Cricket and Maths

Editor: Cricket, lovely cricket! I desire not to remind us that our beloved West Indies cricket team has just lost yet another test series. Instead, I desire to challenge us as learners of mathematics to reflect on two aspects of mathematics, as used in the cricket domain.

Why is this necessary? {{more}} The issue of relating classroom mathematics to real life situations continues to receive much attention. Indeed, many teachers are beginning to see how this translates into rich benefits for the learner. But there is another side to the argument. What are the implications for the mathematics curriculum when local cultural practices appear to twist universally accepted mathematical structures? And this is where, cricket, ‘the game of glorious uncertainties’ seems to be sending down some no-balls within the boundaries of the mathematics classroom.

To solicit a third umpire’s decision on the issue, I draw attention to the use of two mathematical concepts in connection with the “gentleman’s game” called cricket.

Mean or arithmetic average is calculated by adding the scores that are being considered, and dividing the sum so obtained by the number of scores. If a student spent $130 on Monday, $220 on Tuesday and $250 on Wednesday, he would have spent an average of $200 per day over the three-day period. This is sound mathematics. Now consider a similar scenario in cricket. In a test series, Brian Lara scores 130, 220 and 250 runs in the three innings that he batted. What then is Lara’s average score over the three innings? Most children will more than likely shout 200 runs. Mathematically, this is correct, but is it necessarily so in the cricket domain? Yes, if Lara was out on all three occasions. However, if he was not out once, his average score will be given as 600÷2; if not out twice his average is 600÷1. It gets even more complex. If Lara was not out on all three occasions, I believe that his performance will be more often talked of in terms of an aggregate of 600 runs rather than an average score.

Then there is the issue of the use of decimal to record fractional parts of an over. An over in cricket consists of six legal deliveries. When six legal deliveries have been bowled an over is declared. Similarly, twelve deliveries constitute two overs; eighteen deliveries three overs etc. Mathematically speaking nine (9) deliveries should equal 1.5 overs. Oops! Not so in cricket at all! One point five (1.5) overs in cricket is interpreted as one over and five deliveries which translates into 11 deliveries. So nine (9) deliveries recorded in the cricketing domain as a comparison to a whole over is talked of as 1.3 overs.

These seemingly contradictory uses of the concepts of decimal and mean average seem likely to pose some concerns for the mathematics learner, especially as emphasis is placed on getting the learner to make connections between his school mathematics and real life occurrences. How then should the curriculum respond to this seemingly confusing situation? Do we in mathematics, as is often the case with almost every grammatical rule, introduce a clause called an exception to the rule where arithmetic average and decimal are concerned? Or do curriculum planners and developers strive for closer collaboration with personnel within the cricket world?

The first question implies an easier route to be taken, but a third umpire’s decision may yet broaden the discussion.

Kenneth Holder