{"id":260,"date":"2012-01-10T02:50:38","date_gmt":"2012-01-10T06:50:38","guid":{"rendered":"http:\/\/www.cricmetric.com\/blog\/?p=260"},"modified":"2012-01-10T02:50:38","modified_gmt":"2012-01-10T06:50:38","slug":"a-proposal-for-deciding-the-outcome-of-rain-terminated-matches","status":"publish","type":"post","link":"https:\/\/www.cricmetric.com\/blog\/2012\/01\/a-proposal-for-deciding-the-outcome-of-rain-terminated-matches\/","title":{"rendered":"A proposal for deciding the outcome of rain-terminated matches"},"content":{"rendered":"

The Duckworth-Lewis method<\/a> (henceforth referred to as the D\/L method) is a well-known method used for resetting targets, or deciding the outcome of rain-affected limited over Cricket games. Ever since the method was officially adopted by the International Cricket Council in 2001, the method has been dissected, analyzed and criticized by players, commentators, reporters and fans alike.<\/p>\n

\nBriefly speaking, in the D\/L method, both the balls remaining in the inning and the wickets in hand are viewed as “resources”. A table<\/a> lists the resources percentages remaining for a given number of balls left and the wickets in hand. Using this percentage, the target is accordingly reset if the number of overs in the games is to be reduced, or the outcome of the game decided if the game ends because of the rain interuption.<\/p>\n

\nAs the title of the article suggests, we focus exclusively on those matches where the game ends early because of rain. At present, the D\/L method is used to decide the outcome of the game only if both the teams have played at least 20 overs in a 50-over game (5 overs in a Twenty-20 game). If the score of the team batting second is greater than the par score, the team batting second wins, and if the score is below the par score then that team loses. The game is called a tie if the two scores are equal. <\/p>\n

\nMy main argument against the use of this method is that it uses an absolute, fixed par score to decide the outcome of the game. However, the D\/L method is a statistical model, and like any other statistical model, it has a margin of error. If the game has not been played to completion, how can we be absolutely sure about the eventual outcome of the game based on a single score given by the D\/L method?<\/p>\n

\nConsider for example, the one day game between Pakistan and West Indies<\/a> played on May 2, 2011 at Barbados. Pakistan batted first and scored 248 runs in 50 overs. Because of rain after the first innings, the target for West Indies was reset to 223 runs in 39 overs. However, the game was interrupted again near the end of the 30th over, at which point West Indies had scored 154 runs and still had 6 wickets in hand. The game ended right there, and West Indies was declared the winner, winning the game by 1(!) run.<\/p>\n

\nThis is indeed a very close victory margin for a game, whose result was decided by the D\/L method. One can argue that the game was evenly poised at this stage, and so the most fair outcome of the game was a tie. However, because the ICC believes that the D\/L method is a gold standard (it is clearly far from being one), therefore the right outcome of the match was West Indies as the winner. There is a good chance that 1 run is within the error margin of the D\/L model, and so the game should have been ruled a tie. Consider this: if this was a league match of the World Cup, then West Indies would have been awarded 2 valuable points and Pakistan 0 – which could eventually decide which team reaches the knock-out stage. That a statistical model like D\/L should lead to a quantum difference of 1 point awarded to the teams, is grossly unfair.<\/p>\n

\nA better way of deciding the outcome of the rain-terminated matches would be to declare the match a tie if the difference between the second inning score and the D\/L par score is not significant. A good margin for the 50 over game will be, say 10 runs. If the difference is more than 10 runs, then there is a good chance that the team ahead at this stage of the game would have eventually won the game. Otherwise the game is too close to call in favor of one team over the other.<\/p>\n

\nYet another bold proposal that I put forward for deciding the outcome of games in such situations is to use the win probability<\/a>. If the win probability of the batting team when the game ended is, say, between 0.25 and 0.75, then the game is a tie. If it is less than 0.25, then the batting team loses, and if it is more than 0.75, the batting team wins. In the above example, the win probability of West Indies at the time the match was called off was 0.68, therefore according to our method the outcome will be a tie. In fact, one can extrapolate the method for awarding points in rain-terminated matches in the league stage of a tournament. If this was, for example, a league match in the world cup, then West Indies would be awarded 1.36 points (twice the win probability), whereas Pakistan would be awarded 0.64 points, instead of splitting the points 1-1 to the two teams. In the end, this may not make a difference in which team eventually gets to the knock-out stage. However, it will be a more fair way of deciding the outcome of rain-terminated limited over games.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Duckworth-Lewis method (henceforth referred to as the D\/L method) is a well-known method used for resetting targets, or deciding the outcome of rain-affected limited over Cricket games. Ever since the method was officially adopted by the International Cricket Council in 2001, the method has been dissected, analyzed and criticized by players, commentators, reporters and… Read More »A proposal for deciding the outcome of rain-terminated matches<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-260","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/posts\/260","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/comments?post=260"}],"version-history":[{"count":11,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/posts\/260\/revisions"}],"predecessor-version":[{"id":271,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/posts\/260\/revisions\/271"}],"wp:attachment":[{"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/media?parent=260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/categories?post=260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cricmetric.com\/blog\/wp-json\/wp\/v2\/tags?post=260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}