Cricket Batting Averages and Not-Outs: Why the Average Misleads

Cricket loves averages. A batter's career is summarized as one number: total runs divided by the number of times they were dismissed. It looks innocent, but a hidden detail, the not-out innings, makes this one of the most interesting problems in sports statistics.

The not-out problem

The traditional average divides runs by dismissals, not by innings. A not-out innings adds runs to the top of the fraction but nothing to the bottom. The innings is unfinished, which statisticians call censored: the true score the batter would have reached is unknown.

Consider two batters with 20 innings and 900 runs each. Batter A was not out 10 times, so his average is 900 / 10 = 90. Batter B was not out twice, so his average is 900 / 18 = 50. Yet both scored exactly 45 runs per innings. The ranking by average makes A look nearly twice as good.

Extreme cases

Push the idea further: a batter with 20 innings, 19 of them not out, and a total of 950 runs would have an average of 950, far above any score they ever made. Research on improved batting averages notes examples where the traditional average even exceeds the highest score (IIM Bangalore working paper).

The descriptive statistics calculator lets you compare runs per innings, the mean of completed innings and the median for any list of scores, which already reveals these differences.

The geometric idea

A simple model says each ball faced carries a constant chance of dismissal, so the number of balls survived follows a geometric distribution. With a 2% chance per ball, the expected innings lasts 50 balls, and the geometric distribution calculator shows that the batter survives 30 balls about 55% of the time.

Real batting is not that tidy. A classic analysis found that the geometric assumption fails for many players, largely because of the excess of early dismissals, and used survival-analysis methods instead (Kimber and Hansford, 1993). Batters are more vulnerable early in an innings and settle later, a pattern called getting your eye in (Brewer).

Treating not-outs properly

Survival analysis, such as the Kaplan-Meier approach, treats a not-out as an innings that survived at least as far as it went, so it contributes information without being miscounted as a dismissal.

The exponential distribution calculator gives a continuous version of the same waiting-time logic, and our article on mean versus median explains why a single number rarely tells the full story.

Why limited-overs cricket makes it worse

In limited-overs formats, innings often end because the overs run out, so even good batters finish not out regularly. The traditional average then rewards batters who are left stranded at the end of an innings as much as those who build one patiently. Comparing a Test average with a one-day average without thinking about not-outs can mislead.

None of this makes the average useless. It remains a handy summary, and for batters with few not-outs it is close to the runs-per-innings figure. The point is to know when it needs a second number beside it.

Next time you compare two batters, ask how often each was not out.

An average is a good start for a conversation, not an end to it.