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Duckworth–Lewis–Stern method
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===During team 1's innings=== ====Strategy for team 1==== During Team 1's innings, the target score calculations (as described above), have not yet been made. The objective of the team batting first is to maximise the target score which will be calculated for the team batting second, which (in the Professional Edition) will be determined by the formula: <math>\text{Team 2's par score }=\text{ Team 1's score} \times \frac{\text{Team 2's resources}}{\text{Team 1's resources}}.</math> For these three terms: *'''Team 1's score''': Team 1 will always increase Team 2's target by increasing their own score. *At the start of Team 2's innings, '''Team 2's resources''' will be 10 wickets and the number of overs available, and Team 1 cannot affect this. *'''Team 1's resources''' are given by: <!--<div style="background: white; border: 1px solid rgb(153, 153, 153); padding: 2px;">--> <div style="background: white; border: 2px solid rgb(0, 255, 0); padding: 2px;"> {| |- |Total resources available = 100% − Resources lost by 1st interruption − Resources lost by 2nd interruption − Resources lost by 3rd interruption − ... |} </div> If there will not be any future interruptions to Team 1's innings, then the amount of resource available to them is now fixed (whether there have been interruptions so far or not), so the only thing Team 1 can do to increase Team 2's target is increase their own score, ignoring how many wickets they lose (as in a normal unaffected match). However, if there will be future interruptions to Team 1's innings, then an alternative strategy to scoring more runs is minimising the amount of resource they use before the coming interruption (i.e. preserving wickets). While the best overall strategy is obviously to both score more runs ''and'' preserve resources, if a choice has to be made between the two, sometimes preserving wickets at the expense of scoring runs ('conservative' batting) is a more effective way of increasing Team 2's target, and sometimes the reverse ('aggressive' batting) is true. {| class="wikitable" style="float: right; margin: 1em 1em 1em 1em; text-align:center; width:25%;" |+ Percentage total resources remaining reference table (D/L Standard Edition)<ref name="DLMethod"/> |- ! rowspan="2" style="background: #ffdead;" | Overs remaining ! colspan="5" style="background: #ffdead;" | Wickets in hand |- | '''10''' || '''8''' || '''6''' || '''4''' || '''2''' |- | '''50''' || 100.0 || 85.1 || 62.7 || 34.9 || 11.9 |- | '''40''' || style="background: #ACE1AF;" | 89.3 || 77.8 || 59.5 || 34.6 || 11.9 |- | '''30''' || 75.1 || 67.3 || 54.1 || 33.6 || 11.9 |- | '''20''' || 56.6 || 52.4 || 44.6 || 30.8 || 11.9 |- | '''10''' || 32.1 || 30.8 || 28.3 || style="background: #ACE1AF;" | 22.8 || style="background: #ACE1AF;" | 11.4 |- | '''5''' || 17.2 || 16.8 || 16.1 || 14.3 || 9.4 |} For example, suppose Team 1 has been batting without interruptions, but thinks the innings will be cut short at 40 overs, i.e. with 10 overs left. (Then Team 2 will have 40 overs to bat, so Team 2's resource will be 89.3%.) Team 1 thinks by batting conservatively it can reach 200–6, or by batting aggressively it can reach 220–8: {| class="wikitable" |- | style="background: #ffdead;" | Batting strategy | align="center" style="background: #ffdead;" | Conservative | align="center" style="background: #ffdead;" | Aggressive |- | Runs Team 1 thinks it can score | align="center" | 200 | align="center" | 220 |- | Wickets Team 1 thinks it will have in hand | align="center" | 4 | align="center" | 2 |- | Resource remaining to Team 1 at cut-off | align="center" | 22.8% | align="center" | 11.4% |- | Resource used by Team 1 | align="center" | 100% − 22.8% = 77.2% | align="center" | 100% − 11.4% = 88.6% |- | Team 2's par score | align="center" style="background: #ffdead;" | 200 + 250 x (89.3% - 77.2%) <br />= '''230.25 runs''' | align="center" | 220 + 250 x (89.3% - 88.6%) <br />= '''221.75 runs''' |} Therefore, in this case, the conservative strategy achieves a higher target for Team 2. {| class="wikitable" style="float: right; margin: 1em 1em 1em 1em; text-align:center; width:25%;" |+ Percentage total resources remaining reference table (D/L Standard Edition)<ref name="DLMethod"/> |- ! rowspan="2" style="background: #ffdead;" | Overs remaining ! colspan="5" style="background: #ffdead;" | Wickets in hand |- | '''10''' || '''8''' || '''6''' || '''4''' || '''2''' |- | '''50''' || 100.0 || 85.1 || 62.7 || 34.9 || 11.9 |- | '''40''' || style="background: #ACE1AF;" | 89.3 || 77.8 || 59.5 || 34.6 || 11.9 |- | '''30''' || 75.1 || 67.3 || 54.1 || 33.6 || 11.9 |- | '''20''' || 56.6 || 52.4 || 44.6 || 30.8 || 11.9 |- | '''10''' || 32.1 || style="background: #ACE1AF;" | 30.8 || style="background: #ACE1AF;" | 28.3 || 22.8 || 11.4 |- | '''5''' || 17.2 || 16.8 || 16.1 || 14.3 || 9.4 |} However, suppose instead that the difference between the two strategies is scoring 200–2 or 220–4: {| class="wikitable" |- | style="background: #ffdead;" | Batting strategy | align="center" style="background: #ffdead;" | Conservative | align="center" style="background: #ffdead;" | Aggressive |- | Runs Team 1 thinks it can score | align="center" | 200 | align="center" | 220 |- | Wickets Team 1 thinks it will have in hand | align="center" | 8 | align="center" | 6 |- | Resource remaining to Team 1 at cut-off | align="center" | 30.8% | align="center" | 28.3% |- | Resource used by Team 1 | align="center" | 100% − 30.8% = 69.2% | align="center" | 100% − 28.3% = 71.7% |- | Team 2's par score | align="center" | 200 + 250 x (89.3% - 69.2%) <br />= '''250.25 runs''' | align="center" style="background: #ffdead;" | 220 + 250 x (89.3% - 71.7%) <br />= '''264.00 runs''' |} In this case, the aggressive strategy is better. Therefore, the best batting strategy for Team 1 ahead of a coming interruption is not always the same, but varies with the facts of the match situation to date (runs scored, wickets lost, overs used, and whether there have been interruptions), and also with the opinions about what will happen with each strategy (how many further runs will be scored, further wickets will be lost, and further overs will be used? How likely are the coming interruptions, when will they happen, and how long will they last – will Team 1's innings be restarted?). This example shows just two possible batting strategies, but in reality there could be a range of others, e.g. 'neutral', 'semi-aggressive', 'super-aggressive', or [[timewasting]] to minimise the amount of resource used by slowing the over rate. Finding which strategy is the best can only be found by inputting the facts and one's opinions into the calculations and seeing what emerges. Of course, a chosen strategy may backfire. For example, if Team 1 chooses to bat conservatively, Team 2 may see this and decide to attack (rather than focus on saving runs), and Team 1 may both fail to score many more runs ''and'' lose wickets. If there have already been interruptions to Team 1's innings, the calculation of total resource they use will be more complicated than this example. ====Strategy for team 2==== During Team 1's innings, Team 2's objective is to minimise the target score they will be set. This is achieved by minimising Team 1's score, or (as above), if there will be future interruptions to Team 1's innings, alternatively by maximising the resource used by Team 1 (i.e. wickets lost or overs bowled) before that happens. Team 2 can vary their bowling strategy (between conservative and aggressive) to try to achieve either of these objectives, so this means doing the same calculations as above, inputting their opinions of future runs conceded, wickets taken and overs bowled in each bowling strategy, to see which one is best. Also, Team 2 can encourage Team 1 to bat particularly conservatively or aggressively (e.g. through [[Fielding (cricket)#Tactics of field placement|field settings]]).
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