





Will Mathematics decide the Finalists Once Again?By Karthik K Ramamurthy & Sripriya V Narayanasamy4 July 1998 "Rain, Rain, Go Away! The Kiwis, Lankans & Indians want to play cricket today!" That may well have been the refrain of thousands of cricket fans as the raingods played spoilsport almost throughout the Singer Akai Nidahas tournament. As many as three matches were abandoned without a ball being bowled, and two were declared noresults since the minimum 25 overs for both teams could not be completed. The final League match of the tournament, between the home team Sri Lanka and the Kiwis is to be played tomorrow, July 5^{th}, 1998. The final matchup will read: Sri Lanka v. India, if this match too is washed out or abandoned. The points table would then read: Sri Lanka 7, India 6, New Zealand 5. If Sri Lanka win this match, they will meet the same opponent India in the final, as the points table would read: Sri Lanka 8, India 6, New Zealand 4. The only other possibility is for New Zealand to win this match. If they do, all three teams will end up with 6 points. With the factor of Nett Run Rate (NRR) coming into the picture, Mr. Mathematics will decide the finalist. The current Nett Run Rate position is as follows:
The computer was put through the drill again. It's mission: Calculate the various scenarios that will decide the finalists if New Zealand wins the match. After some intense wracking of its brains, the computer came up with its results. The following is a summary: If New Zealand win with a big margin (the definition of the term "big margin" is provided in the tables below), then, the finals will be played between New Zealand and India. This is because the Kiwis would then have improved their nettrunrate beyond Sri Lanka's (whose NRR would have deteriorated below New Zealand's). In any case, India's current NRR of + 0.320 will not be affected. If New Zealand win, but their margin of victory is not large enough, then the finals will be played between Sri Lanka and India. To summarize again, here is a table of the possibilities:
From the above, it is clear that, for all practical purposes, India is already in the final. The race, then, is between Sri Lanka and New Zealand. The following are the various mathematical scenarios and targets for New Zealand to reach the final. Since a rainshortened game is a distinct possibility, the scenarios have been calculated for 30, 40, and 50 over matches. Possibility 1: Sri Lanka bats first. Column 1 in each of the tables 1.1 to 1.3 represents Sri Lanka's score in the allotted number of overs (30, 40, or 50, as the case may be). Column 2 represents New Zealand's winning score (assumed to be one more than Sri Lanka's) Column 3 provides the "magic figure"  the maximum number of overs New Zealand can take to reach the winning target to nudge out Sri Lanka on better Nett Run Rate (NRR). Columns 4 and 5 in these tables represent the final NRRs of each of these teams. Note that neither of the NRRs come close to India's final NRR of + 0.31994! Table 1.1  30 over match:
Table 1.2  40 over match:
Table 1.3  50 over match:
Possibility 2: New Zealand bats first: Column 1 in each of the tables 2.1 to 2.3 represents New Zealand's score in the allotted number of overs (30, 40, or 50, as the case may be). Column 2 represents the minimum margin of victory for New Zealand. This too is a "magic figure" in the sense that a victory by this margin will ensure that New Zealand's NRR will then be better than Sri Lanka's, thereby paving the way for the Kiwis to reach the final. Column 3 represents the maximum number of runs the Kiwis can allow the Sri Lankans to score to ensure the margin of victory in column 2. Columns 4 and 5 in these tables represent the final NRRs of each of these teams. Note that neither of the NRRs come close to India's final NRR of + 0.31994!
Table 2.1  30 over match:
Table 2.2  40 over match:
Table 2.3  50 over match:



 
 
