What to Do With Your Penalty Kick

DESCRIPTIONDylan Martinez/Reuters
Asamoah Gyan’s successful penalty kick down the center.

Our latest Freakonomics Radio podcast discussed the fact that soccer players are generally reluctant to aim penalty kicks at the center of the goal even though the data show that is the most effective spot.

We expanded on this topic in a (U.K.) Times article yesterday.

And then Asamoah Gyan of Ghana went out and made us look smart in a match against Serbia. In the 84th minute of a nil-nil game, Gyan took a penalty and went center with it, producing a big 1-0 upset. (As of this writing, Gyan’s was the only penalty kick taken in the World Cup, although there will be plenty in the knockout round, when tie games are decided by shootouts.)

The method is effective because keepers usually commit to jumping left or right on penalty kicks just as the ball is struck. Kicking to the center seems to work with English keeper Robert Green as well, but for different reasons.

(Hat tip: Collin Campbell.)


Mike

Of course, if players did start aiming for the center more often, keepers would obviously adjust accordingly.

Ben D

Low blow on Green! I love it!

Alex

As a former soccer player I will tell you that game theory is not really applicable to this situation.

The kicker can, if he stikes the ball well, guarantee a goal no matter what the keeper does if he puts it in the side netting.

I had a state series game go to PKs and took the last kick. I kicked right, the keeper went right, and the ball went in anyways because the placement was perfect. My teammates all told me they thought I had missed until the ball went in. You can't guarantee success on an up-the-middle kick like you can going "Upper 90".

Mike B

What players should do is roll a die before each kick with left, right and center each given a 1/3 share of being chosen. Humans are notoriously bad at being random and will remain predictable even if they properly weight a center kick option. By making a public display of choosing one of the three options at random a Penalty Kicker can absolve himself of looking dumb as he is taking the most effective strategy.

Abhishek

Its natural human tendency to look stylish rather than mundane like shooting at the middle.

Reader

Cute article, but it falls short on two counts. First, if you had conducted ethnographic fieldwork (ie attended games, interviewed players) you would have learned that players often pause before hitting the ball, the goalie jumps, and the shooters decides what to do then.

And second, even if you are right that private cost of shooting down the middle (and missing) is higher than the collective cost, you just pushed the puzzle back: to explain the "irrational" shooter, you resort to the "irrational" market for soccer talent. Please explain that!

DaveyNC

Hit any 90 and it's GOOOOOOOOOOOOOOOLLLLLLLLLLLL!!!!!!!!!

Jon

Conversely, the best tactic for goalkeepers is not to dive, but to wait for the shot and try to react to it. That makes almost any sub-par penalty saveable (excluding weird ball behaviour of course), especially anything down the middle.

As a previous commenter noted, if it's a perfectly struck penalty into the side netting, you're very unlikely to save it anyway.

But goalies seem equally reluctant to look foolish by ending up not diving for a shot that goes in the corner: they seem to feel more comfortable diving. At least then they've demonstrably tried, I suppose.

So then what would happen if the rational penalty taker goes for the middle, and the rational keeper stays in the middle?

OJ

you should roll your dice twice: once to decide which way to go and once tot ell the goalkeeper which way you are going to kick it - nothing like a little bit of mind games....

Zack Brown

@3 You still have to consider the odds of actually hitting 'upper 90.' If it were so easy to hit, professional footballers would just do that every time. But, as we know empirically, knockout round games don't go forever with each teams' players perfectly placing the ball into the top corner of the goal. So game theory does apply here. Which part of the goal offers you the most reward with the least failure?

Tim L

Another factor often forgotten in connection with the on-center PK issue deals with end of overtime PKs. That has to do with the "tired legs" syndrome after participants have already spent regulation time +overtime periods on the field.

I am surprised more coaches don't encourage their leg-warn players to kick on-center and take max advantage of the variance from the intended perfect placement the fatigue factor will create. Many more miss-struck kicks might become winners.

Nikki

What everybody should stop doing is kicking Robert Green. It's just one data point, but everybody already makes conclusions. Seriously, people, give him a break.

More to the point, penalty kicks are obviously a situation that calls for a mixed strategy. Always hitting 90 would work in a world without emotions, but in reality players face so much pressure that even the best of them occasionally miss. Think Roberto Baggio in the final game in 1994, just one of the many examples.

Alex

@ Zach/Nikki

That is why you aim for about 7/8 to the side of the net and put alot of pace on it. The best keepers in the world will probably get some hand on it, but the best strikers should be able to hit it hard enough for that to not matter.

Even a decent High Schooler can kick a PK hard enough for a correct guess to be totally irrelevant. Unless you both go middle, which makes for the easiest stop.

I would make a graphic of what I'm trying to say, but that seems frivolous.

Bobby G

Been kinda mentioned above, but I imagine the rare case of kicking middle and the goalie correctly staying middle is a pretty humiliating miss. Contrast that to a dive-stopped PK on the side or a miss wide, where you were either a bit too aggressive or the goal keeper made a great play, and a miss down the middle looks pretty pathetic.

That said... imagine if the guy from Ghana gets another PK and shoots down the middle again and scores. Goalies across the tournament will remember that (I'm sure they're already thinking about it with the one kick). Will they hesitate a bit before jumping on the next PK? Does this open up opportunity for a side shot? Perhaps there is an option that one's sixth penalty kick earns a slower side-reaction from a goalkeeper if 2 of the previous 5 PKs were down the middle.

MikeM

Gyan definitely hesitated in his run-up to see if the keeper was going to commit. When he committed, the down-the-middle strategy was a no-brainer. Before the hesitation, maybe not so.

William Spaniel

I like everything about this and the (U.K.) Times article, but I am a little sketchy on a particular detail in the (U.K.) Times article. I am looking into the penalty kick problem myself. However, whenever I solve for the mixed strategy Nash Equilibrium, I find that the kicker should be going to his weaker side more often than his strong side. I was wondering how you obtained your (contrary) result.

nounet

You can't shot in the middle of the goal AND low (i.e height lower than 1m), because no matter where the goalie dives, he'll have a chance at kicking the ball away.

So, for a "minimal-risk" center penalty kick, you have to place the ball in the air, between 1m and 2m32, obv.

But on the other hand, kicking a penalty high has the added risk of placing the ball over the bar.

Generally, players opt for low kicks for that reason. If players had complete mastery over height and direction of shots, they would shoot the ball left or right, height between 1m50 and 2m30.

relaxing

Players kick low because the keeper can jump faster than he can fall.

EB3

Love the podcast, but I think Steven confused Roberto Baggio with Ronaldo...

Trilok Khairnar

Ironically, it was a penalty kick in the center by Sebastien Abreu of Uruguay in the quarter final against Ghana that sealed the match. Abreu used the same logic and asked why his kick was not magical if Zidane's (in the 2006 final against Italy) was.
Watch both the kicks on YouTube.
http://www.youtube.com/watch?v=3JsJuhzMynk&feature=related

Zidane's kick was a dipping shot that hit the top post after traveling in air excruciatingly slow before going in (goal!!) and then popping out. Sorcery!

And minutes earlier before Abreu's kick, the same Gyan missed the penalty as his kick rebounded from the right post. He was understandably inconsolable after the match.