Monday, June 19, 2006

Elementary (Arithmetic), My Dear Watson

Is what it will take to see the US into the next round now.

To get down to brass tacks, we must beat Ghana, and one of the following things must happen (in order of descending likelihood):

  1. Italy beat Czech, or

  2. Czech beat Italy by at least three goals, and we beat Ghana by at least three goals, or

  3. Czech and Italy draw, and we beat Ghana by at least six goals.

In the former case, the final Group E table sees Italy well clear at the top, with seven points, followed by the US, with four points, and Czech and Ghana with three. Easy to see what happens here: Italy and the US go through as the top two finishers in the group.

In the second case, we get into the somewhat arcane magick of goal differential. Which is actually not that arcane, as my example will show. Here's what happens:

  • Czech beat Italy 3-0

  • US beat Ghana 3-0

This leaves Czech clear at the top of the group with six points, but Italy and the US tied in second place with four points each. How to break the tie? Simple: just add up all of the goals scored for and against both teams. Before the final match, Italy had three goals for and one against, a differential of +2, while the US had one goal for and four against, for a total of -3. After the final, add no goals to Italy's differential and subtract three, leaving them with -1. But add three to the US's differential and subtract none, and you get +0. So the US moves on.

So the best strategy for the US is to beat Ghana by a metric shit-tonne of goals. That way, even if Italy cannot beat Czech, we still might be through on differential. Still, six goals more than Ghana scores is a tall order, so we'd better all don our Italy jerseys on Thursday.

Japan's road through to the next round is similar in terms of mathematics, but worlds different in terms of difficulty. For they must beat defending world champions Brazil , and they must do it by two more goals than the difference between Croatia and Australia if Croatia wins, or three more goals if Australia wins. Take a look at the current Group F standings to see what I mean.

If Japan can beat Brazil by four or five goals (since the slimmest margin of victory for either Australia or Croatia is one goal), they certainly deserve their place in the second round.

Chances of the US going through? 75%, since both the US and Italy are likely to win, thus making all my talk of goal differential a moot point.

Chances of Japan going through? 1%, since nobody beats Brazil by four or five goals.

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