In my paper with Tim Groseclose and Pierre-Andre Chiappori, we test the predictions of game theory using penalty kicks in soccer. We find that the players’ actions conform very closely to the theoretical ideal.
There is one big deviation that we see between what players actually do and what the theory predicts: kickers kick the ball right down the middle much less than they should. Or put another way, in practice, kicking it down the middle scores at a higher rate than kicking it either to the left or right (at least in our data set).
Why? If you kick it right down the middle and you don’t score, it is damn embarrassing. So even though the middle is a great play statistically, kickers don’t choose it very often. There are some things that are even more important than winning, like not looking like a fool.
Today’s shootout between Switzerland and Ukraine is the ultimate case in point. The first kicker from Ukraine missed his shot. Then it was the Swiss player’s turn. The story from the AP describes the Swiss player’s shot as follows:
Marco Streller’s effort for Switzerland was worse — low and directly at Shovkovskyi.
The second Swiss player also missed. Here is the AP’s description:
Barnetta hit the crossbar.
Not pejorative at all…hitting the crossbar is apparently acceptable.
But then the third Swiss player kicked it, to the following description:
Ricardo Cabanas looked almost amateurish on his shot directly into the middle of the goal — and again, right at the Ukranian goalkeeper.
My guess is that the Swiss kickers who kicked it down the middle will forever be remembered as the ones who blew the game in the World Cup by amateurishly kicking it right down the middle.
It is not just whether you win or lose, but how you play the game. Which is why from a game theory perspective, with the world laughing at the Swiss, there is no better time for the next shooter to kick it right down the middle one more time if all he cares about is winning.
19 Comments
I don’t get it - it’s much easier for a goalkeeper to stop a ball going directly towards him rather then jumping left or right (having to choose the right side) for sideway balls. Kicking to the middle is indeed amateurish.
— amit_goldi“I don’t get it – it’s much easier for a goalkeeper to stop a ball going directly towards him rather then jumping left or right”
The “problem” is that most keepers will guess left or right and jump in that direction. Realistically, at the speed the ball is travelling and from the distance it’s kicked from, the keeper is totally guessing. Sure he can TRY to look at body language for a hint here or there, but when you look at how successful penalty kicks are, on the whole, you realize that most saves are just plain luck.
Thus, if the keeper is going to guess left or right the majority of the time, which is the case, then why not just shoot it where the keeper was, instead of potentially shooting it to where he’s going to be?
By the way, why don’t they ever call the keeper amateurish for leaping to the left when the ball gets slammed into the right corner of the goal? Why do they call that a great penalty kick by the kicker? Because the whole world knows the keeeper’s mostly guessing. And if the keeper’s guessing, it’s best to bank on him moving, which leaves the middle of the goal wide open.
— ftelegdyAs far as I can tell, the PKs are basically considered a game of Hot Hands between the kicker and the goalie.
The whole strategy is for the kicker to try and convince the goalie he’s going one way and then kick it the other, since once the goalie commits to a specific direction it’s hard for him to reverse directions in time to stop a kick.
This, combined with the fact that it’s harder for a goalie to stop a kick aimed for the top corners since it’s farther for him to travel, make it the obvious choice.
And on the goalie’s part, it’s all about reading the kicker and trying to predict which we he’s actually going to kick. Once you’ve predicted the correct half of the net, you’re 2/3 of the way there. (Watch a goalie and defense during field play - half of what they do it all about positioning to cut down the possible angles a shooter has at the net, all aimed at channeling him into an easy-to-block shot).
I’m sure there’s scouting reports involved as well, listing a particular player’s habits and weaknesses.
— misanthrope…not to mention that the distance to the goal line in a straight-on penalty kick is shorter than the distance to either side. not that it makes that much difference (probably only a couple of meters either way) but this may be to the kicker’s advantage.
Also consider that an outstretched goalie (one who is diving in one direction or the other) covers more lateral space than a goalie who stays put in the middle (probably crouched down a little) so from the goalie’s perspective if at least they get the direction of the kick right, they have a better chance of blocking the ball…
— NiebylskiTo address the comment from amit_goldi, Table 4 in the paper shows that if the kicker kicks right down the middle, and the goalkeeper stays in the middle of the goal, the probability of scoring is indeed zero. However, the reality is that the goalkeeper almost never stays in the middle of the goal. 98% of the time, he jumps to the left or the right. And with the goalkeeper off to one side, a kick down the middle results in a score 81% of the time.
So it appears that kicks down the middle will have a higher probability of scoring only so long as they remain extremely rare. If they are expected, they are very easy to defend.
— John S.Kicks down the middle are harder to execute, though, as there’s a much smaller margin of error for locating the kick. A down-the-middle kick has to have elevation, for example, to be really successful, which isn’t necessarily the case in either direction.
— tim in tampaUkraine’s first two (of three) successful kicks were more or less right down the middle. The Swiss keeper kept diving to his right.
The difference from Streller was that whereas he kicked it on the ground, the Ukrainians put it in the air, so the keeper couldn’t stop it with his feet.
— lemrobotryMaybe the reason the success rate of “down the middle” is artificially inflated because shooters kick it there intentionally when the keeper has commited early. (In other words, the keeper has dived at a point in time where the kicker can still change the direction of the shot.)
Down the middle should be the easiest area to hit, since there is more allowable margin of error. The problem with putting it in the air is the risk of blowing it over the bar greatly increases.
As a keeper, I tended not to dive before the shot. At the level of game I played, players that aimed for the corners were not deadly accurate. If I was able to get to the shots that were in the middle, the only ones I missed were the perfect shots I probably wouldn’t have gotten anyway, and there weren’t that many perfect shots. An slow shot to the corner would have been the best option against my strategy, but given that most players hadn’t taken penalties shots on me before, it would have been hard to know what to do.
I guess a more complete analysis would include high vs. low shots, and some measure of how hard it is kicked.
— memcknightTheory:
Swiss kickers read the paper, decided to kick down the middle.
Unfortunately, Ukranian goalie found out Swiss kickers had read the paper and figured if they were going to outsmart him, he would outsmart them.
I’ll put $10 that the next penalty kicker against the Ukranian goalie doesn’t kick it anywhere near the middle. Any takers?
— zbicyclistHow about how much ridicule the goal keeper would be given if he just stood in the middle and didn’t move. If he stood in the middle of the goal while a kick sailed by him on the left the fans and media would castigate him more than any kicker, that is, unless he blocked it. If we have many goal keepers reading this blog we may just see more goalies just staying put during penalty shots and shootouts.
— kongziI hate the concept of shootouts, whether it is in soccer or hockey. You played the game, if it is a tie, then why not just play rock-paper-scissors to decide it? Maybe have a game of twister or play Tetris to decide the winner? Shootouts are not the game. At least in baseball they will play innnings after extra innings to decide a winner based on the game rules.
I think this is one factor in why the NFL and the NBA and even MLB are more popular in the US. While technically, an NFL game can end in a tie it very rarely happens. NBA goes to overtime and MLB plays extra innings, and the NFL at least has a period of sudden death.
— jwI watched the match, and those two “amateurish” shots *were* amateurish — they were slow, rolling shots that were easily defended. The shot that hit the crossbar wasn’t amateurish — it was fast and high, and certainly would have scored had it been 4 inches lower. And it was down the middle, like the other two.
— John Hawksjw, I agree with you about everything except the NFL. Sudden death as practiced in the NFL gives far too great an advantage to the team that wins the coin toss. I prefer the college football overtime, with the teams taking turns at possessions. It is much more like baseball. But the soccer shootout is just such a crappy way to win or lose. (The only two shootouts I was in as a player my team won, and it never felt as good as an “honest” win.) Why not just keep playing 5 or 10 minute overtime periods until someone wins?
In any event, I have another question. Can anyone think of a way to test the effect of “pressure” on kick success? I ask because the success rate of penalty kicks during play is so much higher than for penalty kicks in a shootout.
— mathkingmathking, I agree with you 100% about the unfair advantage to the coin toss in the NFL.
Actually, there was a coach (can’t remember the teams or the game) a few years ago that won the OT coin toss and chose to defend a goal instead of choosing posession. They lost, and the coach got raked over the coals by the press and fans.
I agree that the college system is better, but at least in the NFL, while an unfair advantage is given to the coin toss winner, at least the outcome is decided on the field instead of a field goal kicking contest or something.
— jwNFL overtime is off topic, but interesting, so here goes. The current coin flip is unfair (although less so in practice than theory), but there are much more elegant fixes than the overly complicated college system. Alternative 1. Start the overtime by having teams bid for possession of the ball, based on how deep in their own territory they are willing to start. 2. If you really like kickoffs, let them bid based on how far forward they will let the opponent kick off (but remember the onside kick). 3. A rule that in overtime, a team my not kick a field goal unless the opponent has run at least one play from scrimmage, reducing the value of first possession.
— Ken D.Re: comment 3
“This, combined with the fact that it’s harder for a goalie to stop a kick aimed for the top corners since it’s farther for him to travel, make it the obvious choice.”
Actually, a ball on the ground in the corner is usually farther for the goalie to travel since s/he has to travel dive at some upward angle — effectviely passing by the upper corner before reaching the final destination.
— mlibbeyKen D. Wow, your option 1 is great food for thought. I help moderate a sports board and I think I will bring this up as a topic for discussion.
— jwI agree with misanthrope that a big part of penalty kicks is the goalie and the kicker reading each other.
So I don’t think I buy the statistical game theory ideas. It just seems much more complicated then that, as several people have pointed out.
When there are elements of bluffing and faking out going on, then it’s not completely a matter of blind guessing.
— tragulaThank you, jw. Please post the name of your sports board.
— Ken D.