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Graeme Smith declares

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Graeme Smith’s Test career ended in defeat and South Africa’s first series loss in five years and 15 series. He must have drawn satisfaction from his final, albeit unsuccessful, day of Test cricket as his middle and lower order battled and came so close to eking a draw from a game in which they were profoundly outplayed.

Smith’s records as captain – most matches, most victories – have been celebrated. There’s another record he holds, less well known, but which makes the denouement of his final Test ironic. Australia won at Cape Town with time almost, but not quite, up after declaring in the third innings. Smith is the most prolific declarer in Test history, having called time on South Africa batting in the third innings of a match 25 times. Yet, only eight of those declarations were converted into victories – producing a success ratio of 32%, below the average for the game and a long way short of the proportion achieved in recent years of Test cricket.

South Africa have become known for being a team hard to beat and one that finds it hard to speculate to accumulate if the victory isn’t coming comfortably their way. Smith’s statistic of only converting 32% of declarations – made when ahead in the game – into victories gives fuel to this notion of a risk averse South African side. The purpose of this post is to assess whether, from the perspective of the target-setting declarations, this is a fair assessment of Smith’s career, which in so many respects deserves to be remembered for the effectiveness of his leadership.

Smith’s third innings declarations spanned from his third Test as captain (v England at Edgbaston in July 2003) to his 107th and penultimate Test (v Australia at Port Elizabeth). In total, these declarations yielded eight victories, 16 draws and a single defeat. How many of the draws were likely victories spurned through over-caution?

Three of the draws can be discounted immediately. These weren’t ‘target-setting’ declarations, but decisions to close the innings to end a match that hadn’t progressed beyond the third innings. Adjusting for these, Smith’s win rate increases to 36%. A further adjustment, to take out two games where the fourth innings was prevented by rain from running its course, lifts the success rate to 40%.

The chart below shows the target set and estimated number of overs remaining in the match for each of the 22 ‘live’ declarations (including the two rain-affected games). Matches that were won by South Africa are green, defeats in red and draws in blue. The dotted turquoise line indicates the current record fourth innings chase in Test cricket (418). On ten occasions, Smith has challenged opponents to set a new Test fourth innings record.

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Smith’s teams have won each of the matches where they have given themselves over 150 overs (five sessions) to bowl out the opposition. They have won only one-third of the nine games when they had 100-150 overs. Not a single game has been won with the declaration leaving a day’s play (90 overs) or less.

To test for examples of over-cautious captaincy, it makes sense to start with the four matches where Smith set a target of over 400 and gave his team over 100 overs to secure the victory (a fifth, when the final day was rain affected is excluded). Should he have declared earlier?

In only one of the matches (v England, Cape Town – Jan 2010) does it appear, with the benefit of hindsight, that more overs could have delivered a victory. England were nine wickets down and 170 short of the target after the 141 overs were delivered. In the other matches, the opposition were three, four and five wickets down at the close of play. In each case, bringing forward the declaration by an hour would not have substantially increased the chance of a South African defeat, but may have helped a victory push, although that seems unlikely given the position of the game at the end of day five.

Teams batting third create time to bowl the opposition out by batting, if not aggressively, then enterprisingly. The chart below shows the run rate per over achieved by South Africa for each of the 22 ‘live’ declarations. The colour of the bar indicates the match result: green – win; blue – draw; red – defeat.

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The picture is mixed. Three of the four third innings with run rates below 3 per over presaged draws. But three of the five third innings with the highest run rates were also in matches that concluded in draws.

Smith has earned praise for several of his declarations. The defeat against Australia at Sydney in 2006, when South Africa were 1-0 down in the final Test of the series, came about following a “sporting declaration” by Smith – and tremendous attacking innings by Ponting. His next declaration, against India at Durban in December 2006, showed no signs of being scarred by defeat. Smith set the visitors 354 at a rate of almost one run per over slower than his team had amassed their third innings total. He was rewarded with a comfortable victory and a squared series. At Headingley six years later, Smith was credited with “happy daring” when 1-0 up in the series with two to play, he set England 253 in 39 overs.

Taken together, these observations point to criticism of Smith’s negative approach as a captain when setting the opposition a target being overstated. There are examples where he could have ventured more in pursuit of victory. But there are also examples of bold declarations, just as there are of frustration in the face of stubborn, unanticipated fourth innings salvage jobs.

Where Smith’s team appears to vary from the norm in Test cricket declarations is the failure to convert the majority of situations where 100-150 overs remain in the game into victories. In an earlier analysis of target-setting declarations in Tests between 2009-11, All the time in the world, I found that only four of 17 (24%) declarations made with 100-150 overs left in the game resulted in draws. Smith’s career record is 67% (six of nine).

The key to Smith’s apparently low conversion of declarations into victories has not been the timing of his declarations, nor has it been the urgency with which his side has batted in the third innings of the match. If there is a deficiency it lies with the concoction of factors that have made South Africa relatively ineffective at dismissing sides in the fourth innings. In that mix may be: the lack of top quality spin bowling, unhelpful wickets, unadventurous captaincy in the field and, of course, ill-fortune. What do you think accounts for Smith’s mediocre record of driving home match advantage into victory?

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2012: the year in declarations

Michael Clarke, in his first full year of captaincy, has the honour of ‘declaration of the year’. At Bridgetown in April, Clarke declared Australia’s first innings 43 runs behind West Indies, curtailing a 77 run tenth wicket partnership. The following day, in their second innings, Australia chased a target of 192, making Clarke only the second captain in test history to win a match after declaring behind.

Other significant declarations in 2012 will follow after an overview of target-setting, third innings declarations (which Clarke’s was not).

In an earlier review of target-setting declarations, I have shown that they occur in approximately one-quarter of all Test matches. 2012 fell into line with this long-term average, with 11 of the 42 matches in the year featuring this kind of declaration. The proportion of victories arising from these declarations (30% – excluding one declaration made to bring a game to an end) was considerably lower than the typical figure achieved in recent decades: 40-50%.

This brings us to an apparent paradox. Declarations tend to occur when one team is on top in the game. Yet 80% of the drawn matches in 2012 involved a target-setting declaration, while only 9% of the victories did so. The longer-term picture is more balanced, with target-setting declarations featuring in 21% of victories and in 27% of draws.

It revives the question posed in my post, Making the Game Safe, over whether the captains of sides batting third take too long over bringing their innings to an end. Mike Brearley, in The Art of Captaincy, concedes:

most of us already err on the side of caution; fielding is hard work (so postponements are tempting); and we enjoy watching our batsmen demolish the bowling.

Eliminating two games ushered to draws by fifth day rain and a third where the match’s third innings began 40 overs into the final day, four merit review.

SA v NZ at Wellington (Mar 2012)

SA skipper, Graeme Smith, declared 15 overs into the final day, setting a target of 389. Overnight, the lead had been 280, but had built rapidly in the opening hour of the day five. Smith’s declaration did not maximise the time available for pursuing the victory in the fourth innings, where Kane Williamson’s obdurate century and some sloppy SA fielding contributed to the result.

Pak v SL at Pallekele (July 2012)

Misbah-ul-Haq set SL 270 in 71 overs. This was a well-balanced target, although Pakistan may have wanted to risk more given they were one-nil down in the final match of the series.

SA v Eng at Leeds (Aug 2012)

Leading the series and having experienced Kevin Pietersen at his destructive best in the first innings, Smith’s declaration was justifiably cautious but managed to create an exciting final afternoon.

Aus v SA at Adelaide (Nov 2012)

faf du plessisClarke declared with a lead of 430 and almost 150 overs left in the game. That the game was drawn had very little to do with his declaration judgement and a lot to do with the determination of debutant Faf du Plessis, a flat track and the Australian attack being a man down.

So, in only one instance – Smith’s declaration at Wellington – was the judgement awry and culpable in the match being lost. It is also worth noting that rain had taken time out of this match, as it had in the Headingley and Pallekele examples.

The other noteworthy target-setting declaration was made by Mahela Jayawardene at Galle against Pakistan in June 2012. Sri Lanka’s second innings happened as Jayawardene opted not to enforce the follow-on when 370 ahead after dismissing Pakistan in 54 overs. By batting again, a lead of 500 was established and a declaration made. Jayawardene was criticised for opting to bat again. The decision whether to enforce the follow-on has been analysed by academic statistician Philip Scarf, whose work informed my earlier pieces on declarations. Scarf’s conclusion is that the decision makes no significant difference to the outcome of the match.

I end this round-up where it began: with a record-holder. Graeme Smith set a record in 2012 when he became the captain who has made the most target-setting declarations in test history. With 23 he is two clear of Ricky Ponting, the previous record holder. Their fortunes are quite different as Smith has only converted 26% into victories, compared to Ponting’s 81%. Smith hasn’t always been over-cautious, but as at Wellington in April, his reluctance to get out in the field has on occasions cost the South Africans a win.

Who dares is occasionally defeated – part 2

Barely one in fifty target-setting declarations in Test cricket results in a loss for the team who make the declaration. Just eleven in Test cricket history. With the odds seemingly so heavily stacked against it happening, a match-by-match review should produce some treasures – and numbers six to eleven of this series throw up some magnificent innings and even a turning point in the history of the game. The first five were described in Who dares is occasionally defeated.

Clive Lloyd West Indies v India, Port-of-Spain (April 1976)

Lloyd’s 13th match as captain was to have a far-reaching impact on test cricket. His team had been well ahead from early on day 1 of this match. With a comfortable lead of 400 on a slow turning pitch, with three spinners in his side, Lloyd declared after lunch on the fourth day. India had almost five sessions to score the runs.

Generous or not, it required a magnificent, record-breaking effort from India’s upper order – centuries for Gavaskar and Vishwanath and a sheet-anchor 85 from Mohinder Armanath. The other triumvirate whose role was significant were the three West Indies spinners – Jumadeen, Padmore and Imtiaz Ali. Their impotency – absolutely (two wickets in 105 overs) and relative to the Indian spinners – set Lloyd on the path to the all pace attack of the next two decades. It was a rapid transformation with four quick bowlers in place two tests later.

Bishen Bedi Australia v India, Perth (December 1977)

The calculation made by captains approaching a declaration is between size of lead and time available to win. In this case, Bedi’s calculation was how long he dare bat on without an injury to a key bowler. With nine wickets down, himself and Chandrasekhar at the crease and Thomson at full-throttle, he was not sacrificing much run-scoring potential cutting short the innings.

The match had been closely fought with neither team able to secure a telling advantage. This was true through most of the fourth innings, where a nightwatchman’s century (AL Mann) played a major part in a creating a dramatic finish with Australia reaching their target of 339 with two wickets to spare and time running out. Bedi became the second captain in test history to have both suffered and benefited from a loss after a declaration.

David Gower England v West Indies, Lord’s (July 1984)

This is the only one of the eleven matches that I saw any of in the flesh – day 3 when Botham’s bowling took England to the unusual position of a first innings lead against the West Indies. One of his eight wickets in the innings was Richards, given LBW after a half-hearted appeal. At the time it felt as though the umpire, Barry Meyer, was as carried away as the crowd with England’s competitiveness.

Gower declared with nine wickets down early on day 5, setting a target of 342. More controversial than this decision was Lamb’s, and presumably Gower’s, to leave the field for bad light the previous evening when England’s lead was building. Greenidge’s response would have made any such cavils academic as he powered to 214* and a nine wicket victory. The West Indies’ progress was updated on my classroom blackboard by a chemistry teacher who was invigilating some low key afternoon-long test, wearing headphones.

Despite the defeat, this was England’s highpoint of a five-nil series defeat. Lloyd became the third captain in test history to have both suffered and benefited from a loss after a declaration.

Adam Gilchrist England v Australia, Headingley (August 2001)

Stand-in captain Gilchrist brought his attacking frame of mind to Test leadership setting England a target of 314 in a possible 110 overs. Poor weather meant that the full allotment would not be bowled and an inspired innings from Mark Butcher (174*) took England to a rare and unlikely victory when the loss of early wickets on day 5 had made a draw a more reasonable aspiration.

Asked about how he had prepared himself for the afternoon assault on Australia’s magnificent four bowlers, Butcher memorably explained that at lunch he had sat in the shower with a fag and cup of coffee.

Of losses following declarations, this was one of the most comprehensive turnarounds: 1st innings lead of 139, which became a lead over 300 with four wickets down on day four when Gilchrist waved his batsmen in. Steve Waugh was fit for the next test and Australia continued on their winning ways.

Graeme Smith Australia v South Africa, Sydney (January 2006)

Graeme Smith holds the test record for most target-setting declarations (23) and the most drawn matches (16) following those declarations. This is his single defeat.

Losing one-nil, on the final morning of the series, Smith gambled: setting Australia 287 in 76 overs. An onslaught from Ponting saw the target swallowed in just 60 overs, for the loss of only two wickets – setting a new record for a fourth innings winning total at Sydney. Smith’s positive outlook was evident throughout the game as he had declared the 1st innings, becoming the second captain to lose a match after declaring both innings.

Kevin Pietersen India v England, Chennai (December 2008)

Oh the ups and downs of KP. In this, his second (of three) test matches in charge, he cut short England’s innings and set India’s galacticos a target of 387 in around 110 overs. The declaration wasn’t reckless, or even particularly bold, as nine wickets were down and Panesar due to join Anderson.

In sharp contrast to England’s meandering afternoon of batting on the 4th day, Sehwag launched India that evening with 83 from 68 balls. On day 5, Tendulkar and Yuvraj guided India on a record-breaking run-chase.

Despite the loss, Pietersen’s stock was high, having led his team back to India after the Mumbai terror attacks. Within months, at loggerheads with Coach Peter Moores, he had had to step down. Perhaps more significant for his current predicament, at least one of his teammates was unimpressed by his conduct.

The difficulty chasing a substantial total in the fourth innings is the cricketing truism that informs every captain setting a target. These six examples, despite the success of the run-chase, support that belief, as each was driven by one or more outstanding batting performance.

Only Lloyd and Gilchrist made declarations that allowed a fundamental alteration to the course of the game. In three of the matches featured, the declaring captain probably sacrificed little as his team was already nine wickets down. In the remaining case, Smith’s was motivated by the need seize the last opportunity to draw level in the series.

Did you follow, watch or even attend any of these matches – perhaps as one of the sparse fifth day crowd rewarded with a brush with cricket history? Your recollections would be a very welcome addition to this project.

This article is the sixth in a series investigating target-setting declarations in Test cricket. The full series is found by selecting ‘Declarations’ from the top menu bar.

Who dares is occasionally defeated

Test cricket can be construed as a game of scarce resources: wickets, time (in playable conditions), overs, new balls, fresh bowlers and in recent years, unsuccessful DRS reviews. The captain’s job is to eke out the greatest return from those resources. He is competing in a sport where, as in warfare and chess, it’s not enough to gain a position superior to the opponent, one has to defeat the opponent by exhausting their resources (or their ability to call on those resources).

My interest in the third innings declaration stems from it being a juncture where one captain has to weigh up, from a position of superiority, how much to risk, sacrificing one scarce resource to make the most of another, in order to increase their chance of victory. I have presented evidence that captains sometimes err towards caution, costing their team victories. This is the first of two posts which looks at the captains whose experience helps persuade the majority to keep batting for a few more overs, to extend their lead. These are the captains who declared and lost.

Jackie (George Copeland) GrantWest Indies v England, Kensington Oval, Bridgetown – January 1935

Grant was the first captain to have surrendered the scarce resource of third innings wickets in a losing cause. Wisden records he was “a sound tactician and an admirable captain.” So what went wrong? Grant’s declaration is the most unusual of this odd bunch. He declared when his champion bat, George Headley was the sixth man out, setting England a total of 71. Seventy-one. At 7-2, 29-4, 48-6, it was, as surely no-one at the match said, game on. Wally Hammond though, ensured England prevailed, making 29*.

Such abnormal tactics were a response to an abnormal, rain-affected pitch. The two captains took turns hurrying the opponents to the crease in the hope of finding more benign conditions for their batsmen. Wyatt declared England’s first innings 21 runs behind. Batting again, Grant altered his batting order, but when Headley, down the order  at seven, failed, the declaration came.

Modern captains may think there is nothing to learn from Grant and Wyatt’s battle of wits, so anachronistic the conditions in which the game was played. I think everyone can learn from the series result: 2-1 victory for the West Indies. Everyone except the modern captains playing two-off tests, where resources are so scarce that ground lost cannot be made up.

Norman Yardley: England v Australia, Headingley – July 1948 (see header picture)

I cannot resist the cliche that Yorkshiremen aren’t known for their generosity, yet Yardley lost a match in front of his home crowd, England having scored 496 in the first innings. The match is rightly known for Bradman, in his penultimate game, making an unbeaten 173 and batting with Arthur Morris in a partnership of 301 on day five. So, was Yardley at fault, 2-0 down, with two to play, to set Australia 404 in five minutes under a day’s play? I don’t think so, although the top six: Morris, Hassett, Bradman, Miller, Harvey, Loxton are amongst the best ever.

The contemporary account, in Wisden, is clear: England made ‘a succession of blunders’. Pre-match: selection (omitting Young, a left-arm spin bowler); and fifth day: poor leadership from Yardley, poor bowling that didn’t make the most of the wicket taking turn, and sloppy fielding. But it’s not the declaration that’s criticised, although many were surprised to see England’s ninth wicket pair bat for two overs on the fifth morning. Hindsight has been kinder to Yardley and England, as Australia’s achievement is recognised. It remains the fourth highest fourth innings total made to win a Test match.

Dudley Nourse: South Africa v England, Port Elizabeth – March 1949

This match had the tempo of a track cycling race. Three and three-quarter days of steady accumulation, scoring at around two runs per over, and then a burst of activity in the final 95 minutes as England accepted the challenge of chasing 172. Crapp hit ten from three successive balls and the game was won with a minute to spare.

Nourse’s declaration came as a surprise and appears as an afterthought. Trailling in the final test of the series, his team had an 85 run lead before losing the first wicket of their second innings. But they batted on, slowly, into the final session of the match. If a lesson is to be drawn from Nourse’s experience at Port Elizabeth, maybe it is that a single, isolated bold move only serves to make a team vulnerable. However, England lost seven wickets in their chase, so Nourse was not far from conjuring a victory from very little, if any, match advantage.

Gary Sobers: West Indies v England, Port-of-Spain, Trinidad – March 1968

It was another 300 tests before the error was repeated and it has become the decision that is most associated with the captaincy of cricket’s finest ever all-rounder. Sobers lost the match, but only nine West Indies wickets fell in the game. Their first innings total topped 500 and they led England by over 100 as they began their second innings. The declaration set England 215 in two and three-quarter hours. Weighed against Sobers’ men was the injury to Charlie Griffith.

To have had a meaningful chance of victory, Sobers could not have delayed the declaration. But it showed a little too much leg to the England batsmen who won for the loss of just three wickets and with three minutes to spare. Wisden records that Sobers had been “fatally persuaded” that England would be vulnerable to Butcher’s occasional leg-spin, as they had been in the first innings. It was the only positive result of the series, with England’s tailenders twice hanging on at the end of a match for a draw.

Graham Dowling: New Zealand v West Indies, Auckland – February/March 1969

Sobers, fewer than 12 months later, became the first of only two captains to have been on both sides of an unsuccessful third innings declaration. Sobers and Dowling both lost matches they might easily have drawn – although Dowling sacrificed fewer third innings resources, declaring eight down. Neither lost when behind in the series. Indeed, this was the first of a three test series.

Dowling gave the West Indies five and a quarter hours to chase 345. A third innings partnership between Nurse, who scored 168, and Butcher accounted for half of the requirement. The victory was achieved deep into the final hour – a very fine batting performance on a final day that lacked the excitement of three (or four) possible results as New Zealand did not threaten. One week later, they won the second test, which was followed by a drawn match, leaving the series tied.

Declarations six to eleven will follow in a future post. The first five feature two captains chasing victory when behind in a series, two setting inviting targets that were expertly chased down and one captain who saw sacrifice as the only road to success in extreme conditions. All the matches happened long before I was aware of cricket and I have relied on Wisden accounts. I would be fascinated to hear of other perspectives on these matches.

My series of articles on test match declarations are now found together under the menu title ‘declarations’ at the top of this page.

Making the game safe

Not a post about the advisability of batsmen wearing helmets, teenage quicks bowling eight over spells or crowds being prevented from ambling across the ground at the end of match. No, safe here means cannot be beaten, having an unassailable lead. I am returning to my theme of Test match declarations.

The story so far: in the history of Test cricket 37% of third innings declarations end up in victories and only 2% as defeats. Looking at the last three calendar years, successful declarations are associated with major nations playing minor nations, many overs remaining for the fourth innings, higher targets and lower target run-rates. This post looks at the drawn matches in the sample period to query whether the declaring captains were over-cautious.

I am going to draw on, and so want to prominently acknowledge, the fascinating work of Dr Philip Scarf and Sohail Akhtar of the University of Salford. I came across Dr Scarf’s work while researching this piece and am very grateful that he has allowed me to draw on some of it. In brief, Dr Scarf is an academic statistician who has analysed ten years of Test matches to model their results. The statistical proofs used are beyond me, but the conclusions illuminating. A full reference to the paper I borrow from is at the end of this post. I am making use of a table on p8 of his paper which calculates the probability of the three outcomes of a third innings declaration. For example:

Scenario – Target: 300. Overs remaining: 100.

Result probability – Win: 0.465   Draw: 0.274   Defeat: 0.261

What follows is a distillation of a review of the 18 drawn tests following third innings declarations in the sample period. Distilled out are: three declarations made to end the match early without a fourth innings getting under way; four declarations which were made for the purpose of nuisance – i.e. to discomfort the opposition late in the game, rather than as a serious attempt at winning the game (England at Brisbane in November 2010 is the archetype.)

The review comprises three perspectives:

  1. hindsight – how close to victory (or defeat) did the declaring captain get and so would an earlier declaration have made the crucial difference? I calculate and depict closeness to victory as a percentage – for the bowling team, not of the 10 wickets required, but using the average duration (in balls) of each completed wicket partnership (1st to 10th) in the sample period. This gives a more meaningful weighting of the significance of top order wickets and the proximity to victory when amongst the tail – on average!
  2. anecdotal – did the captain appear to delay the declaration? What was in it for the captain to make a bold declaration (e.g. Series situation, relative strength of the two teams)
  3. Scarf predictive analysis – according to Dr Scarf and Sohail Akhtar’s model, how much could the skipper have altered the balance of odds in favour of a victory (or defeat) with an earlier declaration?

And then I judge: Captain Cautious, Skipper Intrepid or just Captain Sensible. Five captains were the decision-makers and each is dealt with in turn.

Andrew Strauss

Eng v WI in Antigua (February 2009)

Strauss declared mid-way through the second session of the fourth day, over 500 ahead. Just one West Indian wicket remained between England and victory (96% of the target requirement) the following evening. Hindsight says that any additional time could have secured a win for England, who had the incentive of being behind in the series (although two more matches were to be played).

Dr Scarf’s analysis doesn’t consider targets above 450. However, the likelihood of winning has peaked for fourth innings with 140 overs remaining with a target of 400. The model suggests that batting on for 20 overs cost England a 90%+ probability of winning, reducing the probability to below 80%. Captain Cautious

Eng v WI in Port-of-Spain (March 2009)

Two matches later and Strauss was able to set a total of 237 at lunch on the final day of the series. England had the West Indies eight wickets down (91% of target requirement) at the close of play. Just a few more overs and Strauss may have had the satisfaction of levelling the series.

Dr Scarf’s table shows that Test matches are rarely won by sides setting totals below 250. With as few as 66 overs remaining, a draw was the most probable result, but a successful chase more likely than the side being bowled out. The model indicates there was little to be gained from an earlier declaration. Captain Sensible

Eng v SL at Lord’s (June 2011)

Strauss made this declaration during the final afternoon of the match. England’s three wickets and Sri Lanka’s total of 127 both represent 37% of their respective targets. While this suggests Strauss required a lot more time, his attack had skittled Sri Lanka on the final day at Cardiff the previous week. One-nil up with two to play, Strauss had no incentive to gamble.

The model would have given England a one-in-eight chance of victory. Declaring 20 overs sooner would have more than doubled the probability of an England success, but given Sri Lanka a 15% chance of squaring the series. Captain Sensible

MS Dhoni

Ind v NZ in Wellington (April 2009)

Dhoni set New Zealand 617 in 160 0vers. They survived due to the loss of 70 overs to the Wellington weather when eight wickets down before play was ended ahead of lunch on day five. India were defending a one-nil lead in the final game of the series, which influenced their decision to carry on batting, setting a target over 30% higher than the record fourth innings chase.

Dr Scarf’s model doesn’t cater for targets so large, but he does conclude: “if a very large target is set, the team batting last will not attempt to play for a win and a draw becomes more likely.” Captain Sensible

Ind v WI in Bridgetown (June 2011)

Dhoni’s declaration set the West Indies 283 in 83 overs. With 15 overs lost to rain, India still managed 85% (7 wickets) of their target. Dhoni was praised for his boldness, which gave a filip to a rain-affected match with a tense final day. What’s more, India led the series one-nil with the third Test still to play. On the debit side for the Indian captain, he was fined for a slow over rate, which may have reduced his team’s chances of winning.

The probability table suggests a pretty even chance of each of the results and nothing to be gained from an earlier declaration. Skipper Intrepid

Younis Khan

Pak v SL at Colombo (July 2009)

Pakistan declared three overs into the afternoon of the fourth day, with their tenth wicket pair at the crease. A day later and 15 overs before the scheduled close, Sri Lanka were closer to victory – 79% of the way towards their target of 490 – although both teams attracted criticism for not pursuing victory more urgently. The game was a ‘dead rubber’.

Extrapolating from the probability table, Pakistan were very heavy favourites (c.90%), giving themselves 160 overs to bowl Sri Lanka out. Captain Sensible

Graeme Smith

SA v Eng at Centurion (December 2009)

Smith set England 364 in 96 overs and came within 4% (or one wicket) of the victory on a fifth day of swinging fortunes. It was the first match of the series and Smith was without Steyn, the spearhead to the attack. The England tenth wicket pair survived three overs, with number 11, Graham Onions, facing 12 balls (shown at the head of this post).

The probability tables suggest a victory as the most likely outcome, and defeat at under 10%. Chances of victory grow steadily however, with the more overs available with targets between 300-400. Captain Cautious

SA v Eng at Cape Town (January 2010)

Three weeks later, now one-nil down in the series and Smith again declares to set England a target: 466 in 141 overs. 47 more overs than South Africa had available at Centurion. The result, in graph form, is identical, but England’s dogged defence more consistent than in the earlier Test.

Scarf’s table put the chance of a South African victory at over 80%. The same probability as if Smith had declared 20 overs earlier and set a target 100 runs fewer (as would have been the case). The probability of an England victory would have been much higher, however, with the earlier declaration. Captain Sensible

SA v Pak at Dubai (November 2010)

Smith set Pakistan 451 in 131 overs in the first of this two match series. While the declaration was seen at the time as ‘on the conservative side’, Smith’s side were the clear favourites. As the graph shows, however, Pakistan were closer to their target than South Africa with the largest percentage point advantage to the batting side in these drawn matches (76% v 37%).

The probability table suggests a c.70% chance of victory and only 1% chance of defeat. A declaration at lunch on day four would have lifted that probability to 80% but increased the chance of defeat to 16%. Captain Cautious

SA v Pak at Abu Dhabi (November 2010)

One week later, Smith again set Pakistan a total, but from a less commanding position: early on the fifth day with a lead of 353. The value of batting for five overs on day five was questionable, but seems unlikely to have tipped the balance as Pakistan lost only three wickets before the match was brought to a close. The series ended in a ni-nil draw.

Scarf’s table suggests a two-thirds chance of a draw, with only marginal improvements to South Africa’s odds (and larger increases to Pakistan’s chances) with an earlier declaration. Captain Sensible

Tillakaratne Dilshan

SL v Pak at Sharjah (November 2011)

Rain delayed the start of day five, with Sri Lanka 237 ahead with 67 overs remaining. The slow scoring rate in the match would mitigate the risk to Dilshan, whose outfit were one-nil down in the last of three tests. But Dilshan batted on for four overs, increasing the target by 18.

The probability tables show the draw was the favourite (50-60%), with a successful chase more likely. With lower targets rarely producing victories, Sri Lanka’s chances would not improve with an earlier declaration. Captain Sensible

Acting as judge of the positive intent of these Test captains, I’ve concluded that on three occasions (out of eleven) the timing of the declaration was over-concerned with making the game safe, reducing the chance of victory. There were two other tests where declarations came later than appeared to be necessary, but I judge the delay as having little impact on the result.

There exists some evidence, from a minority of declarations, to support my original contention that ‘losing feels worse than winning feels good’. None of the delays to declarations was flagrant, but each were in series still ‘live’ and so could have made a difference beyond the match itself.

In this review, I have isolated the timing of the declaration decision, but do acknowledge that what followed in the fourth innings, e.g. quality of bowling, fielding, determination of the batting, umpiring decisions, pitch and weather conditions, all played a part alongside the declaration in bringing about result.

Acknowledgement: An analysis of strategy in the first three innings in test cricket: declaration and the follow-on. Philip Scarf and Sohail Akhtar. Salford Business School Working Paper Series. Paper no. 337/10.

All the time in the world

Graeme Smith called in his batsmen 40 minutes into the afternoon session of the fourth day. Smith’s declaration left England 141 overs to survive, and a target of 466 to chase. Three weeks earlier, Smith’s South African team had been defied by England’s tenth wicket partnership, which had batted out the last four of 96 overs. Smith wasn’t going to leave anything to chance this time, one down in the series and only one further match to play.

Roll forward 28 hours and improbably England had once again clung on to draw, nine wickets down.

Ask Graeme Smith if there is a formula to a successful declaration and I suspect he’d answer with a withering look. The pitch condition, weather, fitness of bowlers, state of the series and tenacity of the opposition are all complicating factors. This post continues a series that began with the psychological insight that captains may be hindered in their search for victory as ‘losing feels worse than winning feels good‘; and continued with a high level survey of third innings declarations in test cricket that showed a victory conversion rate of only 34%.

In this post, I start to assess, through a series of charts and brief comments, whether there are features of declarations that are associated with success. I use a non-random sample, but one that is most relevant to Test captains of today. It takes in the 38 third innings declarations made in the last three completed calendar years of Test cricket.

53% (20) of the declarations in this period led to victories – a higher proportion than in the history of Test cricket. Three of the declarations leading to draws are excluded from the analysis as they were made to end the game early, with no fourth innings occurring, leaving a sample of 35. There were no defeats for the captain who made the declaration in this sample.

Chart 1 shows how results relate to match-level factors: venue, state of the series and strength of the two teams (minor = Bangladesh and Zimbabwe; Major = the rest).

There’s a lot of inter-relationship between these factors, but they point to stronger teams and home teams being more likely to turn the advantage of being in a situation to set a total into victory. I’ll move on quickly as I sense Graeme Smith’s attention wandering at the predictability of those results.

The remainder of the analyses look at the match situation at the point of the declaration being made.

Chart 2 shows the size of the target set in each declaration, team by team. The black diamonds represent the targets, with the highest ever fourth innings total conceded by each team in defeat shown as a blue square.

Captains are, as predicted, risk averse. 57% of targets set required Test record breaking chases of the side batting last (i.e. above the 418 hit by an inspired West Indies in Antigua against Australia in 2003). 80% of the targets, had they been achieved, would have set new national records for totals conceded in the fourth innings of a match in defeat.

Chart 3 sets the result of the game against the target total and required run rate.

The higher the target set in this sample of matches, the greater the chance of victory. None of the ten lowest targets produced a victory (or a loss). The lowest target to result in a victory was 366 set by New Zealand for Zimbabwe to chase in Bulawayo last November. In a tight finish, Zimbabwe fell 35 runs short. There was also a strong relationship to run rate required. Only one total with a required run rate above 4 runs per over had a winning outcome for the declaring captain: Jayawardene had set Bangladesh a target of 624 at 4.22 runs per over in Chittagong in January 2009. The remaining victories came in chases where required run rates varied from 2.33 to 3.91.

Chart 4 refines this analysis, by providing a context in which the target is set. The horizontal axis shows the ‘relative target’ – i.e. difference between the target and the highest innings of the three earlier in the game. The vertical axis plots the ‘relative run-rate’ – i.e. difference between the required run rate and the run-rate achieved across the first three innings of the match.

Victories were more likely to occur if the ‘relative target’ was high (i.e. above or not much less than the highest score in the match at that point). An exception (the red diamond furthest to the left) was New Zealand’s victory over Bangladesh in Hamilton in in February 2010 having set a target of 404, some 149 below the hosts’ total of 553.

Victories are associated, however, with lower ‘relative run-rates’. Over half required a lower run rate of the team batting last than had been achieved in the match to that point. This was true of only two of the draws.

Chart 5 depicts the overs available for the fourth innings.

There is a very clear association of victories with having more time to dismiss the opposition. The drawn match furthest to the left (India v New Zealand at Wellington in April 2009) is misleading as 70 of the fourth innings overs available, were lost to poor weather. Sri Lanka were the team that survived the longest fourth innings without defeat, lasting 150 overs (the match was declared a draw after 134 overs) at Colombo in 2009 against Pakistan. Not a single Test was won in this period with a team declaring on the final day.

In summary, this analysis of results following declarations shows that:

  • captains are conservative, generally only being prepared to set targets that would establish new national records for sides batting fourth were they to lose
  • higher totals, lower run rates and more overs are all positively associated with victories.

Does this mean that, as I hypothesised, captains are too cautious and are missing out on victories, fearing defeat? In the next article in the series, I’ll look in detail at the drawn matches in this sample to ask whether their caution is costing their team success.

Setting a target

What was AE Stoddart the first to do, Michael Clarke (above) the most recent, and Ricky Ponting the most frequent? The answer is that they are three of the 148 captains in Test cricket who have declared a third innings to set a target for the opposition.

In a recent post, Does losing feel worse than winning feels good?, I committed to researching Test match declarations. My aim was to find out whether captains are too cautious in the timing of their declarations, drawing matches that they should have won. This post, the first in a short series, begins to explore the question by taking an overview of the third innings declaration in Test history.

Those 148 captains have declared 483 times in Test cricket. It’s a frequent occurrence, happening in 24% of matches played. The next statistic, depicted below, throws some early light on the object of my quest.

The left-hand bar shows the spread of results of all Test matches for the team batting first. The right-hand bar shows the results of all matches that involved a third innings declaration – a sample that is a subset of the matches comprising the bar to the left (NB ties are excluded from both). The most evident variation is the great reduction (16-fold) in the incidence of defeat. That is consistent with the observation that declarations are usually made when a team has the upper-hand in a match. The incidence of draws almost doubles, while the proportion of victories rises by one-tenth.

Based on my theory of over-cautious captaincy, I suggest this points to skippers, their teams having built up a strong position in the match, batting on until their lead and the target set for the opposition, makes losing such a remote possibility that drawing has become more likely than winning. I have often heard commentators express the view that the best thing for a team beginning its second innings with a healthy lead on first innings is to be bowled out. With control of the progress of the match removed from the captain’s hands, his team are more likely to capitalise on their advantage than if it is left to the skipper to decide when to bring his batsmen in.

It is easy to develop theories behind two more charts of declaration outcomes. The first shows the spread of results for each of the top eight Test playing nations in games where they have made a third innings declaration.

Only Australia and Sri Lanka have converted one-half or more of the games where they have declared into victories. Bold captaincy or potent fourth innings bowling attacks could be part of the answer. India, England and New Zealand languish at the bottom.

The second charts match outcomes following declarations decade-by-decade through Test history.

The highest proportion of victories for the team declaring have occurred since 1990. This tallies with a sense that Test cricket is played more positively – e.g. higher scoring rates. I also suspect the higher proportion of all Tests played by the ‘minnows’ – Bangladesh and Zimbabwe – is playing a part in the higher victory conversion rate.

The final set of ‘global’ analyses look for evidence to support or refute my general theory of over-cautious captaincy from the state of the third innings when the declaration came – specifically, how many wickets were down. This provides a very limited view of that innings and its progress, which would ideally include run-rate, lead, overs/time remaining, etc. However, it is the only one that I am able to obtain at the ‘global’ level.

The more wickets that have fallen, the more limited the remaining run scoring potential. Therefore, it could be argued, the captain who declares with, say, eight wickets down is not taking much a risk in terms of his team’s match position by bringing his innings to a close. 29% of third innings declarations came with eight or nine wickets lost. However, 42% came with five or fewer wickets down, and so considerable run scoring potential un-tapped. The picture is ambiguous.

A more telling analysis may come from relating result to the number of wickets lost at declaration. Does a prolonged innings (using wickets lost as the proxy) reduce the chances of having a positive outcome?

In fact, there is no clear association of wickets lost at a declaration and the result. Declarations with five wickets down have produced the highest proportion of victories; those with three wickets lost, the highest proportion of draws.

In summary, this overview of the third innings declaration in Test match history has shown:

  • a team that declares and sets a target very rarely loses, but doesn’t greatly increase its likelihood of winning compared to the results spread of all teams batting first
  • there is a large variance in the rate at which different Test match countries convert declarations into victories
  • victories following declarations have become more frequent in recent decades
  • there’s no association between the match result and how far the captain has allowed the third innings to run – in terms of wickets lost – before declaring.

The next article in the series will move down a level of detail to a sample of third innings declarations. It will consider the impact of the size and required run rates of targets set, as well as how they relate to other scores and scoring rates achieved in each match.

This series owes everything to the mathematical and programming genius of the people behind Cricinfo’s Statsguru. Any errors are mine, not theirs.

Does losing feel worse than winning feels good?

Struggling to understand the European economic crisis and where it may lead, I have found my most trusted source is in America: the NPR programme, Planet Money. Recently, the show sought an explanation for the slow-down in the US housing market in psychology. The first link to cricket is that the psychological insight comes from a coin toss. But instead of batting first or bowling being at stake, it was $6 win for heads and $1 lose for tails. All comers took that deal. But, apparently, when the stake was changed to $6 win for heads and $4 lose for tails, lots of people turned down the bet.

At this point, you can put the finding down to the parlous state of numeracy in the US population or persevere with the promise of a deep psychological truth being revealed.

Sticking with it, the following insight was offered: “our brains feel losses and gains unevenly: Losing feels worse than winning feels good.” Cricket made its second entry – in my mind, not the broadcast.

One of the fixtures of Test cricket media coverage is that the commentators, writers and analysts want to see, argue for and even defy a captain to make a declaration 30 minutes, or an hour before he does call his batsmen in. The people most vocal in calling for an enterprising
declaration are very often those who, one cricketing generation previously, were carefully accumulating runs to put the game beyond the opposition before calling time on their own innings.

Empirical psychology gets criticised for carrying out artificial experiments, often with university students, and developing theories of underlying human behaviour based upon the results. So, I don’t want to fall into the same trap. A stranger asking you to have a bet on a coin toss where you don’t stand to win enough to buy a round of drinks is in no way equivalent to being required to set the terms for the denoument of an international sporting event, followed by millions of devoted fans and whose outcome could determine your fate at the highest level of the game. Except that phrase, losing feels worse than winning feels good seems to ring true for both.

At its simplest the decision to declare an innings (and I’m really thinking of the third innings of a match) in a Test is a balance between time needed to take the ten wickets for the victory and runs the opposition need to score to inflict a defeat. But it’s rarely a simple calculation. The other factors that will usually influence a captain are: the state of the series – are they level, ahead, behind, playing the first test, last test; fitness and freshness of his bowling attack; pitch condition and prognosis; weather forecast. There are well known occasions when the closeness of one of the not out batsmen to a milestone plays a part in the captain’s thinking. And everyone likes to have modern sports’ most ubiquitous virtue on their side: momentum – so much better to end with a flurry of boundaries than a middle-order collapse.

I have set myself the task of reviewing a sample of declaration decisions in Test matches to see if there is support for the idea that the brain feels losses and gains unevenly. In scientific tradition, I will begin with a hypothesis: captains are five times as likely to delay a declaration and end up with a draw than have any target they set chased down by the opposition. I’ll come up with a framework so there is some consistency in how a declaration is assessed based on the game position and balance of bat and ball at the time it was made and I’ll also record the other factors likely to have influenced the captain and any evidence of media comment on the timing of the declaration. I’ll report back in a few weeks. In the meantime, let me know of any matches you think I should review and look out for tweets as I conduct the research. Look out also for a change in my twitter name to Declaration Game – time for some brand reinforcement.