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.