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The mathematics of football
Location of goals scored in Premier League 2011-12 Season. Look at
0.094! That means a goalie scored from his own area? Any idea who it
was? We will show you at the end if you don’t!
Break down of Attacking areas in Premier League 2010- 2011. Most Shots are
targeted from 0 degree position. Further breakdown of this data shows that 44% of
shots are outside the area, 49% are inside the 18 yard box and only 7% come from
the six yard box.
What a strike force Liverpool had in season 2013-14. One Slip up Away from the Premier League! Remember
Suarez, Sturrridge and Sterling scoring the goals with Gerrard and Coutinho providing the Ammunition? Look at
the shot breakdown. The data shows how confident they were. These guys were attempting to defy Science!
42 shots from Deep centre! Wow! I wonder how many goals did they Score?
Well they didn’t just try to defy Science. They absolutely did!!! Look at the goals data. 2 goals from what
appears 85 degrees left and look closer again, one goal sored from deep centre!! The Science still stacks up
though, the majority of goals scored from 0 degrees. Liverpool's left side also appeared to out perform the
right side with another goal scored from wide left. How did they not win the league with all these goals? Well
you have to keep out goals as well and that’s why Man City won the league in the end.
Liverpool really channelled goals through 0-65 degrees that season. The data shows
that the team really focussed their tactics around Suarez and Sturridge, with most
goals coming from inside the area.
37% of the 19 goals Arsenal had scored to this point had been low centre indicating that they
are tap ins from about 6 yards. This tells us that the ball arrives at the goal scorer’s feet from
a pull back at the bye line. Keep an eye out for this the next time you watch the Gunners.
The next graphic shows where Arsenal had created chances on the pitch. Over half had come
from the area in front of the 18 yard box but no goals had been scored from this position.
Maybe they needed to buy a new right sided midfielder or striker to convert these chances?
This proved unnecessary as a year later Ozil is now the assist king of the Premier League, Giroud
is scoring too and Arsenal are favourites for the league. How times change!!
Below is Arsenal’s shot accuracy for the early part of the 2014-15 season. Less than half of the
attempts had hit the various targets. So for example high left resulted in only 5% of the shots
aimed at this area, resulting in one goal. Time for a new striker Mr Wenger? According to the
data he needed one at this point, however he stuck to his guns and kept faith with the players he
had resulting in Arsenal being top of the league a year later. A perfect example of practice
makes perfect.
When Mr Maloney was in 5th and 6th class, Nottingham Forest were brilliant! They won two
European cups and umpteen other trophies but unfortunately they’ve hit on hard times. Here's
another breakdown of their goals scored in the Championship last season. Only 2 goals scored
from 0 degrees inside the 18 yard box! The data shows that the midfielders need to contribute
more as most of their goals are coming from their centre forwards. 41 goals in 42 games isn’t
going to get promotion. The data tells us they need more goals from midfield.
Nottingham Forest’s Assist areas. We call setting up a goal an assist The crossing looks very
poor from the data. Only 7 assists from 0 to 65 degrees left and right. No assist from corners
on the right side from 90 degrees. Not good enough!!!Break down where and how Premier League goals are scored over the course of Season 2014-15
in Premier League. Interesting to note first time strikes from centre of goal from 0 degrees to
65 account for most goals. Most headers are also scored inside the penalty area from angle 0-65
degrees.Ruud Van Nistelrooy scored 150 goals for Manchester United. Only one of those goals was
scored from outside the box. Arguments were made by some fans saying that Henry was better
in terms of all round game and could do more in midfield areas of the pitch. (Mr Maloney was in
the Henry camp). Other fans claimed that the mark of a striker was the ability to get in free
positions at close range and hit the target. We will leave that debate for another time, but one
guy who scored a 150 goals and more was actually a midfielder! His name was Frank Lampard!
Here's a break down of the 150 goals he netted.
About 78% of his 150 goals were scored from inside the box and 9% from inside the 6-yard
box. The majority of his goals, 53 percent, were scored from around the penalty spot -- mainly
because some of them were, well, penalty goals. From the data this guy really understood the
concept of angles and distance!!! Pity he’s not here today to explain it to us.
WELL, THAT'S ENOUGH statistics on the 150 Premier League goals by Frank Lampard -- a
striker trapped inside a midfielder's body. I'm sure this goal record will stand the test of time
for many years to come.Barcelona have revolutionised the game of football in the last decade.
Football statistics, analysis and studies proved that the zone 14, the area immediately outside
the penalty box, is vital to use in order to score goals from assists begun from that area. By
effective use of that area more goals can be produced from open play. Barcelona looked to
dominate that area by placing more players in this area with great technical skills. While other
teams in the past (France 1998 / 2002 – Zinedine Zidane) used one player in that area Barcelona
set up their team with no less than three skillful players in this zone with Xavi, Andres Iniesta
and Lionel Messi. These players are all able to make those final passes which unlock defences,
either with excellent vision, sublime technique or a lethal mix of balance, low centre of gravity,
acceleration and dribbling!!! While these players looked to dominate that area, the two inside
forwards (Suarez, Neymar, Henry, Eto or Messi himself would stay right outside zone 14 looking
to run into the penalty box penetrating the defensive line. While these players focused on
creating goal scoring opportunities, the holding midfielder in Busquets would give cover forming a
solid diamond or a rhombus. Who knew shapes could be so interesting.Here’s more on Zone 14. The first example of a team using this zone is the France national team from 1998-
2000. In July 2000, France became the first nation to win the European Championship (2000) as World
Champions (1998). (In Mr Maloney’s opinion they were better than Barca or Spain.)
It was found that 81.3% of their assists in the two competitions came from this central area. In other words,
France’s attacking play was narrow. Another finding showed that the majority of France’s attempts at goal came
from the central attacking area just outside the penalty area (The second example is Manchester United FC
(1998-99), which was the first English side to win Premiership, F.A. Cup and European Champions League in the
same season.More Maths Facts
How to win at penalties using
The perfect football statistics
• A lot of research has been done into • Football statistics appear
what makes the perfect football. everywhere, but could you actually
Applied mathematics research has
shown that the smoothness of a win at penalties using statistics?
football affects the spin and speed Researchers from the University of
of its flight. In 2006 the traditional Amsterdam have studied World Cup
32 panel football was radically Penalty shoot outs and found that
modified to have fewer panels which
caused the ball to have less spin and statistically goalkeepers are twice
to move much faster. To overcome as likely to dive to the right when
this, researchers added pimples onto their team is behind. (Psychologically
the ball to create less drag. The there seems to be some reason that
design of the football continues to
evolve based on mathematics and people have a bias to the right when
physics research and now has even under pressure.) Penalty takers on
fewer panels than in 2006 the other hand were shown to shoot
to the left or right in equal measure.
If you were England manager then
this kind of statistic might just help
you!Optimal Angle for a Throw In
• Researchers at Brunel
University have shown that the
angle which will maximise the
distance of a throw in is around
30 degrees. Anyone learning
mechanics will know that 45
degrees is the usual angle which
will maximise the distance that a
projectile travels when launched
at a certain speed. The
researchers have however shown
that footballers can usually
throw at higher speeds from
lower angles meaning that the
best angle is around 30 degrees,
not 45 degrees as you might
have thought.Referees and Maths
• In professional football
referees use what is called the
diagonal system of control
(DSC). This is where two
assistant referees move up and
down diagonally opposite
touchlines and the referee
moves in a diagonal movement
Southeast to Northwest. This
formation has been chosen to
maximise the amount of the
pitch which is in the sight of the
referees. If the referee just
ran up and down the centre of
the pitch then there would be
parts of the pitch which weren’t
covered as well, whereas
geometrically this formation
covers the pitch much more
efficiently.Football managers need maths
• There is no doubt that a successful football
manager needs mathematics in order to do well.
Football is big business and managers can only
pick their dream team by carefully balancing a
multi-million pound budget; deciding whether to
pick a few expensive players or build a better-
rounded team.
• Managers not only need to have a sound financial
head on them, they also need to pay attention to
the finer mathematical detail as Manchester
City’s Manuel Pellegrini found out in 2013 when
he incorrectly calculated goal difference in a
Champions League match against Bayern Munich.
• Manchester City had previously lost at home 1-3
and Pellegrini then told his team that they
needed a 5-2 away win. When the score was 3-2,
Manchester City then incorrectly believed they
needed to score an extra two goals to win, when
in fact they only needed one more goal to win 4-
2.
• Pellegrini had forgotten to calculate using the
away goals rule where away goals count double if
there is a draw on aggregate goals. If Pellegrini
had done his maths right then maybe
Manchester City would have pushed that bit
harder to get one more goal and win.9 ideas for maths jobs in football.
If you are good at maths and also love football then maybe you could choose a
career combining your two passions
• 1. Accountant - helping your
favourite club to succeed financially. • 6. Statistician - football is now full
of statistics and you could be needed
• 2. Web developer - every club needs by a broadcaster or the club itself
an excellent website. to help fans understand as much as
• 3. Engineer or architect - designing they can about the game.
or checking the safety of a stadium. • 7. Bookmaker - statisticians
• 4. Computer games designer - using determine football odds so that
maths and physics to develop the overall the bookmaker will win and
latest football game. the gamblers will lose money in the
• 5. Biomechanics researcher - looking long run.
at the science of football and how • 8. Financial adviser - footballers are
players can play at their best. now some of the best paid people in
the country and will need
professionals to help them manage
their money.
• 9. Broadcast expert - there are lots
of technical roles which ensure your
favourite match is broadcast
correctly each week.• Famous mathematician and Arsenal fan Professor Marcus Du Sautoy said in a fantastic interview recently "Those players who intuitively have a good sense of geometry and calculus, they're the ones who will have the edge... My mathematics is so subconscious that I do it without thinking, and in a sense the footballers are doing that as well
What are Expected Goals?
• This is another example of how Maths
Data has taken the Premier League by
Storm. Managers and coaches can now
work out how statistically likely they
are to win soccer matches. So what is
it called I hear you say? Its called the
Expected Goals Model. Expected Goals
or (ExpG for Short), is just that; it's
a measure of how many goals a team
should have scored based on where a
shot was taken and (sometimes) a few
other factors: if it came from a
corner, if it was headed, or if it was
taken against an opponent reduced to
10 men, etc. Coaches then look at the
differences between shots conceded
and shots taken, the bigger the number
between both means your team has a
higher chance of winning. So for
example Man City and Arsenal have the
highest shots taken and fewest shots
conceded in the Premier League giving
each an ExpG of 1.65 and 1.72 which
is higher than a Sunderland that have a
ExpG of 0.9. So again if you know your
Maths you can win the Premier League!!!• Above is a picture of Billy Beane. Billy is the General Manager of the Oakland A’s Baseball
Team. This means he is responsible for purchasing and selling players for his Baseball team.
Sounds boring but Billy made it very interesting!!! This guy has become the king of
Mathematical data usage in Sport. In 2002 Billy was becoming really frustrated and angry
in his job. He had a budget of $40 dollars to spend on players but some of his rivals like
the New York Yankees had budgets of up to $200 which was 5 times more than Billy’s. His
team was always reaching the playoff, which is like getting to an All-Ireland Quarter Final
but they were being beaten by other teams who could afford to buy the best players.
• But did Billy give up? Absolutely Not! With the help of a friend called Paul DePodesta they
turned to Science and Maths to get more competitive. So by using Mathematical Data and
Statistics they were able to identify better players to buy for a cheaper price. Other
teams were using data but not at the same level as Billy. The result was that Billy’s teams
consistently outperform teams who have more money to spend.
• Soccer became interested and Billy now works closely with teams like Arsenal, AZ Alkmar in
Holland and Liverpool using statistical data to buy players at a good price who can be sold
on at a profit!! Sir Alex Ferguson wanted to meet him so much that he drove from
Manchester to London!! That’s a four and a half hour drive!! Billy states that “We think
we’ve got some tools that will make us evaluate teams and players much more accurately.
With data it’s easier to evaluate players instead of relying on the human eye.” Many other
clubs are taking on the Billy Beane approach and trying to use a more scientific way of
picking players instead of relying solely on the human eye. It’s basically a way of minimising
the risk of losing lots of millions of euro on buying the wrong players. It will be interesting
to see if other clubs start using the approach in the future but Billy and his Maths have
got people talking!!!!Below are two tables. The Table on the right shows the final league table of 2012-2013. The table on the left
shows how much money was taken in by Premier League teams that season. Notice anything? The most money a
team makes is a good way of estimating where a team will finish in the table at the end of the season. Can you
spot the teams that under performed and over performed. For example look at Everton in both tables. How did
they do?Link between wage bill and League Standing
• Good wage bill data exists for the Premier
League from 2000-01 up to last year.
This is how much money teams pay their
players every year. There have been 56
top-four places available over that time,
and 47 of those (over 80 percent) have
been won by the teams with the top four
wage bills in the league. Only nine times in
14 seasons has a team outside of the top
four in wage bills finished in the top four
places; adding in the current season would
almost certainly make nine in 15. Clubs
without the economic power of the biggest
clubs can win occasionally, but most of
them fall well short year after year.
• The following chart shows the rate at
which clubs with a certain payroll rank
have finished in the top four. The club
with the league's top wage bill has only
twice finished outside the top four over
this span: Manchester United in 2013-14
were the first since Ken Bates' Chelsea in
2000-01. On the other side, no team with
a wage bill in the bottom half of the
league has finished in the top four.Billy Beane Again!! • So has anybody beaten the Maths! Well Step forward Liverpool! Since 2000, they are the only club without a top-four wage bill not only to compete for the title but to finish within 10 points of first place. Liverpool in 2013-14 season are also the only club in the past 15 years with a wage bill outside the top four to achieve more than 75 points. Billy Beane and his Moneyball approach had beaten the money men!!
Great Maths Quotes from Footballers and Mathematicians
• “When I played in Holland, • Gary Lineker the great
I always tried to lob the England Centre Forward and
Match of the Day Presenter
goalkeeper. People used to said “Playing football is
say, ‘Oh, you’re always only more mathematical than it
trying to make a nice goal’. might seem. Knowing which
But I said, ‘listen, if the angle to use to direct the
ball towards the goal and
goalie is a little bit off his judging how far to kick it
line, how much space do you down the side line to
have on his left or right? another player requires
It’s not a lot. And how precise calculations. I now
realise why school teachers
much space do you have have always stressed the
above him? There is more. importance of maths
It’s a question of because even as a
mathematics.” Dennis footballer you can still
apply the techniques.”
Bergkamp Arsenal and
HollandImpossible is Nothing! Even though our Experiment showed us the Science of goal
scoring, sometimes Science can be turned on its head! Enjoy!
• https://www.youtube.com/watch?v=cbGG37SHBOo
• 20 Impossible angle goals in the above link
• https://www.youtube.com/watch?v=gvZViKmh5qY
• 10 goals from the half way line in the above link
• The answer to the question at the start is Tim Howard. He scored for Everton v Bolton in January
2012. Here’s the link below
• https://www.youtube.com/watch?v=JftOZQQ2PCE
• Lastly we learned today that the closest you are to a 90 degree angle the less chance you have of
scoring but click on the link below! It can be done! You can score from 90 degrees! Remember
Impossible is Nothing! Football is the beautiful game because it can turn logic and Science on its
head! It’s what makes football and Sport so compelling.
• Here’s a Message from Caherconlish National School: Science + Sport = AWESOME
• https://www.youtube.com/watch?v=jtHXdcsZ904You can also read
