A Harvard economist plays goalkeeper for the USMNT at the World Cup. He wrote a research paper on penalty kicks years ago, but he won't tell anyone what's in it. Here's why that's the perfect way to understand game theory.
The goalkeeper has to defend the area he can actually stop the ball. Basically where he's actually standing.
Then there is an zone where the goalkeeper has a good chance to save.
Then there's a zone which is difficult, top and bottom corners near the post.
To increase the chance of a save. Just don't move until the ball is kicked. The three zones come into play.
Green easy, yello great possibility, red a good penalty kick.
The trick then is posture. This is a key. Crouched position as if you were a cat. Your in a pounce position, you spring to where the ball is going.
If you were standing, in order to get to the ball you have to bend the knees and that initial motion loses a valuable second and makes it easier for the penalty taker.
When I played in goal, I applied this approach and it worked. Even a penalty stopped near a post.
If a goalkeeper does this and is known to be a stopper, all future penalty takers are under pressure.
That in my experience and opinion is probably the best way for goalkeepers to be more successful.
Key.. just keep your eye on the ball. Ignore the penalty taker..more pressure on them.
I remember PKs being an example in game theory lessons in my early Econ courses!
It's such a fun way to introduce interdependence to them.
The goalkeeper has to defend the area he can actually stop the ball. Basically where he's actually standing.
Then there is an zone where the goalkeeper has a good chance to save.
Then there's a zone which is difficult, top and bottom corners near the post.
To increase the chance of a save. Just don't move until the ball is kicked. The three zones come into play.
Green easy, yello great possibility, red a good penalty kick.
The trick then is posture. This is a key. Crouched position as if you were a cat. Your in a pounce position, you spring to where the ball is going.
If you were standing, in order to get to the ball you have to bend the knees and that initial motion loses a valuable second and makes it easier for the penalty taker.
When I played in goal, I applied this approach and it worked. Even a penalty stopped near a post.
If a goalkeeper does this and is known to be a stopper, all future penalty takers are under pressure.
That in my experience and opinion is probably the best way for goalkeepers to be more successful.
Key.. just keep your eye on the ball. Ignore the penalty taker..more pressure on them.
He should've focused on passing
https://www.npr.org/2026/07/03/nx-s1-5879357/world-cup-penalty-kick-game-theory