TOP 15 – Ngjyra dhe Kupa

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A ranking is a relationship between a set of items such that, for any two items, the first is either ‘ranked higher than’, ‘ranked lower than’ or ‘ranked equal to’ the second.[1] In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are the same in rank it is considered a tie.

By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria.[2] Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see.

Analysis of data obtained by ranking commonly requires non-parametric statistics.
It is not always possible to assign rankings uniquely. For example, in a race or competition two (or more) entrants might tie for a place in the ranking.[3] When computing an ordinal measurement, two (or more) of the quantities being ranked might measure equal. In these cases, one of the strategies shown below for assigning the rankings may be adopted. A common shorthand way to distinguish these ranking strategies is by the ranking numbers that would be produced for four items, with the first item ranked ahead of the second and third (which compare equal) which are both ranked ahead of the fourth. These names are also shown below.

Standard competition ranking (“1224” ranking)[edit]
In competition ranking, items that compare equal receive the same ranking number, and then a gap is left in the ranking numbers. The number of ranking numbers that are left out in this gap is one less than the number of items that compared equal. Equivalently, each item’s ranking number is 1 plus the number of items ranked above it. This ranking strategy is frequently adopted for competitions, as it means that if two (or more) competitors tie for a position in the ranking, the position of all those ranked below them is unaffected (i.e., a competitor only comes second if exactly one person scores better than them, third if exactly two people score better than them, fourth if exactly three people score better than them, etc.).

Thus if A ranks ahead of B and C (which compare equal) which are both ranked ahead of D, then A gets ranking number 1 (“first”), B gets ranking number 2 (“joint second”), C also gets ranking number 2 (“joint second”) and D gets ranking number 4 (“fourth”).

Modified competition ranking (“1334” ranking)[edit]
Sometimes, competition ranking is done by leaving the gaps in the ranking numbers before the sets of equal-ranking items (rather than after them as in standard competition ranking).[where?] The number of ranking numbers that are left out in this gap remains one less than the number of items that compared equal. Equivalently, each item’s ranking number is equal to the number of items ranked equal to it or above it. This ranking ensures that a competitor only comes second if they score higher than all but one of their opponents, third if they score higher than all but two of their opponents, etc.

Thus if A ranks ahead of B and C (which compare equal) which are both ranked head of D, then A gets ranking number 1 (“first”), B gets ranking number 3 (“joint third”), C also gets ranking number 3 (“joint third”) and D gets ranking number 4 (“fourth”). In this case, nobody would get ranking number 2 (“second”) and that would be left as a gap.

Dense ranking (“1223” ranking)[edit]
In dense ranking, items that compare equally receive the same ranking number, and the next item(s) receive the immediately following ranking number. Equivalently, each item’s ranking number is 1 plus the number of items ranked above it that are distinct with respect to the ranking order.

Thus if A ranks ahead of B and C (which compare equal) which are both ranked ahead of D, then A gets ranking number 1 (“first”), B gets ranking number 2 (“joint second”), C also gets ranking number 2 (“joint second”) and D gets ranking number 3 (“third”).

Ordinal ranking (“1234” ranking)[edit]
In ordinal ranking, all items receive distinct ordinal numbers, including items that compare equal. The assignment of distinct ordinal numbers to items that compare equal can be done at random, or arbitrarily, but it is generally preferable to use a system that is arbitrary but consistent, as this gives stable results if the ranking is done multiple times. An example of an arbitrary but consistent system would be to incorporate other attributes into the ranking order (such as alphabetical ordering of the competitor’s name) to ensure that no two items exactly match.

With this strategy, if A ranks ahead of B and C (which compare equal) which are both ranked ahea