Become good at games with the help of mathematics

When hockey audiences see the hockey player Nicklas Lidström making a decision on the ice, they see one of the world’s best players doing what he is better at than most others.
When the mathematician Jan Lennartsson sees Nicklas Lidström making a decision in the ice, he also sees a player who is making optimal use of mathematics.

The fact that Jan Lennartsson’s research is in the field of sport should perhaps come as no surprise: he has been playing handball all of his adult life, and can list 125 international matches on his CV.

“As an elite sportsman I’ve kept hearing the message that I’m able to win in any situation. Go for it! Run! And I agree. But maybe the best thing is not to be involved in every situation but rather choose which situations one would like to be involved in.”

He believes that there is more to lose in a situation where one chooses to be involved than there is in a situation where one chooses not to be involved at all. This is where the term game intelligence comes in; an abstract skill that some people are mostly presumed to have been born with. Jan Lennartsson, his colleague Carl Lindberg and Nicklas Lidström have produced a study showing that game intelligence can in fact be taught, and that it is a matter of assessing the results of different actions and the consistent use of those actions to maximise the value of a given situation.

Jan Lennartsson's interest in the connection between mathematics and sports is no coincidence – he can count 125 international matches in handball among his achievements.

Jan Lennartsson’s interest in the connection between mathematics and sports is no coincidence – he can count 125 international matches in handball among his achievements.

Carl Lindberg had analysed Lidström’s game and believed that his style differed from that of other hockey players.

“Nicklas maybe wasn’t the strongest or fastest hockey player, or if he was he didn’t have to demonstrate it on the ice. That said, he was incredibly effective because his way of playing was consistent once he had minimised the best alternatives open to his opponent. We are able to demonstrate together that his strategy is, on average, optimal.”

Lidström’s actions can be broken down in terms of statistics. In any situation one can assess the probability of succeeding by the use of certain actions and also assess the value of succeeding. This can then be weighed up against the probability of not succeeding by using an alternative form of play. The three authors have mapped several examples of situations that are common in hockey and handball, and have counted up the optimal choices for each situation.

“Nicklas has experience of these situations and knows how he should assess them. He has based his fantastic career on a mathematical model, and the interesting thing is not only that it worked for him at that particular time but also that it is the optimal in mathematical terms.

So does that mean that anyone can become a better player in their own sport with the help of this research?

“Physical accomplishments such as strength, technology and swift action are essential for all players, but categorising game strategies and making choices on the basis of a scientific perspective can make you a better player.” By using actions that minimise the opponent’s best alternatives in situations that typically arise again and again in a match, one can on average achieve the best possible results.