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.