LONDON: Excitement is mounting ahead of the Rugby World Cup, which kicks off on 18 September at Twickenham, when England take on Fiji.

Twenty teams will do battle for the Webb Ellis Cup, currently held by New Zealand, who remain the world’s number one team and are favourites to become the first side to retain the trophy.

The 38cm high cup is named after William Webb Ellis the Rugby schoolboy who, according to legend, first picked up the ball during a game of football and ran with it. Whether the story is true and the sport owes its existence to Webb Ellis is doubtful. Yet his name will forever be associated with the sport and its biggest prize, which was nicknamed Bill by the victorious Australia team of 1991.

The trophy is now in England, having toured the world from Argentina to Australia, from Fiji to France in the build-up to this year’s tournament, which is being hosted by England for the first time. In 1991 England’s hosting duties were shared with Frace, Wales, Scotland and Ireland, and while nine games were played in England in 1999, Wales were the official hosts.

This time around, 40 of the 48 games will take place in England, with eight in Wales. England and Wales may have collaborated off the field, but on it they will be at each other’s throats as they both find themselves in the ‘Group of Death’ in this year’s competition.

As things stand, Pool A at Rugby World Cup 2015 contains four of the world’s top ten teams. England are fourth in the world, with Wales ranked sixth. Between them is Australia who are also in Pool A, while Fiji, ranked ten in the world are also in the same pool. With only two teams progressing to the quarter finals, the competition is sure to be tough.

As Yogi Berra, once said: ‘It’s tough to make predictions, especially about the future’. Like most future events, it is impossible to know for certain who will win the 2015 Rugby World Cup, but we can estimate probabilities of various outcomes occurring. We do this by building a rating system for international rugby matches and using these ratings to estimate expected score margins (like who will win and by how much.) We can then characterize uncertainty around these predictions.

rankingIn the following analysis, I use the algorithm to rate teams. This scheme is an Elo-type system specifically designed to represent international rugby games. The Elo system, named after Arpad Elo, was originally invented to rank chess players and is now used in various other games and sports. In the Elo system, ratings points are based on past performances and differences in ratings points reflect relative strength. Our ratings employ a different system to that used for the official world rugby (formerly International Rugby Board) ratings, so our rankings differ from the official ones.
The rankings and rating points for the 2015 World Cup qualifiers are displayed in the table above.

By design, the average rank across all teams is 100. New Zealand and South Africa are, respectively, the number one and two ranked teams. The next tier of teams is relatively tightly bunched and includes Australia, England and Ireland, with Wales just behind this group. Despite France’s win of England on August 22, Les Bleus have only won five of their last 14 matches and are ranked seventh.

Differences between rating points can be used to predict the average score margin for games played at neutral venues. For example, in a match at a neutral venue, New Zealand would be expected to, on average, beat South Africa by 8.5 points (130.3 minus 121.8) points, or 9 points when rounded to the nearest whole point. Home advantage is estimated to be worth 4 points, so this amount is added to the home team’s rating if applicable. In the 2015 World Cup, England will play all of their games at home, and Wales will have home advantage in two pool matches.

Predicting game scores using ranking points and (when applicable) home advantage, provides an estimate of the ‘average’ margin in a game between two teams. As a weaker team will sometimes beat a stronger team, to get the full picture, we also need to know the distribution of scores around the predicted average. To see why this is important, consider our New Zealand versus South Africa example: If the score margin was always within plus or minus nine points of the predicted average, New Zealand would be expected to win all games between the two teams.

However, if the score margin sometimes deviated from the predicted score by more than plus or minus nine points, South Africa would be predicted to win some matches in which the score deviation went in its favour. This uncertainty is characterised by estimating the shape of the distribution of score margins around the predicted averages. It turns out that, at current rating points at a neutral venue, South Africa is expected to win 27% of matches against New Zealand. By combining team ratings and the distribution of score margins around the predicted averages, we can calculate the probability of teams reaching various stages of the 2015 World Cup.

According to these calculations, New Zealand will almost certainly qualify for the quarterfinals, where they will likely play France, and there is a high probability (85.5%) that the All Blacks will qualify for the semifinals – there are no ‘ghosts’ from 1999 or 2007 lurking in these simulations!

New Zealand will likely play South Africa in the semifinal, and their probability of making the final is 63.5%. The All Blacks will probably have to beat England in the final and have a 47.1% chance of winning the tournament.

Despite their recent loss to France in Paris, England is the next most likely team to win the tournament with a 21.8% chance of lifting the Webb Ellis Cup. Although England are seeded in the ‘pool of death’ and are fourth in our global rankings, if they win Pool A, they will likely avoid playing New Zealand or South Africa until the final. Additionally, when home advantage is added to England’s rating points, they are expected to, on average, beat all teams except New Zealand.

South Africa have the second highest probability of making the quarterfinals (behind New Zealand), but only have a 9.5% chance of winning the tournament. This is because, should they make the final, South Africa’s likely opponents in the knockout matches will be Australia, New Zealand and England (at Twickenham).

Ireland have a 62.1% chance of making the semifinals, a 27.7% chance of making the final, and an 9.2% chance of winning the tournament. Ireland would likely have to beat England in a semifinal and New Zealand in the final to win the tournament.

Of the teams that do not play in either the Rugby Championship or the Six Nations, Samoa is the most likely to progress past the pool stages, and has a 30.9% chance of  qualifying for the quarterfinals

So who will win the 2015 World Cup? New Zealand have a much higher probability of winning than any other team, but there is still more than a 50% chance that another team will be crowned champion. []

Here are the knock-out matchups assuming that the team with the most rating points (including points for home advantage) always wins.

mapBetting Odds
New Zealand 13/10
England 9/2
South Africa 11/2
Australia 8/1
Ireland 9/1
France 12/1
Wales 25/1
Argentina 66/1
Scotland 75/1
Samoa, Italy 500/1
Fiji, Japan 1000/1
Georgia, Canada, Tonga 2000/1
USA 3000/1
Uruguay, Romania, Namibia 5000/1