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.