When is a batting average not a real batting average?

That's the question posed by University of Otago economics professor John Howells in an article which appeared in Dunedin's Albion Cricket Club's annual report.

Always one of the more quirky, humorous and best presented club annual reports, the Albion club is onto a thought-provoking and contentious matter here.

Howells asks after looking at the averages of the 1999 World Cup: "How could [Lance] Klusener have a batting average of 140.5 if his highest score was 52? How did [Tom] Moody, over five innings, have an average of 117 when his aggregate of runs was 117?

"The reason for such statistical absurdities is the convention that batting average is calculated by counting only completed innings.

"It is, in effect, the mean number of runs per completed innings of any batsman.

"In simple terms, the score for not-out innings is counted but the innings itself is ignored when dividing the total of innings into the total of runs to determine average," he wrote.

Howells said not-out innings seriously inflated batting averages and pointed out that [Trevor] Bailey had 215 and [Wilfred] Rhodes 237 in their first-class careers. While in Test cricket, Steve Waugh had 18.9% (at the time of writing - Ed) and Imran Khan 19.8% of their innings as not outs.

He also made the point that of 57 players listed in Wisden 1999 with an average of 50 or better and a minimum of 10,000 runs, 45 had 10% or more of not-out innings, 12 had 15% or more as not-out innings.

"Given the incidence of not-outs, the procedure for calculating batting average generates results that are often bizarre and produces inflated averages which undermine the effectiveness of batting average as an honest and accurate measure of a player's performance.

Furthermore, it is not clear what sort of average is being calculated.

"It is not a batting average for completed innings because not-out innings are included in the numerator.

"It is not a batting average for not-out innings are excluded from the denominator.

"The purpose of an average is to represent a group of individual values, but it is not obvious what it is that a batting average represents.

"The public has been presented with an imposter dressed in the robes of a batting average," he said.

The answer was a simple and sensible alternative.

"By removing the distinction between completed and not-out innings, batting average can be calculated simply by dividing total runs by total innings [call it RBA or 'real batting average']," he argued.

In his article, Howells also refutes the arguments put up by those who would retain the status quo.

He said there was no real difference between not-outs and completed innings and as a result no logical reason for not counting all innings as completed in calculating average.

Of the 57 players with a first-class average of 50 or more in Wisden 1999, batting averages fell by 10% or more for 45 of them when the RBA was applied. Forty-eight players missed the 50 mark with only Don Bradman, Bill Ponsford, Vijay Merchant, Bill Woodfull, Sachin Tendulkar, Arthur Morris and Walter Hammond remaining in the elite category above 50.

Howells concluded: "This review seeks to show how far the conventional batting average is out-of-line with actual on-field performance.

"As a classic example of this, consider Bradman's last Test innings. From press reports in 1948, and since, he was bowled within four runs of averaging 100 in Test cricket.

"Not so!

"To score 100 runs, 'on average', in every Test innings, Bradman needed 1004 runs from his last innings.

"Again, recent statistics give Steve Waugh a Test average of 50.8.

"Not so!

"To score 50.8, 'on average', in every Test innings, he still needs 1778 more runs.

"These two examples, and there are others, patently expose the schizophrenic nature of the conventional batting average, namely, its inability to recognise reality," he argued.

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