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# Cricket mix optimization using heuristic framework after ensuring Markovian equilibrium

#### Abstract

International Cricket Council, in consultation with its member boards, prepares the Future Tours and Programme (FTP) which is an eight year long itinerary covering world championships in three formats of cricket, bilateral series and other tournaments. However, the FTP (2015–2023) had been criticized for its asymmetric itinerary and the point system for World Test championship and the FTP (2023–2031) is being criticized for including eight championships in limited formats and enhanced workload for players. Cricket mix standardization like marketing and product mix can work in homogeneous markets. This study derives three homogeneous markets of four teams each using hierarchical cluster analysis. For each market, it finds out the Markovian equilibrium analyzing cricket mix transition over past years. While the same can be used to derive the number of games per format per country, the study proposes a heuristic approach for fine tuning the same taking care of major stakeholders’ (e.g. Administrators, Players and Spectators) aspirations. Despite scores of criticisms and articles on the issue, there is hardly any scholastic contribution on game scheduling in the extant literature. This study thus is a pioneering effort in helping the policy makers to create a balance between cricket formats within each homogeneous market.

## 1Background

The game of cricket has over five hundred years of legacy with International Cricket Council (ICC) being the apex body regulating it since 1909. Currently there are three ICC recognized international formats namely, Test, ODI and T20I and 104 ICC affiliated member countries (International Cricket Council, n.d.). Out of these only twelve elite countries play all the three formats whereas rest can play limited over cricket i.e. ODI and T20I.

The underlying rules of all these 3 formats are same and have some similarities with the game of baseball. The game is played between two teams consisting of 11 players each where the batting team attempts to score as much runs as possible against a fielding team until the innings terminates. There is a role reversal between the batting and bowling teams in the next innings. A bowler on the fielding team “bowls” in groups of six deliveries referred to as overs. Overs are bowled alternatively from two ends of the pitch. At any point, two batsmen of the batting team occupy the two ends of the pitch, called the crease. The striker batsman tries to score runs by hitting the bowled ball with a bat. Runs are scored by running between the two stumps located at opposite ends of the pitch. Runs are counted by the number of times the striker and non-striker interchanges their ends and they can run anything between 0,.., 3. If the batsman can hit the ball out of the boundary, he gets a 4 and scores 6 runs for clearing the boundary without a bounce inside. A loss of a wicket, also called out can occur in various ways with the three most common being a) the ball is caught in midair after being hit by the batsman, b) the ball hits the stump located behind the batsman as he fails to hit it and c) a batsman is run-out if the fielding team breaks the stump before the any of the two batsmen reaches the corresponding crease. When a wicket is lost, a new batsman is introduced in the batting order. An innings terminates when all 10 wickets are lost (one batsman remains ‘not out’ as there is no one at the other end of the pitch). A test match is played over 5 consecutive days, each day permitting 90 overs to be bowled where each team bats for 2 innings alternatively. At the end, the team wins which scores more runs than the other team after successfully terminating their both the innings. However, there is a possibility of a draw if the other teams’ both innings are not terminated. On the contrary, the limited over versions e.g. ODI and T20I are played over one inning per side consisting of 50 overs and 20 overs respectively. Here also the team wins which scores more runs than the other side in the stipulated overs before being all out and by design, these formats ensure a ‘result’. This is a very brief introduction to the rules of the game; more detail on the rules (laws) of cricket can be found in http://www.lords.org or http://www.wisden.com.