2012-06-15

Ranking rules of group matches and scientific research

The ranking system for the current group match stage of Euro 2012 seems far from complex. A senior fan should be familiar with the rules and fake-fans (like me) may check with the official website for the rules as below (found from http://www.uefa.com/multimediafiles/download/competitions/euro/91/87/57/918757_download.pdf). Eight 'if...then' provisions and an extra complement are given there, somewhat confusing but clear enough and well defined.

8.07 If two or more teams are equal on points on completion of the group matches, the
following criteria are applied, in the order given; to determine the rankings:
a) higher number of points obtained in the matches among the teams in question;
b) superior goal difference in the matches among the teams in question (if more
than two teams finish equal on points);
c) higher number of goals scored in the matches among the teams in question (if
more than two teams finish equal on points);
d) superior goal difference in all the group matches;
e) higher number of goals scored in all the group matches;
f) position in the UEFA national team coefficient ranking system (see Annex I,
paragraph 1.2.2);
g) fair play conduct of the teams (final tournament);
h) drawing of lots.
8.08 If two teams which have the same number of points, the same number of goals
scored and conceded play their last group match against each other and are still
equal at the end of that match, the ranking of the two teams in question is
determined by kicks from the penalty mark (Article 16), provided no other teams
within the group have the same number of points on completion of all group
matches. Should more than two teams have the same number of points, the criteria
listed under paragraph 8.07 apply.


Now assume that you are only aware of the match outcomes, i.e. how teams are assigned to the four groups, who have beaten who by what scores, and at last, who have qualified the quarter finals. You are asked to deduce the underlying rules and not allowed to refer to the above 8+1 rules as the standard answer, like a scientist looking for natural rules based on a data set in one or a few experiments. You don't even know the basic rule that 'higher scores are better' when starting off, although you can easily assume it as your hypothesis at the beginning. How confident are you to be able to infer all the 8+1 rules?

I haven't tried this and I believe it's really a hard task.  

If the relatively rare cases didn't happen in your observation when two or three teams shared identical points, goal numbers, and yellow/red number, of course you won't be able to infer the existence of the relevant rules as they had no chance to apply.

So you need large data sets based on many experiments/observations, I mean, you need to watch a large number of matches, to make it possible that all the 8+1 rules find their use. Unfortunately this won't happen in reality as there are only 24 matches this year, and the rules in previous tournaments may have varied. But let's make it easier and assume we have 10,000+ matches to give enough data sets.

Then can you imagine there are 8+1 rules organized as such, and reveal them one by one? More likely you are confused why sometimes a higher score seems essential and why sometimes the win-lose relationship determines the outcome. We are so likely to be trapped but can hardly get one step away from a local mistake.

In fact such works of large-scale data research are proactively taking place in modern biology, where high-throughput post-genomic studies are carried out and astronomical data sets are being obtained. Yet the rules underlying the biological phenomena are (likely) far more complex than the 8+1 ranking rules here. It looks really a scary and impossible mission. Can the scientists make it?

More and more tools are being invented to to organize and analyze huge data sets, and to make interpretation based on them. I don't expect we can find the ultimate rules within a few years, but even a small discovery as a side product of the research may be helpful to solve some pf the realistic problems.

Personally I think a scientist has to beware what a 8+1 rule may look like and how it could be tested before they invent any new tools to deal with data. We need to establish more complex logic before proposing any new hypothesis to be tested.

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