Stack is a way we can store information. It follows the simple process of Last In, First Out or LIFO. Adding an item to the top of the stack is called a “push” operation. Removing an item from the top of a stack is called a “pop” operation. Another operation is “top”. Top simply returns the latest item that has been pushed the stack. Depending on the application, sometimes the pop operation can also be used as a top by returning what has been removed to the caller. These operations have a constant time or a time complexity of O(1).
We can implement a stack using arrays or a linked list. In array implementation, you can push a stack only until you reach the size of an array. We can have a situation where we consume the array and we cannot push anymore. This is what we call a stack overflow. There a few ways to avoid a stack overflow:
1. Add a semantic check before you push a new item to the stack
2. We can create a new large array and copy the contents of the older filled up array. The cost of copy is O(n) where n is the size of the filled up array. Simple strategy of deciding the size of the new array is doubling n
Here is a simple example of a stack implementation in C
#include <stdio.h>#define STACK_CAPACITY 10//A int stack data Structurestruct Stack {
int list[STACK_CAPACITY];
int size;
};
typedefstruct Stack Stack;
//Initialize stackvoidinitStack(Stack *s)
{
s->size =0;
}
//Return the top of stackinttop(Stack *s)
{
if (s->size ==0) {
printf("Error: stack empty\n");
return-1;
}
return s->list[s->size-1];
}
//Returning the current size of a stackintsize(Stack *s)
{
return s->size;
}
//Push an item to the stackvoidpush(Stack *s, int item)
{
if (s->size < STACK_CAPACITY)
s->list[s->size++] = item;
else
printf("Error: stack full\n");
}
//Pop an item to the stackvoidpop(Stack *S)
{
if (S->size ==0)
printf("Error: stack empty\n");
else
S->size--;
}
intmain()
{
//Create local variablesint item=-1, currentSize =-1;
//Create a stack strucuture
Stack s;
//Initialize stack
initStack(&s);
//Get the current size of a stack
currentSize = size(&s);
printf("Current size of a stack %d\n", currentSize);
//Push three items to a stack
item =2;
push(&s, item);
item =1996;
push(&s, item);
item =203;
push(&s, item);
//Get the current size of a stack
currentSize = size(&s);
printf("Current size of a stack %d\n", currentSize);
//Get the current top item of the stack
item =-1;
item = top(&s);
printf("Current top item of the stack %d\n", item);
//Use the pop operations couple of times
pop(&s); //pop 203
pop(&s); //pop 1996//Get the current size of a stack
currentSize = size(&s);
printf("Current size of a stack %d\n", currentSize);
//Get the current top item of the stack
item =-1;
item = top(&s); //returns 2
printf("Current top item of the stack %d\n", item);
item =0;
//Try to overlow the stack by push "0" ten timesfor(int i=0; i < STACK_CAPACITY; i++)
{
push(&s, item);
}
//Get the current size of a stack
currentSize = size(&s);
printf("Current size of a stack %d\n", currentSize);
//Try to empty the stackfor(int i=0; i < STACK_CAPACITY; i++)
{
pop(&s);
}
//Get the current size of a stack
currentSize = size(&s);
printf("Current size of a stack %d\n", currentSize);
//Empty the stack while it is empty
pop(&s);
return0;
}
Here is an output of our simple C program:
Some of the applications of a stack data structure in Computer Science are:
1. Stack Memory Management
2. Text Parsing
3. Expression Evaluation
4. Backtracking Algorithms
For more resources on the applications of the stack data structure see the following: Stack Applications
“Four things come not back: The spoken word, The sped arrow, The past life, The neglected opportunity.” An Arabian Proverb.
When asked why the Manchester United forward Andy Cole was not picked for the 1998 World Cup Squad, former England Coach Glenn Hoddle said: “Andy Cole needed five chances before he converted.” This quote has always stuck with me when evaluating an attacking player. As a forward, you usually only get few chances to convert a goal during a game. Sometimes, missing a crucial chance might even subject you to the unforgiving wrath of the Internet.
After thinking about who is the most efficient striker in Europe currently, I could not come up with an answer. I guessed Suárez or Lewandowski but I was not 100% sure. So I decided to do some research based on data from last season. Statistically, there are two ways you can do this. Count the number of goals per-minute played or count the number of goals per shots taken. I prefer the latter because it normalizes the number of minutes played between the players. In this method, I do not have to worry about Ronaldo playing 18 hours and 15 minutes more than Charlie Austin when comparing the two.
I decided to research the players from the following leagues and tournaments from last season because of the perceived quality of the competition: UEFA Champions League, Italian Serie A, English Premier League, Spanish La Liga, French Ligue 1, Dutch Eredivisie, German Bundesliga and UEFA Europa League. I also decided to only look at players who scored at least 18 goals. An obvious limitation of this research is that the quality of opprutunities or shots taken were not compared.
Here is what I found:
Player Name
Total Shots
Goals
Ratio(%)
1. Bas Dost
54
18
33.33333
2. Carlos Bacca
89
27
30.33708
3. Alexandre Lacazette
96
27
28.125
4. Antoine Griezmann
94
24
25.53191
5. Karim Benzema
88
21
23.86364
6. Alexander Meier
80
19
23.75
7. Neymar
136
32
23.52941
8. Diego Costa
94
20
21.2766
9. Luis Suárez
113
23
20.35398
10. Aduriz
94
19
20.21277
11. Lionel Messi
270
53
19.62963
12. Cristiano Ronaldo
296
58
19.59459
13. Zlatan Ibrahimovic
109
21
19.26606
14. Sergio Aguero
167
32
19.16168
15. Harry Kane
112
21
18.75
16. Thomas Müller
107
20
18.69159
17. Carlos Tevaz
152
27
17.76316
18. Luca Toni
125
22
17.6
19. Arjen Robben
110
19
17.27273
20. Mark Uth
116
20
17.24138
21. Edinson Cavani
143
24
16.78322
22. Gonzalo Higuaín
150
25
16.66667
23. Luuk de Jong
133
22
16.54135
24. André-Pierre Gignac
130
21
16.15385
25. Mauro Icardi
140
22
15.71429
26. Pierre-Emerick Aubameyang
123
19
15.44715
27. Robert Lewandowski
151
23
15.23179
28. Charlie Austin
131
18
13.74046
29. Alexis Sánchez
142
19
13.38028
30. Memphis Depay
188
25
13.29787
Based on the research, VfL Wolfsburg’s Dutch striker Bas Dost was the most efficient striker in Europe with a impressive ratio of 33.333% chances of scoring a goal per shot. The 26 year old 6’5 striker had a wonderful season in the Bundesliga and Europa League. The big man is an excellent finisher, moves wonderfully off the ball and is great in the air. AC Milan’s new Colombian summer signing Carlos Bacca came in second with 30.337% chances of scoring, while Lyon’s French striker Alexandre Lacazette came in third with 28.125%. These three players have two things in common: they are currently not house hold names and do not start for their national teams. Maybe another season with 18 or more goals with the same level of efficiency will cement them with the elite of European football.
If you know the enemy and know yourself you need not fear the results of a hundred battles. Sun Tzu.
Introduction
My first introduction to football tactics was playing Sega’s Football Manager 2008. I was introduced to weird concepts such as defending deep or playing a high-line which made no sense to me. Today most people who watch at least one football match a week have a good understanding of the basics of football tactics because of YouTube videos of Gary Neville and his over-sized iPad on Monday Night Football or reading Michael Cox’s zonal marking blog.
“Good tactics” is only a single factor for a football team’s ability to beat another football team or reach its objective. Other components such as technical proficiency, physical ability, physical condition, mental strength and motivation of the players are just as important. Harry Redknapp, former QPR, Tottenham and West Ham manager, once said: “You can argue about formations, tactics and systems forever, but to me football is fundamentally about the players, Whether it is 4-4-2, 4-2-3-1, 4-3-3, the numbers game is not the beautiful game in my opinion. It’s 10% about the formation and 90% about the players. If you have the best ones and they do their jobs, then they can pretty much play any way you want them to.” I fundamentally agree with Redknapp but the ratios are more like 30 to 40% vs 60 to 70%.
Legendary basketball coach John Wooden once told Roy Williams (University of North Carolina’s basketball coach): “Roy, you can coach talent. Some guys can’t. Nobody can coach no talent, but you can coach talent.” I believe this principle also applies in football. No matter what great plan you come up with to defeat another opponent, if you do not have the personnel to execute the plan effectively then tactics become almost useless. Almost useless instead of just useless because teams can use tactics as damage control, for example instead of losing 10-0, you only lose 3-0. Good tactics are an effective tool but not the whole piece of the pie.
A football match consists of 5 important reference points: your team, the opponent, the space, time and the ball. Tactics is an overall strategy or framework or game plan or philosophy to balance all these factors to gain a competitive advantage in a match. There is no one single perfect way of achieving that balance but instead multiple ways or different schools of thought. Barcelona and Chelsea have won the league effectively in their respective countries in the 2014/2015 season by playing two completely different brands of football when facing their competition rivals. Chelsea beat Manchester United 1-0 in Stamford Bridge with only seeing the ball 29.6% of the time while Barcelona beat Atletico Madrid in the Vicente Calderón Stadium with the same score with 77% of the ball. With respect to effectiveness, both strategies are sound, however when it comes to entertainment value there are criticisms from a majority of football fans against the “Chelsea way.” Argentina’s 1986 world cup winner Jorge Valdano once said “Playing against a defensive opponent is just as bad as making love to a tree.” Personally, I agree with Valdano, but I also enjoy watching a top team trying to break down Chelsea and being extremely frustrated.
In this article series, I will try to comprehensively explain the basics of football tactics. Initially, I will introduce an important component of football tactics that has survived for more than half a century.
Principles of Play
In 1967, The English Football Association also know as The FA published a manual called “The FA Guide to Training and Coaching.” It was written by Allen Wade who was the “Director of Coaching” at the time. This book became a Bible to a generation of coaches, especially to Roy Hodgson who currently leads the English National Team. In the manual, Wade introduces 5 attacking principles countered by 5 defending principles:
Attack
Defence
Penetration
Delay
Support
Depth
Width
Compactness
Mobility
Balance
Improvisation/Creativity
Discipline/Patience
10 Principles of Play
These principles have stood the test of time because of their effectiveness. Each principle can easily be transmitted into practice drills which represents a specific situation during a match. Before we present the principles, we must first clarify and prioritize the objectives of teams when attacking and when defending:
Attacking Objectives
Defending Objectives
1. Score
1. Stop Scoring
2. Advance
2. Delay the Attack
3. Maintain Possession
3. Regain Possession
The principle of play aid teams to reach these objectives during the course of a game. Let us explore the practicality of each principle.
Penetration
As soon as possession is regained by a player or they receive the ball in an advance position the player now becomes the “first attacker.” The first attacker should ask themselves if they can score. If not, then is there a player we can pass to in an advance position or can we move to an advance position closer to the opponent’s goal. If not, then is there space closer to the opponent’s goal they can dribble the ball into. Players are required to make a lot of decisions in half a second. Therefore, repetitive drills that emphasize these decision making skills are great in order to improve a player’s intuition(speed of execution) during a game.
Delay
As soon as a defender becomes the closest player to the first attacker they then become the “first defender.” The first defender now has a choice either to press, delay or concede the space away from the goal to the first attacker. Depending on your location on the pitch you can concede space towards the touchline. According to Pep Guardiola, FC Bayern’s Head Coach, “The touchline is the best defender in the world.” The player must not over-commit when pressing the first attacker because it may lead to a goal scoring opportunity or an overloading situation (more attackers vs. defenders). To delay the first attacker try to maintain an arms length distance away from them. For pacy attackers back off a little bit more than arms length or they will knock the ball to space and blow past you.
Support
In order to keep possession, the first attacker needs passing options if he cannot penetrate the defence. Guardiola also said “If you want to help your teammates, don’t move towards them, move away from them, so you can open up a passing line, open up the game, give more space to the player with the ball. So moving away from them is a good thing if you do it right.” The more options you provide for your teammate the more chances you will have in keeping possession. Players supporting the first attacker are known as the “second attacker” or “second attackers.” Ideally, second attackers should always be looking and moving to the largest space where a clear passing lane exists. Sometimes this identified space is in between a couple of opponents. This is sometimes termed as “playing between the lines” or working the “channels.”
Barcelona’s legend Xavi is the perfect role model to observe how to provide support for your teammates. In a interview with The Guardian’s Sid Lowe , Xavi explained the process behind mastering this skill: “Think quickly, look for spaces. That’s what I do: look for spaces. All day. I’m always looking. All day, all day. Here? No. There? No. People who haven’t played don’t always realise how hard that is. Space, space, space. It’s like being on the PlayStation.”
Barcelona players supporting Xavi (first attacker). Barcelona vs. Manchester United in the 2010/2011 Champions League Final.
Depth
One of the main objectives of a “second defender” or “second defenders” is to take away the first attacker’s passing lanes. This is done by trying to get tight on the second attackers or blocking the path between the first attacker and the second attacker. The latter involves a lot shoulder checking. By getting tight on a second attacker the defender makes it difficult for them to make a turn once they receive the ball from the first attacker (only if the second attacker has their back to goal). Being a second defender also involves being ready to take the loose ball as the first attacker tries to get past the first defender.
Manchester United players supporting Park Ji-sung (first defender).
When the first defender commits but does not win the ball, then the closest second defender should quickly move into space and becomes the new first defender. The previous first defender should now drop back as quickly as possible and become a seconder defender.
Second Defender becoming a First Defender
Manchester United’s holding midfielder Michael Carrick is an excellent second defender. Carrick’s critics focus on why he does not make Roy Keane/Bryan Robson type of tackles when plays in front of his back four as reason why he is not a great holding midfielder. I completely disagree with this notion because another great second defender Xabi Alonso once described tackling as not a really quality or skill but “more something you are forced to resort to when you don’t have the ball.” In a interview with FourFourTwo Performance, Carrick discusses the principles of how he defends: “Shut off the angles. If you press the player on the ball you’re creating space in behind you and they can pass into that space. Force the opposition to play the ball where you want. Do this by stepping off the player you’re marking and drawing them into a pass, then trying to intercept it. If their biggest threat is out on one wing, focus on defending that area, pushing them to the other side. If they have someone playing off the front, like Messi, cut the space through the middle by bringing your wide men in, forcing them out wide.” In another interview with FourFourTwo, Carrick adds “A lot people are screaming at you press the ball, press the ball specially the fans because they want you to be serious and defend, which is fair enough but it is not the right thing to do.”
Here is a clip of Gary Neville illustrating what Carrick does off the ball:
Width
Legendary Dutch coach and player Johan Cruyff once remarked “If you have the ball you must make the field as big as possible, and if you don’t have the ball you must make it as small as possible.” The objective of making the field as big as possible is to stretch your opponent’s defence to free up the space in front of goal. The opponents can be stretched laterally(horizontally) by having players in wide areas or making runs into wide areas. Players away from the ball in areas outside the opposition’s first or second defender’s field of vision are called “third attackers”, while that area of the pitch is known as the “blindside” or “weakside.” Passing the ball to a third attacker in the weakside is called “switching the play.” In a Four Four Two Magazine Interview, Former West Ham Academy Director Tony Carr explains the objective of switching the play “You want to try and catch the opposition off guard by dragging them over to one side of the pitch, where we can quickly change the play to the other side of the pitch to exploit the space…It needs to be done quickly, it needs to be done sharply. Once we’ve got the ball into that wide position, we’re asking the wide player to cross the ball as early as possible for the two strikers waiting in the middle.”
Below is a famous example of how using the width of the field can catch the opposition off guard. Pele’s pass to Carlos Alberto secured Brazil a comfortable 4-1 win in the 1970 World Cup Final against Italy.
Compactness
Being compact means decreasing playing space in the most vulnerable areas to scoring opportunities by grouping players between the goal and the ball. This also means giving up space in less dangerous parts of the field. Once the ball is lost to the opposition, players should quickly drop back towards their goal and be “goalside” with the ball. In the example below, Ryan Giggs needs to be goalside of Andrés Iniesta because Messi can execute a lob pass to the dangerous space marked as red or Messi could pass to Xavi who has clear passing lane to that space.
All the Manchester United Players are correctly positioned expect for Ryan Giggs.
The most vulnerable area in the field is the space in front of goal. Other dangerous parts of the field are referenced by the position of the ball. Therefore, the space a player should be covering, changes dynamically as the ball moves. In an interview with Elite Soccer Magazine, Real Sociedad’s coach David Moyes describes practical ways to help players apply this concept. For example, one drill requires the length of the field to be divided into six narrow segments of 12 meters each. The defending players should always try to occupy the nearest zones to ball. Based on the diagram below, the yellow team always gives up the space least dangerous to them using the ball as a reference. If the blue team had some width in the zones the yellow team is not occupying then they can have the option of switching the play. If the blue team decides to switch the play, the yellow team can counter by quickly shifting to zones as the ball travels to the weakside of the field.
Players shifting based on the position of the ball
Blue attacking on the left side of the field (a)
Blue attacking through the middle of the field (b)
Blue attacking from the right side of the field (c)
Mobility
A very compact defence can comfortably combat against a very static group of attackers since the defenders can easily adjust themselves in a way where they can see both the attacker and the ball. Therefore, attackers should make runs into different areas to drag defenders out of their position or distract them from their duties for a split second. However, making runs should be intelligent and purposeful. Former Manchester United Manager Sir Alex Ferguson once remarked: “When forwards attack from wide to inside, they are far more dangerous. It’s funny when I see centre-forwards starting off in the middle against their markers and then going away from goal. Strikers going inside are far more dangerous… Trying to escape and create space by drifting from the centre to wide positions…actually makes them less dangerous.”
While talking about how the Barcelona Youth Academy La Masia trains its youth players, Pep Guardiola said “We teach our players how they can run less.” Tony Carr feels the same way “Players must know when to run and where to run. Running just for the sake of running and flying about all over the pitch is a trait of poor players who let their heart rule their heads. Running must be intelligent.” Finally, current Manchester United Manager Louis van Gaal discusses the matter “Running is for animals. You need a brain and a ball for football.”
When an attacker makes a run a defender has to decide whether to track them or continue to cover their zone or their original assigned player. If the defender chooses to follow, he leaves some spaces that can be exploited by other attackers. Prime example of this is the following goal for Bayern Munich against Arsenal in the 2013/2014 Champions League. Claudio Pizarro drags Per Mertesacker to create space for Thomas Muller to exploit. Barca Sanga realizes what has happened and tries to cover that space but he is too late.
Balance
If the objective of mobility is to drag defenders out of position to create space to exploit then the principle of balance is to counter that. It is the “third defender” who gives balance to the team and not the first defender or the second defender. Players covering the weakside of the field or third attackers are called third defenders. Third defenders should not track attackers who are going away from their goal or to an area that is already covered by another defender. A defending team is considered to have “good balance” if they apply pressure on the ball and they can naturally cover dangerous areas if the ball is switched.
Improvisation/Creativity
This principle encourages players to use their individual skills to create space or shooting opportunities for themselves or their teammates. Individual skills such as dribbling, fakes, turns, back-heel passing is used to beat the first defender and/or second defenders. This principle works well against an opposition that is very compact and has good depth and balance. Messi’s goal against Atletico Bilbao in the 2015 Copa Del Rey final is one of my favourite examples of utilizing individual skill to create a brilliant goal:
Patience/Discipline
If a team is observing all the first 4 defending principles then it should not practice reckless and impatient defending. First defenders should not make poorly timed tackles or attempts to go for the ball. Second defenders should not try to leave large amounts of space to intercept passes between a first and second attacker. If an attempt to retrieve the ball fails, then most likely a team has broken one of the defending principles. Defending teams should look for visual cues on when to press or try to intercept the ball and not base their decisions on instinct or emotions. Below are some examples of precise indicators to look for before attempting to retrieve the ball:
If an opponent controls the ball badly
If the ball bounces off the ground
If a opponent has their back to goal or they do not have an overview of the pitch
If an opponent is looking around for their teammate
