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.
|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|