CricketPlayerRatings

 Introduction Since this past summer (2005), thanks in the main to the exciting Ashes series between England and Australia, the public's interest in cricket has increased dramatically. Before the series, it was well founded that Australia were the best side in the world, due to the high number of world class players they had in their team. Several pundits claimed that England now had a lot of world class players also and would be strong challengers to Australia, and so this proved to be the case. But how can we determine what makes a player "world class" and how can we compare these players with one another to decide who is the best? One way is to rate all the international players in the world by their batting and bowling abilities. The official ICC Players Ratings can be found here. If you look at the ratings you will see that each player has gained a particular score, which changes after each match depending upon their performance. But how are these ratings calculated? For this instance, we are going to look at the performances of batsmen.

 Exercises Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

 Where answers have more than 2 decimal places, please round them to 2 decimal places. If the answer is a letter, please type the letter as it appears in the question.

Question 1
Let's first look at simple batting averages.
The scores made by two batsmen so far in this cricket season are:

 Batsman A:    27, 15, 39, 36, 25 Batsman B:    76, 23, 37, 2, 4

 (a)    What is each batsman's average score so far? Batsman A Batsman B

 (b)    Which batsman would you pick for your side given          their performances so far? (Type either A or B in the box)

Question 2
Often during a cricket season, a batsman will have innings were he is not out. This is usually shown by a * next to his score. When calculating a batsman's average score, you don't divide by the innings where he is not out.
The scores made by three batsmen so far in this cricket season are shown below:

 Batsman 1:    10, 0, 56*, 93 Batsman 2:    61, 47, 53, 51 Batsman 3:    72*, 0, 5, 101*,2

 (a)    Calculate each batsman's average score so far Batsman 1 Batsman 2 Batsman 3

 (b)    Which batsman would you pick to play in your side          given their averages so far? (Type 1, 2 or 3 in the box)

Question 3
In the ICC official ratings, more credit is given to a player's most recent performances. This is done, with batsmen, by weighting their most recent score highest, then their next score is worth 1% less, the next another 1% less and so on.

(a)     Using the batsmen's scores in Question 1, recalculate their average score, applying the weightings
1, 2, 3, 4, 5 to the scores in those respective positions.

 Averaged weighted score for Batsman A: Averaged weighted score for Batsman B:

 (b)     Using this analysis, which batsman would you pick           in your side now? (Type A or B in the box)

Question 4

(a)     Using the batsmen's scores in Question 2, recalculate their average score, applying the weightings
1, 2, 3, .... to the scores in those respective positions.

 Averaged weighted score for Batsman 1: Averaged weighted score for Batsman 2: Averaged weighted score for Batsman 3:

 Using this analysis, which batsman would you pick           in your side now? (Type A or B in the box)

(b)     Again using the batsmen's scores in Question 2, recalculate their average score, applying the weightings
1, 2, 4, 8, .... to the scores in those respective positions.

 Averaged weighted score for Batsman 1: Averaged weighted score for Batsman 2: Averaged weighted score for Batsman 3:

 Using this analysis, which batsman would you pick           in your side now? (Type A or B in the box)

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