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. In mathematics, this is known as a 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.

By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an evaluation 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.

Examples of ranking

• In many sports, individuals or teams are given rankings, generally by the sport's governing body
• In football (soccer)n national teams are ranked in the FIFA World Rankings and, unofficially, in the World Football Elo Ratings.
• In the Olympic Games, each member country (NOC) is ranked based upon gold, silver and bronze medal counts in the Olympic medal rankings.
• In snooker, players are ranked using the Snooker world rankings
• In ice hockey, national teams are ranked in the IIHF World Ranking
• In golf, the top male golfers are ranked using the Official World Golf Rankings
• In relation to credit standing, the ranking of a security refers to where that particular security would stand in a wind up of the issuing company, i.e., its seniority in the company's capital structure. For instance, capital notes are subordinated securities; they would rank behind senior debt in a wind up. In other words the holders of senior debt would be paid out before subordinated debt holders received any funds.
• Search engines rank web pages depending on their relevance to a user's query. See HITS algorithm, PageRank, TrustRank.
• In video gaming, players may be given a ranking. To "rank up" is to achieve a higher ranking relative to other players, especially with strategies that do not depend on the player's skill.
• The TrueSkill ranking system is a skill based ranking system for Xbox Live developed at Microsoft Research
• A bibliogram ranks common noun phrases in a piece of text.
• In language, the status of an item (usually through what is known as "downranking" or "rank-shifting") in relation to the uppermost rank in a clause; for example, in the sentence "I want to eat the cake you made today", "eat" is on the uppermost rank, but "made" is downranked as part of the nominal group "the cake you made today"; this nominal group behaves as though it were a single noun (i.e., I want to eat it), and thus the verb within it ("made") is ranked differently from "eat".