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The Elephant RankingsAbout the System Click on one of the links below if you want to jump down the page: How does the System Work? How does the system work?It's very simple. The basic principle is that every time you play a match, your rating points will change, based on two main factors:
The way this works is that:
We can illustrate these principles with the 'Elephant Rating Table':
Looking at the table, if you win against weaker opposition your rating goes up +1, and if you win against stronger opposition, your rating goes up +5. The table above is just for illustration because, in practice, an opponent is not just 'weaker' or 'stronger' - life isn't that simple. They may be much weaker or much stronger. So we use a sliding scale, which varies for each sport. What counts as a 'win'? Any win at all, whether in extra time, or after a penalty shoot-out, or after a controversial refereeing or umpiring decision. Allowing for Home AdvantageThe Elephant Ranking System deals with home advantage by treating sides playing at home as if they are stronger than their current rating suggests. The effect of this is that home sides pick up fewer points for winning, and give away more points for losing. The net result is that home advantage is cancelled out. We have thousands of results in our databases, and these help us to work out how much home advantage is worth - and this can change over time. Which Competitions Count?World Football Our research has indicated that 'friendly' matches are not good indicators of future performance. Rankings could be applied prior to the Second World War, but as there was a 12 year gap in the World Cup at that time, the ratings would probably need to be re-started in 1949 anyway. Test Cricket
This means that if two countries played a four match series, the rating points change for each side at the end of the series would be twice as big as if they played a two match series. Start RatingsYou have to start somewhere. Every country that joins the rankings is given a start rating. The Elephant Rankings work on the basis that new countries have to prove themselves - so they tend to start at or near the bottom of the rankings, in a consistent system for each sport. This is done without discrimination - there is no bias, whether your country is from a strong or a weak region of the world. World Football Test Cricket Margin of VictoryIt is a feature of the Elephant Ranking System that margin of victory is not normally treated as particularly significant. This is because our analysis indicates that who you beat, and who beats you, is a far better indicator of current strength - and future performance - than the margin by which you beat much weaker opposition. We have found, however, that it is of some significance, so:
Regional AdjustmentsIn some sports, countries or competitors can play the vast majority of their matches in particular regions of the world. This can lead to a lack of alignment between the ratings of countries from different Regions, as they hardly ever play each other. The Elephant Rankings deals with this - where necessary - by treating participating countries as being representatives of their Region during World Finals, and we apply an adjustment to the countries of each Region based on the performances of their representatives. Currently, we only do this in World Football, once every 4 years, following the World Cup Finals. We use a consistent, unbiased system, which generates relatively minor adjustments, but this does help us to keep up with changes in relative regional strength. Discussing the Merits of the SystemIn World Footbally, why don't we include Minor Tournaments and Friendly Matches?The Elephant Rankings attempt to present an accurate picture of current strength, based on matches that matter. In football, the fixture lists for top players are very crowded with important matches for club and country, and we don't believe that friendlies are taken very seriously. Are the Elephant Rankings Credible? They are - and we believe that we can prove it. As we've said above, we believe that a ranking system is about presenting an accurate picture of current strength, and this can be assessed using statistical measures. We have set up a testbed for each sport, using all available results, which allows us to measure the performance of the ranking system as we alter variables and weighting factors. This means that the Elephant Rankings are fully tested on historical data, and the values that we use are based on what works on historical results - noting trends over time.. Do World Cup winners always go top of the rankings?Only England, in 1966, and Argentina, in 1978, have won the football World Cup and not gone top of these rankings. There are three main reasons for this:
WIth the number of matches played, winning the Football World Cup these days will almost invariably put you at the top of the Elephant Rankings. The Cricket World Cup is not, of course, relevant here as it is not based on Test Cricket. The 1999 Copyright Statement for The Elephant Ranking System (ERS)1) Factual statements about the Elephant Ranking System The ERS is a calculation process that can display the relative strengths of competitors in any sport that is based on matches between pairs of competitors. The ERS can be used for individuals (e.g. boxing, chess) or teams (e.g. football, rugby). The calculation process uses the results (i.e. win, lose or draw) of matches to generate a numerical "rating value" for each competitor. These rating values reflect the underlying "strength" or "performance" of each competitor. The rating values calculated by the ERS allow teams to be placed in a sequence from strongest to weakest. This is the "ranking sequence". As further matches are played the ERS calculation process uses the new results to generate updated rating values and ranking sequences. 2) What we claim to have invented We claim the following elements of the ERS calculation process. Individually and together these elements are the source of the benefits described in section 3. a. Each competitor is given a ‘start rating’ when admitted to the system. b. Competitors’ ratings are then adjusted on the basis of match results, according to the following key principles.
c. The following table shows how these principles could be applied. Down the left are match results, across the top are relative ratings of opponents, and the figures are indicative of the pattern of rating adjustments that could be made.
From the table, if a competitor wins against opposition that is lower-rated then their rating will go up by just 1 point, whereas if they beat opposition that is higher-rated they will go up 5 points. A draw against same-rated opposition will result in no change to the rating of either competitor. The ERS principles can also be expressed as a mathematical function, of this general form:
Features of the form of this function are:
Note that the general shape of the function drawn is important, but the details are not. So, bend points can be altered, straight lines can be curved, the slope can be changed, whilst still retaining the essential invented features of the ERS process. d. Adjustments to the rating of competitors are calculated from each match result. These adjustments can be accumulated over fixed cycles of time or applied after every match. e. Additional optional calculations may be made on the following bases:
3) The benefits of the ERS process The benefits given to the ranking outputs are stability, attraction to true value, and independence from starting value. a. Stability: Playing a number of matches against mixed opposition, a competitor’s rating adjustments will tend to stabilise the rating to a central value. This can be considered the "true" strength of the competitor. b. Attraction to true value: If the "true" strength of a team varies over time, or is different from the calculated value due to freak match results, subsequent matches will tend to move the calculation rapidly towards the "true" value. And, due to stability, the value will then remain steady in the long term if the competitor’s strength really is steady. c. Independence from starting value: An effect of stability and attraction-to-true-value is that, when matches are played, the rating will rapidly move from the start value to the "true" value. Copyright ©1999 Mike Henry and Andy Newton .oOo.
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