Goalkeeping and Game Theory

With the World Cup now history, Asia Sentinel celebrates with this piece, originally written for a literary journalism course at the Journalism and Media Studies Centre of the University of Hong Kong. It was recently chosen to be published in an upcoming book to commemorate the 10th anniversary of the JMSC.

In my sweaty, seasoned blue jersey and black shorts, with my palms in white gloves close to my hips and my football boots shoulder-width apart in a ready stance, I stood motionless and focused on the eyes of the man behind the ball planted on the white-rounded spot.

The man to take the penalty, lanky and tanned in a yellow jersey, stood motionless three yards behind the ball. His eyes focused on me for any sign of my tendency to lean to one side or another. It was a dreaded moment for both of us. For a while, neither of us moved. Neither did his teammates, the men in yellow tops locked in a straight line another few yards out, nor mine. Spectators writhed in their seats, their eyes moving left and right like the dial of a grandfather's clock between the man behind the ball and the goalkeeper on the line.

Goalkeeping is the only role that lured and kept me in the game since my first taste of football at the tender age of 8, when I discovered the thrills of denying shots and frustrating even the most prolific strikers. Casual fans have this gross misconception that goalkeeping is for the fat, slow and lazy. On the contrary, the modern game requires goalkeepers to have agility and lightning-fast reflexes, explosive speed over short distances, and the mental and physical toughness to charge at unforgiving blades-laden boots and execute acrobatic moves above the rest for the ball that may lead to awkward, body-twisting landings. Goalkeeping, in the last line of defence and first line of attack, is not for the faint-hearted.

For goalkeepers, facing a penalty is another way to prove themselves – and to be a hero.

But now, standing on the white strip between the two poles on a late August evening, the anxiety heightened. Warm salted sweat dribbled down my forehead to my locked-jaw chin and fell between my feet. I was tempted to wipe the perspiration welling in my eyes but withdrew the thought to focus on his intention – in which direction would he kick the ball? Right? Left? Straight? – as much as he concentrated on anticipating my horizontal commitment at the moment of his kick. The intensity grew in the mounting silence. The men on the horizon began shoving each other to sprint for any possible rebound. Any second now and…the ball somehow glided off the white spot. Shoulders dropped for deep exhales, breaking the dreadful stance of my team.

My team is known as Stanley Milan in Cantonese. The Milan refers to the famous Italian football club Inter Milan and is symbolized by our vertical, blue-black striped jerseys, although we sometimes puzzle our opponents by also wearing the white tops of Spanish giant Valencia. Our team was atop the Hong Kong district league table after five matches into the new season. As the goalkeeper and only foreigner on the team, I took great pride in my five consecutive clean-sheets – no goals conceded in five straight matches – thanks of course to a lot of great defence by my teammates.

My teammates are local residents whose families have lived for generations on the southern tip of Hong Kong Island. Many of their forebears were fishermen, but many of them now own family-run shops and restaurants in Stanley, a popular stopover for tourists by day and lovers and diners at night.

Billy, the right-back defender, was accepted by the University of Hong Kong but ended up in the family business, which has changed over the years from eateries to souvenirs and most recently to toys. Wai Yip, the team captain, runs a few stalls with some teammates that sell China-made souvenirs, mostly to Westerners.

Not all my teammates work in Stanley. Toa, the muscular centre-back who lives alone in a little run-down hut with his brown mongrel, works as a plumber in Aberdeen. The left-back defender, nicknamed Chicken Wings, is an electrician for a shop in Causeway Bay while his family runs a clothing shop in Stanley. The right midfielder Superboy, a speed demon on and off the pitch, drives the number 40 public minibus between Causeway Bay and Stanley.

And there are also jobless ones like Fai, the athletic striker, who spent the last two years playing football,

basketball and any activities that cost him nothing. Many teammates belong to the Stanley sports association and the Dragon boat team. They formed half of the Stanley lion-dance troop on one festive day. After a hard day's work, many like to hang around the Stanley waterfront to enjoy the beautiful sunset and chat over beers. The team, many unmarried and even unattached, will often throw barbeques on weekends and eves of public holidays and spend the night arguing any trivial matters that suddenly seem to matter so much. What a life!

I was never part of these activities until I was recruited after a game three years ago at the Stanley Prison ground between Stanley Milan and the local Baptist church that I played for occasionally. Stanley Milan won by a large margin, although I made many saves on that busy night.

"You're welcome to join us, we need a keeper,'' one of them said after the game.

And right now I am the goalkeeper this squad is counting on. Not just because we are two goals down minutes before half-time, a situation this squad is unaccustomed to, but because we have been slapped with a highly controversial penalty from what seemed like a bribed referee.

The short, stern referee is no stranger to our team. He has ruled blatantly against us previously. His whistles against our squad in this match, especially the one leading to this penalty I am now facing, were so bluntly and jaw-dropping biased that they seemed to surprise even the opponents. There were whistles against our seemingly harmless moves, but none against the ankle-slamming and body-flipping tackles from the opponents.

The scene that night was really chaotic for our squad. The first goal we conceded, the first this season, was a result of a sloppy back pass between Billy and Toa that was picked up by their striker, who fired the ball from such close range that my impulsive leap to my left failed to reach the high goal-bound shot. The squad felt confident it could compensate for that mistake, only to see Toa violently brought down without a whistle by two opponents who then charged forward for a two-on-one play for another goal.

As I remained beaten to the ground in shock, the squad surrounded the referee screaming in protest while the opponents hopped away in joy. Firm in his decision, the referee showed the bruised Toa a yellow card instead for his threatening words.

The squad held the ball firm when play resumed, looking forward to the interval to review the situation when the most unthinkable happened. A lost possession of the ball led to a long through-pass from the opposite end, which sent Billy and an opponent racing towards my territory. In a most dramatic fashion, the opponent pulled and dropped Billy flat on the pitch and pushed the ball alone towards me. As my squad waved and shouted in protest, I sped out of the box to narrow the angle of his shot but he did exactly what every goalkeeper fears in such situation – a lob.

The ball was lobbed well and fast over me and as I twisted my body abruptly around, I saw the ball ending its parabola near the left upright pole and heading for the third goal… when Chicken Wings flew like a torpedo to collide with that ballistic missile.

And I watched in awe from close range his entire airborne feat. His flight originated from a 45-degree takeoff at the edge of the goalkeeper box, the smaller rectangular area in front of the two poles. His hands were close by his sides like a cannonball man in the circus just shot into the air. He timed his leap perfectly to intercept the ball right before the goal line and altered the path of the ball with an upward jolt from his top left shoulder, the horizontal part of the shoulder down from the neck. His heroic effort cleared the ball for a corner-kick but a loud "Piiiii" from a few feet to my right pierced my ears. The referee stood firm and pointed at….What? The penalty box?!

"You must be kidding!" I howled as I lumbered my six-foot-one frame in three giant steps towards the five-foot-five referee.

"Are you blind? It was my collar bone!" Chicken Wings yelled and shoved the referee a few feet back.

"Who paid you? How much?" Billy, who had just arrived at the scene, shouted.

By then, it was complete chaos as our entire squad, the opponents and the linesmen converged to deal with the situation and filled the air with profanity.

"He's obviously bribed," one angry voice thundered.

"Everyone can see what's going on. Teach him a lesson." The last four words were repeated a couple of times and prompted a few advances toward the referee.

As it always turns out in football, the opponents somehow managed to play successful diplomacy and divide the angry men. The linesmen persuaded my squad to back off for the match to resume. The men took their positions, but with outrage still on their faces and their profanity still slicing the hot summer air.

Now the ball that somehow had moved off the rounded-spot was planted back in place. This match, which eventually sparked a run of bad results before our squad recovered and ended the season in mid-table, has to resume. I took my spot and adopted a ready stance again.

Left or right? I can almost hear everyone asking the same question. Statistics show some interesting facts. For one taking the penalty, he actually has three options – left, right or centre? – after eliminating vertical concerns. If he aims for the center, he can almost guarantee a goal as goalkeepers more often than not commit themselves either way. The major risk of this strategy is the goalkeeper may still be able to use his leg to block the shot whilst in mid-flight sideways. The worst nightmare, however, is when the goalkeeper stays rooted to the ground and the ball goes embarrassingly straight into his hands. That scenario is very rare, according to statistics, and chances are the ball will go either left or right.

For the goalkeeper, statistics show the ball will almost certainly end up on his right if the penalty-taker is left-footed – he will kick to his left (goalkeeper's right) 90 percent of the time. However, the probability is split almost evenly if the penalty-taker is right-footed.

"So what's your strategy facing a penalty?" my colleague Raymond Wang asked me over dinner one day.

My strategy was actually very logical, and echoed the famous game theory of "The Prisoners' Dilemma" as it was applied in economics by Nobel Prize winner John Nash and featured in the Hollywood movie, "A Beautiful Mind". In The Prisoners' Dilemma, the question is whether two prisoners will cooperate to minimize total loss of liberty or will one, trusting the other to cooperate, betray him so as to go free.

Of course I can never expect the opponent to cooperate in a penalty kick but what the Prisoners' Dilemma came to mean to me as a goalkeeper was the need to betray the opposition by engaging in mind games. As a kid, I somehow managed to find success at outsmarting others in penalty situations – by making my moves after foreseeing my opponent's intentions – a method I instantly recognized when I later heard about The Prisoners' Dilemma game theory.

I always pondered: if I knew he was kicking to my right, I will dive right. But if he knew I knew he was aiming right, he will shoot to my left. Now, if I actually figured he knew that I knew he was aiming right in the first place and he will shoot to my left instead, I will dive to my left! However, if he managed to read my mind on this, then he knew I knew that he knew that I knew that he will shoot right at the beginning, he will still shoot to my right! Ha, but if I knew...and I wasted many of my younger days perfecting my game theory of goalkeeping this way.

"I will fool him to slot the ball to my stronger side," I told Raymond, providing my more mature, manageable and modern version of the theory: I will tell him where to shoot.

Goalkeepers can only move along the line before the ball is kicked. I tend to dive a farther distance to my right. By moving slightly off the center to my left and exposing a bigger gap on my right, he is likely to shoot into the generous space that is still possibly within my reach. And even if he did otherwise, I have my left well covered.

And that is the strategy I have in mind with this penalty. My squad is counting on me. I embarked my horizontal solo dance, hopping equal distances to the left and right, at first at a slow rhythm, but tilting evidently more and more to my left as he geared up towards the ball. With one step away from executing his shot, I deliberately gave him full confidence of my wayward commitment by making one big hop to my left – but I was almost ready for a great leap to my right where the ball is definitely targeted.

He did exactly what I expected and the ball headed to my right and I…I slipped off the spot marked for my take-off!

I laid on my back absorbing the cacophonous atmosphere, down and out from the suffocating pressure, sensing that our successful run into the season was cruelly over.

Vanson Soo is a commercial investigator in private practice and a freelance writer.