You’re standing at the penalty line; your next kick could decide which team wins the football World Cup. You’ve trained your whole life for this moment, but where should you aim? It depends on where the goalie will be.
No matter the playing field, our pay-offs in life often depend on other people’s choices. The likelihood of a goal increases if the ball goes somewhere the goalie can’t reach. And part of the decision might be based on understanding your opponent’s motivation.
Beyond sport, you might be coordinating a birthday surprise, or working out the best way to deliver bad news. Typically, success means negotiation among a group of people with different opinions on the matters at hand. Many activities work out best if we can understand and anticipate how others might respond.
Don’t just do something
Statistics have shown that football goalkeepers tend to jump either left or right when facing an opponent’s penalty kick, even though staying near the middle of the net increases their chance of a save. This bias towards action can make us feel as if we have tried and given our all, which can be particularly relevant in an important event like a World Cup decider.
Mixing up your moves
With these statistics about football goalies in mind, it’s probably best for us to aim our penalty kick towards the centre. But if we do this too many times, goalies will catch on. They will learn that we are only going for the middle of the net and very quickly boost their goal-saving average.
We will need to be less predictable: start adding some uncertainty, sometimes going left and sometimes going right, mixing things up so the goalie can’t anticipate our next kick. This is referred to within game theory as a mixed strategy, reflecting that playing just one strategy all the time is unlikely to get the best results.
Instead, having many strategies and choosing between them with a certain probability can increase our chances of winning.
Once more, with feeling
However, a mixed strategy is not without risk. Emotions run high in situations such as the World Cup; this may encourage us to try harder to minimise the chance of missing the net. In its turn, this may be why kickers have been proven statistically to avoid aiming for the top part of the net, even though it has been shown that this is the area where the goalie is least likely to stop a goal.
Kickers might aim low due to the risk of missing the goal altogether when kicking high. And with kickers being relatively risk averse – just like investors – when it comes to potential loss, they can be tempted to play it safe.
Testing, testing 4:4:2
Goal kicking has been widely studied by game theorists because there are clear winners and losers, as well as obvious strategies. Football provides fabulous real-world examples of player interaction. And although many factors play a role, not all assumptions hold and the final analysis can become rather complex.
Typically, though, we find that people play as game theory expects: they randomise their strategy so their opponent doesn’t know what they are going to do. Game theory seeks to understand how people interact with each other in different environments and conditions.
Just like the player in the World Cup final, your future and current needs will be different. Just like him or her, winning is emotional and surprising the other player is key (it can be useful to put yourself in your opponent’s shoes). On or off a playing field, acting in your best interests depends on how others act too.