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The Actuary The magazine of the Institute & Faculty of Actuaries

Batting on a statisticky wicket

When a cricketer goes out to bat, his career statistics are shown on the television screen. The most important figure quoted is his average score, but nothing is indicated about his consistency. This information, however, should be of considerable interest to the viewer. In this article I shall explain why.

Tossing up
The standard deviation is a good measure of consistency, but in itself it is not useful for comparing players of different abilities. If you averaged 100, for example, your standard deviation would naturally be higher than for someone who averaged 5. Therefore, we need to ‘normalise’ the standard deviation by dividing through by the average score:
We calculated a consistency coefficient (CC) statistic for 200 international cricket players using data up to 14 February 2005. In recognition of the notion that bigger is better, we defined the CC as the inverse of the above ratio (so that more consistent players had a higher CC statistic) and we also introduced a slight variation in order to handle any not-out scores. We then allocated cricketers to different classes, both for one-day international (ODI) matches and for test matches, as shown in table 1 above.
We then plotted 10 different players’ averages (y-axis) against their CCs (x-axis) for both ODI and test cricket, as shown in figures 1 and 2.
A declaration
The ODI graph indicates that in one-day cricket, Herschelle Gibbs averages second-lowest of the ten players analysed, with very low consistency around his average. Seeing that he is inconsistent around his average of 35, if may be inferred that he is more likely to produce a score much higher than his average. So in this sense, his inconsistency could be considered a virtue!
The above reasoning can also be applied to the selection of players with low averages. As a captain, I might find myself favouring a batsman who scored 10 on average, but with frequent low scores and occasional very high scores, over a batsman who scored consistently 10 every time he played.

Drawing stumps
The CC serves as an additional statistic by which to compare batsmen. In particular, it is very useful when used in conjunction with the average score. With the advances in cricket statistics shown on television screens, the CC may be appropriate for use in cricket broadcasts. It would definitely give cricket fans something else to discuss in post-match debates in the pavilion.