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Stats Analysis

What looking at the halfway mark of Tests and innings tells us about them

A deep dive into patterns of runs scored and wickets taken at halfway points of Test matches and innings

Ashton Agar and Phil Hughes added 163 together, England v Australia, 1st Investec Test, Trent Bridge, 2nd day, July 11, 2013

Australia's halfway score of 140 in the first innings at Trent Bridge in 2013 was only crossed during their tenth-wicket partnership  •  Rui Vieira/PA Photos/Getty Images

A few years back, I wrote an article containing one of my most intriguing measures, called the Halfway Value. I have decided to revisit that theme now, and have widened its scope considerably.
I have expanded the halfway concept to the wickets taken in the innings, and broadened the measure to cover entire matches, and both teams, not just one innings. This allows for greater insight. About 200 more Tests have been played since then and some of these factor nicely in this concept set.
There has always been a lot of discussion about the contributions of lower-order batters. One day, during a shower, I had a brain wave, a la Archimedes - why not use the halfway score as a reference point? Fortunately, unlike Archimedes, I stayed in the bathroom. I have developed this concept further over the past few years. I can say honestly that I have never been so excited by the possibilities of a measure like I am with this one. It is also very easy to understand, and derive, for the regular cricket follower.
The idea is simple. The measure, let us call it IW-HS (Innings Wickets at Half-Score), is the exact wicket equivalent of the innings when the halfway score was reached. The measure is applicable only to completed innings. Say, a team scores 410. The halfway mark is 205. When the score of 205 was reached, the fourth-wicket partnership was in progress. The third wicket fell at 180 and the fourth at 270. The IW-HS value is 3.28 (3.0 + (205-180)/(270-180)). In another innings, the team scores 283. The halfway mark is 142. When the score of 142 was reached, the eighth-wicket partnership was in progress. The seventh wicket fell at 131 and the eighth at 201. The IW-HS value is 7.16 (7.0 + (142-131)/(201-131)).
Let me define IW-HS in simple terms. A team scores "rrr for ww", in a completed innings. If the halfway mark is "hhh", the IW-HS is defined by the phrase "hhh for IW-HS", with IW-HS being the exact wicket value, in decimals.
This measure, a ridiculously simple one indeed, packs a punch. It is a clear indicator of how the innings progressed. A lower IW-HS values indicate that there have been collapses in the middle and late order. A higher IW-HS values indicate recoveries by the late-order batters. Let me illustrate this.
Let us say that the IW-HS is 0.91. There was a terrific first-wicket partnership, which exceeded the halfway score mark. Soon after the first wicket fell, there was a huge collapse and the last nine wickets contributed less than half the score.
Say, the IW-HS is 2.42. The top order performed quite well and the team reached the halfway mark, two wickets down. There was a collapse of sorts and the last seven wickets did not contribute a lot, well below half the score.
If the IW-HS is, say, 6.91 instead, there was loss of top-order wickets and the halfway mark was reached six down and the seventh wicket was lost soon afterwards. However, the last three partnerships saved the day and added nearly half the final score.
If the IW-HS is 8.75, it tells us there was a huge collapse and the ninth wicket fell soon after the halfway score was reached. The last wicket pair played outstandingly well and helped reach the final score. And so on.
For this article, in the first place, I have extended the concept to wickets also. What was the score reached at the fall of the fifth wicket (not forgetting that we only consider situations where all ten wickets have fallen in an innings)? The only requirement is that this is not a number like IW-HS. It was possible for IW-HS to be fixed as a number because the total number of wickets was fixed (at ten). In this case, since the final score could be just about any number up to about 700, the IS-5W (Innings Score at five wickets down) is a percentage value.
Here are a couple of examples taken from the England-India Test played at The Oval in September. In their first innings, England reached 290, after losing their fifth wicket at 62. The IS-5W is 21.3%. In their second innings, India reached 466 after being 296 for 5. Their IS-5W is 63.5%.
A reader may raise a valid query: Aren't both measures the same? Shouldn't the results be similar? Surprisingly, no. The collection of Tests that are featured are quite different. I have checked the collections of featured Tests and there is almost no common Test between these. That is because the innings dynamics change considerably when we look at different aspects, especially the middle-order partnerships.
I will present the results with a brief coverage of the top few Tests in each category. I leave it to the readers to look at the other Tests and derive their own conclusions.
In the second part, I will look at Tests as a whole. If I set a minimum limit of 40 wickets, only wins by runs will be included, which is wholly inadequate. It is also clear that innings wins have different dynamics and should be excluded. If the winning team bats first, it is a high score followed by two low scores and the halfway stage will perforce be somewhere in the first innings. If the winning team bats second, it is low-high-low and the halfway stage will appear in the second innings. It is also true that teams are chalk and cheese in their batting in such matches. As such, I have to exclude all innings wins and also ten-wicket wins. This is done by the simple method of fixing the minimum cut-off at 31 wickets. A total of 1266 Tests (of the 2433 played to date) qualify.
In the analysis of Tests, I will look at the same two things. However, in this case, both measures will be percentage values since both the total match runs and total match wickets vary between Tests. The runs could be anything and the wickets will range from 31 to 40. The first measure, let us call it MW-HS (Match Wickets at Half-Score), is the exact wicket equivalent in the innings when the halfway score was reached. This could be in any innings. The second measure, let us call it MS-HW (Match Score at Half-Wickets), is the runs accumulated until the fall of the halfway wicket. It could be in any innings but the first.
I recently analysed pitches using Pitch Quality Index (PQI) values. This measure is similar but it offers a lot more insights since it straddles the two teams and recognises the primacy of the pitch. The PQIs are innings-dependent and the two teams could have been chalk and cheese.
Finally, I look at the Test as a whole, but from the innings point of view. What were the IW-HS values reached and what was the mean for the Test? This highlights the Tests in which in almost every innings there was a either a significant recovery or a significant collapse.
A feature of the IW-HS table above is that the top is almost totally dominated by recent matches. There are eight Tests played before 1982 and eight after 2000, indicating that late-order batters have come to the party in a significant manner recently.
In the first Test featured, at Trent Bridge in 2013, Australia collapsed disastrously to 117 for 9 and then had a last-wicket partnership of 163, well over half the score. Philip Hughes and Ashton Agar staged this recovery. The IW-HS value was an incredible 9.14. Agar was unfortunately dismissed for 98.
In November 2011, it was a different sort of recovery for Australia. After having taken a big lead in the first innings in Cape Town, they slid dramatically to 21 for 9 - five runs short of the all-time low score. Somehow, Peter Siddle and Nathan Lyon managed to add a "whopping" 26 runs to the total, which let Australia finish at 47. That South Africa won comfortably is another matter. The IW-HS was only a fraction lower than for the first entry on the table - at 9.11.
England were in a similar predicament against New Zealand in Auckland in March 2018. Batting first in a day-night match, they managed to go past 26 but slid to 27 for 9 before Craig Overton and James Anderson took them total past 50. The IW-HS was 9.06.
A year later, Ireland, playing in Dehradun against Afghanistan, slumped to 85 for 9 before recovering to 172 with a good partnership between George Dockrell and Tim Murtagh. The IW-HS was 9.01.
In August 2019 in Antigua, chasing 419 to win, West Indies collapsed dramatically to 50 for 9 against India. Their last-wicket pair, Kemar Roach and Miguel Cummins, put on 50 runs, leading to an IW-HS value of exactly 9.0.
In the table above we see the other end of the spectrum as far as the IW-HS is concerned: amazing collapses after excellent starts. It is dominated by matches between 1980 and 2010.
The first of these matches contained, in some ways, the strangest innings ever played. When Adrian Griffith and Sherwood Campbell had taken the score to 276 for no loss in Hamilton in December 1999, their captain, Brian Lara, must have had visions of a 500-plus score and an innings win. Instead, West Indies collapsed to 365, losing all ten wickets for 89 runs, and New Zealand won by nine wickets. After 276 for 0, West Indies lost 20 wickets for 186 runs. The IW-HS was an amazing 0.66 - all of two-thirds of a wicket.
At Old Trafford in 1946, Vijay Merchant and Mushtaq Ali were sitting pretty at 124 for no loss before an avalanche of wickets, and India could only reach 170. They managed to hold out for a draw, but the IW-HS for the first innings was a measly 0.68.
Against West Indies in Karachi in December 1997, Pakistan reached 298 for no loss, courtesy Aamer Sohail and Ijaz Ahmed, but could add only 119 more before being bowled out by West Indies. That Pakistan still won comfortably is another thing. The IW-HS for Pakistan was only 0.70.
That figure was emulated by Zimbabwe against West Indies in December 2001. They were over 400 runs behind on the first innings, but Dion Ebrahim and Alastair Campbell launched a fightback with 164 for no loss. However, the inexperienced West Indian attack ran through the line-up for a mere 64 runs more.
In October 2018 in Dubai, Australia collapsed to 202 all out after being 142 for no loss against Pakistan. The IW-HS was 0.71.
Four centuries and two 450-plus scores did not prepare anyone for what happened on the fourth day of the Ahmedabad Test between India and New Zealand in November 2010. India's top order - Gautam Gambhir, Virender Sehwag, Rahul Dravid, Sachin Tendulkar and Suresh Raina - was back in the pavilion, with the score reading 15 for 5. But VVS Laxman scored a magnificent 91 and Harbhajan Singh an unlikely 115 to take India to 266, an amazing recovery indeed. The IS-5W was an unbelievable 5.6% (15/260).
A few decades earlier, India had performed a similar escape at The Oval, in 1952. Their top order, led by Vinoo Mankad and Pankaj Roy, scored 5, 0, 0, 1 and 0 and slid to 6 for 5. Then they recovered to 98 all out and, aided by heavy rain, managed to draw the match. India's IS-5W was 6.1%.
Sri Lanka set Pakistan an imposing target of 357 in Sialkot in September 1995. The hosts slid disastrously to 15 for 5 before Moin Khan played one of the great retrieving innings and took Pakistan to a respectable 212 - an IS-5W value of 7.1%.
On the opening day of the Colombo Test against Australia in August 2016, Sri Lanka slid to 26 for 5 before recovering to an excellent 355, thanks to hundreds by Dinesh Chandimal and Dhananjaya de Silva. The IS-5W was 7.3%.
Bangladesh were down in the dumps in Harare in February 2004, at 14 for 5 before reaching a respectable 169 - the IS-5W being 8.3%.
This is the other end of the five-wickets-down situations, in which the last five batters did very little before returning to the pavilion.
In Melbourne in March 1979, Pakistan claimed one of their most memorable victories, defeating Australia by 71 runs, through arguably the greatest bowling spell in away matches - Sarfraz Nawaz's 9 for 86. Australia, who were set 382 to win, were well placed at 305 for 5 when they lost their last five wickets for five runs. The scores of the batters who were dismissed from Nos. 6-11 were 0, 0, 0, 0, and 0. Australian IS-5W value was an amazing 98.4%.
Pakistan had inflicted a similar assault in Wellington in January 1965. New Zealand were sitting pretty at 261 for 5 when the bottom gave way and they were dismissed for 266. The IS-5W value was an imposing 98.1%.
In the Boxing Day Test at the MCG in 1990-91, England, having secured a first-innings lead of 46, were well placed at 147 for 5, when lightning struck a few times. They could add only three more runs and Australia won the Test comfortably. The IS-5W was 98.0%. These are the fewest runs added for the last five wickets.
At Trent Bridge in 1953, Australia moved from 244 for 5 to 249 all out. England nose-dived from 493 for 5 to 507 all out in Karachi in February 1962. The IS-5W values for these two Tests are either side of 97%.
Now I will move on to the new idea incorporated into this article. The idea of half-score or half-wickets, taking the entire match into consideration. This offers great insights since it's across teams.
First, let me take a look at the half-score state in the match. For this purpose, the total runs is the match aggregate runs. Since there is no other consideration, this helps tell us how the pitch performed across the two halves. In this table, I will feature matches in which there was a great recovery in the second half since the pitch improved dramatically.
When India played New Zealand in Wellington in February 2014, the match aggregate was a huge 1476. However, when the 738th run was scored, the match scoreline was New Zealand: 192, India: 438 and New Zealand: 108 for 5. A huge innings defeat stared New Zealand in the face before Brendon McCullum, BJ Watling and Jimmy Neesham rescued them. New Zealand finished at 680 for 8 and India rattled up a quick 166 for 3. The wicket value was 25.04 (out of 31) and this resulted in an amazing 80.8% MW-HS value. Here, even the wicket count is a percentage value since the total number of wickets varies from match to match.
When West Indies toured Pakistan in 1974-75, the match aggregate in the Lahore Test was 1044, which meant that the halfway mark was 522. After two low first innings, of 199 and 214, Pakistan were floundering at 58 for 3. The halfway mark was reached at a match wicket value of 23.6 and this represented an MW-HS value of 76.3%. Then Mushtaq Mohammad, Asif Iqbal, Len Baichan and Clive Lloyd produced valuable innings and the match finished in an eventless draw.
A total of 1348 runs were scored by Sri Lanka in Pakistan in Colombo in July 2009. The halfway point was 674. The match scoreline was 299, 233, 425 for 9 and 391 for 4. It took 23.7 wickets (out of 33) to reach the halfway mark, which gives this match an MW-HS Rating of 74.6%.
The highest value of MW-HS when all 40 wickets have fallen comes in a match much later in the table. The match scoreline of an Ashes Test at the MCG in 1901-02 tells a resounding story: 112, 61, 353 and 175. The halfway mark of 350 in a low-scoring Test was reached when 28.2 wickets had fallen - an MW-HS value of 70.4%.
Now, on to matches in which the pitches turned square as the match progressed. Pakistan and West Indies scored 1348 runs in Dubai in October 2016. The halfway mark, of 674, was reached just after the fall of the fifth wicket and the MW-HS value is 15.8%. The scores tell the story - 579 for 3, 357, 123 and 289. A sea change in the pitch, for certain.
At the WACA in December 2009, Australia scored 520 for 7 and West Indies responded with 312. Then Australia collapsed to 150 but won, dismissing West Indies for 323. The halfway mark of 652 runs was reached around the fall of the first West Indies wicket; 8.0 wickets, out of 37, leads to an MW-HS of 21.5%.
In the Pallekele Test between Sri Lanka and Bangladesh earlier this year, the match scoreline was 493 for 7, 251, 194 for 9 and 227. The halfway stage was reached at 7.9 (out of 36) and the MW-HS was 22.1%.
In matches where all 40 wickets were taken, the highest value of MW-HS is in an Ashes Test - at The Oval in 1934. The scores were 701, 321, 327 and 145 - leading to a monumental 562-run win for Australia. The halfway stage, of 747 runs, in a high-scoring match was reached with as few as 10.4 wickets taken, leading to an MS-HW value of 26.1%.
Now, we move on to the half-match-wickets analysis. The main difference between this and the corresponding Innings analysis is that there the numbers were fixed at ten and five respectively. However, here the total number of wickets varies from 31 to 40. So, the halfway mark is fixed at 50% of the total wickets. It is variable. If the total number of wickets is odd, say 35, the exact score is calculated by adding half the partnership value for the 18th wicket.
Eighteen wickets fell on the first day of the Delhi Test between India and West Indies in November 1987. India scored 75 and West Indies could only take a 52-run lead. In the second innings, India made 327 and West Indies chased down the target of 276 with some difficulty. Only 124 runs were scored at the fall of the 17th wicket (match total 35) and this represented just 18.7% of the match total of 805 runs - that being the MS-HW value.
Going back nearly 100 years from then, to the MCG Ashes Test in 1894-95, the first-innings scores were almost identical to the Delhi match - England 75, and Australia 123. Then the pitch improved and England, with a second-innings total of 475, managed to win comfortably by 94 runs. The match wicket aggregate was 40. This meant that the first two innings could be taken to determine the MS-HW value rather easily - 198 runs out of 1006 comes to a MS-HW value of 19.7%,.
The first two innings of the Centenary Test, between Australia and England in Melbourne in March 1977, were miserable efforts - 138 and 95. Then came two virtually identical 400-plus totals and Australia's first-innings lead gave them a 45-run win. The match total was 1069 runs and the first-two-innings' total was only 233, leading to a MS-HW value of 21.4%.
Still in Melbourne, for the New Year's Ashes Test in 1936-37 - the two first innings were forgettable but tactically brilliant efforts - 200 for 9 and 76 for 9. Then Don Bradman came in at 97 for 5 (having reversed the batting order to deal with a drying pitch) and played one of the all-time great innings, of 270. England were set 689 but could not get even halfway there. The match aggregate was 1163 runs and the first-two-innings' total was only 276, leading to a MS-HW value of 23.7%.
Now on to situations in which the pitch got considerably worse. When West Indies played in Mirpur in November 2012, the two first innings were huge 500-plus run-bonanzas, for only 14 wickets. The next two innings were contrasting efforts - 273 and 167 - and West Indies won by 77 runs. The total runs scored at the fall of the 17th wicket were 1295, which formed a huge MS-HW value of 85.0% of the total match aggregate of over 1500 runs.
When South Africa toured England in 1951, Trent Bridge showed its Jekyll-and-Hyde qualities. The two first-innings scores were 483 for 9 and 419 for 9. Then there were two miserable efforts - 121 and 114. South Africa won the topsy-turvy match by 71 runs, mainly because of their first-innings lead. The MS-HW is a rather high 80.4%.
When Pakistan toured Australia in 1972-73, the MCG Test again proved to be a yo-yo match. Australia declared at 441 for 5 but saw Pakistan take a lead of 133. The hosts stitched together an excellent third innings of 425 and then won by 92 runs. All this meant that at the halfway mark of 16 wickets (out of 33), the MS-HW was 79.8%.
In this concluding part, I have taken the IW-HS as the base and looked at Tests as a whole. This has allowed me to identify Tests in which both the teams either recovered superbly or collapsed dramatically. Only Tests in which there were three or more such occurrences are considered. And all IW-HS values should be greater than 5.0. Let us first look at the recoveries.
In the 1999 Edgbaston Test, there were three good recoveries. First, New Zealand came back from 104 for 6 to 226 (IW-HS of 6.11). Then England fell to 45 for 7 before making it to 126, leading to an IW-HS of 7.26. New Zealand slumped disastrously to 52 for 8 before getting to a three-figure score. The IW-HS was a huge 8.04. This Test had the highest IW-HS average of 7.13.
In Kanpur in 1983-84, India lost by an innings to West Indies. All three innings had excellent recoveries. First, West Indies, from 157 for 5 to 454. Then India, from 90 for 8 to 207, and in the follow-on, from 43 for 5 to 164. The three IW-HS values were 5.46, 98.11 and 5.62 respectively.
At the SSC in Colombo in 2005, West Indies slumped to 113 for 5 before scoring 285 (IW-HS 5.37). Then Sri Lanka reached 227 after being 113 for 7 (IW-HS 7.02). Finally West Indies slid again, to 48 for 6, before crossing 100, although still losing the Test by a large margin.
There are two occurrences of all four innings exceeding IW-HS values of 5.0. The first was in Lahore in November 1996. The four values were 5.50, 6.19, 5.39 and 6.74 respectively. Pakistan and New Zealand recovered from five-down and six-down situations. In 2015 at the SSC, India and Sri Lanka posted five-plus values of IW-HS in all four innings. Sri Lanka's recovery from 47 for 6 to 201 was the most noteworthy one.
Finally to Tests in which both teams suffered collapses. All IW-HS values should be lower than 3.0 to qualify.
In Antigua in July 2012, New Zealand reached 223 for 2, yet managed a total of only 351 (IW-HS of 2.47). Then, West Indies were 304 for 1 and could add only 218 more (IW-HS of 1.13). Finally, New Zealand were 170 for 1 and could put on only 102 more (IW-HS of 1.72). The average was a very low 1.78.
West Indies went from 114 for 2 to 216 (IW-HS of 1.98) in December 1997 in Karachi. Then it was Pakistan's turn to fritter away a good start of 298 for no loss to 417 all out (a very low IW-HS of 0.70 - this innings was featured earlier). In their second innings, West Indies were doing reasonably well at 140 for 2, but could only reach 212 (IW-HS of 2.71).
At the SCG in January 1968, Australia could not capitalise on a start of 219 for 2, and reached only 317. India responded in kind, converting a good position of 178 for 2 to 268 all out. In the third innings, Australia were sitting very well at 222 for 2 (a bogey score indeed) and could only add 70 more. To complete the sorry tale, India reached 120 for 1 but were dismissed for 197. This is the only Test featured in which all four innings had sub-2.50 IW-HS values (2.27, 2.34, 1.63 and 1.43 respectively. The average was an incredible 1.92, across all four innings.
Calling for an all-time XV
In 2013, I ran a readers' poll to determine a group of 15 players to be considered for an all-time World team. There was excellent response and the results were very insightful and interesting. I now call for submissions again, since new contenders have emerged, as also new measures for selection. You can email your entries through one of the three routes below, with the subject "All-time XV - 2021".
- Send an email to my personal mail id, if you have it
- Send an email to the email id at the bottom of this article
- Send an email to the Talking_Cricket group, more on which is below.
When sending in your XV, provide your name, place of residence, and your list of 15 players (no more, no less). The team must be an all-terrain one. A manager/coach is optional. If you send multiple entries from one email id, I will consider the last one sent. Thus, you have the opportunity to change your selections. You don't have to justify your selections; I prefer short emails. The entries should reach me by November 30. I will write a summary article, which will probably be published in January. The entry that matches the final selection or comes closest to it will be acknowledged.
- eight batters/allrounders
- one wicketkeeper
- four pace bowlers
- two spinners
Talking Cricket Group
Any reader who wishes to join the general purpose cricket-ideas-exchange group of this name that I started last year can email a request for inclusion, giving their name, place of residence and what they do.
Email me your comments and I will respond. This email id is to be used only for sending in comments. Please note that readers whose emails are derogatory to the author or any player will be permanently blocked from sending any feedback in future.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems