Bomber this is from
here <hr>
<h1>An analysis of the Duckworth/Lewis System</h1> The Duckworth/Lewis system is the system now used to determine the winning score in rain-interrupted one day matches. It is superior to the previous rules that were used and, despite a number of comments to the contrary, is quite simple to apply. The system was updated in September 2002 to take account of the higher scoring in recent times. For example, the average 50 over score has been increased from 225 to 235. This page analyses the accuracy of the system, using 399 one day internationals played between 22 November 1998 and 11 April 2002. The over by over scores were collected for matches where the team did not have its maximum number of overs reduced due to interruptions by rain or due to slow over rates. For each over, we compare the final score against the expected score by Duckworth/Lewis. In the case of a team batting second achieving the winning target with balls to spare, a final score is estimated by applying the D/L system to the team's winning score. The D/L system converts the number of overs remaining and the number of wickets lost into a "resources remaining" figure. At the start of the innings, this is 100, but as overs are completed or wickets fall the "resources remaining" falls. The expected score is the current score plus 235 times the resources remaining divided by 100. The system assumes that the average innings score for an ODI is 235. The formula used by the D/L system is: Z(u, w) = Z<sub>0</sub>(w)[1 - exp{-b(w)u}] where Z(u, w) is the expected number of runs to be scored in u overs when w wickets have been lost. Z<sub>0</sub>(w) is the average total score if an unlimited number of overs were available and when w wickets have been lost. b(w) is a decay constant that varies with w, the number of wickets lost. Duckworth and Lewis do not list the values of the constants Z<sub>0</sub>(w) and b(w) due to commercial confidentiality. The following table lists values based on fitting the above formula to the actual over by over scores in the one-day internationals mentioned above. The values are calculated separately for the side batting first and the side batting second. The values for 9 wickets down are not listed as they don't seem to follow the above formula. For example, suppose that a team had lost 2 wickets after 10 overs. The table estimates that a team batting first would score 182 runs in the remainder of the innings. It estimates that the team batting second would score 178 more runs. For comparison, the D/L method estimates 183 more runs (the pre-2002 D/L method estimates 175 more runs). <table border=1> <tbody> <tr> <th class=Col1C></th> <th class=Col1C colspan=2>Team batting first</th> <th class=Col1C colspan=2>Team batting second</th></tr> <tr> <th class=Col1C>Wickets lost (w)</th> <th class=Col1C>Z<sub>0</sub>(w)</th> <th class=Col1C>b(w)</th> <th class=Col1C>Z<sub>0</sub>(w)</th> <th class=Col1C>b(w)</th></tr> <tr> <td class=Col1R>0</td> <td class=Col1R>313.66</td> <td class=Col1R>.028118</td> <td class=Col1R>399.61</td> <td class=Col1R>.016984</td></tr> <tr> <td class=Col1R>1</td> <td class=Col1R>260.79</td> <td class=Col1R>.035523</td> <td class=Col1R>471.81</td> <td class=Col1R>.012129</td></tr> <tr> <td class=Col1R>2</td> <td class=Col1R>225.01</td> <td class=Col1R>.041292</td> <td class=Col1R>437.88</td> <td class=Col1R>.013001</td></tr> <tr> <td class=Col1R>3</td> <td class=Col1R>170.71</td> <td class=Col1R>.056870</td> <td class=Col1R>265.40</td> <td class=Col1R>.023914</td></tr> <tr> <td class=Col1R>4</td> <td class=Col1R>155.30</td> <td class=Col1R>.059565</td> <td class=Col1R>160.64</td> <td class=Col1R>.044013</td></tr> <tr> <td class=Col1R>5</td> <td class=Col1R>117.66</td> <td class=Col1R>.073572</td> <td class=Col1R>128.93</td> <td class=Col1R>.048669</td></tr> <tr> <td class=Col1R>6</td> <td class=Col1R>87.029</td> <td class=Col1R>.095344</td> <td class=Col1R>121.38</td> <td class=Col1R>.046397</td></tr> <tr> <td class=Col1R>7</td> <td class=Col1R>55.706</td> <td class=Col1R>.15467</td> <td class=Col1R>45.653</td> <td class=Col1R>.15884</td></tr> <tr> <td class=Col1R>8</td> <td class=Col1R>31.470</td> <td class=Col1R>.30022</td> <td class=Col1R>23.521</td> <td class=Col1R>.25859</td></tr></tbody></table> The following table lists the number of runs difference between the D/L score and the actual score, the standard deviation and the number of innings that reached that number of overs. The table also includes the difference that would be obtained by using the pre-2002 D/L table. Rain interrupted matches will only be decided using Duckworth/Lewis if at least 25 overs have been completed. The table shows that if 25 or more overs are completed, the predicted D/L score was within four runs of the average score actually obtained for the team batting first. The discrepancy is greater for the second innings, but this may be due to using the results of matches back to 1998 when the average scores were lower than today. Note that in the first table entry we can see that the average innings by a team batting first was 234.0 runs (235 - 1.0) and the teams batting second averaged 226.4 runs (235 - 8.6). <hr> more:
here
I dont think I'll ever really get this whole system but if concensus says it's the way to go then so be it. But in saying that I'm still not convinced that after hitting a million the other night the Aussies should have lost if India scored bugger all in 25 overs. I realize the answers above but it just doesnt make sense.
