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