As recently as last month, Metropolitan division teams had won only about 35% of their games against the West and 45% of their games against the Atlantic. But they have been on a good run lately, and as of today, have won 45% of their games against the West and 51% of their games against the Atlantic. Suddenly, the Metropolitan division has a similar record (in fact, marginally better as of this post's writing) as the Atlantic division.
In fact, the whole "West is so much stronger than East" thing is less and less true. Again, as of early December (or was it late November?), Eastern teams had won only about 36% of their games against the West. Now, it's 45%, meaning the in the past few weeks, the East has actually had a winning record against the West.
I wonder when the hockey commentators will catch on to the new reality. (Or maybe they don't need to, if the Metropolitan/East goes back to sucking in the coming weeks.) All this is masked by the fact that the West still has 9 of the top 13 teams in the league (and the Metropolitan has only one), but if the current trend continues, that'll change.
As a Habs fan, I have to point out that the Leafs have just two regulation wins in their past 25 games - yes, 2/25. I blame this for the Metropolitan catching up to the Atlantic. On second thought, nah, just keep doing what you've doing, Leafs - I like you this way.
Showing posts with label Sports. Show all posts
Showing posts with label Sports. Show all posts
Sunday, January 12, 2014
Monday, August 13, 2012
Why So Few Gold Medals?
Canada's low gold medal count in London - one - is raising eyebrows: it is lower than our "usual" total of three (achieved in every summer Games after 1984, except in London and in Barcelona, where seven were won). However, even three is low compared to how much silver and bronze our athletes bring home. Indeed, gold accounted no more than a third of Canada's medals in every postwar summer games except Barcelona! This Vancouver Sun blog post has more stats.
As it turns out, this can be explained by simple math and the following two facts:
- Canada does not have a very large population; and
- Canada is competitive in many sports.
To see this, consider the following situation: a sport has 5 elite athletes, two from China, two from the US, and one from Canada. For simplicity, we will assume there there's no luck involved at the Olympics - the final results perfectly reflect the quality of athletes.
What happens if every athlete receives the same quality of support and training, so that everyone has an equal opportunity? Our Canadian then has an equal chance of being in each position from 1st through 5th - 20% chance of gold, 20% chance of silver and 20% chance of bronze.
But now suppose that the sporting federation imposes a rule: each country can only enter one athlete. To win gold, our Canadian athlete would still need to be the best. But she can win silver either by being second, or by being third if the top two athletes are from the same country. And of course, she is now guaranteed at least a bronze. Simply by virtue of being a smaller country, Canada now has a 20% chance of gold, ~27% chance of silver and ~53% chance of bronze!
In other words, having limited entries hurts large countries chances of winning bronze much more than it hurts their chances of winning gold: they still get to send their best athlete(s), but might not get to send all of their medal contenders. Thus, small countries will tend to win disproportionately many bronze medals.
Of course, even though Canada isn't the US or China, we're still larger than most countries. But the same effect applies: suppose a sport has 100 elite athletes, with 50 from the US, two from Canada, and one each from 48 other countries, so that Canada is actually the second largest country out of 50. Again, assume that each country has one entry. Canada's chances of winning gold are 2%. We don't necessarily win silver if one of our athletes is second: we won't send her to the games if the other one is first. But it is very unlikely that the two Canadian athletes happen to be the top two in the world (~0.02% chance). It is much more likely that the top Canadian, even if she is third, still ends up with a silver because the top two are American (~0.50%). She could even rank worse and still get silver if all of the superior athletes are American. The probability of winning silver turns out to be about 2.97%, and the probability of winning bronze, roughly 3.92%. So if there were 100 such events, you would expect Canada to win roughly two gold, three silver and four bronze. Thus, limited entries help even relatively large countries like Canada, as long as some other country/countries are much larger. Canada is a significant player in diving, but think about what would happen to Canadian medal hopes in diving if all countries including China were allowed to send all medal contenders.
By the way, this also explains why, even excluding Vancouver, Canada has no gold medal problems in the winter: we are a relatively large winter sports nation. (We don't actually dominate any winter sport except for hockey and curling, which yield few medals - this is why you also wouldn't expect a disproportionate amount of gold. But we are a significant presence in all the ice sports, freestyle skiing and snowboarding, where we win most of our medals.)
What about small countries like New Zealand that rack up the gold medals? As it turns out, these countries focus on a small number of sports. New Zealand might have a smaller population than BC, but it has lots of rowers focusing on small boats (i.e. not Eights) and sailors. At these Olympics, we also saw North Korea and Kazakhstan focus on weightlifting, which brought results. On the other hand, Spain, whose talent is also spread out (outside male soccer and basketball, which don't give many medals), has the same problems as Canada: apart from Barcelona and two pre-WWII games where it only won one medal, Spain's gold medal count has never even reached one third of its total haul. In summary, what matters is a country's "effective size" within each sport. So small countries can earn a disproportionate amount of gold if they focus on certain sports. Canada, by contrast, is spread quite thin.
Does this mean that Canada should start focusing on few sports? No: spreading out makes our gold count low relative to our total medal count because it enhances our total medal count by allowing us to be a "small" country benefiting from the limited entries effect. (To be sure, there are other arguments, such as economies of scale, for focusing on a small number of disciplines - especially cheap ones like weightlifting.) Also, being competitive at a large number of sports may be more effective in encouraging athletic activity, which is the larger goal of participating in the Olympics.
By the same token, this analysis only explains why we have few summer gold medals relative to silver and bronze. It does not explain why our total count is high or low, though as I hypothesized in my previous post, our total count is probably right around where it should be.
That said, the single gold performance at these Olympics is very poor: just 0.3% of total gold medals, while we account for 0.5% of the global population and are comparatively very well off. Even accounting for the mathematical effect described here, you'd expect more than one gold out of 18 medals. Of course, throw in luck, and such a thing will happen once in a while - so let's hope that this is just a one-off.
As it turns out, this can be explained by simple math and the following two facts:
- Canada does not have a very large population; and
- Canada is competitive in many sports.
To see this, consider the following situation: a sport has 5 elite athletes, two from China, two from the US, and one from Canada. For simplicity, we will assume there there's no luck involved at the Olympics - the final results perfectly reflect the quality of athletes.
What happens if every athlete receives the same quality of support and training, so that everyone has an equal opportunity? Our Canadian then has an equal chance of being in each position from 1st through 5th - 20% chance of gold, 20% chance of silver and 20% chance of bronze.
But now suppose that the sporting federation imposes a rule: each country can only enter one athlete. To win gold, our Canadian athlete would still need to be the best. But she can win silver either by being second, or by being third if the top two athletes are from the same country. And of course, she is now guaranteed at least a bronze. Simply by virtue of being a smaller country, Canada now has a 20% chance of gold, ~27% chance of silver and ~53% chance of bronze!
In other words, having limited entries hurts large countries chances of winning bronze much more than it hurts their chances of winning gold: they still get to send their best athlete(s), but might not get to send all of their medal contenders. Thus, small countries will tend to win disproportionately many bronze medals.
Of course, even though Canada isn't the US or China, we're still larger than most countries. But the same effect applies: suppose a sport has 100 elite athletes, with 50 from the US, two from Canada, and one each from 48 other countries, so that Canada is actually the second largest country out of 50. Again, assume that each country has one entry. Canada's chances of winning gold are 2%. We don't necessarily win silver if one of our athletes is second: we won't send her to the games if the other one is first. But it is very unlikely that the two Canadian athletes happen to be the top two in the world (~0.02% chance). It is much more likely that the top Canadian, even if she is third, still ends up with a silver because the top two are American (~0.50%). She could even rank worse and still get silver if all of the superior athletes are American. The probability of winning silver turns out to be about 2.97%, and the probability of winning bronze, roughly 3.92%. So if there were 100 such events, you would expect Canada to win roughly two gold, three silver and four bronze. Thus, limited entries help even relatively large countries like Canada, as long as some other country/countries are much larger. Canada is a significant player in diving, but think about what would happen to Canadian medal hopes in diving if all countries including China were allowed to send all medal contenders.
By the way, this also explains why, even excluding Vancouver, Canada has no gold medal problems in the winter: we are a relatively large winter sports nation. (We don't actually dominate any winter sport except for hockey and curling, which yield few medals - this is why you also wouldn't expect a disproportionate amount of gold. But we are a significant presence in all the ice sports, freestyle skiing and snowboarding, where we win most of our medals.)
What about small countries like New Zealand that rack up the gold medals? As it turns out, these countries focus on a small number of sports. New Zealand might have a smaller population than BC, but it has lots of rowers focusing on small boats (i.e. not Eights) and sailors. At these Olympics, we also saw North Korea and Kazakhstan focus on weightlifting, which brought results. On the other hand, Spain, whose talent is also spread out (outside male soccer and basketball, which don't give many medals), has the same problems as Canada: apart from Barcelona and two pre-WWII games where it only won one medal, Spain's gold medal count has never even reached one third of its total haul. In summary, what matters is a country's "effective size" within each sport. So small countries can earn a disproportionate amount of gold if they focus on certain sports. Canada, by contrast, is spread quite thin.
Does this mean that Canada should start focusing on few sports? No: spreading out makes our gold count low relative to our total medal count because it enhances our total medal count by allowing us to be a "small" country benefiting from the limited entries effect. (To be sure, there are other arguments, such as economies of scale, for focusing on a small number of disciplines - especially cheap ones like weightlifting.) Also, being competitive at a large number of sports may be more effective in encouraging athletic activity, which is the larger goal of participating in the Olympics.
By the same token, this analysis only explains why we have few summer gold medals relative to silver and bronze. It does not explain why our total count is high or low, though as I hypothesized in my previous post, our total count is probably right around where it should be.
That said, the single gold performance at these Olympics is very poor: just 0.3% of total gold medals, while we account for 0.5% of the global population and are comparatively very well off. Even accounting for the mathematical effect described here, you'd expect more than one gold out of 18 medals. Of course, throw in luck, and such a thing will happen once in a while - so let's hope that this is just a one-off.
Sunday, August 12, 2012
Canadian Medal Count: Not Bad
Every summer Olympics, some Canadians despair at our low medal count: not only do all more populous developed countries (except for Spain, who can console itself with its soccer team) beat us hands down, but Australia, with just 2/3 of our population, does so too. Certainly, the COC's objective of a Top 12 finish at summer games has once again been missed - Canada was 13th by total medals, two shy of the Netherlands and Ukraine. However, the obvious explanation for this is that much of our athletic talent is involved with winter sports, so one should take the winter Olympics into account before despairing.
(We should also note that with 18 medals, Canada ties its best performance at summer games conducted outside the US, albeit with less gold than in Barcelona or Beijing.)
Are summer and winter medals comparable? I think so. While fewer countries contest winter sports, there are also many fewer medals available at the winter Olympics: just 86 events in Vancouver versus 302 in London. The ratio is probably roughly right.
Here's a list of countries with at least 10 medals total from Vancouver and London (ties are broken by the number of gold, then silver) [updated to account for the doping incident in women's shot put]:
1. USA 141
2. CHN 99
3. RUS 97
4. GER 74
5. GBR 66
6. FRA 45
9. KOR 42
10. AUS 38
11. ITA 33
12. NED 28
13. NOR 27
14. UKR 20 (all summer)
15. SWE 19
16. HUN 17 (all summer)
17. ESP 17 (all summer)
18. BRA 17 (all summer)
19. CZE 16
20. AUT 16 (all winter!)
21. POL 16
22. BLR 15
23. KAZ 14
24. CUB 14 (all summer)
25. SUI 13
26. NZL 13 (all summer)
27. IRI 12 (all summer)
28. JAM 12 (all summer)
29. KEN 11 (all summer)
30. AZE 10 (all summer)
As you can see, Canada, in fact, does quite well, drawing level with much more populous countries like Japan and France, and handily beating Italy and Spain. And this is not a host country effect: Canada won only two more medals in Vancouver than in Turin. (Britain, however, increased its medal count by 18 between Beijing and London.) The only countries that are well ahead of Canada are the US, China, Russia, Germany and Britain. The first four all have more than twice Canada's population, while Britain is over 80% more populous and would likely have a much smaller lead had it not been the host country this year.
We also notice that there's a clear Top 13: the G8 countries, China, Korea, Australia, the Netherlands and Norway, who is 118th by population... (If only it produced as high quality soccer referees as athletes!)
One might be tempted to look at population per medal in order to establish a "fair" comparison. However, this ignores the fact that the number of entries into the competition is far from proportional to population: in most team sports, only one entry per country is allowed, and even in most individual sports, the limit is one, two or three. As a result, you just can't expect the US to win 9 times as many medals as Canada.
Then of course, there's the issue of each country's resources. Obviously, given similar populations, rich countries will have a much easier time than poor ones. Witness hapless India, with just 6 medals despite having more than 1/6 of the world's population. Pakistan, Nigeria and Bangladesh, the world's 6th, 7th and 8th most populous countries with over 150 million people each, have no medals at all!
A better way of looking at this data might be to plot the number of medals against total GDP. You wouldn't be looking for a straight line, but rather a concave curve, due to the lack of proportionality of competitive entries to population. And what to put on the GDP axis is not clear. First, it should likely be some mix of GDP at market prices and GDP at purchasing power parity (PPP, which adjusts for differing price levels between countries): a top-level athlete's consumption basket has a significant international component, so going by PPP alone would be misleading. Second, it should exclude "subsistence" GDP - something between the $1.25/day = $457/year/person poverty line used by the UN and $1,000/year/person, which is roughly the number for Afghanistan, the poorest country to win a medal in London (both figures PPP). Somebody should do this - looking at the various news outlets, many people have been paid for doing much less...
If we look only at rich countries, though, plotting medals against population works pretty well, since almost everyone's GDP PPP per capita is between $25,000 and $50,000. (It's still true that you'd want to fit a concave curve rather than a line.) Now, I'm feeling lazy, but just looking at the numbers, Norway and Australia would, unsurprisingly, be the big overachievers, while Japan, Italy and Spain would be the worst underachievers. Canada would likely lie above the fitted curve.
In terms of gold, however, the story might be different for Canada. Of course, in this cycle, thanks to the gold explosion in Vancouver, Canada has 15 gold medals out of 44. But usually, gold accounts for much less than one third of Canadian medals (3 in the summer and 7 in the winter is normal).
So, given the concentration of Canadian athletic resources in winter sports, our athletes' performance at the London games is right about what you'd expect - a bit better in terms of total medals, though a bit worse in terms of gold.
(We should also note that with 18 medals, Canada ties its best performance at summer games conducted outside the US, albeit with less gold than in Barcelona or Beijing.)
Are summer and winter medals comparable? I think so. While fewer countries contest winter sports, there are also many fewer medals available at the winter Olympics: just 86 events in Vancouver versus 302 in London. The ratio is probably roughly right.
Here's a list of countries with at least 10 medals total from Vancouver and London (ties are broken by the number of gold, then silver) [updated to account for the doping incident in women's shot put]:
1. USA 141
2. CHN 99
3. RUS 97
4. GER 74
5. GBR 66
6. FRA 45
7. CAN 44
8. JPN 439. KOR 42
10. AUS 38
11. ITA 33
12. NED 28
13. NOR 27
14. UKR 20 (all summer)
15. SWE 19
16. HUN 17 (all summer)
17. ESP 17 (all summer)
18. BRA 17 (all summer)
19. CZE 16
20. AUT 16 (all winter!)
21. POL 16
22. BLR 15
23. KAZ 14
24. CUB 14 (all summer)
25. SUI 13
26. NZL 13 (all summer)
27. IRI 12 (all summer)
28. JAM 12 (all summer)
29. KEN 11 (all summer)
30. AZE 10 (all summer)
As you can see, Canada, in fact, does quite well, drawing level with much more populous countries like Japan and France, and handily beating Italy and Spain. And this is not a host country effect: Canada won only two more medals in Vancouver than in Turin. (Britain, however, increased its medal count by 18 between Beijing and London.) The only countries that are well ahead of Canada are the US, China, Russia, Germany and Britain. The first four all have more than twice Canada's population, while Britain is over 80% more populous and would likely have a much smaller lead had it not been the host country this year.
We also notice that there's a clear Top 13: the G8 countries, China, Korea, Australia, the Netherlands and Norway, who is 118th by population... (If only it produced as high quality soccer referees as athletes!)
One might be tempted to look at population per medal in order to establish a "fair" comparison. However, this ignores the fact that the number of entries into the competition is far from proportional to population: in most team sports, only one entry per country is allowed, and even in most individual sports, the limit is one, two or three. As a result, you just can't expect the US to win 9 times as many medals as Canada.
Then of course, there's the issue of each country's resources. Obviously, given similar populations, rich countries will have a much easier time than poor ones. Witness hapless India, with just 6 medals despite having more than 1/6 of the world's population. Pakistan, Nigeria and Bangladesh, the world's 6th, 7th and 8th most populous countries with over 150 million people each, have no medals at all!
A better way of looking at this data might be to plot the number of medals against total GDP. You wouldn't be looking for a straight line, but rather a concave curve, due to the lack of proportionality of competitive entries to population. And what to put on the GDP axis is not clear. First, it should likely be some mix of GDP at market prices and GDP at purchasing power parity (PPP, which adjusts for differing price levels between countries): a top-level athlete's consumption basket has a significant international component, so going by PPP alone would be misleading. Second, it should exclude "subsistence" GDP - something between the $1.25/day = $457/year/person poverty line used by the UN and $1,000/year/person, which is roughly the number for Afghanistan, the poorest country to win a medal in London (both figures PPP). Somebody should do this - looking at the various news outlets, many people have been paid for doing much less...
If we look only at rich countries, though, plotting medals against population works pretty well, since almost everyone's GDP PPP per capita is between $25,000 and $50,000. (It's still true that you'd want to fit a concave curve rather than a line.) Now, I'm feeling lazy, but just looking at the numbers, Norway and Australia would, unsurprisingly, be the big overachievers, while Japan, Italy and Spain would be the worst underachievers. Canada would likely lie above the fitted curve.
In terms of gold, however, the story might be different for Canada. Of course, in this cycle, thanks to the gold explosion in Vancouver, Canada has 15 gold medals out of 44. But usually, gold accounts for much less than one third of Canadian medals (3 in the summer and 7 in the winter is normal).
So, given the concentration of Canadian athletic resources in winter sports, our athletes' performance at the London games is right about what you'd expect - a bit better in terms of total medals, though a bit worse in terms of gold.
Tuesday, April 26, 2011
Saturday, April 10, 2010
Adjusted Final NHL Regular Season Ranking, 2009-2010
As I explained in this post, to gauge the relative performances of NHL teams during the 2009-2010 season, a reasonable adjustment for the differing strengths of the two conferences is to add 3 points to Western teams, and subtract 3 points from Eastern teams.
Below are the final standings with this adjustment. I broke ties between teams in different divisions by considering the strength of the other teams in the division relative to the strength of the conference (since the difference in the latter has already been taken into account). If I had actually computed the appropriate divisional adjustments, all would be less than 1 point, and most would be less than 0.5 point. Ties between teams in the same division are resolved the usual way.
1. Washington 118
2. San Jose 116
3. Chicago 115
4. Phoenix 110
5. Vancouver 106
6. Detroit 105
7. Los Angeles 104
8. Nashville 103
9. New Jersey 100
10. Pittsburgh 98
11. Colorado 98
12. Buffalo 97
13. St. Louis 93
14. Calgary 93
15. Anaheim 92
16. Dallas 91
17. Ottawa 91
18. Boston 88
19. Minnesota 87
20. Philadelphia 85
21. Montreal 85
22. NY Rangers 84
23. Columbus 82
24. Atlanta 80
25. Carolina 77
26. Tampa Bay 77
27. NY Islanders 76
28. Florida 74
29. Toronto 71
30. Edmonton 65
7 of the top 8, and 12 of the top 16 teams are in the West - only 4 Eastern teams "deserve" to make the playoffs (WSH, NJ, PIT, BUF), while only 3 Western ones "deserve" to miss it (EDM, CBJ, MIN). The 8th seed in the West, Colorado, ranks ahead of Buffalo, the Northeast division champ!
Now, wouldn't it be awesome if the 21st regular-season team in the league wins the Cup?
Below are the final standings with this adjustment. I broke ties between teams in different divisions by considering the strength of the other teams in the division relative to the strength of the conference (since the difference in the latter has already been taken into account). If I had actually computed the appropriate divisional adjustments, all would be less than 1 point, and most would be less than 0.5 point. Ties between teams in the same division are resolved the usual way.
1. Washington 118
2. San Jose 116
3. Chicago 115
4. Phoenix 110
5. Vancouver 106
6. Detroit 105
7. Los Angeles 104
8. Nashville 103
9. New Jersey 100
10. Pittsburgh 98
11. Colorado 98
12. Buffalo 97
13. St. Louis 93
14. Calgary 93
15. Anaheim 92
16. Dallas 91
17. Ottawa 91
18. Boston 88
19. Minnesota 87
20. Philadelphia 85
21. Montreal 85
22. NY Rangers 84
23. Columbus 82
24. Atlanta 80
25. Carolina 77
26. Tampa Bay 77
27. NY Islanders 76
28. Florida 74
29. Toronto 71
30. Edmonton 65
7 of the top 8, and 12 of the top 16 teams are in the West - only 4 Eastern teams "deserve" to make the playoffs (WSH, NJ, PIT, BUF), while only 3 Western ones "deserve" to miss it (EDM, CBJ, MIN). The 8th seed in the West, Colorado, ranks ahead of Buffalo, the Northeast division champ!
Now, wouldn't it be awesome if the 21st regular-season team in the league wins the Cup?
Sunday, April 4, 2010
Which 16 NHL Teams Would Make the Playoffs with a Balanced Schedule?
The last inter-conference game of the NHL regular season was played yesterday - the next time that teams from the East and the West meet will be in the Stanley Cup Finals. Teams from the Eastern Conference only won 115 of the 270 inter-conference games this season, a success rate of 42.6%.
The West being stronger than the East and yet getting the same number of playoff spots is a sore point for some Western hockey fans. For example, the Flames now only have a 5.5%-chance of making the playoffs according to Sports Club Stats even though their record would guarantee them a spot in the East. Some have therefore proposed to simply allocate playoff spots to the top 16 teams, regardless of conference.
However, the actual situation is worse: Western teams also suffer from facing stronger Western teams for 64 games, and weaker Eastern ones for only 18 games. How many points is that worth?
Well, to a first approximation, to make the schedule fair, each team should play 23 fewer games against teams in its own conference, and 23 more against ones in the other conference. In those 23 games, Eastern teams would have a success rate of 42.6% instead of 50%. On average, they would therefore win about 1.7 fewer games.
Each win is not quite worth 2 points, since the losing team gets 1 point for making it to OT. That has happened in 23.6% of games played this season. Thus, a win is worth 2-0.236 = 1.764 points.
Bottom line: One should subtract 3.005 points from each team's total in the East, and add 3.005 for Western teams.
Of course, ideally one would also adjust for the strength of divisional opponents (against whom each team plays 6 times instead of 4 against non-division rivals in the same conference), and the strength of the 3 teams from the other conference a team plays against twice instead of once. However, those adjustments are bound to be much smaller, so to a first approximation, adding 3 points to Western teams and subtracting 3 from Eastern teams is appropriate. Equivalently, we could simply add 6 to Western totals.
(The appropriate adjustment for now is not 6, but about 5.5 since the season isn't over yet.)
Looking at the current standings, counting each game left beyond 3 as 1.1 points (i.e. teams with 4 games left get +1.1, while the Predators get -1.1 for having just 2 remaining), and adding 5.5 to Western teams, my homemade NHL ranking is:
1. Washington 115.1
2. San Jose 112.5
3. Chicago 111.6
4. Phoenix 107.5
5. Vancouver 105.5
6. Nashville 102.4
7. Los Angeles 101.6
8. Detroit 101.5
9. New Jersey 98.1
10. Pittsburgh 98.1
11. Colorado 97.6
12. Buffalo 97.1
13. Calgary 94.5
14. Anaheim 91.6
15. St. Louis 91.6
16. Ottawa 91
17. Dallas 89.5
18. Minnesota 86.5
19. Montreal 86
20. Boston 85.1
21. Philadelphia 84
22. NY Rangers 83.1
23. Columbus 82.5
24. Atlanta 81
25. NY Islanders 77.1
26. Carolina 76
27. Florida 75.1
28. Tampa Bay 75.1
29. Toronto 72
30. Edmonton 62.6
Instead of being already guaranteed to win the President's Trophy, Washington would be in a tough fight with San Jose and Chicago for the top spot, especially if you additionally adjust for divisional strength. Fully 7 of the 8 best teams in the league are in the West, and the East has 10 of the 12 worst teams! The Devils, Penguins and Sabres suddenly look a lot less likely to hoist the Cup in June: they are only about as good as the Avalanche, ranked 8th in the West. Overall, 11 Western teams and 5 Eastern teams deserve to make the playoffs.
In terms of Canadian teams, instead of having Ottawa in, Montreal almost in and Calgary almost out, we'd have Calgary almost in, Ottawa on the bubble (but looking good) and Montreal almost out.
I will update the homemade standings at the end of the regular season, next week.
The West being stronger than the East and yet getting the same number of playoff spots is a sore point for some Western hockey fans. For example, the Flames now only have a 5.5%-chance of making the playoffs according to Sports Club Stats even though their record would guarantee them a spot in the East. Some have therefore proposed to simply allocate playoff spots to the top 16 teams, regardless of conference.
However, the actual situation is worse: Western teams also suffer from facing stronger Western teams for 64 games, and weaker Eastern ones for only 18 games. How many points is that worth?
Well, to a first approximation, to make the schedule fair, each team should play 23 fewer games against teams in its own conference, and 23 more against ones in the other conference. In those 23 games, Eastern teams would have a success rate of 42.6% instead of 50%. On average, they would therefore win about 1.7 fewer games.
Each win is not quite worth 2 points, since the losing team gets 1 point for making it to OT. That has happened in 23.6% of games played this season. Thus, a win is worth 2-0.236 = 1.764 points.
Bottom line: One should subtract 3.005 points from each team's total in the East, and add 3.005 for Western teams.
Of course, ideally one would also adjust for the strength of divisional opponents (against whom each team plays 6 times instead of 4 against non-division rivals in the same conference), and the strength of the 3 teams from the other conference a team plays against twice instead of once. However, those adjustments are bound to be much smaller, so to a first approximation, adding 3 points to Western teams and subtracting 3 from Eastern teams is appropriate. Equivalently, we could simply add 6 to Western totals.
(The appropriate adjustment for now is not 6, but about 5.5 since the season isn't over yet.)
Looking at the current standings, counting each game left beyond 3 as 1.1 points (i.e. teams with 4 games left get +1.1, while the Predators get -1.1 for having just 2 remaining), and adding 5.5 to Western teams, my homemade NHL ranking is:
1. Washington 115.1
2. San Jose 112.5
3. Chicago 111.6
4. Phoenix 107.5
5. Vancouver 105.5
6. Nashville 102.4
7. Los Angeles 101.6
8. Detroit 101.5
9. New Jersey 98.1
10. Pittsburgh 98.1
11. Colorado 97.6
12. Buffalo 97.1
13. Calgary 94.5
14. Anaheim 91.6
15. St. Louis 91.6
16. Ottawa 91
17. Dallas 89.5
18. Minnesota 86.5
19. Montreal 86
20. Boston 85.1
21. Philadelphia 84
22. NY Rangers 83.1
23. Columbus 82.5
24. Atlanta 81
25. NY Islanders 77.1
26. Carolina 76
27. Florida 75.1
28. Tampa Bay 75.1
29. Toronto 72
30. Edmonton 62.6
Instead of being already guaranteed to win the President's Trophy, Washington would be in a tough fight with San Jose and Chicago for the top spot, especially if you additionally adjust for divisional strength. Fully 7 of the 8 best teams in the league are in the West, and the East has 10 of the 12 worst teams! The Devils, Penguins and Sabres suddenly look a lot less likely to hoist the Cup in June: they are only about as good as the Avalanche, ranked 8th in the West. Overall, 11 Western teams and 5 Eastern teams deserve to make the playoffs.
In terms of Canadian teams, instead of having Ottawa in, Montreal almost in and Calgary almost out, we'd have Calgary almost in, Ottawa on the bubble (but looking good) and Montreal almost out.
I will update the homemade standings at the end of the regular season, next week.
Tuesday, March 2, 2010
Assessing Vancouver 2010
So our athletes did great. But how good of a show did we put up? Below, I grade several aspects of the Games, using the following scale:
A = Excellent
B = Above average
C = Below average
D = Unsatisfactory
F = Failing
Venues: Things were pretty nice overall, but there was no exclamation point, so I start with a B. However, having competitions at Cypress Mountain turned out to be too audacious. Also, the ice track in Whistler should obviously have been safer. Still, the Georgian luger's death cannot be solely blamed on the organizers (the luge federation, track designer and luger himself must share responsibility), so I won't knock the grade down too much. C.
Security: Media from all over the world marveled at the non-intrusiveness and efficiency of the security apparatus. A.
Logistics: A few transportation glitches here and there (especially with buses early on), and a few minor ticketing issues, but nothing out of line with other Olympics. No significant technical problems with broadcasting (just a few occasional problems with timers). Good, but not great, website. B.
Non-sporting Organization: Slight lack of French at the opening ceremony, but adequate representation at the closing one, and great presence during the Games. Incredibly stupid arrangement for the Olympic Cauldron, but adequate fix found, with closer access to the flame than ever before. Embarrassing glitch at the opening ceremony, but brilliant recovery at the closing one. Up to now, not great, but OK.
All the live concerts and lively public gathering places are a nice plus. VANOC and the COC were also accessible and transparent. Outstanding Olympic village. So I'm tempted to give a B, BUT (and here I go on a 3-paragraph rant) -
I cringed at the response to Nodar Kumaritashvili's death. Suppose your clumsy friend Ronald falls on a knife and kills himself while helping you cook for a party, and his family inquires about what happened. Other people present are already telling the family that it's indeed your friend's maladroitness. What would you say? "I'm terribly sorry for your loss." or "I'm terribly sorry for your loss, but this was entirely Ronald's fault, and I reject any responsibility." VANOC opted for the latter. Perhaps it was for legal reasons, but couldn't VANOC have let the RCMP and Luge Federation do the talking about the investigation?
Also, publicly congratulating yourself that, after several days, you finally found a partial solution to a problem arising from an inexplicable brain cramp (the fence around the cauldron), is rather rich. Something like, "This is what we're doing. We're glad to have solved the problem, but regret that it was there in the first place. We hope that the public will like it" would have been much more appropriate (and Canadian) than "Aren't we great? We managed to move the fence, make a cutout, and allow people to go up an adjacent building in a matter of just a few days! This shows how adaptable and flexible we are." A stuffed nose could smell the insecurity from St. John's.
It wasn't just VANOC: Mayor Robertson also said in the middle of the first week, when all the glitches were going on and not yet resolved, that these were the best organized games ever. Ha! Try saying that with a straight face - especially at that point - to an organizer from Beijing, Salt Lake City, Sydney or Nagano. This type of childlike defensive attitude reflected poorly upon Canada, and unfortunately cast a shadow over VANOC's and Vancouver's legitimate achievements.
This explains the feeling in the international media that while Canadian organizers did a good job and met high expectations, they also appeared to be some of the most arrogant, graceless and thin-skinned people in the world. B for performance, F for optics. Given that actual performance is still more important, I'll average these out to a C.
Sporting Organization: The ice resurfacing problems at the Oval were ridiculous. So even if everything else under VANOC's control (i.e. not counting the weather and the biathlon pursuit starting snafus, which were entirely under the control of the biathlon federation) went right, it deserves no more than a C.
Atmosphere: The Sydney Morning Herald said that Vancouver embraced the Games more than Sydney did. That's the best Vancouver could possibly have hoped for - no big city can match Lillehammer's magical ambiance. Given that Winter Olympics will probably be held in big cities from now on, no Games is likely to be as fun as Vancouver's for decades to come. Will the city carry this energy and shed its 'No Fun' label? A+.
Overall: 1 A+, 1 A, 1 B, 3 C's. The average is just below a B. The atmosphere, though, is probably the most important of these ratings, so I'll go with a solid B: above average. Canada and Vancouver did a good job. But despite what Stephen Harper says, we were not quite as good as Lillehammer (who can ever beat that?), and only matched Sydney in the 2nd week. That said, overall, we at least equaled, if not slightly topped, the better recent Games (Nagano, Salt Lake and Beijing, especially if you don't count the latter's ceremonies), all of which were a bit stronger organizationally, but not nearly as fun. And we were clearly better than the weaker ones (Atlanta, Athens, Turin).
So good job VANOC, Vancouver and Canada! But let's not congratulate ourselves too hard, so that we can remember to draw the lessons that we should.
(And to Britons: this Canadian understands that your media are always this vicious, and that if you screw up in London, we won't need to criticize - by the time we notice, your own journalists will probably have already eaten Lord Coe alive.)
A = Excellent
B = Above average
C = Below average
D = Unsatisfactory
F = Failing
Venues: Things were pretty nice overall, but there was no exclamation point, so I start with a B. However, having competitions at Cypress Mountain turned out to be too audacious. Also, the ice track in Whistler should obviously have been safer. Still, the Georgian luger's death cannot be solely blamed on the organizers (the luge federation, track designer and luger himself must share responsibility), so I won't knock the grade down too much. C.
Security: Media from all over the world marveled at the non-intrusiveness and efficiency of the security apparatus. A.
Logistics: A few transportation glitches here and there (especially with buses early on), and a few minor ticketing issues, but nothing out of line with other Olympics. No significant technical problems with broadcasting (just a few occasional problems with timers). Good, but not great, website. B.
Non-sporting Organization: Slight lack of French at the opening ceremony, but adequate representation at the closing one, and great presence during the Games. Incredibly stupid arrangement for the Olympic Cauldron, but adequate fix found, with closer access to the flame than ever before. Embarrassing glitch at the opening ceremony, but brilliant recovery at the closing one. Up to now, not great, but OK.
All the live concerts and lively public gathering places are a nice plus. VANOC and the COC were also accessible and transparent. Outstanding Olympic village. So I'm tempted to give a B, BUT (and here I go on a 3-paragraph rant) -
I cringed at the response to Nodar Kumaritashvili's death. Suppose your clumsy friend Ronald falls on a knife and kills himself while helping you cook for a party, and his family inquires about what happened. Other people present are already telling the family that it's indeed your friend's maladroitness. What would you say? "I'm terribly sorry for your loss." or "I'm terribly sorry for your loss, but this was entirely Ronald's fault, and I reject any responsibility." VANOC opted for the latter. Perhaps it was for legal reasons, but couldn't VANOC have let the RCMP and Luge Federation do the talking about the investigation?
Also, publicly congratulating yourself that, after several days, you finally found a partial solution to a problem arising from an inexplicable brain cramp (the fence around the cauldron), is rather rich. Something like, "This is what we're doing. We're glad to have solved the problem, but regret that it was there in the first place. We hope that the public will like it" would have been much more appropriate (and Canadian) than "Aren't we great? We managed to move the fence, make a cutout, and allow people to go up an adjacent building in a matter of just a few days! This shows how adaptable and flexible we are." A stuffed nose could smell the insecurity from St. John's.
It wasn't just VANOC: Mayor Robertson also said in the middle of the first week, when all the glitches were going on and not yet resolved, that these were the best organized games ever. Ha! Try saying that with a straight face - especially at that point - to an organizer from Beijing, Salt Lake City, Sydney or Nagano. This type of childlike defensive attitude reflected poorly upon Canada, and unfortunately cast a shadow over VANOC's and Vancouver's legitimate achievements.
This explains the feeling in the international media that while Canadian organizers did a good job and met high expectations, they also appeared to be some of the most arrogant, graceless and thin-skinned people in the world. B for performance, F for optics. Given that actual performance is still more important, I'll average these out to a C.
Sporting Organization: The ice resurfacing problems at the Oval were ridiculous. So even if everything else under VANOC's control (i.e. not counting the weather and the biathlon pursuit starting snafus, which were entirely under the control of the biathlon federation) went right, it deserves no more than a C.
Atmosphere: The Sydney Morning Herald said that Vancouver embraced the Games more than Sydney did. That's the best Vancouver could possibly have hoped for - no big city can match Lillehammer's magical ambiance. Given that Winter Olympics will probably be held in big cities from now on, no Games is likely to be as fun as Vancouver's for decades to come. Will the city carry this energy and shed its 'No Fun' label? A+.
Overall: 1 A+, 1 A, 1 B, 3 C's. The average is just below a B. The atmosphere, though, is probably the most important of these ratings, so I'll go with a solid B: above average. Canada and Vancouver did a good job. But despite what Stephen Harper says, we were not quite as good as Lillehammer (who can ever beat that?), and only matched Sydney in the 2nd week. That said, overall, we at least equaled, if not slightly topped, the better recent Games (Nagano, Salt Lake and Beijing, especially if you don't count the latter's ceremonies), all of which were a bit stronger organizationally, but not nearly as fun. And we were clearly better than the weaker ones (Atlanta, Athens, Turin).
So good job VANOC, Vancouver and Canada! But let's not congratulate ourselves too hard, so that we can remember to draw the lessons that we should.
(And to Britons: this Canadian understands that your media are always this vicious, and that if you screw up in London, we won't need to criticize - by the time we notice, your own journalists will probably have already eaten Lord Coe alive.)
Monday, March 1, 2010
Not All Medals Are Created Equal
I can't resist a quick post about the Olympics!
Much has been said about the US setting a new Winter Olympics medal record (37), and Canada setting a new Winter Olympics gold medal record (14). But what would the medal count look like if we weighted each medal according to some measure of significance?
Obviously, what's significant for a country may not be for another. Even then, I'm pretty sure even Koreans would agree that hockey medals mean more than speedskating ones. I used the following simple formula for determining the weight of each medal, and I think it produces intuitive results:
Square root of number of athletes on a team, rounded to the nearest integer
+1 if the event is the only Olympic event for (almost) every athlete competing in it
+1 if the event features a weeklong tournament
For example, hockey medals are worth 5+1+1=7, curling medals are worth 2+1+1=4, while 33 other medals are worth 2 and the remaining 49 are worth 1. This produces the following weighting of sports:
Cross-country 14
Hockey 14
Speedskating 14
Biathlon 12
Freestyle Skiing 12
Snowboard 12
Alpine Skiing 10
Short Track 10
Curling 8
Figure Skating 8
Luge 6
Bobsleigh 5
Nordic Combined 4
Skeleton 4
Ski Jumping 4
Freestyle and snowboard appear overweighted at first glance. But I would argue that each of these "sports" is actually 3 sports: for example, ski cross and aerials are just as far apart as alpine skiing and cross-country, and more so than the two kinds of speedskating.
The total weight for the 86 events is 137 (69 for ice sports and 68 for snow sports), so I then multiply by 86/137 and round to the nearest integer to produce the adjusted medal count.
Top 10 Countries by Weighted Medals (actual in parentheses)
USA 42 (37)
CAN 37 (26)
GER 27 (30)
NOR 20 (23)
AUT 14 (16)
RUS 13 (15)
CHN 13 (11)
FIN 12 (5)
FRA 10 (11)
SWE 10 (11)
Canada and Finland are the big winners. The US gains as well, while all other countries lose out, but only slightly.
Top 12 Countries by Weighted Gold Medals (actual in parentheses)
CAN 24 (14)
USA 9 (9)
GER 8 (10)
NOR 7 (9)
SWE 6 (5)
KOR 4 (6)
SUI 4 (6)
CHN 4 (5)
AUT 4 (4)
NED 3 (4)
RUS 3 (3)
AUS 3 (2)
O Canada! Even if I had weighted the hockey and curling medals at 2 instead of 7 and 4, Canada's normalized gold total would still be 18. That's right - not only did Canada win the most medals ever, but it tended to win them in team events and in events where athletes did not have multiple chances. The latter means that to get to 14, Canada couldn't rely on a handful of sports that happen to have lots of events: amazingly, despite the huge overall total, Canada did not win more than 2 gold medals in any sport, and no Canadian athlete got more than 2 medals of any colour. Canada is also the only country to have won gold in a majority of the 15 sports (9).
So, in summary: once you apply some kind of sensible weighting scheme to events, the Canadian performance at the Games is even more impressive!
Much has been said about the US setting a new Winter Olympics medal record (37), and Canada setting a new Winter Olympics gold medal record (14). But what would the medal count look like if we weighted each medal according to some measure of significance?
Obviously, what's significant for a country may not be for another. Even then, I'm pretty sure even Koreans would agree that hockey medals mean more than speedskating ones. I used the following simple formula for determining the weight of each medal, and I think it produces intuitive results:
Square root of number of athletes on a team, rounded to the nearest integer
+1 if the event is the only Olympic event for (almost) every athlete competing in it
+1 if the event features a weeklong tournament
For example, hockey medals are worth 5+1+1=7, curling medals are worth 2+1+1=4, while 33 other medals are worth 2 and the remaining 49 are worth 1. This produces the following weighting of sports:
Cross-country 14
Hockey 14
Speedskating 14
Biathlon 12
Freestyle Skiing 12
Snowboard 12
Alpine Skiing 10
Short Track 10
Curling 8
Figure Skating 8
Luge 6
Bobsleigh 5
Nordic Combined 4
Skeleton 4
Ski Jumping 4
Freestyle and snowboard appear overweighted at first glance. But I would argue that each of these "sports" is actually 3 sports: for example, ski cross and aerials are just as far apart as alpine skiing and cross-country, and more so than the two kinds of speedskating.
The total weight for the 86 events is 137 (69 for ice sports and 68 for snow sports), so I then multiply by 86/137 and round to the nearest integer to produce the adjusted medal count.
Top 10 Countries by Weighted Medals (actual in parentheses)
USA 42 (37)
CAN 37 (26)
GER 27 (30)
NOR 20 (23)
AUT 14 (16)
RUS 13 (15)
CHN 13 (11)
FIN 12 (5)
FRA 10 (11)
SWE 10 (11)
Canada and Finland are the big winners. The US gains as well, while all other countries lose out, but only slightly.
Top 12 Countries by Weighted Gold Medals (actual in parentheses)
CAN 24 (14)
USA 9 (9)
GER 8 (10)
NOR 7 (9)
SWE 6 (5)
KOR 4 (6)
SUI 4 (6)
CHN 4 (5)
AUT 4 (4)
NED 3 (4)
RUS 3 (3)
AUS 3 (2)
O Canada! Even if I had weighted the hockey and curling medals at 2 instead of 7 and 4, Canada's normalized gold total would still be 18. That's right - not only did Canada win the most medals ever, but it tended to win them in team events and in events where athletes did not have multiple chances. The latter means that to get to 14, Canada couldn't rely on a handful of sports that happen to have lots of events: amazingly, despite the huge overall total, Canada did not win more than 2 gold medals in any sport, and no Canadian athlete got more than 2 medals of any colour. Canada is also the only country to have won gold in a majority of the 15 sports (9).
So, in summary: once you apply some kind of sensible weighting scheme to events, the Canadian performance at the Games is even more impressive!
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