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Who will win the Rugby World Cup? Statistical predictions

16th September, 2015
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Dan Carter is in trouble. (AFP/Marty Melville)
Roar Guru
16th September, 2015
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8658 Reads

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 characterise uncertainty around these predictions.

In the following analysis, I use the rugbyvision.com algorithm to rate teams. This scheme is an Elo-type system specifically designed to represent international rugby games.

2015 RUGBY WORLD CUP LADDER

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 rugbyvision.com ratings employ a different system to that used for the official World Rugby ratings, so our rankings differ from the official ones.

The rugbyvision.com rankings and rating points for the 2015 World Cup qualifiers are displayed in in the table below.

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By design, the average rank across all teams is 100. New Zealand, South Africa and Australia are the top three teams. England are considered the strongest Northern Hemisphere team fourth followed by Ireland, Wales and France. Argentina, Scotland and Samoa round out the top 10.

Differences between Rugby Vision 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.

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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 with an algorithm that estimates the number of tries scored by each team, we can calculate the probability of teams reaching various stages of the 2015 World Cup.

Probabilities of winning the RWC for the main title contenders are shown in the figure below and detailed probabilities for each team and displayed in the following table.

According to these calculations, New Zealand will almost certainly qualify for the quarter finals, where they will likely play France, and there is a high probability (86.7%) that the All Blacks will qualify for the semi finals – there are no ‘ghosts’ from 1999 or 2007 lurking in these simulations!

New Zealand will likely play South Africa in the semi final, and their probability of making the final is 64.1%. The All Blacks will probably have to beat England in the final and have a 47.8% chance of winning the tournament. Here are the knock-out matchups assuming that the team with the most rating points (including points for home advantage) always wins.

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Despite their recent loss to France in Paris, England is the next most likely team to win the tournament with a 21.3% 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 9.9% 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).

Even though Australia are ranked above England, the Wallabies are expect to finish second in Pool A (due to England’s home advantage) and have a 71.3% chance of qualifying for the quarter finals, and an 8.4% chance of winning the Webb Ellis Cup.

Ireland have a 58.6% chance of making the semifinals, a 25.2% chance of making the final, and an 7.4% chance of winning the tournament. Ireland would likely have to beat England in a semi final 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 29.7% chance of qualifying for the quarter finals.

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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.

Join in the analysis and discussion of the World Cup predictions on our Facebook page and on Twitter by following @rugbyvision. Rugby Vision will also make live, minute-by-minute predictions for key World Cup games (see an example below).

About the author
Niven Winchester is an economist at the Massachusetts Institute of Technology and the founder of rugbyvision.com. He specialises in quantitative analysis of climate and energy policies. His interests in sports economics focus on ranking systems and improving rugby’s bonus point system. He has published widely in leading academic journals and is co-editor of the Journal of Global Economic Analysis. He has a PhD from the University of Nottingham and also studied at the Australian National University and the University of Otago. He supports the Highlanders and the All Blacks.

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