Thursday, December 13, 2012

The King and the Vampire - 2: Cricketing Conundrum

This is the second episode in our 'King Vikram and the Vetaal' (Vampire) series, based on the simple but nice Indian story-telling format. Read the first K&V story here.

Dark was the night and weird the atmosphere. It rained from time to time. Eerie laughter of ghosts rose above the moaning of jackals. Flashes of lightning revealed fearful faces. But King Vikram did not swerve. He climbed the ancient tree once again and brought the corpse down. With the corpse lying astride on his shoulder, he began crossing the desolate cremation ground. "O King, it seems that you are generous in your appreciation for the analytics-based Duckworth-Lewis method used in weather-interrupted cricket matches. But it is better for you to know that there are situations where the D/L method invariably results in complaints, especially in T20 cricket. Let me cite an instance. Pay your attention to my narration. That might bring you some relief as you trudge along," said the vampire that possessed the corpse

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The cricketing vampire went on:
In a recent Australian T20 match, the D/L method did not just perform badly, it actually failed. Here's why:
Team-A batted first, played terribly and made just 69 runs.
Team-B chasing 70 for a win, got off to a flyer and scored 29 of 2 overs before rain interrupted the match. However, the D/L  revised target for Team-B only comes into play when at least 5 overs have been completed by both teams... Anyway,  here's what transpired, per cricinfo:
".. Under the Duckworth/Lewis method the target for the Stars (Team-B) was recalculated. The calculation, which itself has been disputed, ensured that the Stars required just six runs from five overs. Even though the Stars had already reached and exceeded the target, given the D/L target had changed when overs were lost play needed to resume to set the revised target. Play resumed at 7.52pm after a minor delay. Hilton Cartwright bowled one ball to Rob Quiney, who allowed it to pass through to the keeper, and the match was over as the Stars had reached their revised target after 2.1 overs."

So tell me King Vikram, What is the correct result? Did the Stars win because they achieved the revised target, or should the points be shared because the required five overs were not completed?  Answer me if you can. Should you keep mum though you may know the answers, your head would roll off your shoulders!"

King Vikram was silent for a while, and then spoke: "Vetaal, unlike the last time, this is a tough one, so first consider this counter-factual: 

The Stars continue to play for another 1.4 overs, and are bowled out for 29. If the revised target when they were 29/9 was 30, then Team-A (Scorchers) would have won the match. Therefore, even though the Stars were temporarily ahead of the revised target, that target is not static since the minimum overs were not completed. The D/L based revised target is computed based on two resource constraints, taking into account the runs to be scored and wickets lost. It can change over time and the Scorchers still had a theoretical chance, however small, of winning the match by taking wickets.
However, here's another situation. Suppose Team-B was 29/9 after 2 overs, and the revised 5-over D/L target was 52. Team-B gets to 57/9 in 4.5 overs, hitting the last ball for a six before rains come down and and stop the game permanently. In this case, the D/L target cannot increase further, given that Team-B is already 9-down. In this case, Team-A has zero chance of winning the match. Team-B should be declared the winner even though the minimum overs have not been bowled.

1. For the current game, the points have to shared. This answers your specific question.

2. If a match ends before the minimum overs are completed, the chasing team can be declared the winner only if they have achieved a score that equals or exceeds the highest of all possible revised D/L targets that can occur for the fixed number of overs possible. In this example, Team-B would have been declared the winner if they scored at least 52.

3. However, I suspect that the cricket council will simply enforce the minimum-over rule as a hard-constraint that must be satisfied before the match can be decided in favor of one team over the other.

No sooner had King Vikram concluded his answer than the vampire, along with the corpse, gave him the slip.

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The Vetaal apparently agreed with Vikram's answer, but do you? If not, explain why. There's no penalty for trying!

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