Cricket: An Unfairly Random Game?

In sports competitions, a variety of measures are often taken to make conditions about equal for all competitors. In tennis, for example, players must changes sides every other game so as to neutralize impact of angle of the sun, among other ‘side’ specific problems. In basketball, due precaution is taken to balance home court advantage. In cricket however, a curious thing happens – conditions are made randomly unequal.

In many cricket matches, there is a clear advantage in bowling or batting first. This fact is often pointed out by commentators, and by captains of the competing teams in the pre-toss interview. However the opportunity to bowl or bat first is decided by a coin toss. While this may seem ‘fair’ – it really just means that one team is randomly handed the shorter end of the stick. Hence games are not decided on ability alone. One can derive estimates of the advantage by comparing results in cases where teams won the coin toss, and when they lost it.

At first glance, the imbalance may seem inevitable – after all someone has to bat first. One can however devise a baseball like system where short innings are interspersed throughout the day. If that violates the nature of the game too much, one can easily create pitches that don’t deteriorate heavily over the course of a game, or come up with an estimate of the advantage and adjust the target for the team by that estimated amount (something akin to an adjustment issued when matches are shortened due to rain).

Empirical Analysis
Data are from nearly five thousand one-day international matches, and all international test-matches.

Toss likely plays a more crucial role on sub-continent pitches as the typically dry dusty pitches deteriorate faster under the harsh sunlight. It is also likely that toss is more crucial in day and night matches, due to dew and lower visibility of the white ball in the lights. It may well be case that toss is more important in tests than one-day matches.

The team that wins the toss wins the match approximately 46% of the times. This brings up the question as to whether the teams are choosing wisely.

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