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:
- 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!
- 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)
- 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.
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
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
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
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
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.