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.
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.
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.
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.
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.
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.
lesley trinder
Guest
How can England be considered stronger than Ireland! We won six nations two years in a row! and now they are out of Rugby World Cup! what have they won recently!!!
Geoffrey Potgieter
Guest
OK so redo the numbers if South Africa miraculously loose to Japan. Sorry did you say South Africa New Zealand Final? What and Australia soften New Zealand up going in? Madness.
James in NZ
Guest
Pardon being a bit late to the conversation but we're both currently on 86% wins Boks RWC win rate 86.2% P29 W25 L4 (2 Oz, 1 each Eng, NZ) ABs RWC win rate 86.0% P43 W37 L6 (2 each Oz, Fra, SA). Well at this point at least, SA will statistically leap ahead with wins from here with the smaller no. of games. So first one to drop a game will fall behind. At least if neither of us win Bill, we have this little side comp. Feeling confident that a SH team will do it this time though, just a matter of which one.
Harry Jones
Expert
Yep! 'South Africa’s likely opponents in the knockout matches will be Australia, New Zealand and England (at Twickenham).' That last word is the key. SA recent record at that ground is superb.
taylorman
Roar Guru
I would have thought one way to enhance the reality of the figures would be to somehow embed the actual results of the past into the equation. Each of the tournaments so far will have started with these types of ratings somewhere in the midst and could potentially be recreated by the data at the time and as we know, the actual outcomes did not necessarily reflect those with the highest %'s. By re-comparing the actuals of each tournament with the pre tournament numbers over the seven tournaments, plus perhaps weighting towards the later tournaments, the historical influence of each country to either do better or worse than its original predictions might be valid here as an additional weighting in terms of a prediction. For example, France I'm guessing have outperformed their expectations of each tournament so on that basis a positive % might be applied to their initial prediction. Say 105% . If applied against the global vision rating of 112.9 France instead get 118.5% and move from 7th to 6th on the table, ahead of Wales on 116. NZ on the other hand may end up with a weighting of 97% which would bring their score lower. And so on with every country, the table gets adjusted purely to take into account whether they perform better or worse than expected. Now history may have no influence at all but it might serve to add an element that simply takes into account those conversations we all have...'NZ might be favourites, but they don't always win', or, 'don't underestimate France' fans in a way get 'rewarded' or 'reminded' by their sides performances of the past.
Nobrain
Guest
Pumas lost in semi in 2007 and 1/4s n 2011, the intresting thing about it is that the teams that beat them went on to win ths RWC, SA and NZ .Ireland may have chance then.
Charging Rhino
Roar Guru
You are incorrect. 1999. Jerry... whatever makes you feel better ;-)
I am a bit of a stats geek, so I love these kinds of statistical analysis. Good work.Niven.
Squirrel
Roar Rookie
Boks will win it vs England final. Fiji to make semis. NZ will crack with a lot of injuries due to the age of their workhorses . Crash easily if not by France the semis.
Paul from Melbourne
Guest
Very interesting and original article. It would be interesting also to know the model behind the predictions. What is good about this compared to all other predictions is that it is updated as the tournament progresses and the model becomes more and more accurate. My own gut feeling is that All blacks' chances of winning the cup again is not as high as it is stated. Although it is not explicitly stated, you seem to imply that the ability of a team to win test matches outside the normal world cup window is the same as that in the world cup finals. I think the extra intensity in these matches do affect the outcomes. It would be good to treat ratings based on match results outside worldcup as prior rating and treat history match results within the worldcup, particularly the finals, as the actual experimental results to obtain some kind of posterior rating - a kind of Bayesian treatment.
dsat24
Ooh WBs to not get past the qtrs, doubt you'll get many Aussie day BBQ invites.
Jerry
Guest
There was also the 1999 "Who wants to kiss their sister the most" playoff for 3rd place. It's 1-1 in matches that count for anything.
austrartsua
Guest
2-1? I believe the record between NZ and SA stands at 1-1. 1995 final. 2003 QF.
Ralph
Roar Guru
Statistics are like accounting, they are only ever accurate in arrears. The trouble with that being, the longer you spend looking into the rear view mirror the more likely you are to crash in the near future. But it is very interesting to see how tight everything is; a single converted try the different between 2,3,4,5 and 6; and a single 3 point drop goal the match between SA, Aus, Eng and Ireland. Naturally, this suggests the home ground advantage (four points) is huge and alone catapults England into second rated. I hope the hospital cardiac wards are cleared out before the Cup starts, there is going to be a lot of broken hearts.
Charging Rhino
Roar Guru
Boks have only ever lost 4 games in RWC history over 5 World Cups. 2 of those losses were in 1 tournament in 2003 with an awful team. The other two were against Australia. They have a 2-1 win record over New Zealand in RWC's, but haven't played each other since the 2003 RWC so I guess that doesn't mean too much.... Boks to take the big prize!!! :-)
moa
Guest
What these stats DO show is the gulf in class between some of the so-called contenders---coupled with the evidence of how tournament play is a great leveller. All that is required to win a tournament is a dollop of luck and the resilience & durability to dodge bullets until you are last man standing.
kombiutedriver
Guest
Means nothing. Statistics and probability are only an indication not a definite outcome. What part does the human factor bring to paper?
Stray Gator
Roar Rookie
Well! THAT'S certainly put a dampener on things. Where's the cat whenever I need to kick something??
moa
Guest
Interesting how these results mirror intuitive predictions made by many of us at least 6 months ago.