# “Double the 30-over score” — a cricket analysis

In one-day cricket there is an old maxim about trying to predict a team’s score, mostly referred to by commentators. It states that, on average, a team’s score at the end of its allotted 50 overs will be roughly double its score from the 30-over mark. Or, put more commonly, “Take the 30-over score and double it.”

To those unfamiliar with cricket this may seem odd, as basic arithmetic tells us that half of 50 overs is 25 overs, not 30. Where this maxim comes from, however, is the change in attitude of a batting team towards the end of its innings. Many factors contribute to this: various rule changes around fielding restrictions; batsmen who have had enough time batting to feel in good form; bowlers and fielders getting more tired; and so on. This means that batting teams generally score far more runs in the last 25 overs than in the first 25.

2015 The recent ICC Cricket World Cup 2015 saw a high frequency of large scores, with a flurry of runs coming in the last 10-15 overs. We became accustomed to seeing teams scoring 150 runs in the last 10 overs, having only scored 200-odd runs in the previous 40 overs. This new pattern of scoring has been attributed to several factors that have changed in recent years (e.g. bigger bats, two new balls at the start of an innings, more restrictive fielding regulations). Each change would have some impact on its own, but when all changes are combined together there is a significant difference in the way teams approach a one-day innings.

During the 2015 World Cup, many commentators were heard to say that the old 30-over marker for half a team’s score was now redundant, and that many teams are reaching half their score at around 35 overs. This sounded like a “gut-feel” call to me, so I set out to find data that would sort it out.

My primary aims were to find out:

1. Was the 30-over score ever a reliable guideline or just anecdotal data?
2. Has the overall pattern of scoring changed in recent years in a statistically significant way?

Disclaimer: I am not a statistician, and quite possibly there’s a prominent statistical technique that I’ve missed. If so, let me know on Twitter or GitHub.

## The data

3646 In order to properly study scoring patterns, I needed ball-by-ball data for as many ODI (One-Day International) matches as possible. At the time of writing (just after the 2015 World Cup finished), since the first ODI in 1971 there have been 3646 ODIs where at least one ball was bowled (so this number excludes matches that were abandoned before play started, generally due to rain).

1899 Ball-by-ball data was not collected in the early years of one-day cricket. The first match I could find on Cricinfo with ball-by-ball data was in 1999, leaving 1899 matches with data that I could analyse.

1858 However, there was only ball-by-ball data for a handful of matches in 1999 and none at all in 2000. It wasn’t until mid-2001 that ball-by-ball data was available for each match. Including a small number of matches from 1999 and then jumping forward 2 years wouldn’t provide accurate data trends, so I had to exclude all matches before June 7th, 2001. This reduced the count to 1858 matches.

The next task was to filter down individual innings to only those which lasted a full 50 overs. (Early ODI matches were 60 overs per innings, but these were all well before the 2001 data cut-off.) The “double 30 overs” rule only works for teams that complete a 50 over innings. Any team having its innings cut short (e.g. by losing all its wickets, or rain reducing the overs available) loses the ability to pace its innings properly and would skew the statistics.

1348 1858 matches with 2 innings per match gives 3716 innings in total (not all of which will have been played, due to rain or other interruptions). Restricting to only those lasting a full 50 overs reduces the list to 1348 innings, or 36%. Of these, 1173 (87%) are from the first innings of the match. This is hardly surprising, as the team batting second is most likely to either lose by being bowled out chasing a target score, or win by chasing the target before reaching 50 overs.

With the data gathered, I could finally start analysing these 1348 innings to determine at what point teams hit their halfway scores. Or, going back to the questions above, was the 30-over score ever a reliable guideline? Short answer: Yes (close enough, anyway).

Over the last 14 years, teams that have played their full 50 overs have, on average, reached half their score at 29.2 overs (using standard cricket scoring notation, where “29.2 overs” means 29 overs and 2 balls, with 6 balls per over). This is close enough to 30 overs to give a Mythbusters-style confirmed to the old maxim.

IMAGE: A graph showing the average halfway mark as described in the next paragraph.

Graphing out the data reveals that, since 2001, the average has been consistently within 2 overs of the legendary 30-over mark. The average started high at 30.3 overs (mostly due to an insufficient amount of data) then dropped down to its lowest value of 28.0 overs in 2002. Since then it has been slowly but steadily increasing to its current value of 29.2 without any decrease along the way. This suggests that modern teams are indeed consistently reaching half their score later in their innings than they were 10-15 years ago.

## Digging deeper

The second question I wanted the answer to was: Has the overall pattern of scoring changed in recent years in a statistically significant way?

In order to find the answer, I graphed out a 100-innings rolling average, to give a better indication of trends over time.

IMAGE: A graph showing a rolling average halfway mark as described in the next paragraph.

This shows a few more peaks and troughs, reaching a lowest point of 27.5 overs in 2002, then jumping up to 29.4 overs in 2004. After another drop to 28.3 overs in 2006, the rolling average remained relatively stable between 29.1 and 29.4 overs for many years. Since the beginning of 2013, the scoring rate has significantly increased, bringing the average for the most recent 100 innings (which reached 50 overs) up to 30.5 overs – the highest it’s ever been.

One reason for the higher scoring – given by commentators and armchair experts alike – has been the change in rules for fielding restrictions in late 2012. The reduction from 5 to 4 fielders outside the 30-yard circle (in the non-Powerplay overs) has provided more opportunities for batsmen to score boundaries by hitting over the top of fielders. But does this theory hold true?

The rolling averages listed above certainly indicate a change in scoring patterns around the same time. Just how much of an effect did the fielding restriction changes have? I compared two groups of innings: One from the rule change on October 30, 2012 until the World Cup final on March 29, 2015 (a period of 2 years, 5 months), and one group from the equivalent time period before the change (giving a start date of May 30, 2010).

IMAGE: Two highlighted sets of data show consistently different averages for two equal time periods either side of the restriction changes.

Here we see that in the 2-and-a-half years leading up to the changes the average halfway mark never got above 30 overs, hovering consistently between 29 and 30 overs (with a highest point of 29.5 overs). After the rule changes there is a dinstinctly different pattern, where the average never drops below 30 overs.

Although it’s only a 1-over difference in the average, the consistency of the higher marks indicates a definite change in scoring patterns. So the answer to the second question, then, is also a yes. Confirmed

## Other explorations

With my primary questions answered, I set about playing with the data to see if there any other interesting little stats jumped out at me. Below are some of the findings.

### Data extremes

16.2 The earliest point that a team reached its halfway score was at 16.2 overs, by England against Pakistan at Manchester in 2003. Having scored at a run-rate of 6.24 runs per over to reach 102/3 at that point, England slowed down and scored only 3.03 runs per over from then on, finishing at 204/9 in 50 overs. Pakistan then scored 208/8 in 49.2 overs to win with only 4 balls to spare.

40.3 Conversely, the latest point in an innings for a team to reach its halfway score was at 40.3 overs, by Bangladesh against New Zealand at Dunedin in 2010. Bangledesh started extremely slowly, only scoring at 2.27 runs per over to reach 92/6 at 40.3 overs. From then on, the innings finished with a bang as the remaining 91 runs were scored at 9.58 per over to finish at 183/8. Unfortunately for Bangladesh, New Zealand then scored 185/5 in 27.3 overs for a comprehensive victory.

### 1st vs 2nd innings

IMAGE: A graph of scores in the first innings of a match only. IMAGE: A graph of scores in the second innings of a match only.

There is a stark difference in averages for the two phases of a one-day match. The average halfway mark for teams in the first innings is 29.3 overs, while in the second innings it’s only 27.5 overs. It is harder to construct and pace an innings when chasing a total, meaning there a fewer teams managing to effect the same kind of increase in scoring rates in the last 10-15 overs.

I should note, though, that the sample sizes are vastly different for the two sets of data. As mentioned earlier, there are 1173 data points for the first innings but only 175 for the second innings. Therefore, the above stats should be taken with healthy dose of skepticism.

### Test-playing nations vs the rest

IMAGE: A graph of scores from test-playing nations. IMAGE: A graph of scores from non-test-playing nations.

The 10 nations with Test-playing status play One-Day Internationals far more regularly than those nations who do not play Test matches. They also generally score higher (and therefore faster). But do the two groups of nations (those with Test status and those without) have different scoring patterns?

Given how infrequently the non-Test-playing nations (the “Associate nations”) are able to play fully qualified ODIs, the data should be viewed with the same skepticism as the 2nd-innings data in the previous section (only 135 innings are counted). Most of the non-Test innings are clustered around tournaments such as the World Cup. These stats also include special temporary teams such as the ICC World XI.

Surprisingly though, there is little difference between the two groups in their scoring patterns. The halfway mark averages since 2001 are 29.2 overs for Test nations and 29.3 overs for the others.

## Credits

The main inspirations for this were the MBTA (Boston subway) data analysis and some random conversations with fellow cricket tragics at work.

Statistics include all men’s One-Day Internationals from June 7th, 2001 to March 29th, 2015.

All data originally came from Cricinfo and are probably under copyright, but it’s very hard to find any data usage guidelines on their website. These analyses were done as a personal hobby project only. Cricinfo also did an analysis of run-rates in the 2015 World Cup that is worth reading.

The rest of the content here is © 2015 Gilmore Davidson. The source code is available on GitHub for those interested.

A write-up of the technology used to build this article was posted on my personal blog: Responsive graphs and custom elements.