Rejigging The Olympics Medal Tally

Commonly, the Olympics medal tally for countries is ordered in terms of number of gold medals won. Under this system, countries that have won a lot of medals but only a small proportion of them are gold are disadvantaged (in the current Olympics this includes the Russian Federation, Japan, Germany and Australia). On the other, countries could be ranked by number of medals won, but this treats all medals as being of equal value.

So how about this system - what if 3 points were awarded for a gold medal, 2 for a silver medal, and 1 point for a bronze medal? Under this system, the top 10 for the current 2012 Olympics medal tally would look like this:

This order seems more reflective of who the historically strong sports nations are. Over the long run, one would expect the proportions of medals of each colour won by each country to even out, so that the all-time table under this system would have a similar order to the all-time table ordered by gold medals won. Here are the top 12:

China drops a few places under the adjusted system, but other than that it's pretty close.

AFL Power Rankings: Round 19 2012

The Western Derby had the biggest effect on the rankings this week, with the winner Fremantle moving up from 12th to 10th (and into positive territory on ranking points), and the loser West Coast falling from 5th to 7th, losing touch with the top five.

Twelve teams are now in positive territory, with a massive gap between 12th-placed Carlton and 13th-placed Brisbane.

1 (1) Hawthorn 45.8 (46.9)
2 (2) Sydney 31.9 (30.5)
3 (3) St. Kilda 20.7 (21.4)
4 (4) Adelaide 19.6 (19.3)
5 (6) Collingwood 19.5 (18.2)
6 (7) Geelong 14.2 (12.3)
7 (5) West Coast 11.0 (18.4)
8 (8) North Melbourne 10.2 (7.3)
9 (9) Richmond 6.8 (1.7)
10 (12) Fremantle 5.5 (-3.6)
11 (10) Essendon 3.8 (0.8)
12 (11) Carlton 0.8 (0.7)
13 (13) Brisbane -16.9 (-14.1)
14 (14) Port Adelaide -25.1 (-21.1)
15 (15) Western Bulldogs -30.0 (-28.9)
16 (16) Melbourne -33.6 (-36.4)
17 (17) Gold Coast -46.9 (-46.8)
18 (18) Greater Western Sydney -68.3 (-74.1)

The Finger Points Outwards - No. 43

Revisiting the "bootleg Batman".

The problems with making friends after 30.

"Medalball": which sports is it most cost-efficient to win Olympic medals in.

Comparing the pace of Olympic gold medallists over time (it's interactive!)

American baby names are getting worse.

And music is becoming more homogenous.

Quick ... Name The Five Sports In Modern Pentathlon

AFL Power Rankings: Round 18 2012

Hawthorn extend their lead at the top after smashing the Bombers over the weekend. The Saints edge back up to third, while the Eagles and Pies close the gap with fourth-placed Adelaide after they both had massive wins.

(And for those who are wondering: how can the Tigers move further up after losing to Carlton?!  ... Don't overthink the ranking positions. Essentially, the Tigers and Blues were close to even before their game on the weekend, there was very little between them in that game, and so they are still close to even after it.)

1 (1) Hawthorn 46.9 (39.9)
2 (2) Sydney 30.5 (29.5)
3 (4) St. Kilda 21.4 (17.1)
4 (3) Adelaide 19.3 (19.2)
5 (5) West Coast 18.4 (12.5)
6 (6) Collingwood 18.2 (12.5)
7 (7) Geelong 12.3 (10.2)
8 (8) North Melbourne 7.3 (6.2)
9 (10) Richmond 1.7 (0.4)
10 (9) Essendon 0.8 (5.0)
11 (11) Carlton 0.7 (0.2)
12 (12) Fremantle -3.6 (-6.0)
13 (13) Brisbane -14.1 (-10.8)
14 (14) Port Adelaide -21.1 (-20.2)
15 (15) Western Bulldogs -28.9 (-26.4)
16 (16) Melbourne -36.4 (-36.9)
17 (17) Gold Coast -46.8 (-47.1)
18 (18) Greater Western Sydney -74.1 (-70.2)

The Most "Efficient" Premiership Winning Team In VFL/AFL History

Alright, Carlton and Essendon have the most VFL/AFL premierships, with 16 each, but looking at who has won the most premierships is not a very interesting blog post (and doesn't fill our quota of at least one mathematical formula per post). Another question is which team has been the most "efficient" at winning premierships? To answer this, I've devised the following formula:

Premiership Efficiency Rating = (Premierships Won / Number of Seasons Played) - Average Probability Of Winning Premiership

The average probability of winning the premiership is calculated as the average of one divided by the number of teams over all the seasons a club has played. In 1897, the probability of winning was 0.125 (1/8); in 2011 it was 0.059 (1/17). Hence, the average probability is lower for newer clubs because a far higher proportion of their seasons were played in a larger league.

The "premiership efficiency rating" for each team is as follows:

Brisbane (Bears/Lions) 0.056
West Coast 0.056
Essendon 0.055
Carlton 0.051
Collingwood 0.042
Hawthorn 0.037
Adelaide 0.032
Melbourne 0.021
Richmond 0.011
Port Adelaide 0.004
Geelong -0.007
Fitzroy -0.013
North Melbourne -0.032
Sydney -0.052
Gold Coast -0.059
Fremantle -0.062
Western Bulldogs -0.067
St. Kilda -0.078
University -0.100

Brisbane and West Coast come out on top, narrowly ahead of Essendon, assuming that the Brisbane Lions are counted as a continuation of the Brisbane Bears. If they're not, then the Brisbane Lions come out way ahead, with a PER of 0.138, as they have won 3 premierships since they began in 1997 in a league no smaller than 16 teams.

One could apply this formula to other competitions, and you would get more interesting results for the American professional sports associations, where there has been a wide variation in the degree of expansion over time. Indeed, I first had this idea in relation to the Davis Cup for tennis, in which the US and Australia won a lot of titles when fewer countries competed (and the format was different). Depending on how enthusiastic I feel, I might look at other leagues at a later date.

The Best Sporting Nation On Earth (Per Capita)

In their book "Soccernomics" Simon Kuper and Stefan Szymanski came up with a system for determining which countries have historically performed the best at sports given their population. They awarded points to countries based on their success in the following sports: rugby union, karate, cricket, baseball, basketball, women's soccer, men's and women's tennis, golf, chess, cycling, auto racing, the Summer and Winter Olympics, and the men's soccer World Cup. They then divided each country's total points by population to work out each country's sporting efficiency rating.

The winner? Norway, and by a considerable margin. Norway has been very successful at the Winter Olympics and women's soccer, and has a population of only five million. Sweden finished second on the table, Australia third, and New Zealand fourth.

Unsurpisingly, on the "raw" points total, the US came out as the most successful sporting nation.

The top 10:

Norway - 4 points per million inhabitants
Sweden - 1.22
Australia - 0.98
New Zealand - 0.97
United Germany - 0.91
Britain/England - 0.85
Hungary - 0.80
West Indies - 0.77
France - 0.67
Italy - 0.54

AFL Power Rankings: Round 17 2012

The big mover this week in terms of positions is Adelaide, who jump from sixth to third after their big win against the Eagles, while the teams near them all lost this weekend. Another big mover is Geelong, who move back to seventh after their 11-goal win against Essendon.

The top three ranked teams are also now the top three teams on this season's ladder, but the Hawks are still ranked No.1.

1 (1) Hawthorn 39.9 (38.0)
2 (2) Sydney 29.5 (28.8)
3 (6) Adelaide 19.2 (15.1)
4 (3) St. Kilda 17.1 (17.4)
5 (4) West Coast 12.5 (16.0)
6 (5) Collingwood 12.5 (15.1)
7 (9) Geelong 10.2 (5.3)
8 (8) North Melbourne 6.2 (6.5)
9 (7) Essendon 5.0 (9.1)
10 (11) Richmond 0.4 (-0.3)
11 (10) Carlton 0.2 (2.1)
12 (13) Fremantle -6.0 (-8.5)
13 (12) Brisbane -10.8 (-7.4)
14 (14) Port Adelaide -20.2 (-22.0)
15 (15) Western Bulldogs -26.4 (-27.5)
16 (16) Melbourne -36.9 (-35.0)
17 (17) Gold Coast -47.1 (-49.5)
18 (18) Greater Western Sydney -70.2 (-67.6)