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 19982000. 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 The perfect football •

A lot of research has been done into what makes the perfect football. Applied mathematics research has shown that the smoothness of a football affects the spin and speed of its flight. In 2006 the traditional 32 panel football was radically modified to have fewer panels which caused the ball to have less spin and to move much faster. To overcome this, researchers added pimples onto the ball to create less drag. The design of the football continues to evolve based on mathematics and physics research and now has even fewer panels than in 2006

How to win at penalties using statistics •

Football statistics appear everywhere, but could you actually win at penalties using statistics? Researchers from the University of Amsterdam have studied World Cup Penalty shoot outs and found that statistically goalkeepers are twice as likely to dive to the right when their team is behind. (Psychologically there seems to be some reason that people have a bias to the right when under pressure.) Penalty takers on 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 •

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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 betterrounded 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 42. 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 •

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1. Accountant - helping your favourite club to succeed financially. 2. Web developer - every club needs an excellent website. 3. Engineer or architect - designing or checking the safety of a stadium. 4. Computer games designer - using maths and physics to develop the latest football game. 5. Biomechanics researcher - looking at the science of football and how players can play at their best.

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6. Statistician - football is now full of statistics and you could be needed by a broadcaster or the club itself to help fans understand as much as they can about the game. 7. Bookmaker - statisticians determine football odds so that overall the bookmaker will win and the gamblers will lose money in the long run. 8. Financial adviser - footballers are 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?

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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!!!

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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.

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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.

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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

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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, I always tried to lob the goalkeeper. People used to say, ‘Oh, you’re always only trying to make a nice goal’. But I said, ‘listen, if the goalie is a little bit off his line, how much space do you have on his left or right? It’s not a lot. And how much space do you have above him? There is more. It’s a question of mathematics.” Dennis Bergkamp Arsenal and Holland

• Gary Lineker the great England Centre Forward and Match of the Day Presenter said “Playing football is more mathematical than it might seem. Knowing which angle to use to direct the ball towards the goal and judging how far to kick it down the side line to another player requires precise calculations. I now realise why school teachers have always stressed the importance of maths because even as a footballer you can still apply the techniques.”

Impossible 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

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https://www.youtube.com/watch?v=gvZViKmh5qY 10 goals from the half way line in the above link

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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

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https://www.youtube.com/watch?v=JftOZQQ2PCE

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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

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https://www.youtube.com/watch?v=jtHXdcsZ904