Archives for: October 2007

08/10/07

Permalink 01:01:24 am, by RayTomes Email , 1081 words, 206 views   English (NZ)
Categories: miscellaneous

May the Best Team Win?

It is the 2007 World Rugby Cup. The team play has occurred and then the quarterfinals. The semifinals are about to take place.

My home country of New Zealand is in deep shock and mourning as a result of the All Blacks being beaten by France in the quarterfinals by 20-18. The NZ coach Graham Henry resigned the next day. The inquiry (or is it inquisition) is about to start. But before that I want to look at the record of the All Blacks over the last few years and look at the issue of whether the best team is really expected to win. I am sure that people think that the best team is the one that won, but that isn't really true. Not winning does not mean that you have failed. In a game of rugby, one funny bounce of the ball can mean 7 points difference on the score board. There are usually a number of such events in a game. Anyway, first the facts:

1. Over the last 3 years New Zealand has indisputably been the best team and the IRB ranked them as number one team. They have a better than 50% result against every other team they have played.

2. My own analysis is based on all International Rugby Board games between countries from 16th April 2005 and 1st September 2007 determines a points ranking for each team so that if you want the expected winning margin then you take the difference between the points for the two teams. For example, from the table if NZ plays Australia the expected margin is the difference between NZs 79 and Australia's 70 or 9 points in NZ's favour. In that period NZ met Australia 5 times and the average margin was 8 points to Australia, so you can see that it works OK. Of course one of those games was a win to Australia and 4 to NZ.

New Zealand 79
Australia 70
South Africa 65
Ireland 61
France 57
Argentina 54
Italy 50
England 50
Scotland 48
Samoa 46
Wales 46
Fiji 34
Canada 27
Tonga 25
Japan 13
Romania 8
United States 3
...
India -124

2. Rugby balls are not round. This means that when a team kicks up and attackers and defenders are chasing the ball over the try line to dive on it there is every chance that someone gets a lucky bounce (unlucky for the other team). There are many other chance events in a game of rugby, such as a referee not blowing the whistle for a forward pass (we will leave that particular matter rest there, simply mentioning that such a thing did happen in the game between France and NZ and it did in fact decide the game). Anyway, for all these reasons the expected result is not really expected, but rather we expect some result in the general vicinity of that margin. A statistician will say that there is scatter with standard deviation of about 16 points about the expected result. A result will be outside one standard deviation about one third of the time. It will be outside two standard deviations about 5% of the time.

3. If a team such as NZ meets a team such as Australia and the difference between them is expected to be just 9 points with a standard deviation, then a statistician can tell you that there is about a 30% chance that Australia will win. In the previous 5 games that would mean we would have expected 1.5 games to go to Australia and 1 did so that is no big surprise. If NZ plays France then there is just a 10% chance of an upset and if they play South Africa, then a 20% chance.

4. Having reached the quarter-finals of the 2007 IRB World Cup of Rugby, it looked like New Zealand would be needing to beat France, Australia and South Africa to be the cup winners. With the chances of winning based on pre-cup match results that meant that New Zealand had pretty much an exact 50% chance of winning the cup. So there is a full 50% chance that the best team will not win. In past cups where the dominance of NZ was not so great the chances of them winning was generally more like 30% to 40%. So over 6 world cups we would have expected NZ to win 2 or 3 of them but they have only won one. They would very likely have won another if almost the whole team hadn't been suffering from food poisoning in South Africa.

5. It is worth noting that although NZ was expected to beat France by 22 points on average, in their previous encounter they beat them 61-10 or by 51 points. That was 29 more points than expected and the quarter final result was 24 points less than expected. That is the nature of sports results.

6. Graham Henry has been a really great coach for the All Blacks. His policy of rotating players has not been proved wrong by one loss for the team. It is sensible to look at the entire record to assess the value of his coaching and his method. It stands up as second to none. It is a tough result that NZ exited the cup so early and Graham took it on the chin like the man that he is. He has resigned and no doubt the public of NZ will want him gone and a new coach. There are others that are certainly capable, but if the NZ Rugby Union were sensible, they would look at his methods and keep as many as they can.

7. In the 7 world cups up to and including this one, New Zealand have scored the most points and the most tries in all but one of them. This shows that they have clearly been the best team pretty consistently. If anyone can name the year and the team that took that honour off them in one cup then they are good to have in your side in a rugby trivia contest. It totally surprised me.

8. If you really wanted the best team to have the best chance of winning, then you wouldn't have pool play followed by a knockout. Rather you would have section play with maybe three divisions of 6 to 8 teams and a round robin system in each section. There were 20 teams in the cup, so that would make 3 sections of about 7 teams each. That would mean 6 games played against teams of similar strength, no more games than the present tournament, just missing out the mismatches and getting to the meaningful games more quickly. The bottom two teams could be demoted each year and top one promoted with one extra place decided on best results between tournaments or something like that.

Just Thinking

From time to time I have a rave about something. I write letters to the NZ Listener and the NZ Herald but they never publish them. Does that make me a subversive? Probably not, but it seems to me that people with very dim thoughts get given lots of free air while useful thoughts often get ignored. OK, you can ignore the rest of this now ...

Well, these thoughts are about social, political, economic and environmental issues that affect us all, even though most people don't pay much attention to them.

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