# 2015 Rugby World Cup Outcome Probabilities

With the 2015 Rugby World Cup kicking off on the 18th of September, Rugby Vision – a website that uses mathematical optimization and statistical techniques to predict rugby outcomes – has estimated the outcome probabilities for the tournament. Their predictions include the probabilities of each team making the quarter-finals, semi-finals, final and winning the World Cup.

We take a look at these estimates to see if any value can be found in the 2015 Rugby World Cup futures markets.

### Methodology

Rugby Vision have described their methodology here. Basically, they use a similar approach to the Elo rating system, which was designed to determine the relative skill levels of chess players and chess software. With this system, ratings are calculated based on past performances, taking into account the strength of each opponent. Rugby Vision used this system to derive their own ratings for each rugby nation. Each country starts with a rating of 100, with the team’s rating then adjusted based on game results and the ratings of their opponents.

As of the 8th of September the top five teams’ ratings are:

New Zealand – 130.3
South Africa – 121.8
Australia – 121.0
England – 120.6
Ireland – 118.7

Differences between the ratings can are then used to predict the average winning margins for games played at neutral venues. For example, New Zealand would be expected to, on average, beat South Africa by 8.5 (130.3 minus 121.8) points. Rugby Vision have estimated home advantage to be worth 4 points, so 4 points are added to the home team’s rating where applicable. In the 2015 World Cup, England will play all of their games at home, while Wales will enjoy home advantage in two pool matches.

These ratings have been used to estimate the expected margin for each World Cup fixture. A weaker side will sometimes beat a stronger team, however, so Rugby Vision modeled a distribution of scores around each predicted margin. In many cases the distribution includes losses for the stronger team. For example, using the current ratings, South Africa is estimated to have a 27% chance of beating New Zealand on neutral ground.

By combining team ratings and the distributions of score margins around the predicted margins, Rugby Vision has estimated the probability of each team reaching the various stages of the 2015 World Cup. The results are displayed in the following section.

### Outcome Probabilities

Rugby Vision’s latest update was on the 30th of August, with the following knockout stage predictions and outcome probabilities.

Knockout Stage Predictions:

Outcome Probabilities:

WC denotes the winner of Group C, LD denotes the runner up of Group D, and so on.

Pool Country Quarter – finalist Semi – finalist Finalist Champion
A England 88.3% 71.1% 46.8% 22.2%
A Australia 70.3% 44.9% 21.0% 7.6%
A Waes 40.9% 20.0% 7.2% 2.2%
A Fiji 0.5% <0.1% <0.1% <0.1%
A Uruguay <0.1% <0.1% <0.1% <0.1%
B South Africa 99.4% 53.6% 18.9% 9.5%
B Scotland 69.2% 8.6% 1.9% 0.1%
B Samoa 27.0% 1.7% 0.3% <0.1%
B Japan 3.8% 0.1% <0.1% <0.1%
B USA 0.7% <0.1% <0.1% <0.1%
C New Zealand 99.9% 86.3% 65.4% 48.7%
C Argentina 85.5% 23.8% 4.7% 0.6%
C Tonga 13.9% 1.2% <0.1% <0.1%
C Georgia 0.7% <0.1% <0.1% <0.1%
C Namibia <0.1% <0.1% <0.1% <0.1%
D Ireland 99.0% 59.6% 25.4% 6.8%
D France 96.1% 29.0% 8.3% 2.3%
D Italy 4.7% 0.2% <0.1% <0.1%
D Canada 0.2% <0.1% <0.1% <0.1%
D Romania <0.1% <0.1% <0.1% <0.1%

Inversing these probabilities yields the following fair decimal odds:

Pool Country Quarter – finalist Semi – finalist Finalist Champion
C New Zealand 1.00 1.16 1.53 2.05
A England 1.13 1.41 2.14 4.50
B South Africa 1.01 1.87 5.29 10.53
A Australia 1.42 2.23 4.76 13.16
D Ireland 1.01 1.68 3.94 14.71
D France 1.04 3.45 12.05 43.48
A Wales 2.44 5.00 13.89 45.45
C Argentina 1.17 4.20 21.28 166.67
B Scotland 1.45 11.63 52.63 1000
B Samoa 3.70 58.82 333.33 1000
C Tonga 7.19 83.33 1000 1000
D Italy 21.28 500 1000 1000
B Japan 26.32 1000 1000 1000
B USA 142.86 1000 1000 1000
C Georiga 142.86 1000 1000 1000
A Fiji 200 1000 1000 1000
D Canaday 500 1000 1000 1000
A Uruguay 1000 1000 1000 1000
C Namibia 1000 1000 1000 1000
D Romania 1000 1000 1000 1000

### Current Odds

The next step is to compare these estimated fair odds to the current bookmaker odds.

Below are the current futures odds at the time of writing. Based on Rugby Vision’s algorithm, New Zealand look to be good value at 2.40, while England look to be good value at 6.13. Every other team represents poor value according to their analysis.

Team bet365 Betfair (5%) CrownBet Luxbet Ladbrokes Palmerbet Pinnacle Sports Sportsbet William Hill
New Zealand 2.25 2.27 2.30 2.20 2.30 2.40 2.27 2.30 2.40
England 4.50 6.13 5.00 6.00 5.00 5.00 5.91 5.00 5.00
South Africa 7.00 8.22 6.50 9.00 7.00 6.00 6.90 7.00 6.00
Australia 8.50 8.98 9.00 9.00 7.00 8.00 8.21 8.00 8.00
Ireland 10.00 10.50 9.00 7.00 9.00 9.00 8.89 10.00 9.00
Wales 21.00 23.80 19.00 17.00 23.00 17.00 15.90 26.00 17.00
France 17.00 18.58 17.00 19.00 17.00 21.00 12.75 15.00 21.00
Argentina 67.00 66.55 61.00 41.00 67.00 81.00   81.00 81.00
Scotland 201 162 126 201 126 201   201 201
Samoa 201 437 201 151 501 301   301 301
Fiji 1001 855 751 751 1001 501   1001 501
Italy 1001 950 1001 401 1001 501   1001 1001
Tonga 1001 950 1001 501 2001 501   1001 1001
Japan 1501 950 2001 1001 2001 501   1001 1501
Canada 2001 950 2001 1001 5001 501   2001 2001
USA 2001 950 2001 1001 5001 501   3001 2001
Georgia 2001 950 2501 1001 5001 501   2001 2501
Romania 5001 950 5001 1501 5001 501   5001 3001
Uruguay 5001 950 5001 2501 5001 501   5001 3001
Namibia 5001 950 5001 2501 5001 501   5001 3001

Click here to view the latest 2015 Rugby World Cup futures odds

Click here to view the latest 2015 Rugby World Cup fixture odds

### Caveats

The above analysis is excellent, however it can’t account for injuries leading up to and during the World Cup. For example, Wales have been rocked by the news that fullback Leigh Halfpenny ruptured his ACL on Saturday while halfback Rhys Webb picked up a foot injury. Both have been ruled out of the tournament. As it so happens, the algorithm feels bookmakers have overestimated Wales’ chances anyway, but the best approach to the World Cup, or any betting, is to supplement a model such as this with the latest injury news.

Backers of New Zealand should also be wary of the fact that if the tournament plays out as expected, the All Blacks would have to play their bogey team France in the quarter-finals. France are a mercurial side that often plays at its best against New Zealand. If Rugby Vision’s predictions prove to be correct, the All Blacks would have a tough run in the knockout stage, with England having a much smoother run. Much will come down to how Group A plays out, however.