Tag Archives: Euro 2016

The penalty shoot-outs are a lottery

Recently, the 2016 UEFA Champions League final (between Real Madrid and Atletico de Madrid) was decided in a penalty shoot-out, so was the 2016 Copa America Centenario final (Chile – Argentina) and so have already been a couple of matches in the round of 16 and quarter finals of the ongoing UEFA Euro 2016 (Switzerland – Poland and yesterday’s Poland-Portugal). You could expect one or two more matches in that competition to be decided in such a way.

“The penalty shoot-outs are a lottery”

This is a mantra repeated once and again each time the extra time of a football match comes to an end and the score is still a draw. Yet penalty shoot-outs are not a lottery. However, asking TV or radio football commentators to describe this aspect of the game as “two-person zero-sum game that meets von Neumann’s Minimax theorem” would be too much.

Years ago, while reading the book “Soccernomics“, by Simon Kuper and Stefan Szymanski (book review here), I came to know a couple of papers on penalties and penalty shoot-outs published by the Spanish economist Ignacio Palacios Huerta (at the London School of Economics).


In a first paper, Professionals Play Minimax (2002, and its annex) [PDF, 335 KB and 342 KB], by analyzing over 1,400 penalty kicks, he came to confirm that professionals do play Minimax, a game theory rule decision model in which they try to minimize the worst outcome not knowing the strategy of their opponent.

The object of the paper itself is to try to find a natural setting in which von Neumann’s theorem implication can be tested. Penalty kicks turns out to be such a natural setting, the reasons enabling the game to be so are: there are few strategies available to the players (basically shooting left or right for the kickers, or jumping to his left or right for the keepers), it is a two-player zero-sum game and the outcome of the game (goal or no goal) is immediate after a strategy is chosen.

Studying those over a thousand penalties and in particular those of 42 players (kickers and keepers) who have been each one involved in over 30 penalties in the time span of the study (1995-2000), the author came to the following findings:

  • Kickers have practically the same probability of scoring with different mix of strategies (being a strategy alternating between shooting left or right by a given proportion).
  • Players are capable of generating truly random sequences of choices (left – right). This is remarkable, as humans, when asked to produce a random sequence, normally over do it and shy away from what would be truly random.
  • Some figures: players shoot to their natural side (with the interior of the feet, shooting left to a right footed) just above 50% of the times, keepers jump to the natural side of the kicker slightly more often.
  • When the keeper “guesses” the side to which the kicker is shooting, the scoring probability greatly differs depending on whether it was the kicker’s “natural side”, 71%, or the non-natural side, 55%. When the keeper jumps to the wrong side the scoring probability is about 95% with no big difference between natural or non-natural side.
  • During a match the average scoring rate is about 80%, with the rate decreasing as the match comes to an end (73% for penalties in the last 10 minutes).
  • Some players during the years of the study (1995-2000) had significantly better scores; in particular Mendieta (91% and no matter whether he kicked to his natural (68% of the times) or non-natural side (32%)), Del Piero and Juninho (especially strong on their natural side (94%) and above average in their non-natural (87%)) or Bergkamp (91% and 88%).
  • Strategies between players varied greatly. As I said Mendieta had a 68/32 (natural / non-natural), whereas Batistuta had a 81/19 and Baggio a 45/55, all with above average scoring success. Other players like Zidane, Mihajlovic or Chiesa managed an undistinguishable 50/50.

See a couple of interesting tables below:

Minimax table 1

Minimax table 2

Even more interesting is his second paper.

Penalty shoot-outs

In a second paper, “Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment” (2009, with Jose Apesteguia) [PDF, 342 KB], Palacios Huerta wants to find out how emotions play a major effect on performance and to do so he takes a look at penalty shoot-outs from major football competitions.

For this study he reviewed over 2,800 penalty kicks in about 270 penalty shoot-outs. He divides the observations in two blocks, before and after FIFA changed the rules governing the shoot-outs in 2003. Before that date, the team of the captain winner of a toss of a coin started kicking first; after the change in the rules, the captain winner of the toss of a coin chooses which team kicks first.

Before 2003, the fact of kicking first or not was random, and after 1,343 kicks in 129 shoot-outs, the authors found out that the first in kicking in the sequence win the penalty shoot-out 60.5 percent of the time. (1)

As part of his study, Palacios Huerta made a survey questioning over 200 football players and coaches in Spain, professionals and amateurs, what would they choose if they had won the toss of a coin to decide which team kicks first in a penalty shoot-out. The results offer not doubt: over 95% of the cases chose to kick first. When asked why they would choose that option they indicated “to put pressure on the rivals”.

Experience matched the survey. After the change of FIFA rules in 2003, Palacios Huerta gathered data of another 140 penalty shoot-outs up to 2008 (just before writing his paper). Those were the first 140 penalty shoot-outs in which the winner of the toss of a coin had to choose whether he wanted his team to kick first or his opponent to kick first. In just a single case did the winner of the toss of a coin choose to let the opponent to kick first: Gianluigi Buffon playing for Italy the quarter-final of the Euro cup in 2008 against Spain, with the result that Spain won the penalty shoot-out and went to win the Euro, starting a streak of 3 consecutive major competitions at national level (Euro 2008, World Cup 2010 and Euro 2012).

Take a look at the following graphics and tables that let you read how the probabilities of scoring each penalty in a shoot-out evolve depending on previous outcomes (whether the team is behind, even or ahead) and the probability of winning the shoot-out (hence qualifying to the next phase or winning the competition) evolve.



I highlighted in the previous table in blue and yellow the scoring probability for each kick and the winning percent of the shoot-out for a shoot-out in which both teams go about scoring each of the penalties. It is interesting, if not dramatic, to see how while the scoring probability for the first team is always between 72 and 78% (2), for the second team it drops from 82% to 62-66% for rounds 3 to 5. Similarly, the winning probability decreases for the second team down to 21-23% just before attempting kicks 3 and 4 if all previous penalties have been scored.

See below that 2008 penalty shoot-out between Spain and Italy.

After having commented on these two papers and its conclusions, let me share a few comments and anecdotes:

MILAN, ITALY - MAY 28: Cristiano Ronaldo of Real Madrid scores the winning penalty during the UEFA Champions League Final match between Real Madrid and Club Atletico de Madrid at Stadio Giuseppe Meazza on May 28, 2016 in Milan, Italy. (Photo by Shaun Botterill/Getty Images)

MILAN, ITALY – MAY 28: Cristiano Ronaldo of Real Madrid scores the winning penalty during the UEFA Champions League Final. (Photo by Shaun Botterill/Getty Images)

Toss of a coin. Both 2016 Copa America Centenario final and UEFA Champions League final were won by the team which kicked the first penalty, Chile and Real Madrid, respectively. In the draw, using the toss of a coin, to decide which team kicked first Chile chose to kick first (see here the video). However, in the Champions League final, Atletico de Madrid’s captain Gabi chose to let Real Madrid kick first. Apparently, he chose that as they had kicked second in the round of 16 of that same competition against PSV Eindhoven and passed. Somehow he tried to repeat the sequence thinking that this would bring them luck. Well, with that decision he put his team against about 60-40% odds backed by over 30 years of recorded experience and about 270 shootouts. Not a clever move. See this article “La buena mala suerte del Churu” by Manuel Jabois discussing this toss of a coin (in Spanish). See here the video.

“[…] we find a systematic first-mover advantage. Further, professionals are self-aware of their own psychological effects and, when given the chance, they rationally react by systematically taking advantage of these effects.” (Palacios-Huerta)

1024x1024As reflected above, in the paper, Palacios-Huerta indicates that between 2003 and 2008 only once in 140 samples did the winner of the toss chose to let the opponent kick first. That is why it was striking what Gabi did and why it called the attention of some football fans. Well, yesterday, during the first match of the Euro 2016 quarter finals between Poland and Portugal, we had yet another such example, another anomaly. This time it was Robert Lewandowski, the Polish captain, the perpetrator. He won the toss of the coin and chose that Portugal kicked first. I can imagine how Cristiano Ronaldo might have felt at that moment, the second time in just 6 weeks that he was being handed such a present. Portugal won the shoot-out.

Palacios Huerta and other analysts receive requests for dedicated reports about kicking patterns, records and data of different teams when playing knock-out phases. In Soccernomics, Simon Kuper and Stefan Szymanski, describe how that happened during the 2008 UEFA Champions League final between Manchester United and Chelsea. Palacios Huerta had given Chelsea some tips on Manchester kickers and keeper (van der Saar): “Van der Sar tends to dive to the kicker’s natural side”, “most of the penalties that Van der Sar stops are mid-height, thus is better to shoot low or high”, “if Cristiano Ronaldo stops half-way in the run-up to the ball chances are 85% that he shoots to his natural side”…, it is quite interesting to actually see that penalty shoot-out and how the different players acted. See below the video. Apparently Van der Saar saw how Cech, Chelsea’s keeper had some paper in his hands and also noticed how kickers were shooting to their non-natural side, until at the 7th penalty (~9’30” in the video) he defies Anelka by pointing to Anelka’s non-natural side, like saying “I know you have the tip to kick there”, then…

For the record, the final was won by Manchester, first in kicking.

Finally, ever since coming to know all this information I have enjoyed penalty shootouts more than before. I now entertain myself seeing the strategy taken by the keepers and kickers, whether the keeper jumps to the natural side of the kicker more or less than in 60% of the shots, if he changes his strategy depending on whether the kicker is left or right-footed, whether kickers shoot more or less than 60% of the shots to their natural side, etc.

Les grandes personnes aiment les chiffres“, Le Petit Prince.

(1) At the time of the Copa de America Centenario final, the Spanish journalist Alexis Sanchez (better know by his profile @2010MisterChip), expert in providing all kind of football statistics, tweeted that Chile, being the first in kicking in the penalty shootout against Argentina had a 55% chance of winning the tournament. Thus, it may be the case that he has a larger (not public) database including more penalty shootout.

(2) Note how probabilities in shoot-outs decrease from the average of 80% of penalties during the match.


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Forecasting France Euro 2016

I have a work colleague who not only is a tremendous negotiator and aircraft seller but also has a great sense of humor and manages in his free time late in the night to set up a contest for office staff to try to guess winners, matches’ scores, top scorers, etc., of major international soccer competitions. The France Euro 2016 which starts this afternoon could not be missed. Nacho managed to set up the contest in time.

In this post I am going to explain how I went about forecasting the results of the UEFA Euro 2016.

“when in doubt, build a model”, Nate Silver.

The readers of this blog may already know how much I do like to build models to produce forecasts, guesstimates, etc. In relation to forecasting this UEFA Euro 2016 there is some background that has shaped my mind in relation to the subject in the recent years, let me give you some hints:

Having shared this background, you may understand that I tried to remove all the beauty of guessing and my football knowledge out of the forecasting process (1).

I rather made use of:

  • ESPN Soccer Power Index (SPI) ranking, introduced by the economist Nate Silver. I used its offensive and defensive scores plus weight for each of the scores based on a tip indicating that in competitive matches the defensive factor tends to be slightly more important (see “A Guide to ESPN’s SPI rankings”) (2).
  • The frequency of different scores in the group phases of the Euro 2012 and the World Cup 2010, the in the round of 16, quarter finals and semi-finals.


  • A few simple rules about how to allocate results given the difference between SPI ratings of the two nations playing each match. (3)
  • The total number of goals during group phases the latest Euro and World Cup. In order to cross check that the total numbers of goals that my forecast yielded was in check with previous competitions.

It may sound very complex. It is not. It requires a bit of reading (which most of it I did years ago), retrieving the latest ratings, giving it a bit of thought to set up the model and then, not even looking at the names of the teams, you go about allocating the scores based on raw figures. Let’s see how my forecast fares this time! (4)

Porra Euro 2016

Les grandes personnes aiment les chiffres” (5), the Little Prince.

(1) In fact I have not watched a single national team football match from any country since the World Cup in Brazil in 2014.

(2) See here the blog post I published yesterday in which I made a more thorough review of the ESPN SPI index.

(3) I set up rules like “if the difference of the combination of indices of the two nations is below this threshold, I take it as a draw, if it is between x and y as victory by 1 goal, if higher…”, etc.

(4) This way of forecasting allowed me to finish 4th out of 47 in 2010, 15th out of 87 in 2014. As it removes biases it allows to be better than the average, though it prevents you of guessing outliers, gut feelings, etc.

(5)”Adults love figures”.

Note: In the blog post from yesterday I mentioned that the latest complete ranking from the ESPN SPI index that I could retrieve dated from October 2015. That is the one I have used, therefore, Germany results as winner. Of the latest ranking, covering the Top 25 nations, only 13 countries of the 24 competing at the Euro 2016 are included. I could have set up an hybrid ranking taking the latest rankings and ratings for the top 13 from June and using the October figures for the lower 11 teams. I decided to go on with a single set of data. If I had done so, the maing changes would have come from the semifinals onwards. France would have appeared as winner instead of Germany. We’ll see if that was a good decision.

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France Euro 2016: “group of death”?

Tomorrow will start the UEFA Euro 2016. Fans all over Europe start getting excited by it. This year’s competition is played in France, with some matches taking place in Toulouse, one of them Spain – Czech Republic, which some friends and I will be able to watch live!

This post is intended to be a quick one to discuss, as I did for the 2014 World Cup in Brazil, which groups are the most difficult ones, the so-called “group of death“. Media all over Europe states that it is group E, with Belgium, Ireland, Italy and Sweden the one which is the toughest. To discover which is effectively such group I’ll focus on a couple of rankings: FIFA’s and ESPN’s Soccer Power Index, as I did in 2014.

Teams Euro 2016

FIFA world ranking.

In its website, FIFA explains the procedure which it uses to compute the ranking, which is based on the following formula:

M x I x T x C = P

M: winning, drawing or losing a match

I: importance of the match

T: strength of opposing team

C: confederation strength weights

P: points for a game

According to that formula, the latest ranking (June 2nd), filtered for European teams, has the following teams at its top:

FIFA ranking

With the information of both the ranking and the points I went to check which of the groups of the Euro 2016 were the strongest, both taking a look at the overall group and looking from the perspective of the “favourite” team (the one with the highest ranking), which was the one facing a toughest group (total points of the other 3 teams composing the group). See the results below:

Group of death - FIFA ranking

As you can see the most difficult groups in terms of total points are:

  • C (Germany, Northern Ireland, Poland, Ukraine) with 3,897.
  • F (Austria, Hungary, Island, Portugal) with 3,895.
  • E (Belgium, Ireland, Italy, Sweden) with 3,869.

Looking at the average ranking, the most difficult groups are:

  • F (Austria, Hungary, Island, Portugal) with 18.
  • C (Germany, Northern Ireland, Poland, Ukraine) with 18,75.
  • D (Croatia, Spain, Czech Republic, Turkey) with 20,25.

And excluding the points of the favorite team in each group, which is the favorite facing the toughest group?

  • Portugal in group F, facing 2,714.
  • Germany in group C, facing 2,587.
  • Spain in group D, facing 2,576.

Then, combining the 3 approaches, to me, it becomes clear that the toughest group is F, with Austria, Hungary, Island and Portugal, by the total amount of points (2nd), ranking of the teams (1st) and in relation to what Portugal will face (1st).

The second most difficult group would be C, with Germany, Northern Ireland, Poland and Ukraine, by the total amount of points (1st), ranking of the teams (2nd) and in relation to what Germany will face (2nd).

You can see that, using FIFA ranking, and despite of conventional “wisdom” (press), group E would be nothing but the 3rd or 4th most difficult group, i.e. an average group out of 6.

ESPN Soccer Power Index (SPI) ranking.

ESPN Soccer Power Index (SPI) ranking was introduced by the economist Nate Silver of worldly fame, who many readers will know from his forecasts on elections in the USA (check his blog FiveThirtyEight).

In a post from 2009, when the SPI was introduced, just before the 2010 World Cup, he explained how the index was computed (“A Guide to ESPN’s SPI rankings”). As he explained, the process had 4 main steps:

  • Calculate competitiveness coefficients for all games in database.
  • Derive match-based ratings for all international and club teams.
  • Derive player-based ratings for all games in which detailed data is available.
  • Combine team and player data into a composite rating based on current rosters; use to predict future results.

The main difference in relation to FIFA ranking algorithm is that it takes player-based ratings for those players who play in clubs in the Big Four leagues (England, Spain, Italy, Germany) and the UEFA Champions’ League. The player-based rating is merged into the national team coefficient. The player-based rating weighs heavily in national teams with many players playing in the main leagues (e.g. England or Spain national teams) and less heavily in other nations which roster is composed of many players not playing in clubs of the 4 main leagues (e.g. Russia).

Other details of the ESPN’s approach are similar to those used by FIFA: e.g. giving weights to results depending on the opponent, measuring the competitiveness of the match, the different confederations, etc.

ESPN provides a daily update of its ranking, however it includes only the top 25 world-wide teams, out of which 15 are European and only 13 represented in the UEFA Euro 2016, that is about half of those 24 competing.

ESPN - daily rating June 08

In order to review which one would be the group of death using the ESPN SPI I took the latest available complete ranking I could find, dating from October 2015, which is half a year away, but reflected the situation at about the end of the qualifying phase for the Euro 2016. See the ranking below:

ESPN SPI Oct 2015

As I did with the FIFA ranking above, with the information of both the ranking and the ESPN SPI ratings I went to check which ones of the groups of the Euro 2016 were the strongest, both taking a look at the overall group and looking from the perspective of the “favourite” team (the one with the highest ranking), which was the one facing a toughest group (total ratings of the other 3 teams composing the group). See the results below:

Group of death - ESPN SPI ranking

As you can see the most difficult groups in terms of total ratings are:

  • D (Croatia, Spain, Czech Republic, Turkey) with 309.
  • B (Slovakia, Wales, England, Russia) with 307.
  • C and E with 303.

Looking at the average ranking, the most difficult groups are:

  • B (Slovakia, Wales, England, Russia) with 24.
  • D (Croatia, Spain, Czech Republic, Turkey) with 24.5.
  • E (Belgium, Ireland, Italy, Sweden) with 28.

And excluding the points of the favorite team in each group, which is the favorite facing the toughest group?

  • England in group B, facing 224.
  • Spain in group D, facing 223.
  • Belgium in group E, facing 219.

Then, combining the 3 approaches, to me, it becomes clear that the toughest group is B, with Slovakia, Wales, England and Russia, by the total amount of points (2nd), ranking of the teams (1st) and in relation to what England will face (1st).

The second most difficult group would be D, with Croatia, Spain, Czech Republic and Turkey, by the total amount of points (1st), ranking of the teams (2nd) and in relation to what Spain will face (2nd).

You can see that, using ESPN SPI ranking (from October), and despite of conventional “wisdom” (press), group E would be nothing but the 3rd most difficult group.

Some readers may be tempted to think that I arrived at this result because I used a ranking from half a year ago, that if we were to take the latest ratings (if fully available) group E would emerge as the toughest one… not so. See the preliminary table using the information available for those 12 teams:

Group of death - ESPN SPI ranking - June 2016

There you can see that with the latest ratings the most competitive group would be either D or C, very much like with FIFA rating (from June as well).

It is interesting to note how by using FIFA or ESPN SPI the weight given to the group F (Portugal) is completely different.

Finally, in both ratings the big absence in the tournament is the Netherlands, arguably about the 10-14th team in the world, the 6th in Europe. A pity for the competition.

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