Using up your overs

50 overs-page-001Wickets 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.

bowled out-page-001

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.

1st inns win-page-001


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.

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About chrisps

TouchlineDad to three sporty kids; cricket blogger and coach; and the alpha male in our pride.

7 responses to “Using up your overs”

  1. Andy Powell says :

    How typical of Lawson to take the contrarian position. I have enjoyed his thoughtful and perceptive commentary for several years on the ABC.
    Makes you think that genuine “non batsmen” down the order should just cultivate their slogging technique…

    • chrisps says :

      Andy, good to hear from you. Lawson was excellent on radio. Is he still broadcasting in Aus?
      Unfortunately Stuart Broad had taken your advice to heart. Would like to see him graft for some runs – even in an ODI.

  2. Seamus Hogan says :

    Please keep tweeting this post, Chris. It has been a hobby horse of mine for years. Batting teams have two scarce resources–wickets and balls. Why has it become considered a cardinal sin to not use up all 300 balls, but it is not considered poor to bat out 300 balls leaving hard-hitting batsmen in the pavilion with their pads on?

    My reading of your graph is not that there are rises and levellings, but rather that there is small-sample variation and that the true relationship is essentially a straight line. What that means is that the way for the team to maximise its probability of winning is to maximise its expected score.

    • chrisps says :

      Thanks Seamus. This World Cup so far is providing few opportunities to push a piece about the dilemma of whether to go for runs and risk being bowled out in the 1st innings.

      I am sure you are right about the straight line relationship of runs scored and match outcome for 95% of scores. I wonder, though, whether very low and very high scores would show a slightly different relationship e.g. At the low end, prospects of victory are very low and unchanging until, say, 150 is reached.

  3. Seamus Hogan says :

    Chris. There is definitely a flattening of the relationship between first-innings score and probability of winning at low and high scores (as there must be, given that probabilities must be between 0 and 1), but surprisingly, it doesn’t change the conclusion that score-to-date should have no impact on whether a team should bat aggressively or not. I hope to do a post on this soon.

  4. chrisps says :

    Look forward to reading that.

  5. Dave says :

    Hi Chris,
    I covet memories of watching the televised JPL games (often Gloucestershire) in the 70s, and how it appeared that the team batting first often took the nudge and nurdle approach, seeking to achieve a “competitive” score.
    Jim Laker, if he was on commentary first, might describe Jim Foat’s innings of 18 as “useful runs in the middle order” concealing the reality that everyone had turned on to watch Zaheer and Proctor. If John Arlott was on commentary first there were often periods of lengthy silence as the leg byes accumulated possibly denoting that he was either asleep or had gone to find another bottle of Macon Villages.
    Lovely to see that, in these days of playing the percentages, sometimes attack is worth a punt. Viv Richards and Michael Holding at Old Trafford in May 1984 ?

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