Does the 30-over rule hold in one-day cricket?

With wickets in hand, a team should go on and double its 30-over score in a one-day international - you'd have heard commentators make this statement often over the last few years. Intuitively, you'd think this statement is slightly dated: it should have made sense in the early days of one-day cricket, when the norm was to keep wickets in hand through the early overs, consolidate in the middle, and then look for the runs towards the end.

In the last decade or so, you'd think the blueprint for an ODI has changed drastically - with the fielding restrictions in place in the early overs, teams are increasingly willing to take risks and hit over the top at the start. With the introduction of the Powerplays, the trend seems to have increased even more. The only way to verify the theory is by actually checking the numbers - do the stats support it, or has the game indeed moved on so much that this hypothesis no longer holds? The Numbers Game delves into the Cricinfo database - since this analysis requires ball-by-ball data, we can only go as far back as 2002 - to come up with an answer.

Apart from restricting itself to games after 2002, the analysis has only considered the first-innings performances in non-interrupted matches in which teams have lost four or fewer wickets at the 30-over stage. The explanation for the criteria is as follows: too often the second-innings performance is skewed by teams pacing themselves according to the target, or simply batting for practice if the target is out of reach. The four-wicket cap has been enforced since the loss of more wickets will obviously make it a meaningless comparison, with the last 20 overs likely to fetch far fewer runs.

The overall results indicate that on an average, teams don't quite double their 30-over score, but they aren't that far off. In 2002 teams scored 17 runs fewer in the last 20 compared to the first 30 (140 to 123), while in 2006 the difference was 20, but in the other years the average difference has hovered around the ten-run mark. In the 2007 World Cup, teams were, on average, only six runs from doubling their 30-over score: the average score after 30 was 139 (with the qualifications as mentioned above); after 50, it increased to 272.

Overall, since 2002, teams have averaged 138 after 30 overs in games in which they've lost four or fewer wickets at that stage of their innings. In those games, they've gone on to total 262 after 50 overs, which is 14 runs fewer than double the 30-over score. The numbers suggest, though, that teams are closest to their final score after 29 overs. They average 132 at that stage (again, in games when they've lost less than five wickets then) and end up with 261, which means they get to within three of doubling their score. Also, the introduction of Powerplays has had a negligible effect, with the percentage of runs in the last 20 remaining almost the same.

The other interesting angle is to see how the wickets-in-hand scenario has influenced the final score. Since 2002, only seven times have teams finished 30 overs without losing a wicket: in those innings they've averaged 159 after 30, and finished up with a total of 315 after 50, which is only three runs short of doubling their score. The table below lists the average scores for the first five wickets. After that, as you'd expect, the percentage of runs scored in the last 20 overs drops dramatically.

The other way to examine the theory is to analyse it through the Duckworth-Lewis method, the system that is used to get revised targets and projected scores in interrupted matches. The method is based on resources used up by a team - and hence resources left - which makes it possible to check the projected 50-over score at any point in an innings. Since the system also uses a normalisation process, it ensures that a freakish start will be normalised so the projected scores don't become unrealistic. The table below presents one set of projected scores for a team which is 140 for x after 30 overs, where x represents the wickets lost, from zero to three. Note that when one or no wickets have been lost, D-L projects the score after 30 overs to be more than doubled by the end of the innings.

However, as mentioned earlier, these percentages change according to the score at the 30-over stage. If, for instance, a team has scored 190 without loss after 30, D-L projects the 50-over score to be 373 - an addition of 'only' 183 in the last 20, simply because it's unrealistic to expect a team to more than double its score when it has already made 190 in 30. On the other hand, a score of 110 without loss after 30 gets projected to a 50-over total of 247, which translates into 55% of the total runs coming in the last 20.