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22 July 2008

 

COMPARING THE RECORD TEAM SCORES

 

By Charles Davis

 

When comparing the biggest team scores in Tests, the results can be a bit messy. This is because cricket often does not allow teams to carry their innings to completion, and big innings are often truncated by declaration or lack of time. We know for sure that the highest innings in a Test match is Sri Lanka’s 952 for 6 in 1997, but an interesting side question would ask if this is also the most ‘extraordinary’ score in Tests. For example, we know that the West Indies once made a score of 790 for 3. Where might such an innings have gone if it had continued? Can we compare it to Sri Lanka’s record?

 

While we can never know for sure, it is possible to make a statistical estimate. The approach is to look at the way that innings naturally progress over a wide range of scores. Of course, there is plenty of variation between innings (part of cricket’s appeal), but there are statistical patterns. A team that is, say, five wickets down, will on average add a certain number of runs if the innings is played to completion.

 

This average number of runs added depends also on the starting point. A team on, say, 50 for 5, can be expected to add fewer runs than a team on 500 for 5, before being bowled out. But there is a surprising result to be found here. Contrary to expectation, the number of runs at the starting point is not very important, with only a limited effect on the future progress of the innings. This is shown in the following table, calculated from the outcomes of all relevant Test innings, which gives the average number of runs added by teams with five wickets down, at different starting points.

 

Starting Score

Runs Added (average)

Projected All Out Score

50 for 5

85

135

100 for 5

91

191

200 for 5

99

299

300 for 5

114

414

400 for 5

116

516

500 for 5

114

614

600 for 5

110

710

 

What we see here is that above a certain level, in this case about 300 runs, there is very little change in the potential scoring of a team. This is surprising, but it probably comes down to the fact that a batsman coming in at a score of 600 for 5 is likely to bat in a riskier manner, or with less intensity, than one who comes in at 300 for 5. This would appear to balance out any advantage from tired bowling or benign conditions. This pattern is also seen at 6, 7, 8 or 9 wickets down.

 

It should be stressed that these runs added will often be theoretical in practice. For example,  the Projected All Out score for teams that reach 600 for 5 is 710, but in practice most such innings will not reach 700, often because of declarations. What the projected All Out score gives us is an estimate of where the innings was headed if the limits of time and tactics had been removed – its trajectory if you will.

 

With modern computer power, the result of this process is an “Innings Projector” that can give a projected estimate for any score. (In practice, it only works for innings with two or more wickets down.) Estimates for extreme innings must remain provisional because of the rarity of the situations, but the fact that trends are so stable, as illustrated by the first table, adds confidence to the results.

 

So what are the most extreme projected scores? Here is a list of the results:

Team

Opponent

Score

Projected Score

Sri Lanka

India

Colombo4 (RPS) 1997

952/6

1028

West Indies

Pakistan

Kingston, Jamaica 1958

790/3

996

England

Australia

The Oval 1938

903/7

951

Sri Lanka

Zimbabwe

Bulawayo (Queen's) 2004

713/3

919

Sri Lanka

South Africa

Colombo2 (SSC) 2006

756/5

866

West Indies

England

St John's, Antigua 2004

751/5

861

England

West Indies

Kingston, Jamaica 1930

849/10

849

New Zealand

Sri Lanka

Wellington 1991

671/4

821

India

Bangladesh

Dhaka (Mirpur) 2007

610/3

816

Australia

Zimbabwe

Perth (WACA) 2003

735/6

810

Pakistan

India

Lahore (Gaddafi) 1989

699/5

809

South Africa

Zimbabwe

Harare 2001

600/3

806

Australia

England

Lord's 1930

729/6

804

England

India

Lord's 1990

653/4

803

Australia

England

Leeds (Headingley) 1993

653/4

803

Australia

England

The Oval 2001

641/4

791

Australia

West Indies

Kingston, Jamaica 1955

758/8

788

Pakistan

India

Hyderabad (Pak) 1983

581/3

787

India

Pakistan

Multan 2004

675/5

785

Australia

England

Lord's 1993

632/4

782

England

South Africa

Lord's 1924

531/2

779

West Indies

New Zealand

Wellington 1995

660/5

770

England

South Africa

Durban (Kingsmead) 1939

654/5

764

Pakistan

Sri Lanka

Faisalabad 1985

555/3

761

South Africa

England

Lord's 2003

682/6

757

Pakistan

Bangladesh

Multan 2001

546/3

752

India

Australia

Sydney (SCG) 2004

705/7

752

India

Australia

Sydney (SCG) 1986

600/4

750

 

So Sri Lanka retains the #1 position under this calculation. However, the West Indies 790 for 3 moves up to second place, while England’s 849 all out in the Timeless Test of 1930 moves down to seventh.

 

Another aspect to these scores is that the distribution of the scores around these projections can be calculated, which means that the probability of a specific score can also be calculated. For example, the probability of a score of 790/3 actually exceeding the 1028 assigned to Sri Lanka’s record is about 24%.

 

One other possible calculation here is a re-appraisal of the most one-sided innings victories in Tests. Using the projected score, the margin of victory can be re-calculated and compared more evenly. The most one-sided Tests in this analysis are:

 

Team

Opponent

Score

Projected Score

Original Margin

Projected Margin

The Oval 1938

England

Australia

903/7

951

Inns + 579

Inns + 627

Multan 2001

Pakistan

Bangladesh

546/3

752

Inns + 264

Inns + 470

Bulawayo (Queen's) 2004

Sri Lanka

Zimbabwe

713/3

919

Inns + 254

Inns + 460

Kolkata 1958

West Indies

India

614/5

724

Inns + 336

Inns + 446

Dhaka (Mirpur) 2007

India

Bangladesh

610/3

816

Inns + 239

Inns + 445

Wellington 1995

West Indies

New Zealand

660/5

770

Inns + 322

Inns + 432

Johannesburg (New Wanderers) 2002

Australia

South Africa

652/7

699

Inns + 360

Inns + 407

 

(Please, no comments that the ‘highest’ does not mean the ‘greatest’. No one is claiming that it does. We are just looking at extremes here.)

 

[Technical note: the trajectory at large scores must be calculated with care, because teams that continue with great success from a high starting point rarely complete their innings. This must be allowed for in the calculation. The way to do this is through an iterative process, where big innings that are declared closed are themselves calculated through to completion, firstly for innings that are nine wickets down, then eight, seven, and so forth, and these results are then fed back into the calculation for end points starting from fewer wickets down.

 

For example, take a score of 500 for 3. This has occurred 37 times in Test matches. The projected score in this case is 705 all out. However, only three of the 37 teams have actually reached or exceeded a score of 705, while nine have been bowled out for less than 700. The reason that the projected score is above 700 is that many teams continue to do well but declare before reaching 700. Careful iterative analysis of these declared scores produces the average estimate of 205 runs added, or 705 all out for a projected score.]

 

 

17 June 2008

 

Gibbs Update (see also 30 May 2007 and 7 July 2007)

 

Back from holidays, where some more detail was found regards the unique 8 for 6 spell against India by Lance Gibbs at Bridgetown in 1962. The Barbados Advocate gives some useful detail not available elsewhere, including the times of each wicket, and in combination with other sources, an over by over sequence of sorts is possible. One complication is that some sources, including Wisden, give the length of the spell as 15.3 overs with 14 maidens. The Advocate, and one or two other sources, say 16.3 overs with 14 maidens, and on close inspection, this appears to be correct.

 

The following reconstruction distills various sources, but is based on the Advocate account, starting with Gibbs being brought on for Worrell just before 2 o’clock. Prior to this spell, Gibbs had bowled 37 overs without success. The overs in Gibbs’ spell are numbered. The overs at the other end, mostly bowled by Solomon, are given in italics. Note that there was no new ball taken in an innings that lasted 185.3 overs. When Gibbs was brought back on, there had been no wicket for close to 100 overs, and the partnership between Sardesai and Manjrekar had produced just 98 runs. The score, 149/2 off 142 overs at lunch, was now 158/2 off 153 overs.

 

1.      Wicket maiden (Sardesai, 60 in 392 mins) 2:00pm

Solomon, maiden

2.      One run to Umrigar.

Solomon, maiden

3.      Double wicket maiden (Manjrekar 51 in 259 minutes, Pataudi 0, 2nd ball). 2:11

Solomon, maiden. India now 159 off 159 overs.

4.      To 10. Seven overs with six maidens, and one over for 5 runs.

Solomon bowled at the other end, conceding 10 runs. For 25 mins, Borde faced Gibbs and Umrigar faced Solomon.

11.  Wicket maiden (Umrigar, 10 with 1x4) 2:45, Borde 6 not out.

Solomon, maiden

12.  Maiden

Solomon, conceding two runs from Borde plus a bye

13. Double Wicket maiden (Borde, 8 with 1x4, Engineer 0, 2nd ball) 3:00

Solomon, boundary by Durani, plus two singles (Durani, Nadkarni)

14. Wicket maiden (Durani, 5 with 1x4) 3:07. Gibbs spell at this point is 14-12-6-7

Solomon, maiden

15. Maiden. At this point India had scored 183 runs in 182 overs.

Solomon’s last over, with a  single to Nadkarni, single to Desai and 2 leg byes. Solomon’s spell: 21 overs for 24 runs, no wickets.

16. Maiden

Sobers on, maiden

17. Desai (1) out off third ball. 3:22pm

 

All out for 187 off 185.3 overs in 474 minutes.

 

This sequence confirms that Gibbs took his last 5 wickets without conceding a run. Oddly enough, none of the sources mention this, though they mention his 3 for 1 spell earlier. It may have escaped notice because it was stretched over a period of 12 overs during which runs were scored at the other end.

 

For comments, or to contact Z-score (Charles Davis) email

 

statz334  at  iprimus  dot  

com  dot  au

 

(The address is like this to avoid SPAM. Type the address in the usual format)

12 May 2008

 

 

The website/blog Cricket Buzz has produced a list of “50 Best Cricket Blogs”, and included this site on the list. So there is a compliment. Thanks, guys. Actually, I didn’t know there were 50 cricket blogs, best or otherwise, but with millions of people blogging, I suppose it is not surprising.

 

 

 

So Near but So Far (Written for Cricinfo)

 

When Virender Sehwag strode to the Chennai wicket on the fourth day of the recent Test against South Africa, he already had 309 runs to his name. There would have been a great many fans wondering how far he could go: could he top Brian Lara’s 400?

 

Statistics, however, say that the fans were very likely to be disappointed (as they were). The truth is, that while 309 and 400 sound like reasonably similar scores, they are not. In fact, it is harder for a batsman to add another 100 runs if he has already made 300, than it is at almost any other score.

 

There have now been 22 Test triple centuries, enough for some statistics. Only one of those triples has gone on to produce the magic 400, while 17 have been dismissed. Only one out of 18: that is only a 5.6% conversion rate. (The other four innings finished not out between 300 and 399; it is better not to include them in this calculation.) It is interesting to compare this to the conversion rates at other scores:

 

Number of dismissals

Number of successes

Conversion rate

0-99*

33,822

2942

8.0%

100-199

2334

279

10.7%

200-299

192

22

10.3%

300-399

17

1

5.6%

*0-99 data involves only recognised batsmen (#1-#6 in batting order). “Number of successes” refers to the number of innings that have passed through the specified range without dismissal, e.g., for 0-99 it refers to the number of centuries.

 

While interesting, this data is not very robust for the 300-399 range. If the next batsman to make a triple century happens to go on to 400, the conversion rate will almost double (to a rate similar to the 300-400 conversion rate in first-class cricket of 11%). However, the difficulty that batsmen encounter above 300 can also be seen when we look more closely, at 20-run increments

 

Number of dismissals

Number of successes

Conversion rate

100-119

1105

1791

62%

120-139

581

1087

65%