Soccer goalies almost always dive to one side or the other when defending penalty kicks. Instead, they should just stay put. This is the conclusion by Israeli academics after analyzing 311 soccer penalty kicks in their fantastic paper “Action Bias among Elite Soccer Goalkeepers: The Case of Penalty Kicks.”
The Outsized Importance of Penalty Kicks in Games
Soccer is a pretty low-scoring sport — only about 2.5 goals are scored a game (by both teams). Case-in-point is that the US Men’s National Team made it through group play even though it only scored two goals in three games (1-1 vs. Wales, 0-0 vs. England, 1-0 vs. Iran).
So, every goal is HUGE!
That brings us to penalty kicks which occur when a player gets the opportunity to kick a stationary ball located 11 meters from the goal against the goalkeeper who must remain on the goal line until the ball is kicked. It’s super-hard for a goalie to stop a penalty kick and typically, the kicker scores about 80% of the time. Penalty kicks occur in two situations: (1) when a foul occurs within the penalty area (a big box around the goal), or (2) in certain championship situations when a regular game ends in a tie.
Given the low-scoring nature of soccer and the high success rate of penalty kicks, the ability of a goalie to stop a penalty kick is extremely important.
The Difficulty of Defending Penalty Kicks
Given the short 11-meter distance from the kick to the goal, it only takes a ball about 0.2-0.3 seconds to reach the goal. That’s not enough time for a goalie to wait to see the direction that the ball will be kicked by the shooter. Thus, he has to decide to jump left, right, or stay in the center before the kick happens. So, the goalie’s decision about which direction to lunge and the shooter’s decision about where to kick the ball are complex, interrelated decisions that mathematicians describe as “mixed-strategy Nash equilibrium” decisions (like playing rock paper scissors).
But the goalies don’t make optimal decisions with respect to strategy because they almost never just stay put — they almost always dive to one side or the other. This isn’t optimal because in the 311 penalty kicks observed in the study, nearly 29% of the kicks were to the center. Check out the table below. Goalies only stayed put 6.3% of the time yet 28.7% of the kicks were to the center.
Stop and think about this. If you are a goalie, by always diving to a side, you are removing the ability to stop nearly 1/3rd of the stops. So, even if you guessed the right and left kicks correctly, the best you’d do would be 71.3%.
Analyzing the above data, the researchers concluded that a goalie should just stay put.
Why Goalies Always Dive in a Direction
The researchers posited that the goalies nearly always dive to a side because they had an “action bias.” Staying still is inaction — diving is action. And if they just stand there and miss the shot because it’s to either side they look stupid. You can imagine fans saying, “what the hell? He just stood there? I could have done that!”
This makes sense, as much of our decision-making involves regret avoidance. It’s not always about whether we make the best decision but rather making the decision that makes us look the least stupid. The seminal study on this (which was mentioned in the soccer paper) was by Daniel Kahneman and Amos Tversky who asked study subjects the following:
“Paul owns shares in company A. During the past year he considered switching to stock in company B, but he decided against it. He now finds out that he would have been better off by $1,200 if he had switched to the stock of company B. George owned shares in company B. During the past year he switched to stock in company A. He now finds out that he would have been better off by $1,200 if he had kept his stock in Company B. Who feels more regret?”
A large majority of the subjects thought that George, who acted, felt more regret than Paul, who did not act.
So, it’s common to have an “inaction” bias because taking action that doesn’t turn out well often leads to more regret than when we do nothing. The soccer study authors thought that the opposite is true of goalies — that there’d be more regret if they didn’t take action — so taking action was the “norm” for goalies. To prove this point they surveyed 32 professional soccer goalies and found that it supported their conclusion that staying put goes against the norm and would lead to more regret.
It’s like when you got in trouble with your mom and you said, “but all the other kids did it!” And your mom replied, “would you jump off a bridge if all the other kids did?” Well, the answer is if the “norm” is jumping off a bridge, then, yeah, you might just follow the other kids off the bridge because acting differently than the norm could make you look stupid which leads to regret.
So What Should Goalies Do?
The paper concluded that based on the current distribution of shots, a goalie should stay in the middle. By doing so, they’d save a higher percentage of shots than if they dive to a side and guess wrong.
Of course, this would only work until the shooters caught on. As the paper states, “If goalkeepers will always choose to stay in the center, however, kickers will start aiming all balls to the sides, and it will no longer be optimal for the goalkeeper to stay in the center. The distribution of jumps and kicks that will constitute an equilibrium (in which both the kicker and the goalkeeper will be happy with their choices given what the other players does) is therefore one in which each player randomizes among his various possible actions – known as a mixed-strategy equilibrium.”