{"id":144,"date":"2012-11-05T21:11:54","date_gmt":"2012-11-05T21:11:54","guid":{"rendered":"http:\/\/cricbol.com\/blog\/?p=144"},"modified":"2012-12-01T11:05:10","modified_gmt":"2012-12-01T11:05:10","slug":"cricket-team-standings-a-radical-approach","status":"publish","type":"post","link":"https:\/\/cricbol.com\/blog\/2012\/11\/05\/cricket-team-standings-a-radical-approach\/","title":{"rendered":"Cricket Team Standings: A radical approach"},"content":{"rendered":"

The current system of making standings table<\/span><\/strong><\/p>\n

We have at times witnessed a cricket team performing really well in a tournament and still bowing out owing to less number of total wins or may be due to a lower net run rate in case it is tied at the same number of points with another team. The traditional standings system allots 2 points for a win, 1 point for a tie and nil for a loss. Suppose there are 8 teams and after all the teams play against each other, the top four teams qualify for the semi finals. Thus, the total points and the net run rate are the usual basis of selection.<\/p>\n

Let us take a hypothetical situation. Taking the case of an ODI tournament and the team standings after the scheduled 28 matches (each team plays against everyone) is as given in the below table.<\/p>\n

 <\/p>\n

\"Cricket<\/a>
Cricket Team standings in ODI<\/figcaption><\/figure>\n

The need for a different system for calculating team standings<\/h3>\n

Based on the standings, top 4 teams qualify for the semis. However, if we look at the matches, Bangladesh had sprung up a major surprise and had beaten Australia, who in turn is the table topper.\u00a0 There is no importance given to the quality of the opponent whom a team defeats. Had it been the case, Bangladesh\u2019s position might have been better than the current standings.<\/p>\n

Hence, should there be a differentiation in the points a team scores based on opponent team\u2019s quality? A system that differentiates the performance of a team based on the quality of the opponent. The system may allot different credits for defeating a good quality team and different credits if a bad quality team is defeated.<\/p><\/blockquote>\n

But isn\u2019t quality a subjective term? How to measure the difficulty level for an opponent? Yes, quality is tough to analyze but we can figure out something from the stats.<\/p>\n

The new standings system we suggest<\/h3>\n

If we can have a system by which the teams are given points on the basis of teams they beat, the system can give better results. We thus give each team a score that is equal to the sum of the scores of the teams that they beat. The overall scores will look like these 8 equations:<\/p>\n

SL = P + B + NZ + WI
\nA = SL + I + P + NZ + WI + SA
\nI = SL + P + B + NZ + SA
\nP = B + NZ + WI
\nB = A
\nNZ = B + WI
\nWI = I + B
\nSA = SL + P + B + NZ + WI<\/p>\n

The list can be expressed as a matrix equation for the quantity x = (SL, A, I, P, B, NZ, WI, SA) in the form of A x = K x, where K is a constant and A is a 8×8 matrix of 0\u2019s and 1\u2019s denoting defeats and wins. The following table shows the matrix with \u20181\u2019 representing a win and \u20180\u2019 representing a loss, not assuming any ties.<\/p>\n

\"\"<\/a>
Cricket Results Matrix<\/figcaption><\/figure>\n

In order to solve such an equation, we have to find an Eigen-vector of the matrix. This will provide a relative score for each team. Thus calculating the 8×8 Eigen vector using an online matrix calculator (http:\/\/www.bluebit.gr\/matrix-calculator\/default.aspx<\/a>), we find the following result:<\/p>\n

X = (A, I, SA, SL, WI, B, P, NZ)<\/p>\n

= (0.617, 0.451, 0.395, 0.292, 0.236, 0.217, 0.216, 0.160)<\/p>\n

The ranking of the teams given by the magnitude of their scores shows a different story; though the top 4 teams remain the same but there is a change in the order. Moreover, Bangladesh on the basis of its victory over Australia rises to number 6.<\/p>\n

The following table compares the rankings:<\/p>\n

\"Ranking<\/a>
Ranking comparison<\/figcaption><\/figure>\n

Thus we can see that Bangladesh rose in rank owing to its victory over Australia. Pakistan went down a couple of places so as New Zealand since they won matches against lowly ranked (or not so good performing teams). Overall there is a radical difference in the standings.<\/p>\n

Google also uses a similar Page Rank algorithm which rates a webpage on the basis of its content, referring links etc. It creates a matrix of links that exists between various topics and then assigns a numerical value to each page based on the inbound and outbound links. Thus if a website has inbound links from a reputed website, its page rank increases. Have a look at the following image:<\/p>\n

 <\/p>\n

\"How<\/a>
How Google PageRank works<\/figcaption><\/figure>\n

Image courtesy: http:\/\/wikiknowledgee.com\/the-mathematics-and-operation-of-pagerank\/#<\/a><\/p>\n

A large number of pages are referencing to \u2018B\u2019, hence it has a high score of 38.4 and since \u2018B\u2019 is referencing to \u2018C\u2019, this provides \u2018C\u2019 a high score and thus a better page rank. The principle applies to the calculations in our case.<\/p>\n

Thus, the cricket advocates might closely look at this more rational approach to rank the teams? The new model will boost the weaker teams by ranking them higher in case they are able to defeat the better ranked teams. Sounds interesting!?<\/p>\n

PS: With inputs from \u2018100 essential things YOU DIDN\u2019T KNOW you didn\u2019t know about SPORT\u2019 by John D. Barrow<\/p>\n","protected":false},"excerpt":{"rendered":"

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