Jointly Controlled Lotteries and U12 Soccer

I coach my daughter’s U12 travel soccer team. An important skill that a player of this age should be picking up is the instinct to keep her head up when receiving a pass, survey the landscape and plan what to do with the ball before it gets to her feet.  The game has just gotten fast enough that if she tries to do all that after the ball has already arrived she will be smothered before there is a chance.

Many drills are designed to train this instinct and today I invented a little drill that we worked on in the warmups before our game against our rivals from Deerfield, Illinois. The drill makes novel use of a trick from game theory called a jointly controlled lottery.

Imagine I am standing at midfield with a bunch of soccer balls and the players are in a single-file line facing me just outside of the penatly area.  I want to feed them the ball and have them decide as the ball approaches whether they are going to clear it to my left or to my right. In a game situation, that decision is going to be dictated by the position of their teammates and opponents on the field. But since this is just a pre-game warmup we don’t have that.  I could try to emulate it if I had some kind of signaling device on either flank and a system for randomly illuminating one of the signals just after I delivered the feed.  The player would clear to the side with the signal on.

But I don’t have that either and anyway that’s too easy and quick to read to be a good simulation of the kind of decision a player makes in a game.  So here’s where the jointly controlled lottery comes in.  I have two players volunteer to stand on either side of me to receive the clearing pass.  Just as I deliver the ball to the player in line the two girls simultaneously and randomly raise either one hand or two.  The player receiving the feed must add up the total number of hands raised and if that number is odd clear the ball to the player on my left and if it is even clear to the player on my right.

The two girls are jointly controlling a randomization device.  The parity of the number of hands is not under the control of either player.  And if each player knows that the other is choosing one or two hands with 50-50 probability, then each player knows that the parity of the total will be uniformly distributed no matter how that individual player decides to randomize her own hands.

And the nice thing about the jointly controlled lottery in this application is that the player receiving the feed must look left, look right, and think before the ball reaches her in order to be able to make the right decision as soon as it reaches her feet.

We beat Deerfield 3-0.