Who's the best cricketer?
by Aditya Rishi

THE most tempting challenge of all is to know who is the best player in the world, so, today's challenge is to devise a reliable cricket rating. Cricket has always been popular with mathematicians because it is so full of numbers and statistics. Devising a cricket rating, I may warn you, is as "easy" as facing Brett Lee on a fast pitch.

Let's hear it from an expert: In 1987, Rob Eastaway, a young mathematician, was approached by the former England cricketer Ted Dexter to see if Rob could help him devise a better method of rating cricketers statistically. Rob is still involved in running cricket ratings.

Here's what he told Dexter: "Statisticians largely rely on a simple statistic (an average) to rank cricketers. Taking an average is easy: take the number of runs a batsman has scored in his career and divide these by the number of times he has been out. However, in any innings, there is always at least one player who is not out at the end. He's a rather hopeless player who comes in at the end and never scores more than 2 runs. He may have a good season with a string of innings like: 1*, 2*, 0*, 3*, 1*, 2*, 1 , where * indicates that he was not out. His "average" at the end of this season comes out to be 10 runs divided by 1 out = 10 runs per innings, even though he has never made it past 3!

Imagine that the career scores of Waugh brothers are like this: Mark: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100; Steve: 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0. The mean score for each batsman is 50, but there is an obvious trend, in that Mark seems to be getting better, while Steve is getting worse. A raw average, therefore, fails to identify trends. An ideal cricket rating, therefore, will have to be based on a statistic that would identify trends."

Wisden says that, these days, all kinds of persons are floating their cricket ratings (tyre companies, television companies...), but you should go by the Wisden cricket ratings because they are a cricket company. However, for devising the fairest among all cricket ratings, a company of mathematicians would still be the best; and not all cricketers are good mathematicians. If all this is making you think that producing a ranking table is as much an art as a science, then, you would be right. Mathematics is a wonderful logical tool, but when it comes to measuring or representing the real world, it can't always guide you to the right answer on its own. You will have to carefully build your innings there. (Suggestions for devising ideal cricket ratings should be sent to Mind Games, The Tribune, or adityarishi99@yahoo.co.in.)