Using up your overs

Wickets tumble in the first innings of a one day international. Commentators will urge the batting team to do it. Failure to do it will be condemned as a cardinal sin. Using up your overs; batting the full 50 is the very least expected of a side batting first.

It’s a viewpoint that is well supported by the historical records of sides that have been bowled out without using their full allotment. In recent years, between one-quarter and one-third of all matches have featured the side batting first being dismissed. In the period shown in the chart below, only 20% of those sides batting first and losing all their wickets have won the game.

There’s a strong association between the number of balls forfeited and chance of defeat. There’s no magic in that relationship. The shorter the innings, on average, the lower the score.

The importance of batting out the overs is a viewpoint with a critical consensus backed up by some solid data. It was almost shocking to hear a voice of dissent. It came on Test Match Special a few years ago. The batting team were struggling and the commentator made the usual injunction that the lower order see out the overs.

“Why?” asked Geoff Lawson, who went on to rationalise that if all the batting side attempted was to survive the 50 overs, they were very unlikely to set a winning total. Wouldn’t it be better, Lawson argued, to hit out with the aim of setting a challenging target, accepting the risk that they could be bowled out, than to crawl to an unsatisfactory total?

Lawson was positing the batting team, while in adversity, having a tactical choice to make. They had to decide how to balance risk and reward. It felt distinctively Australian to stress there was a route other than that of damage limitation; one that could very well leave the team scoring fewer runs than if they took the conventional approach of using up their overs.

It is also a notion that can be explored statistically. The chart below shows the win % of teams making below par scores (in 5 run intervals) in the first innings of ODIs since 1996 when the 50 over per side format became standard across the world. Matches where weather or playing conditions reduced the first innings to fewer than 50 overs have been excluded.

 

Between 145 and 170, there is a low but steadily increasing probability of winning. From 175 to 199, however, the win percentage levels out, before jumping from 20% to 35% when 200 is reached. Thereafter, it’s not until 230-234 that there’s another increase in win percentage.

The nudge & nurdle method can be measured against Lawson’s long-handle approach by selecting a scenario and applying some probabilities. I have chosen a team on 140-7 after 40 overs.

The approach of maximising the length of the innings can be expected to yield a total in the range of 180-184; although there is, say, a 20% possibility that they will be bowled out, despite their best efforts, for 160-164.

Their chance of winning (based on past results) would be:

(0.8 x 0.21) + (0.2 x 0.13) = 0.194

The long-handle method could take them to a healthier 210-214, accepting that about half the time they would swing and miss and fold for 150-154. Using past results, this produces a win likelihood of:

(0.5 x 0.07) + (0.5 x 0.37) = 0.22

In this particular case, with these probabilities, it’s better to attack, than see out the overs. Other situations, perhaps where, say 190, is the maximum that an aggressive approach could bring may repay the conventional conservation of wickets and seeing out the overs.

Individual match situations – the respective strengths of teams, expected change in playing conditions, the batsmen at the crease, perceptions of par scores for the venue, etc – will all trump the message of this historical analysis. What I hope it does show, however, is that a blinkered trudge towards the final ball of the fiftieth over will not always serve the batting team best.