Reflections on Sport and mathematics
The value of graphical presentation of data: an example from cricket

Iain Skinner, School of Electrical Engineering, The University of New South Wales

I recently found an elegant, instructive example of how some simple mathematics, combined with the power of a small computer, allows a very intelligible graphical presentation of information that is conventionally presented in long, barely comprehensible tables of numbers. Given that finding ways to interpret numerical information is an important function of mathematics, and given that the subject of the example was cricket, I thought there may be wider interest in this instructive example.

In cricket there are three numbers frequently used as summary statistics to indicate the quality of a bowler's performance. The first, and most frequently quoted, is the average (ave), which is defined as the total runs scored off, divided by the number of wickets taken by, the bowler. It is often termed the cost of a wicket, and, in general, the lower the average, the better the bowler. The second number is the bowler's strike rate (SR). It measures how often a bowler captures a wicket and is defined as the total number of deliveries bowled divided by the number of wickets taken. Again, the lower the better. The third number characterizing a bowler is the economy rate (ER). There are several definitions of this. (The definitive source of cricket records, the annual edition of Wisden Cricketers' Almanack, does not calculate one at all.) The one used here (consistent with the definition of Kimber (1993)) is the number of runs conceded per hundred balls bowled. Once again, the smaller the number, the better is the bowling.

By tradition (and cricket is a very traditional game) cumulative bowling figures are gathered for a specified period of time (season, career, etc.), and then ordered and tabulated, necessarily in a small font so that the most numbers can be arranged on the least number of pages. A glance at a typical set (e.g. Tables 1 and 2) of bowling figures shows that it is not immediately clear who has performed best. If the table were ordered by average, as is often the case, the better strike rates would remain obscure. Providing a second table, while helpful, does not solve the difficulty, for comparison across tables is not easy. An improvement in presenting a comparative summary of bowling performances was explained by Kimber (1993).