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Turning the tables on this World Cup madness

By Stephen Lyon posted 25-11-2022 09:14

  

Living, as I do, with a football mad son, its difficult to avoid the men's football World Cup. I have kept up to date with the scores and watched the odd highlights, but for the first time, the other evening, sat down to watch a full 90 minutes. My mind started to wander; how many different final tables can there be in the group stages?

4 teams, 3 games each, 3 points for a win, 1 for a draw. What might the answer be? Lots of 4 and 3s, possibly 12 different final tables? 4x3x2x1 = 24 maybe?

What strategy should be employed? Let’s start with the first team winning all three games. The second team winning their other two games. The third team winning their last game. The fourth team not winning any. Let’s call this a (9,6,3,0) table. Other options starting with 9: (9,6,1,1) (9,4,4,0) and so I went on.

I now looked at tables starting with the winning team winning two games and drawing the third producing final tables such as (7,7,3,0); (7,7,1,1)…

I soon passed my prediction of 12 different tables. Tables starting with 6, then tables starting with 5 took me well past the 24 prediction. Then a couple of unusual tables – all four teams winning one game, drawing one game, and losing one game: (4,4,4,4) – all games being drawn (3,3,3,3). I am now well beyond 30 different possible tables.

How do I check I have got them all? Have I included any tables that are not possible? I looked back through group tables from previous World Cups, ticking off those I have got, adding others combinations I have missed. Some final tables appear quite frequently, others I am yet to find: has (5,5,5,0) ever happened?

Pictured at the top of this blog is some of my working out. Have I got all the possible combinations? Have I got any combinations that are impossible? There is your homework for next week! The game I was watching? Not sure what the final score was – or who was playing!

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Grem Nurker
29-03-2023 23:58

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Stephen Lyon
06-12-2022 09:33

This blog, by Rob Eastaway, explains how a proposed change of format in the next World Cup competition, will change the nature of the group stages.

Stephen Lyon
05-12-2022 16:33

So the group stages have come to an end. The final tables are as follows:

A (7 6 4 0)                   B (7 5 3 1)                   C (6 4 4 3)                   D (6 6 4 1)

E (6 4 4 3)                   F (7 5 4 0)                   G (6 6 4 1)                   H (6 4 4 3)

What do you notice?

 

The result (6 4 4 3) appears three times. Is there a reason for this? Is this combination, in some way more likely than other final tables?

A disappointment is that all these combinations have been seen before in world cups. Which made me wonder whether all my unseen combinations are possible.

Having convinced myself that (7 4 2 1) is not possible, convince yourself that the following are possible.

(9 2 2 2)           (9 3 3 3)           (7 6 2 1)          (6 4 4 2)           (6 5 2 2)

(5 5 5 0)           (5 5 2 2)           (5 4 4 3)           (3 3 3 3)

Have any of these combinations been seen in world cups or any other football competitions?

Steven Cooke
26-11-2022 06:42

Fun stuff!  The American Society for Quality (ASQ) often posted similar examples from members who applied Quality Management principles and statistics to home and leisure situations.
Whether you work them all out, or the math is too advanced for the age level, the example can use the thrill of the sports fan to understand the potential value of scientific studies and math.