National Rankings, quantitatively

So, if you haven't figured out by now, I like quantitative analysis.  Therefore, I was quite chuffed to read a paper by Dr. James Keener^[link], provided by Mr. Skipsey^[link], describing a way of quantitatively analysing the relative ranking of teams.

Now, there are several great systems in this world of ours, but most rely on teams all playing each other.  Derby doesn't do that.  Derby teams play who they want, and rely on subjectivity to guess who's better than whom.  That's where Dr. Keener's paper comes in handy.



See, Dr. Keener was analysing the US college football scheme, which has similarly loose scheduling.  Therefore, he figured he would start with what we yanks call strength of schedule, or S_s.  Normally, this is calculated by a team's winning percentage.  Thus, beating a team that's .800 is better than beating a team that's .200.

What Dr. Keener did, though, was to take that S_s value further.  He suggested further comparing to the teams played by the teams played by the team in question, etc.  Thus, if nation X played nations Y and Z, also analysing how Y and Z did against who they played.

Mathematically, this is actually fairly simple, and for international roller derby I have done it not by win/loss record, but by adjusted score percentage:

Using this system, the following table is produced:

	Nation	Bouts	Rank Score
1	USA	7	224.7
2	Canada	6	152.9
3	England	5	141.6
4	Australia	6	117.3
5	Germany	5	95.4
6	Sweden	8	78.7
7	Ireland	5	74.3
8	Finland	7	70.1
9	New Zealand	6	62.9
10	France	7	58.4
11	Argentina	4	48.5
12	Scotland	6	46.8
13	Brazil	6	35.9

The rank score is just the results of Dr. Keener's scheme, multiplied by a thousand to make the numbers easier to use.  So, what does this mean?

It means that England were about 40 points shy of overtaking Canada after the bout against USA.


Next question: is this ranking system valid?  Well, only 12.5% of all bouts played by the nations were upsets.  That is, the higher ranked team won 87.5% of the time.  As upsets have to happen in sport, and sport wouldn't be awesome without upsets now & again, I reckon this is a pretty good number!  After all, DNN's numbers are usually about 15-18% upset rate.

So, at the end of the day, England did really well, and Finland let themselves down a bit on the weekend several weeks ago.  Now, what would happen if I ran this system on the leagues within the UK?

On that note,
Roll on!