# Everyone is an expert

In discussing sports events children are no different from adults. Some of them like to do an analysis rather than just remembering who won. Tinku is interested in such analysis and guess who is prepared to do this with him. None other than Tanya who is at least equally interested in sports.

On Thursday of December 8, 2011 a one day cricket match (ODI) between India and West Indies was played and Bhagi (Tanya’s mother) recorded the whole game. Tanya and her friends Tinku, Kate and Peter watched it on Sunday. Sehwag scored 219 runs – a record in men’s ODI. There was a buzz in the whole country. Tinku requested Bhagi not to erase this recording. He came the next day after school to look at the scoreboard more carefully. Tanya was waiting for him.

Tanya: What do you want to do – compare performance of all the players?

# Strike rates and run rates

Tinku: First, I want to compare the strike rate and run rate of each batter for the Indian team.

Tinku started with the runs scored by each batter from the Indian team. Then he calculates the strike rate (the average number of runs scored by a batter per 100 balls faced) and the run rate (the average number of runs scored by a batter in an over of 6 balls), and also the average number of runs the Indian batting side scored per over. Here is what he did. For the strike rate he first divided the number of runs by the number of balls. That gave him the number of runs per ball. Then he multiplied it by 100 to get the number of runs per 100 balls. Run rate is the number of runs per over of 6 balls. Therefore, he divided the number of runs by the number of overs and then multiplied it by 6. He got confused and asked Tanya.

Tanya: The run rate for Sehwag comes out to 8 plus 8/10. You can write this fraction using decimals as 8.8. Let us do the same thing for all the run rates. Also the number of balls for the team total will be 300 because it has 50 overs and one over has 6 balls in it.

Performance of the Indian Team Batting |
||||

Player | Runs Scored | Balls Faced | Strike Rate | Run Rate |

Gambhir | 67 | 67 | 100 | 6 |

Sehwag | 219 | 149 | 146 | 8.8 |

Raina | 55 | 44 | 125 | 7.5 |

Jadeja | 10 | 10 | 100 | 6 |

Sharma | 27 | 16 | 168 | 10.1 |

Kohli (not out) | 23 | 11 | 209 | 12.5 |

Patel (not out) | 3 | 3 | 100 | 6 |

Team Total (includes extras) | 418 | 300 | 139 | 8.3 |

They worked hard calculating every strike rate and every run rate, and wrote these numbers. They were admiring their work and then Peter walked in.

Peter: Sorry for being late. I was hungry and mom gave me something to eat. I see you have done some interesting work here. Great job, Tinku.

Tinku: Thanks Peter.

# Peter questioned the numbers

Peter: There is one thing I don’t understand. When I look at the strike rate, the order is: Kohli > Sharma > Sehwag > Raina > Gambhir = Jadeja = Patel. When I see the run rate, it is in the same order: Kohli > Sharma > Sehwag > Raina > Gambhir = Jadeja = Patel. (Note the symbol > is used for greater than, < for less than.)

Tinku: Peter, it is interesting. Maybe Tanya can explain it or I did something wrong.

Tanya: Johnneee..ee (as if a little annoyed), you did everything correct. Why can’t you explain it? For both the calculations you first got the ratio of the number of runs to the number of balls. You multiplied this ratio by 100 to get the strike rate and by 6 to get the run rate. It is the same ratio in both the columns, just multiplied by 100 in one column and by 6 in the other. The two ratios are equivalent. Therefore, they have to be in the same order for all of them whether it is for the strike rate or the run rate.

Peter: The orders of the runs batted by each player and their strike rates are very different: For runs the order is Sehwag > Gambhir > Raina > Sharma > Kohli > Jadeja > Patel but for the strike rate Kohli > Sharma > Sehwag > Raina > Gambhir = Jadeja = Patel. How does this come about?

# Speed versus distance

Tanya: Peter, can you run fast?

Peter: As fast as you can.

Tanya: Let us say that you and I are running. If you start huffing and puffing in 5 minutes and stop but I keep running, I would have run more than you – yes or no?

Peter: Yes but I am not sure that this will happen. What is your point?

Tanya: How fast you run is a rate at which you run but the total distance has to be how fast multiplied by for how much time you run for. Gambhir and Jadeja have the same strike rate of 100 but Gambhir makes 67 runs and Jadeja makes only 10 because Gambhir has this rate playing 67 balls and Jadeja is out after 10 balls.

Tinku: Okay, okay. You can argue all you want but Sehwag has outdone everyone – not just from this match but everyone who has ever played in an ODI. That is what I am impressed with.

*Challenge*

Tinku wanted to determine the bowling performance of the West Indies team against India in this ODI. He wrote the following information in his notebook and then left because his father called him to come home. When a player is run out, the wicket is not given to the bowler. This is why there are only 3 wickets listed in the bowling performance even though 5 players were out. Bowling average (Ave) is the number of runs given divided by the number of wickets taken. Strike rate (SR) is the the number of balls divided by the number of wickets taken. Economy rate (ECON) is the number of runs given per over of 6 balls.

Note that whenever you have to divide a number by zero, the result will be infinite and you can just use some mark.

Complete his notes based on the information in his notebook.

Complete his notes based on the information in his notebook.

Bowling Performance by West Indies |
||||||

Bowler | Overs | Runs | Wickets | Bowling Average | Strike Rate | Economy Rate |

Roach | 10 | 88 | 1 | |||

Rampaul | 9 | 66 | 0 | |||

Russel | 7 | 63 | 1 | |||

Narine | 6 | 46 | 0 | |||

Sammy | 3 | 30 | 0 | |||

Pollard | 7 | 65 | 1 | |||

Samuels | 8 | 59 | 0 |

*Solution*

Bowling Performance by West Indies |
||||||

Bowler | Overs | Runs | Wickets | Bowling Average | Strike Rate | Economy Rate |

Roach | 10 | 88 | 1 | 88 |
66 |
8.8 |

Rampaul | 9 | 66 | 0 | – |
– |
7.3 |

Russel | 7 | 63 | 1 | 63 |
42 |
9 |

Narine | 6 | 46 | 0 | – |
– |
7.7 |

Sammy | 3 | 30 | 0 | – |
– |
10 |

Pollard | 7 | 65 | 1 | 65 |
42 |
9.3 |

Samuels | 8 | 59 | 0 | – |
– |
7.4 |