This post was motivated of course by the last over of the World Cup (2015) semi-final.
When Elliott was batting, Steyn had several options and he is well capable of bowling everything. Yet he chose to bowl a length ball, almost a sin during the slog overs. So, why did Steyn choose to bowl length? Pressure? I don't think so. Here is a game theory explanation. For simplicity, let us discuss just two options for Steyn. Yorker vs Length. Similarly, Elliott also had a few options. For simplicity I am going to consider two: Stay put and Play across.
Now, here are the pay-offs.
1. If Steyn bowls a yorker and Elliott decides to Stay put, it's at best a single for Elliott (So, advantage SA)
2. If Steyn bowls a yorker and Elliott decides to move across and flick, because of the short boundaries, the ball might just go for a boundary. (So, advantage NZ)
3. If Steyn bowls length and Elliott decides to Stay put and slog, it's a boundary. (So, advantage NZ)
4. If Steyn bowls length and Elliott decides to move across and flick, because of Steyn's pace, Elliott is likely to miss the flick (It's not easy to time a flick against Steyn's length ball vs a yorker). So, advantage SA.
So, here is the pay-off matrix. (SA, NZ)
People who understand game theory will immediately realize that there is no pure strategy Nash Equilibrium in this case. That is, there is no one "best" path of action for both players. So, each player has to mix up their strategies a little. In fact, 50% for each action. But if Elliott decides to play across and Steyn know this, then Steyn's best action is to bowl length.
What actually happened? Elliott moved across before the ball was bowled. Steyn tried to outsmart him and bowled length (instead of the yorker). Elliott slogged onside instead of flicking. Game Set and Match!
When Elliott was batting, Steyn had several options and he is well capable of bowling everything. Yet he chose to bowl a length ball, almost a sin during the slog overs. So, why did Steyn choose to bowl length? Pressure? I don't think so. Here is a game theory explanation. For simplicity, let us discuss just two options for Steyn. Yorker vs Length. Similarly, Elliott also had a few options. For simplicity I am going to consider two: Stay put and Play across.
Now, here are the pay-offs.
1. If Steyn bowls a yorker and Elliott decides to Stay put, it's at best a single for Elliott (So, advantage SA)
2. If Steyn bowls a yorker and Elliott decides to move across and flick, because of the short boundaries, the ball might just go for a boundary. (So, advantage NZ)
3. If Steyn bowls length and Elliott decides to Stay put and slog, it's a boundary. (So, advantage NZ)
4. If Steyn bowls length and Elliott decides to move across and flick, because of Steyn's pace, Elliott is likely to miss the flick (It's not easy to time a flick against Steyn's length ball vs a yorker). So, advantage SA.
So, here is the pay-off matrix. (SA, NZ)
Stay put
|
Play across
|
|
Yorker
|
(1,-1)
|
(-1,1)
|
Length
|
(-1,1)
|
(1,-1)
|
People who understand game theory will immediately realize that there is no pure strategy Nash Equilibrium in this case. That is, there is no one "best" path of action for both players. So, each player has to mix up their strategies a little. In fact, 50% for each action. But if Elliott decides to play across and Steyn know this, then Steyn's best action is to bowl length.
What actually happened? Elliott moved across before the ball was bowled. Steyn tried to outsmart him and bowled length (instead of the yorker). Elliott slogged onside instead of flicking. Game Set and Match!
