roberge, Kalyna Outside 0.10      
15 Alpine Ski Slalom - M Cousineau, Julien Outside 0.10      
15 Alpine Ski Slalom - M Janyk, Michael Outside 0.10      
15 Bobsleigh Four-Man - M Rush (Pilot) Outside 0.10      

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