We at Rugby4Cast use the Elo rating system to maintain our own set of rankings which are used in our predictions algorithm, and to rate and compare club sides.
Elo is a method for calculating the relative skill levels of teams in matches and it is named after its creator Arpad Elo, a Hungarian-American physics professor, who invented it as a chess rating system.
The difference in the ratings between two teams serves as a predictor of the outcome of a match, with the difference in rating being the difference in expected score. Therefore, the expected score difference for a team rated 5 points higher than their opponent would be … you guessed it … 5 points.
After each game, points are transferred based on the actual outcome relative to the expectation. In the above scenario, if a team was expected to win by 5 but only won by 4, then the higher ranked team would lose points with the lower ranked team would gain the corresponding amount. The actual amount transferred is dependent on the k-factor (which can be thought of as a sort of ‘refresh rate’) so it takes a while for results to be fully reflected into the rankings, and a greater picture of team form emerges.
We have analysed all the previous matches to find the optimal k-factor for each league, as well as analysing home advantage to see what extra edge the home team should be given. For each league’s specific home advantage please see the individual event page.
Large discrepancies in expected results (say a team winning by 45 points, rather than 30, compared to a team winning by 6 rather than 2) can be quite difficult to normalise. Therefore certain results may lead to a larger rankings change than may actually be indicated by the match outcome.
World Rugby Rankings
World Rugby Rankings World Rugby maintain a set of rankings to judge international sides and their respective strength. International nations are ranked based on match results, with the most successful teams being ranked highest.
Rankings are based on the match outcome, with more significant matches being more heavily weighted to help reflect the current competitive state of a team. The ranking system was introduced the month before the 2003 Rugby World Cup, with the first new rankings issued on 8 September 2003, with England topping the first ever rankings table during their run to World Cup glory.
Unsurprisingly, since then New Zealand have been the most consistently ranked #1 team since the introduction of World Rankings, having held the top spot for more than 85 percent of the time during this period. South Africa and England are the only other sides that have ever held the top spot.
As new results come in, past successes or losses will fade and be superseded by the more recent results and their points gain or loss. Thus, it is thought that it will produce an accurate picture depicting the actual current strength and the rank of the nations.
Team ranking is calculated using an exchange system (zero sum game), in which sides receive points from each other on the basis of the match result – whatever one side gains, the other loses.
The exchanges are based on the match result, the rankings of each team, and the margin of victory, with an allowance for home advantage.
A full explanation with worked example is available here on the official World Rugby website, but essentially a range of up to 2 points can be exchanged in a match, the exact amount depending on the rankings of the two sides before the match.
Should the winning team be more than 10 ranking points ahead of the losing team before the match begins, the winning team will gain no ranking points from victory. They are deemed to be sufficiently far ahead that no points exchange is required to update the rankings. If the winning team is 10 ranking points behind, they will gain a maximum of 2 ranking points from a victory.
Should the difference in team rankings be less than 10 points, then the points exchange is calculated by interpolating between 0 and 2 based on the difference in team rankings. A few scenarios are demonstrated here:
- Winning team 10 or more ranking points ahead: 0 ranking points exchanged
- Winning team 5 ranking points ahead: 0.5 ranking points exchanged
- Team ranks equal: 1 ranking point exchanged
- Winning team 5 ranking points behind: 1.5 ranking points exchanged
- Winning team 10 or more ranking points behind: 2 ranking points exchanged
A few specific things to note
- Home advantage is deemed to be worth 4 ranking points, which is taken into the calculation in the difference in team rankings before the match starts. So if a team is 7 points ahead of another in ranking terms, they are deemed to be 11 points ahead if the match is played at home, and would therefore gain nothing from a victory.
- If the margin of victory is greater than 15 points, the points exchange is multiplied by 1.5, as that is deemed to be a ‘heavy’ win.
- In Rugby World Cup, all points exchanges are multiplied by 2, in order to reflect the importance of the event. This is why you will often see large points fluctuations in the World Cup. It is (apparently!) possible to climb to the top from the bottom (and vice versa) in fewer than 20 matches. As all matches are worth a net of 0 points for the two teams combined, there is no particular advantage to playing more matches. A rating will stay the same until the team plays again.
Whilst this is an excellent system for judging team strength, there are a few limitations (as there are in any ranking system).
It is impossible to gain points from losing a match which, whilst logical from one point of view, can be a little counterintuitive from another. Namely, it doesn’t account for the heroic 1 point loss by a much weaker team (heroic is a purely subjective measure, obviously).
For example, imagine Japan play New Zealand in Eden Park and perform incredibly, losing by just 1 point. They would gain no ranking points from that particular match, which might not be indicative of their current strength given that performance.
Under our alternative rankings for international sides, which uses the ELO system this limitation is accounted for.
Aside from the doubling of points exchanged for World Cup matches, there is no system to reflect game importance. Some matches played outside of the official international windows have much weaker teams and are little more than a warm up match, meaning the outcome may not be indicative of team strength, and points exchange is often meaningless.