Player of the week
Aditya Rishi

IN 1987, statistician Rob Eastaway stumped former England cricketer Ted Dexter with this googly: "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 while Mark is getting better, Steve is getting worse. A raw average, therefore, fails to identify trends."

Rob says that a simple way of doing this is to just pick out the performances over a recent period of time. Taking the last five matches would rate Mark as 400/5 = 80; and Steve as 100/5 = 20. If in his next match, Mark scores 70 runs, this might suggest that his form is dipping slightly (because 70 is worse than his current rating of 80). However if we look at his last 5 performances, this score of 70 will displace the 60 he scored 5 matches ago, so, his rating will actually go up.

One of the best ways of avoiding the anomaly where a bad performance can result in your rating moving upward, or vice versa, is to use an exponentially decaying average, where every score is considered in the calculation, but, as you go back in time, each value is discounted by a certain percentage.

If the decay rate is 4 per cent, we calculate Mark's exponential average as follows: Adjust his total runs over his 11 innings as 100 + 90`D70.96 + 80`D70.962 + 70`D70.963 + 60`D70.964 +...+ 0`D70.9610; that works out to be 489.96. Instead of dividing by 11 innings, you need to divide by 1 + 0.96 + 0.962 +...+ 0.9610, which comes to 9.04. That gives a weighted average of 489.96/9.04, or 54.2 for Mark. This shows truly that Mark has been performing better recently than his career average of 50 would suggest. If Mark scores 60 in his next innings, his decayed average indeed goes up; and if he scores 50, it goes down.

However, while rating cricketers, you also have to allow for the fact that they are not playing in the same conditions as each other. Scoring a 50 against Australia is a much greater achievement than scoring a 50 against Bangladesh.

An ideal cricket rating adjusts each player's individual performance in a match and, then, updates the player's overall decayed average to produce a rating. Fluctuations in ratings over a player's career can be plotted on a graph. Rating a batsman needs to take account of the latest ratings of the opposing bowlers, while a bowler's rating needs to take account of the opposing batsmen's latest ratings. Who, then, should you rate first: the bowlers or the batsmen?

Give each player a "provisional" rating after the match, use it in all the adjustment calculations, and replace the provisional figure with the updated one. (Got better suggestions? Write at The Tribune or adityarishi99@yahoo.co.in)