What are the detailed calculation steps involved in duckworth-lewis method?

The Duckworth–Lewis method (often written as D/L method) is a mathematical formulation designed to calculate the target score for the team batting second in a http://en.wikipedia.org/wiki/Limited_overs_cricketmatch  interrupted by weather or other circumstances. It is generally   accepted to be the most accurate method of setting a target score. The   D/L method was devised by two English statisticians, Frank http://en.wikipedia.org/wiki/Frank_Duckworth and Tony http://en.wikipedia.org/wiki/Tony_Lewis_%28mathematician%29. The  basic principle is that each team in a limited-overs match has  two  resources available with which to score runs: wickets remaining, and   overs to play. Where overs are lost, setting an adjusted target is not   as simple as to reduce the batting team's run target proportionally,   because a team batting second with ten wickets in hand and 25 overs to   play can be expected to play more aggressively than one with ten  wickets  and a full 50 overs, and can consequently achieve a higher run  rate.  The Duckworth–Lewis method is an attempt to set a statistically  fair  target for the second team's innings, based on the score achieved  by the  first team, taking their wickets lost and overs played into  account. Basis of the method The D/L method  works using the notion that teams have two resources  with which to make  as many runs as they can - these are the number of  overs they have  still to receive and the number of wickets they have in  hand.  From any  stage in their innings, their further run-scoring  capability depends  on both these two resources in combination.  The  single table gives the  percentage of these combined resources that  remain for any number of  overs left and wickets lost.  An extract of the  over-by-over table is given in Table 1.   (A ball-by-ball version of the  table has also been produced to enable  scorers to deal with instances  when play is interrupted mid-over.) When  a match is shortened after it has begun, the resources of one or  both  teams are depleted and the two teams usually have different  amounts of  resource for their innings.  In this case a revised target  must be set.  The  D/L method does this in accordance with the relative  run-scoring  resources available to the two teams.  If stoppages cause  the team  batting second (referred to here as Team 2) to have less  resources  available, as is more often than not the case, then their  target will  be revised downwards.  If, on the other hand, as often  happens when  Team 1's innings has been interrupted, the stoppages result  in Team 2  having more resources available, then their target is revised  upwards  to compensate for the extra resources they have at their  disposal. Table 1: Extract from the table of resource percentages remaining                                    Wickets lost                    Overs left             0             2            5            7             9                        60                    107.1        87.9        50.0       26.5         7.6                  50                    100.0        83.8        49.5       26.5         7.6                  40                      90.3        77.6        48.3       26.4         7.6                         30                      77.1        68.2        45.7       26.2         7.6                         25                      68.7        61.8        43.4       25.9         7.6                         20                      58.9        54.0        40.0       25.2         7.6                         10                      34.1        32.5        27.5       20.6         7.5                          5                       18.4       17.9         16.4       14.0         7.0 Reading the table The single table applies to all lengths of one-day matches from 60  overs-per-side downwards.  [In 1997 there was a separate table for all  lengths of matches from 60 to 10 overs per side.]  Because  50  overs-per-side matches are by far the most common, the resources  listed  in the table are expressed as percentages of those available at  the  start of a 50 over innings.  Thus when there are 50 overs  still to be  received and no wickets have been lost, the resource  percentage  available is 100%.  60 over innings start with a resource  percentage of  107.1% compared to a 50 over innings and 40 over innings  start with a  resource percentage of 90.3% compared to a 50 over  innings. In order to determine the correct resource percentage  the batting  side has remaining at any stage of an innings, the number  of overs left  must be identified.  This number of overs left, in  conjunction with the  number of wickets lost, is then used to read the  resource percentage  remaining from the table. For example,  suppose that after 20 out of 50 overs a team have lost 2  wickets.  They  have 30 overs left.  From the table you will see that  the resource  percentage remaining is 68.2%.  Suppose now that there is an  interruption in play and 10 overs are  lost from the innings of the  batting side.  When play can resume there  are only 20 overs left but  there are still, of course, 2 wickets down,  and the table now tells us  that the resource percentage remaining is  54.0%.  Thus the shortening  of the innings has caused the team to lose a  resource percentage of  68.2 - 54.0 = 14.2%. Having started with a resource percentage of  100% and lost 14.2%,  then if they complete their innings with no  further loss of overs, they  will have had a resource percentage  available for their innings of 100 -  14.2 = 85.8%. Applying the D/L method The  procedure for setting a revised target, which is the same for any   number of stoppages at any stage of the match, is as follows. For each team's innings (a) from the table note the resource percentage the team had available at the start of their innings; (b) using the table, calculate the resource percentage lost by each interruption; (c) hence calculate the resource percentage available. If  Team 2 have less resources available than Team 1, then  calculate the  ratio of the resources available to the two teams.  Team  2's revised  target is obtained by scaling down Team 1's score by this  ratio. If  Team 2 have more resources available than Team 1, then  calculate the  amount by which Team 2's resource percentage exceeds Team  1's.  Work  out this excess as a percentage of 225 [the average 50 over  score in  ECB matches and one-day internationals (ODIs)] and this gives  the extra  runs to add on to Team 1's score to give Team 2's target. Worked examples Example 1: Premature curtailment of Team 2's innings Team  1 have scored 250 runs from their 50 available overs and Team 2  lose 5  wickets in scoring 199 runs in 40 overs.  Play is then stopped by  the  weather, the rain refuses to relent and the match is abandoned.  A   decision on the winner is required. Team 1's innings:  this was uninterrupted, so the resource percentage available is100%. Team  2's innings:  resource % available at start of innings =  100%  After  40 overs Team 2 have 10 overs left and have lost 5 wickets. From table, resource % left at suspension of play   =  27.5% As play is abandoned all this remaining resource is lost. Hence resource % available for Team 2's innings = 100 - 27.5 = 72.5% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 72.5/100 Team 1 scored 250, so Team 2's 'target' is 250 x 72.5/100 = 181.25 As  there is to be no further play, the winner is decided according to   whether or not this target has been exceeded.  With 199 runs on the   board, they have exceeded their required target by 17.75 and so are   declared the winners by 18 runs. Note :  The  above result is quite fair as Team 2 were clearly  in a strong position  when play was stopped and would very likely have  gone on to win the  match if it hadn't rained.  Most other methods of  target revision in  use would, unfairly, make Team 1 the winners.  The  average run rate  method gives 201 to win, the http://static.espncricinfo.com/link_to_database/ABOUT_CRICKET/RAIN_RULES/ICC_RAIN_RULE gives 227 and the parabola method gives 226.  [Setting the target by the method of Discounted Total Runs - the http://static.espncricinfo.com/link_to_database/ABOUT_CRICKET/RAIN_RULES/AUS_RAIN_RULE - requires knowledge of the runs made by Team 1 from their most   productive overs but the target would almost certainly be no lower than   that required under average run rate and would probably be much higher   so that Team 2 would very probably lose by this method as well.] Example 2:  Interruption to Team 2's innings In  an ECB Axa Life (Sunday) League match Team 1 have scored 200  runs from  their 40 available overs and Team 2 lose 5 wickets in scoring  140 runs  in 30 overs.  Play is then suspended and 5 overs are lost.   What is  Team 2's revised target? Team 1's innings: At the start of 40 over innings resource percentage available  =90.3% Team 2's innings:  resource % available at start of 40 over innings = 90.3%  After 30 overs Team 2 have 10 overs left and have lost 5 wickets.   From table, resource % left at start of suspension  =  27.5%   5 overs are lost, so when play is resumed 5 overs are left.  From table, resource % left at resumption of play  =  16.4%    Hence resource % lost     = 27.5 - 16.4 =   11.1%   so resource % available for Team 2's innings = 90.3 - 11.1 = 79.2% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 79.2/90.3 Team  1 scored 200, so Team 2's target is 200 x 79.2/90.3 =175.42, or 176  to  win, and they require a further 36 runs from 5 overs with 5 wickets  in  hand. Example 3: Interruption to Team 1's innings In  an ODI, Team 1 have lost 2 wickets in scoring 100 runs in 25  overs  from an expected 50 when extended rain leads to Team 1's innings  being  terminated and Team 2's innings is also restricted to 25 overs.   What  is the target score for Team 2? Because of the different stages  of the teams' innings that their 25  overs are lost, they represent  different losses of resource.  Team 1  have lost 2 wickets and had 25  overs left when the rain arrived and so  from the table you will see  that the premature termination of their  innings has deprived them of  the 61.8% resource percentage they had  remaining.  Having started with  100% they have used 100 - 61.8 = 38.2%;  in other words they have had  only 38.2% resources available for their innings. Team  2 will also receive 25 overs.  With 25 overs left and no wicket  lost  you will see from the table that the resource percentage which they   have available (compared to a full 50 over innings) is 68.7%.    Team 2 thus have 68.7 - 38.2 = 30.5% greater resource than had Team 1   and so they are set a target which is 30.5% of 225, or 68.63, more runs than Team 1 scored. [225 is the average in 50 overs for ODIs] Team  2's revised target is therefore set at 168.63, or 169 to win in  25  overs, and the advantage to Team 2 from knowing in advance of the   reduction in their overs is neutralised. Note: Most  of the other target resetting methods in use make no allowance    for  this interruption. They set the target of 101 to win simply because  both    teams are to receive the same number of overs. This is clearly  an injustice    to Team 1 who were pacing their innings to last 50 overs  when it was curtailed,    whereas Team 2 knew in advance of the  reduction of their innings to 25 overs    and have been handed an unfair  advantage. D/L allows for this by setting Team    2 a higher target than the number of runs Team 1 actually scored, as    described above. Credits: http://www.espncricinfo.com/ci-icc/content/story/566696.html http://thequietus.com/articles/12817-the-duckworth-lewis-method-sticky-wickets-review http://en.wikipedia.org/wiki/Duckworth%E2%80%93Lewis_method http://static.espncricinfo.com/db/ABOUT_CRICKET/RAIN_RULES/DUCKWORTH_LEWIS.html

The following links should be helpful : http://static.espncricinfo.com/db/ABOUT_CRICKET/RAIN_RULES/DUCKWORTH_LEWIS_2001.html http://www.surreydowns.org/DL-Method.htm