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Will Mathematics decide the Finalists Once Again?

By Karthik K Ramamurthy & Sripriya V Narayanasamy


4 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 rain-gods 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 no-results 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 5th, 1998.

The final match-up 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:

Played

Won

Lost

No result

Points

For

Against

NRR

Sri Lanka

5

2

1

2

6

615 / 126

609 / 129.4

0.18340

India

6

1

1

4

6

409 / 79.4

414 / 86

0.31994

New Zealand

5

0

1

4

4

200 / 50

201 / 40

-1.02500

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 nett-run-rate 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:

Result

Implication

The Match is washed off or abandoned

Points: SL 7, IND 6, NZ 5. Finalists: India & Sri Lanka

Sri Lanka win

Points: SL 8, IND 6, NZ 4. Finalists: India, Sri Lanka

New Zealand win, and by a "big margin". For mathematical definitions of "big margin", see tables below.

Points (in order of NRR): IND 6, NZ 6, SL 6. Finalists: India & Sri Lanka

New Zealand win, but not by a "big enough margin". For mathematical definitions of "big margin", see tables below.

Points (in order of NRR): IND 6, SL 6, NZ 6. Finalists: India & Sri Lanka

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 rain-shortened 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:

SL Score

NZ Score

NZ Overs

SL NRR

NZ NRR

up to 161

162

21.4

-0.12034234

-0.12028927

up to 345

346

21.3

-0.16368277

-0.16363636

Table 1.2 - 40 over match:

SL Score

NZ Score

NZ Overs

SL NRR

NZ NRR

up to 142

143

31.5

-0.09611443

-0.09603690

up to 307

308

31.4

-0.12965451

-0.12961723

Table 1.3 - 50 over match:

SL Score

NZ Score

NZ Overs

SL NRR

NZ NRR

up to 107

108

42.00

-0.07442549

-0.07439614

up to 250

251

41.83

-0.09990102

-0.09986206

up to 536

537

41.67

-0.14892891

-0.14891813

 

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:

NZ scores in the range

NZ should win by at least

Sri Lanka scores not more than

SL NRR

NZ NRR

90 - 93

33

57

-0.07017734

-0.06071429

94 - 104

33

61

-0.06958850

-0.06785714

105 - 115

34

71

-0.07437945

-0.07321429

116 - 126

35

81

-0.07917040

-0.07857143

127 - 136

36

91

-0.08396135

-0.08392857

137 - 147

37

100

-0.08889951

-0.08750000

148 - 158

38

110

-0.09369046

-0.09285714

159 - 168

39

120

-0.09848141

-0.09821429

169 - 179

40

129

-0.10341957

-0.10178571

180 - 190

41

139

-0.10821052

-0.10714286

191 - 200

42

149

-0.11300147

-0.11250000

201 - 211

43

158

-0.11793963

-0.11607143

212 - 222

44

168

-0.12273058

-0.12142857

223 - 233

45

178

-0.12752153

-0.12678571

234 - 243

46

188

-0.13231248

-0.13214286

244 - 254

47

197

-0.13725064

-0.13571429

255 - 265

48

207

-0.14204159

-0.14107143

266 - 275

49

217

-0.14683254

-0.14642857

276 - 286

50

226

-0.15177070

-0.15000000

287 - 297

51

236

-0.15656165

-0.15535714

298+

52

246

-0.16135260

-0.16071429

Table 2.2 - 40 over match:

NZ scores in the range

NZ should win by at least

Sri Lanka scores not more than

SL NRR

NZ NRR

90 - 97

30

60

-0.05357696

-0.04027778

98 - 109

30

68

-0.05253546

-0.05138889

110 - 122

31

79

-0.05699730

-0.05555556

123 - 134

32

91

-0.06132895

-0.06111111

135 - 146

33

102

-0.06579079

-0.06527778

147 - 158

34

113

-0.07025263

-0.06944444

159 - 170

35

124

-0.07471448

-0.07361111

171 - 183

36

135

-0.07917632

-0.07777778

184 - 195

37

147

-0.08350797

-0.08333333

196 - 207

38

158

-0.08796981

-0.08750000

208 - 219

39

169

-0.09243165

-0.09166667

220 - 231

40

180

-0.09689349

-0.09583333

232 - 244

41

191

-0.10135534

-0.10000000

245 - 256

42

203

-0.10568699

-0.10555556

257 - 268

43

214

-0.11014883

-0.10972222

269 - 280

44

225

-0.11461067

-0.11388889

281 - 292

45

236

-0.11907251

-0.11805556

293+

46

247

-0.12353435

-0.12222222

 

Table 2.3 - 50 over match:

NZ scores in the range

NZ should win by at least

Sri Lanka scores not more than

SL NRR

NZ NRR

90 - 93

27

63

-0.03826458

-0.03333333

94 - 106

27

67

-0.03780076

-0.03777778

107 - 120

28

79

-0.04197514

-0.04111111

121 - 134

29

92

-0.04603357

-0.04555556

135 - 147

30

105

-0.05009200

-0.05000000

148 - 161

31

117

-0.05426638

-0.05333333

162 - 175

32

130

-0.05832481

-0.05777778

176 - 188

33

143

-0.06238323

-0.06222222

189 - 202

34

155

-0.06655762

-0.06555556

203 - 216

35

168

-0.07061604

-0.07000000

217 - 229

36

181

-0.07467447

-0.07444444

230 - 243

37

193

-0.07884886

-0.07777778

244 - 257

38

206

-0.08290728

-0.08222222

258 - 270

39

219

-0.08696571

-0.08666667

271 - 285

40

231

-0.09114009

-0.09000000

286 - 298

42

244

-0.10076438

-0.08444444

299 - 311

42

257

-0.09925695

-0.09888889

312 - 325

43

269

-0.10343133

-0.10222222

326 - 339

44

282

-0.10748976

-0.10666667

340 - 353

45

295

-0.11154819

-0.11111111

354+

46

308

-0.11560661

-0.11555556

karthik_kumar@hotmail.com



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Date-stamped : 05 Jul1998 - 02:30