Game theory in cricket: batsman vs fast bowler
http://www.economist.com/blogs/gametheory/2012/04/decision-making-cricket
The article considers decision making in cricket, specifically for batsmen facing fast bowlers – defined as bowlers who can consistently bowl at speeds above 90 miles an hour. It starts off with a specific situation in a game in 1981 and then goes on to, in general terms, comment on how and why certain batsmen can play fast bowlers effectively and others cannot.
The concept of game theory, taught in INFO 2040, is applied to a specific scenario in cricket. The game in this case would be the batsman facing the fast bowler, where the players are the batsman and the fast bowler. Each of the players has his own strategies. On a simplified level, the batsman’s and the bowler’s strategies are mentioned below.
For the batsman, his strategies are to:
- Attack the ball
- Defend the ball
- Take evasive action
For the bowler, his strategies are to:
- Bowl at the batsman’s body
- Bowl towards outside the wickets
- Bowl towards the batsman’s head (the article makes mention of aiming for the batsman’s chin – such a ball is called a bouncer)
Based on this, a 3×3 payoff matrix may be drawn to find the Nash equilibria in the game. However, the payoffs may not be arbitrarily chosen to reflect such a real-life game, and would be based on statistical studies.
The idea of a best strategy and a dominant strategy, as taught in the course, can be applied to this game. For example, the article makes mention of the batsman having to take evasive action if the ball is aimed at his chin. This is the batsman’s best response to a fast bowler whose strategy for the given ball was to aim the ball at his head/face/chin. Similarly, if the batsman is determined to defend the ball, the bowler’s best strategy would be to bowl at the batsman’s body.
The article makes mention of how, in a specific game in 1981, Geoffrey Boycott could not play Michael Holding’s fast balls and was dismissed (a term used in cricket to mean that the batsman is out) on the sixth ball of an over after “five balls screeched past Mr Boycott’s flailing bat”. Making a simplification of the situation, it may be stated that while facing Mr holding on that day, Mr Boycott’s dominant strategies could have been to just defend the ball.
While this article makes mention of just one situation, if a given scenario in cricket can be picked in isolation, it may be analyzed using the same concepts of game theory as done here and in the course. These are similar analyses made by coaches and players before a game to maximize the payoffs, and also done by sports betters in an attempt to predict the likely outcome in a given scenario.
Interesting side note: Being a spin bowler in Cornell University’s club cricket team, I, myself have to make similar analyses when I bowl to a batsman (the game), where the batsman and I are the players. However, being a spin bowler, my strategies are different from those of a fast bowler, just as the batsman’s strategies are different when playing a spin bowler vs a fast bowler.
This is one of the great explanation about cricket and batsman vs bowler comparison. But it could be more effective if we could edit it once and add the importance of fielding and spin bowlers.
Fielding is an important part of today’s cricket, especially in T20 cricket format. One brilliant catch can turn around the game.