One of the biggest clichés in the sporting world is the Law of Averages. While there is a real theorem that a random variable will reflect its underlying probability over a large sample (The Law of Large Numbers), the law of averages typically assumes that unnatural short-term "balance" will occur. Television commentators, including former cricketers often claim a batsman is “due” as he hasn’t scored a “big one” for a while.

In order to test this “Law of Averages”, the stats of the 15 batsmen with the most number of innings were studied (Consider it roughly equivalent to the number of plate appearances in baseball). The reason for choosing these 15 was that they provided the largest samples for study. I calculated the number of innings each of them took to score a hundred and used it as a benchmark to test the law of average, rounding it up to N. For example, Allan Border scored 27 100’s in 267 innings, which roughly came out to be a hundred every 9.9 innings. Hence, according to the law of averages, if Border hasn’t scored a 100 in 9 consecutive innings, his tenth (Nth) inning should be a 100. I then calculated the probability of this event using the formula:

**P’ = N**, where

_{2}/(N_{1}+ N_{2})P’ = Probability of scoring a 100 in n

^{th}inning after (N-1) consecutive scores of less than 100N

_{1}=No. of instances when batsman didn’t score a 100 in ‘N’ consecutive innings.N

The P-Factor is a measure of how frequently a batsman scored when he was “due”. A P-Factor of more than 1 indicates a batsman delivered more frequently when he was “due” as compared to his career record. Table 1 shows the analysis of the sample. Of the 15 batsmen sampled, 12 have a P-Factor of less than 1.1, 7 of which have a P-Factor less than 1! Seems to me that even some of the best batsmen don’t fare any better when they were “due”, isn’t it? _{2}=No. of instances when batsman scored a 100 after ‘N-1’ consecutive scores of less than 100.Player | Innings | 100's | Innings/100's | N | N1 | N2 | P | P' | P-Factor |

Allan Border | 267 | 27 | 9.889 | 10 | 87 | 9 | 0.101 | 0.094 | 0.931 |

Steve Waugh | 260 | 32 | 8.125 | 9 | 92 | 8 | 0.123 | 0.08 | 0.65 |

Sachin Tendulkar | 237 | 39 | 6.077 | 7 | 65 | 13 | 0.165 | 0.167 | 1.012 |

Alec Stewart | 235 | 15 | 15.667 | 16 | 86 | 6 | 0.064 | 0.065 | 1.016 |

Brian Lara | 232 | 34 | 6.824 | 7 | 69 | 14 | 0.147 | 0.169 | 1.15 |

Graham Gooch | 219 | 20 | 10.95 | 11 | 63 | 7 | 0.091 | 0.1 | 1.099 |

Sunil Gavaskar | 214 | 34 | 6.294 | 7 | 58 | 11 | 0.159 | 0.159 | 1 |

Michael Atherton | 212 | 16 | 13.25 | 14 | 62 | 4 | 0.075 | 0.061 | 0.813 |

Mark Waugh | 209 | 20 | 10.45 | 11 | 46 | 8 | 0.096 | 0.148 | 1.542 |

Rahul Dravid | 205 | 24 | 8.542 | 9 | 64 | 9 | 0.117 | 0.123 | 1.051 |

David Gower | 204 | 18 | 11.333 | 12 | 69 | 6 | 0.088 | 0.08 | 0.909 |

Desmond Haynes | 202 | 18 | 11.222 | 12 | 62 | 6 | 0.089 | 0.088 | 0.989 |

Inzamam-ul-Haq | 200 | 24 | 8.333 | 9 | 49 | 6 | 0.12 | 0.109 | 0.908 |

Jacques Kallis | 194 | 29 | 6.69 | 7 | 68 | 9 | 0.149 | 0.117 | 0.785 |

Geoffrey Boycott | 193 | 22 | 8.773 | 9 | 55 | 8 | 0.114 | 0.127 | 1.114 |

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