Penalty Kicks: Is guessing a sucker’s bet?

“I think of them [penalty kicks] as no-lose situations for a goalkeeper. All the pressure is on the field player, who is supposed to score”. – Brad Friedel (Liverpool, Blackburn, Aston Villa, Tottenham and US MNT GK)

So much has been said and written about what the best method is to save a penalty kick that yet another entry seems a bit like beating a dead horse. But a lot of research has been done in recent years, and a lot of additional statistical tools have become available so considering that there are a bunch of Cup finals and a WC Tournament coming up, so maybe we should take one more wack at the old nag.

Game Theory

One of the first scientific approaches to saving penalty kicks was a study done by Dr.Ignacios Palacios-Huerta (http://www.palacios-huerta.com/research.html) He used the mathematical game theory approach to analyze several hundred penalty kicks. The conclusion of the study was that both striker and goalkeeper should adopt the “Mixed Strategy” approach to maximize their chance of success. The shooter should go to his “natural side” (left side for right footed players or to the goalkeeper’s right, right for left-footed players or the goalkeeper’s left) 61.5% of the time and to the other side 38.5% of the time. A goalkeeper should dive to the shooter’s “natural side” 58% of the time and choose the other side 42% of the time.

You can’t save a well-taken penalty kick

In 2010 ESPN Sports Science ran a short item comparing the degree of difficulty of hitting a baseball to that of saving a penalty kick. 

Their calculations showed that a 90mph fastball reaches home plate in 440 milliseconds, while a batter needs 150 ms to react and swing his bat. A 70mph penalty kick reaches the goalline in 400 ms while a keeper needs 100 ms to process the information and another 100 ms to initiate a dive. And even though a 6’3” goalkeeper can cover the area of the goal with just a single powerstep, it takes him 730ms to reach the posts in a dive.

That makes for very simple math: You cannot save a well-taken penalty kick. In order to have a chance, the keeper has to give himself a 330 ms head-start. But diving that far ahead of the kick, gives the shooter time to put the ball somewhere else.

It is interesting to note that, even though they have much more information available to them than goalkeepers do (a pitcher will throw between several hundred to well over a thousand times over a season while a batter will have a few hundred “at-bats”, often consisting of multiple pitches thrown, which means that there is an incredible amount of statistical data available on the habits and tendencies of each player in every possible situation) and even though they have three “strikes” available, baseball hitters don’t guess when hitting. They wait until they see the pitch before swinging. Granted, they have 150 ms more to think than a keeper but that’s still not a lot of time.

More Research

Michel Bar-Eli and Ofer H. Azar at the Ben-Gurion University of the Negev have done several interesting studies in regard to goalkeeping, among them Penalty kicks in soccer: an empirical analysis of shooting strategies and goalkeepers preferences. Soccer & Society, 10:183-191) as well as Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology -2005

The conclusion of these studies shows that: “Given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal’s center. When goalkeepers remain in the center of the goal and the shot is placed in the center, they make the save 60% of the time. Given that about 30% of penalty kicks are placed in the center third of the goal, remaining stationary in the center of the goal increases the keepers chances of stopping the shot from about 13% to more than 33%. Thus, the best strategy for goalkeepers is to remain in the center of the goal during the penalty kick. Goalkeepers, however, almost always jump right or left. We propose the following explanation for this behavior: because the norm is to jump, norm theory implies that a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action.

Thus the idea that keepers should jump left or right and hope they guess correctly is not supported by these numbers”  

Let’s look at Lamps.

With the above research in mind, I wanted to take a closer look at how a player takes penalties. I don’t have access to a lot of penalty stats but Paul Riley (@thefootballfactman / http://differentgame.wordpress.com/) did some great research work involving Frank Lampard’s penalty kicks and he graciously allowed me to use it. You can find Paul’s original articles here and here.

Paul does an excellent job breaking down the numbers in relation to the mixed strategy approach so I want to focus on some other numbers: lampard PK2 There are three stats that jump out:

1. Lampard doesn’t have a “tell”. Goalkeepers facing Frank Lampard guessed correctly 48.5% of the time. All the investigating, the data analysis, the cognitive science research, the dvd watching, etc. and the success rate for guessing the correct direction of a Lampard penalty kick is just about equal to tossing a coin. So in 51.5% of the situations, the quality of the penalty kick itself was irrelevant since the goalkeeper went the wrong way. Essentially, 35 out of 58 Lampard goals were “freebies”, because the goal was already scored prior to the kick.

When the keepers guessed correctly, their save percentage was 27.3%. Which means that, even if a keeper guesses correctly, 7 out of 10 Lampard penalty kicks still go in. In my opinion that proves the point: You can’t save a well-taken penalty kick.

2. Lampard is extremely accurate. If a player is aiming for the far corner, you would expect him to occasionally make an error and miss the target. In 68 attempts, Lampard went wide once. The reason for this could be that he places his penalties further inside the post, but that would mean that his shots are easier to save when the goalkeeper guesses correctly. But even when they guess correctly, goalkeepers only save 27% of Lampard’s penalty kicks, which means that his placement is very accurate, once again showing that you can’t stop a well-taken penalty kick.

The second graph shows even more proof of that. In the 16 PKs (23.5% of Frank’s total) taken against Friedel, Reina, van der Sar and Given, these four worldclass keepers guessed correctly 62.5 % of the time, yet saved only 2 penalties, for a save percentage of 12.5%. So even though their guessing correct percentage was 15% above the average, their save percentage was 1.1% lower than average. (Trivia: the only keeper to save more than 1 Lampard PK is Hull City’s Allan McGregor who saved both Lampard spotkicks he faced, one in the Premier League with Hull City and one in a friendly with Rangers).

3. Lampard knows Neeskens. In their research paper “The Penalty-Duel and Institutional Design: Is there a Neeskens-Effect?”, authors Wolfgang Leininger and Axel Ockenfel noticed that the scoring probability in penalty shooting increase by 11% after 1976 compared to rates prior to 1974. They presented evidence that part of this increase was due to Dutch international Johan Neeskens taking a penalty through the middle in the 1974 World Cup final against West Germany. As a result of going through the middle, Neeskens (probably unwittingly) changed the game-theory terms regarding penalty kicks from a 2×2 game to a 3×3 game form where “The scoring probability in equilibrium of the latter institution is higher than in the former one”.

Frank Lampard went through the middle 11 times (16.2%), and scored all 11 times. The research by Bar-Eli and Arfa shows that if a goalkeepers remains in position, he will save 60% of the shots through the middle third. In Lampard’s case, that means that if a keeper had stayed in place, he could have expected 7 (OK, 6.6 to be exact) of those penalties to hit him squarely in the schnoz. In comparison, Lampard had 9 out of 68 penalties saved. In order to match that number a goalkeeper who stayed in position would have to save an additional 2.4 penalties out of 57. When facing Friedel, Reina, van der Sar and Given, Lampard went through the middle three times, which would give them 1.8 “expected saves” almost the same amount as the actual 2 saves they made in 16 total penalties.

Should we track penalty kicks a different way?

With all kinds of new technology at our disposal, maybe it is time that we start thinking about changing the way we track players taking and saving penalty kicks. Maybe use something similar to the “Expected Goals per game” stat. Rather than tracking a kick by placement left, right and center we should use some of Bar-Eli and Arfa’s research and categorize a penalty kick by the save possibility percentage , maybe based on keeper reaction time. The 3 or 4 feet either side of center could be categorized as “high save probability”. I’d imagine that the “unsaveable” area would be a curve from about 2 feet inside the low post to about 4-5 feet inside the crossbar with the rest of the goal area designated “medium save probability”. With that done you could more easily compare performance between both keepers and shooters. Maybe something like this:

goal

A method like this would allow easier performance comparison between goal keepers. For instance, Friedel has a 0% save percentage against Lampard and McGregor has a 100% save percentage. And according to transfermarkt.com, the Scottish international has a career penalty save percentage of 30.3%, almost twice that of the American keeper (15.9%). Does that make McGregor a better penalty stopper than Friedel? Maybe. Friedel guessed correctly on 60% of the Lampard penalty kicks he faced but all three of them went in. Did Lampard put them in the “unsaveable zone”. What if the two kicks saved by McGregor were in the “high save probability” zone? Friedel is one of only two goalkeepers to save two penalty kicks from open play during a World Cup final tournament. (Poland’s Jan Tomazewski is the other). Where were those penalties placed? How about the kicks Tomazewski saved?

By considering where the penalty kicks faced by a goalkeeper were placed would allow us to calculate an “expected penalty save percentage” for each individual keeper which could be compared to actual performance to determine if a keeper over- or under-performs. It would also allow for a better performance comparison between keepers.

The method could also be used to analyze shooters. For instance, if a shooter has a high scoring percentage but places a lot of his shots in the high and medium probability zone, one would have to conclude that this player is very good at making a goalkeeper move prematurely (i.e. Mario Balotelli) Conversely, one could identify players that put a high percentage of his shots in the “unsavable zone” and then separate the ones who tend to go wide a lot from those who hardly ever miss (I would suspect Rickie Lambert and Matt LeTissier fall in that category). Comparing shooter behavior in different situations such as league games vs. shoot-outs could give insight into a player’s mindset in different situations.

Conclusion

Legendary NY Yankee catcher Yogi Berra could have been talking about saving penalty kicks when he stated that: “90 percent of this game is half mental”. The psychological aspect of the penalty kick is crucial, and, unlike the mathematical aspect, favors the goalkeeper. I agree with Friedel that with penalty kicks, all the pressure is on the shooter who is expected to score. That pressure only increases during shoot-outs when the keeper doesn’t have to worry about rebounds.

So make the shooter beat you. By reacting rather than guessing, a goalkeeper can increase the pressure on the penalty taker by forcing the shooter to take a good penalty. Go for the “low-hanging fruit” and give yourself a chance at saving the less than perfect kicks. Eliminate the “Neeskens effect”. If a player knows the keeper is not going to guess, it makes the option of kicking the ball through the middle less appealing. Fewer kicks through the middle mean more shots to the side which increases the chance of a PK being off-target, which, from a goalkeepers perspective, is just as good as a save.

My philosophy for in regard to saving penalty kicks is simple: Don’t guess, go for the low-hanging fruit, make the saves you’re supposed to make and force the shooter to beat you.

Of course, that’s just my opinion. I could be wrong.

Cheers,

Johan

About Coach Johan

I was born and raised in the Netherlands, and have been playing "real football" since I was old enough to identify a ball. Currently residing in Maryland, I hold USSF “D” and NSCAA “National” Goalkeeping coaching licenses, and have been a part-time Assistant / Goalkeeping Coach at the High School, Club, ODP and NCAA Div 1 levels since 1999. When not playing, talking, writing or thinking about football and goalkeeping, I remind airline passengers to keep their seatbelts comfortably fastened around them, in my day job as a pilot for a major US airline. I can be reached at jdevicq at icloud dot com. Please note that I do not do private training or camps
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4 Responses to Penalty Kicks: Is guessing a sucker’s bet?

  1. Steve Saunders says:

    Nicely done Johan. From my own amateur experience and observing youth games I have a very unscientific theory that has found some success (albeit not measurable!). During the game players make passes, shoot and generally behave to their strengths to get the best desired outcome. Their strengths are most evident when they strike the ball. Throughout the game I find myself mentally logging clues about the players who handle the ball the most. In fact, it is necessary for a GK to do this at least to anticipate what a player on the other team is going to do in certain situations. The way a player strikes the ball is the most telling sign of where the ball is going to go. It helps me cheat. Some call it reading the game. I like to take it a step further calling it reading the player. Thus, since a penner is a situation where the pressure is entirely on the striker of the ball he/she usually go with the style of striking the ball that they are strongest. This clue in combination with the run up makes very strong indication of which way the player will go. Look, most of us will not have the pleasure lining up against Stevie G or Lamps. But with some physics and a few observations a youth keeper can cut down the odds dramatically.

  2. de felice says:

    I have my view on this and you can check by yourself if I’m right or wrong. Unless the player shoot the ball in a unusual way here is my method by watching closely the players. This is what I tell my GK to do: look for the position of the player prior his shot. This give the first clue (if the player position himself on the left side of the ball he is right footed and vice versa). Once this is identified then I ask my GK to focus on the arm of the player, if the arm goes wide the he is going to shoot on the same side of his run and if the arm remain close to his body then he is going to shoot the opposite way of his running side, obviously the GK need to wait for this to happen prior to choose where to dive which is a fraction of a second but normally if this is applied correctly no GK should be choosing the wrong diving side. If the penalty is well taken then it is unstoppable anyway so at least choose the right diving side gives you a real chance to save it. Please comments
    Pietro

    • Coach Johan says:

      Pietro and Steve,

      Thanks for the comments. As goalkeepers, we all try to figure out where the kick might go, in order to give ourselves an advantage. Sometimes it works, sometimes it doesn’t. A lot of research has been done in regard to the kinetics and biomechanics in soccer but no method has been found that is 100% accurate. The study by Bar-Ali and Azar acknowledges that: “The data provide evidence that goalkeepers might have some noisy signals, or cues, about the direction of the kick, since they do better (43% match between their jumps and the ball’s direction) than the 33.3% rate they could achieve by choosing randomly, or the 39.2% they could achieve by always jumping to the right (the most common kick direction)”. Another problem with kinetics is that it difficult for a goalkeeper to look at, and process, all the different clues in the very short time available to him.

      So observing players gives keepers an edge. It turns a blind guess into an educated guess. But it’s a guess nonetheless. At the lower / younger levels it might be a little easier to pick up these signals since the player skill is likely to be less. In addition, in these leagues, less players tend to go through the middle, which makes the guessing easier because it increases the chance that you will be guessing correctly (2×2 game theory vs. 3vx3). Both these factors could result in a higher save percentage. The underlying problem still remains though: How do we compare the amount of penalties saved to the amount of penalties a keeper should have saved? In the lower leagues, that problem is increased because of the lack of available metrics.

      Cheers,

      Johan

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