World Cup: First-Round Statistics

So, how do things stand with the Uncertain Principles World Cup Contest at the end of the first round?

We have completed the first set of 16 group play games, and to this point, we have 6 ties. Extrapolating from that to the final result (because, of course, you always start with a linear extrapolation) you would expect a total of 24 tie games. The contest also asked for the total number of goals in the tournament, for use as a tiebreaker (since we can't make commenters do penalty kicks), and there have been 25 goals scored to date, which extrapolates to 100 for the final total.

In the naive linear extrapolation model, Mary Aileen and Rajesh look to be positioned very well to win a signed copy of How to Teach Physics to Your Dog. Of course, the linear extrapolation is probably hopelessly naive, though you can make arguments for either increases or decreases from this point on (increased scoring/ decreased ties: players are nervous in opening games, and will loosen up and score more in later games; decreased scoring/ increased ties: as you move into the elimination rounds, the teams will be more evenly matched, and less likely to score lots of goals). That's why they play the games...

Feel free to treat this as an Open Thread, those of you who care, particularly if you would like to explain Spain's surprising loss to Switzerland...


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Also, when we get to the elimination rounds there will be extra time, which should decrease the number of ties. In the 2002 world cup there were 14 ties in the group stages and only 2 in the elimination rounds, giving tie percentages of ~30% and 12.5% respectively. Having said that, in 2006 there were 11 ties in the group stages and 4 in the elimination rounds, meaning that the percentage of ties actually increased slightly from ~23% to 25%. Therefore, we can't really say anything useful about how the rate of ties varies, although with my meager estimate I have to hope 2010 is more like 2002 than 2006.