How much is this a function of Ferguson or of Manchester United? In order to truly examine this we decided to see if there was a link between which teams were playing and the amount of added time. The problem is that a certain amount of added time is justified due to time wasted during the match due to goals or substitutions etc. We looked at added time from the 2009-2010 season up to and including this season. Built a linear model with different factors for a match that could lead to longer or shorter extra time, then applied stepwise selection to pick out the best model.

Our main question was answered in the stepwise selection of significant variables – individual teams were not found to be particularly favoured, however the strength of a team was found to make a difference. So it’s not that Ferguson is the manager, or that it’s Manchester United, but rather that Manchester United are good. What this means practically for next season is that as long as Manchester United remain a strong team we should continue to see this effect.

The table below shows the effect of different events on added time and the strength of the home and the away team.

Coefficients of the optimised linear model

For example it appears that referees are more aware of events which take place in added time than normal time and add more time for that, like card, goals or substitutions in extra time. A strong team that is losing gets more time added both at home and away.

There is one additional point to mention in reference to Fergie time – although the added time for stronger teams seems to be a function of all teams – what is crucial is what they do with it. As we have previously shown in the Fink Tank (£), Man United out perform at the end of the game. So Moyes may continue to get the extra time, but whether or not Manchester United will use it to score late goals remains to be seen.

Likelihood of First Leg Result

The first question relates to the unlikeliness of the result. Before the match was played the probability of Bayern Munich having a goal difference from the first leg greater than or equal to +3 was 8.9%. When we look at the probability of a +4 goal difference the probability is reduced to 2.7% but this is partly due to the generally low scoring nature of football. The chances of Dortmund finishing the first leg with a +3 goal difference was 8.3%. These results were not quite so unlikely as commentators have made out although the most likely result for both semi-finals would have been a 1-1 draw.

Team Strengths

The truly interesting question is whether there has been a sea change in power in European football.

Team Strengths

The Spanish domination of Europe has been on the slide all season with Real Madrid and Barcelona both weaker than they were in the 2011-2012 season. In addition Bayern Munich and Dortmund have become stronger as the season has continued. Dortmund is still some way behind rivalling the top three though. Perhaps a clearer analysis of the trends would be that the gap at the top between Barcelona and the rest has disappeared.

Predictions

Progression probabilities, before and after the first leg

The Spanish teams both seemed more likely to progress to the finals than their German opponents but since the first leg this has been entirely reversed. Real Madrid has a 14% chance of being able to turn things around, Barcelona a 2% chance.

When the draw was made, there was a lot of discussion about the possibility of an all German or all Spanish final. What do the odds look like now?

Champions League Final

There’s now a 0.3% chance of an all Spanish final, but an 85% chance of an all German final. Even though there may be an all German final this year, the real story of the 2012-2013 season is about Bayern Munich once again joining the elite in European football.

Below is a bar graph showing European teams chances’ of automatic progression (coming top in their group). Teams that have a chance of less than 5% have not been included.

Automatic Qualification for Brazil 2014

Observers won’t be surprised that Germany, Russia, the Netherlands and Spain are all easily narrowing in on another world cup, but Bosnia’s strong showing against an admittedly weak group means that they could take part in their first international competition. Group A continues to be the most interesting group with points currently even between Croatia and Belgium, although we give Croatia the edge. England have a 66% chance of progression even though they trail Montenegro by 2 points.

There are four remaining places up for grabs from the eight best second placed teams. We can use our simulations of the teams positions within their groups to estimate their chance of being in the play-offs and winning their play-off match.

Play offs for Brazil 2014

France has the highest probability of progressing through the play-offs because they are a strong team that is very unlikely to qualify automatically through their group (Spain currently tops it).

We estimate that there are currently 5 serious contenders for the top four positions: Man Utd, Man City, Chelsea, Arsenal and Spurs. Everton and Liverpool remain outsiders for 4th place in the league. Their current respective chances of making the top 4 are displayed below.

Champions League Place Probability

From the graph it is clear that Man Utd and Man City have qualification to the Champions league almost guaranteed at this stage in the season. Chelsea may have slipped to fourth place but given their team strength we still think they have a strong chance of making Champions league football. Whether or not that will help Rafa keep his job seems more difficult to predict.

Team Strengths

Below is a graph displaying how the Champions league contenders team strengths have developed over the season.

Team Strengths

The graph shows how Spurs has cracked the top four over the season, a combination of their improvement and Arsenal’s decline. Manchester United has slowly declined over the season, this is mainly due to our low ranking of their defence.

The Title Decider

The Manchester derby in April was meant to be the title decider, but with City currently 12 points adrift, what effect will it have on the title race even if they are the better team on the day? In order to estimate the answer to this problem we simulated the outcomes of the remaining matches while fixing the result for the derby to be either a draw or a win for either side with a plus one goal difference.

Manchester City's title chances dependent on the Manchester Derby

The answer looks less than encouraging for Manchester City, provided Manchester United don’t have any major slip ups any time between now and April, winning the Derby won’t swing things Manchester City’s way in the race for the title. It might save Mancini’s job though.

3rd and 4th Place

The crucial match in the fixture list would appear to be the Spurs Arsenal match this Sunday as it’s one of the few remaining fixtures in which two of Arsenal, Spurs or Chelsea will play each other. A true “six-pointer”.

Probability of a Champions league place dependent on the outcome of the Spurs Arsenal match

Should Spurs win this weekend their chances of a Champions league place are almost guaranteed (85%). This is also a must win match for Arsenal as it would dramatically boost their chances from 51% to 72%. Let’s hope Sunday’s game is as interesting to watch as it is crucial for Champions League qualification!

Champions League

The most meaningful way to look at how things have been changed by the first leg is to look at the relative percentage change in probability of qualifying for the next round.

Relative change in probability of reaching quarter-finals

Celtic originally had a 24% chance of progression but after a 3-0 dubbing by Juventus their probability has gone down to 0.4%. Manchester United’s away goal really does appear to have helped their chances, increasing  their relative chance of progression by almost 50%. But as their original progression chance was 27% and their new chance 40%, everything seems still to play for in the second leg. PSG’s win at Valencia has also increased their relative chance of progression just under 50%, but they previously had a 60% chance of progression and now have a 89% chance.

For all the excitement promised by the Champions league only the Man United/Real Madrid fixture looks genuinely up for grabs at the moment.

Europa League

But what about the Champions league little brother? The picture is more mixed for English teams in the Europa League. Chelsea’s 1-0 win at Spata Praha has them almost guaranteed to make it through to the quarter-finals, with a 9% chance of an upset. This is partly because we originally thought they had an 82% chance of qualification and the lead and home advantage should be able to help them secure a quarter-final against either Ajax or Steau Bucharest. Chelsea are very much the team to beat with a 24% chance of winning the Europa league at the moment.

For all Brendan Rodger’s claims to the contrary, Liverpool are on the verge of being dumped out of the Europa league. Before the first leg they had a 56% chance of progression, now they have a 14% chance. Newcastle may have felt hard done by in the 0-0 draw against Metalist Kharkiv but their progression chances have slightly improved from 31% to 38%.

The best improvement on our predictions among the Premier league clubs was from Spurs. As we discussed in a previous blog, Spurs was given one of the more challenging draws as Lyon is of almost equal strength. The 2-1 win at White Hart lane has boosted their progression chances from 53% to 65%, but this tie remains difficult to predict.

The overall picture for the competition has a distinctly Eastern-European flavour as shown on the graph below.

Europa Progression Chances

Dependent on how seriously Chelsea takes the Europa league this could be a surprising year.

We have to look further down the groups to discover our tournament surprises. Zambia, the cup-holders, are out, but this year’s surprise quarter-finalists are Burkina Faso and Togo. We can see this more clearly when we look at their probabilities of progressing in the competition before and after the group round.

Difference in Progression probabilites from before the group stage and after it

The biggest losers are Nigeria, who face a tough draw with Ivory Coast in the Quarter-Finals and either South Africa or Mali in the Semi-Finals. Ghana is sitting in the other half of the draw with Cape Verde in the Quarter-Finals and either Togo or Burkina Faso in the semi-finals. Togo and Burkina Faso have benefited from the easier draw but the large difference in progression probabilities is partly due to the low probabilities predicted for these teams before with Togo having only a 10% chance of progression from the group stages and Burkina Faso a 44% chance.

New Progression Chances

Ivory Coast are still the cup favourites, but this is still very much an open field.

Group A

The hosts, South Africa, should have a relatively straight forward group and are the team most likely to top it. They have a 22% chance of being knocked out at this early stage. The second team to qualify from Group A is slightly more up for grabs with Morocco on a 56% chance, ACN debutantes Cape Verde on 37% and Angola on 29%.

Group B

Ghana should qualify with ease from this group with an 83% chance of progression. Mali is likely to finish second with a 71% chance of progress. DR Congo and Niger are the outside contenders for the competition with only a 30% and a 17% chance respectively of making it out of the group.

Group C

Nigeria should qualify with ease with an 88% chance of progression to the next round. The cup -holders, Zambia, may find it more difficult to progress with a 56% chance. Their main rivals in the group are Burkina Faso, who have a 44% chance of progression. Ethiopia haven’t competed in the ACN in 31 years and it seems unlikely that they will do very well with only a 14% chance of progression.

Group D

Ivory Coast face something of a walkover with an 87% chance of progression. The interesting thing to watch out for in this group will be the race for second place between Tunisia and Algeria. Tunisia are slightly ahead with a 54% chance of progression to Algeria’s 50%.

Progression Chances

Champions

Ivory Coast are yet again the favourites with a 28% chance of winning. Nigeria has a 16% chance and South Africa and Ghana both have a 15% chance. Alternatively, there is a 27% chance of the winner not being one of the big 4. Expect surprises!

 Graphic View

The graph below shows the Dectech team strengths for Africa. Darker shading indicates a stronger team. The ACN teams are labelled (except for Cape Verde as it doesn’t show up on a map of this scale).

Team Strengths

The gap between Ivory Coast and every other team is clearly shown in the graphic. Only South Africa looks likely to beat the West African domination of African football.

There are four English teams in the Europa league, Premier League position in brackets: Chelsea (4), Liverpool (8), Newcastle(15) and Tottenham (3).  This is double the amount that have made it to this stage in the previous two years. But how much further can they go?

Team Strengths

The first step in looking at this problem is to see how the English teams match up to the rest of the Europa league. The graph below shows the team strengths of the 32 teams in the Europa League.

Europa League Team Strengths

Athletic Madrid and Chelsea are clearly in another league when compared to Genk and Steaua Bucharest. The imbalance in team strengths has lead to some one-sided ties, like Chelsea v Sparta Prague. Probably the greatest surprise for Premier league fans is how much stronger the Ukrainian team Metalist Kharkiv is than Newcastle as it’s the 10th best team remaining in the competition and Newcastle the 28th.

The Premier league team strengths and that of their opponents in the next round is summarised below.

Round of 32 English matches

Progression

We then simulated 100,000 times the likely progression of the competition. The four teams with the highest chance of winning the Europa league and the remaining English teams progression chances are displayed on the graph below.

Europa League Progression

Chelsea are the team most likely to win the Europa league with a 20% chance of raising the trophy. Whether or not that can get Rafa a permanent position at Chelsea is more difficult to predict. The high probability is partly due to their easy draw, facing Sparta Prague with an 82% chance of winning.  They could then have a  77% chance of facing Ajax or a 23% chance of Steaua Bucharest. Athletic Madrid, their closest rivals, only have a 66% chance of beating Rubin Kazan. They would then have to face either Levante (40%) or Olympiakos (60%).

The Europa league seems unlikely to be bringing good news to Tyneside, with our model predicting Newcastle only have a 30% chance of making it through to the next round and an 11% chance of getting through to the quarter-finals.

Liverpool have benefited from a kinder draw than Tottenham, with a 57% chance of beating Zenit St Petersburg. They then either play Basle (43%) or Dnipro (57%). All the teams that Liverpool is scheduled to play against are weaker than Liverpool, but are not considerably weaker, leaving room to stumble.

Tottenham have a 49% chance of beating Lyon. The opponents in the next round are no easier with a 63% chance of facing Cluj. The Lyon/Tottenham draw is the match to watch in the round of 32 with the teams evenly matched and both likely title contenders, the Real Madrid/Manchester United fixture of the Champions league.

There is good news for a disinterested English supporter, there is a 51% chance of an English team in the final and a 29% chance of an English team raising the trophy. Given the chance of an English team getting to the final of the Champions league is 11% and winning it is 4% this may be the year to start paying more attention to the Europa league.

Causes

The first step in approaching the problem is to understand that there are underlying reasons why host nations (generally) do better when hosting. Firstly after the announcement of the host city the host nation will start to put more funding into Olympic sports. Secondly there is a home advantage for the home athletes. This is particularly pronounced for various disciplines where the marking is more subjective like boxing, gymnastics and diving. We would expect to see some legacy of the funding at subsequent Olympics, but obviously the home advantage would no longer exist. The question then becomes what was the rate of medal decay after hosting and which countries managed to keep the glow that bit longer or found it faded too fast.

Medal Decay Rate

We only considered modern Olympics (London 1948 onwards) when calculating medal decay rates. There are however a number of difficulties with the data due to countries merging, splitting and boycotting each others’ Olympics.  In order to be able to compare different host nations’s Olympic decay rates we need to come up with a similar point of reference. We therefore numbered Olympics relative to hosting, e.g for GB London 2012 = 0, Beijing 2008 = -1, Rio 2016= 1 etc. The decay rates are calculated by looking at the exponential decay rate from the games which they hosted and the next three games (if available). As most medal tables are ordered by the number of gold medals, we’ve included a gold medals decay rate and a total medals decay rate. The decay rate could not be measured for some countries gold medal total because in subsequent games they won 0 medals.

Medal Decay Rate

Some of these results can be explained. Canada in Montreal 1976 managed to have the worst ever performance by a host nation, winning no gold medals. GB’s performance in London 1948 is somewhat unusual as no games had been played since 1936. The stand out failures when considered this way is Greece since Athens 2004, with a total medal decay rate five times the average decay rate. Spain since Barcelona 1992 has had the most dramatic gold medal decay rate, although we can’t compare this to Athens due to the Greek team winning no gold medals at London 2012. Australia’s gold medal decay rate is slightly above average.

Legacy

London 2012 was a huge success for team GB, but as the BOA looks forward the question remains of whether or not there will be a legacy. How one can measure as vague a term as legacy is difficult but it’s simple to see how host nations perform in Olympics after they hosted.

The question of legacy can be phrased as this: “Had a nation not hosted the Olympics, would you be able to tell the difference in terms of medals x number of years down the line?” In order to answer this question, one must consider a country’s normal medal total before they are awarded host nation status. This means that the Olympics before they host the games is not a good benchmark for that nations performance, because in general the Olympics are awarded 7 years before they are hosted so 4 years before hosting funding should already be improving performance. If we compare the medal total two Olympic games before a nation hosts and x years after the nation hosts, we can perform a t-test to determine how much of an impact the Olympics has had on the host nation. The p-value stated below is the probability of something as extreme occuring as getting the number of total medals x years after hosting. A p-value of less than 5% means that it is very unlikely and therefore statistically significant

P-values from T test

12 years after hosting we can still see the Olympic glow when we compare the number of medals in total. But after that it is as though the country didn’t host the Olympics.

It seems unlikely that the British will have to get used to seeing GB third in the medal table every games. An alternative approach is to enjoy the Olympic glow while it lasts, because it won’t be forever!

The first step was to define selfish behaviour. We came up with a ball hogging statistic for each player which refers to the number of passes the player attempted to pass to their own team over the total number of times during the match that they were in possession of the ball. So 0% indicates no ball-hogging whereas 100% would refer to  only ball-hogging. It should be noted that the ball hogging is based purely on attempted passes and ignores whether the ball is being passed up or down the pitch and whether or not the pass is successful. Below is a list showing the worst ball-hogging forwards.

Top ten ball- hogging forwards

The problem with purely looking at ball-hogging numbers and identifying these players as selfish is that we know that we would want a certain amount of selfishness from a forward, as making shots is categorised as a ball-hogging action in our previous definition. Additionally we have to ask if ball-hogging relate to player ability, and if so, how? To measure player quality we used Castrol Rankings as a performance statistic. This ranking system assesses whether or not players actions have a positive or negative impact on their team’s ability to score or concede.  We standardised ball hogging to create a selfishness index and standardised performance statistics. A negative selfishness index score for a player in a match indicates that in that match the player was less selfish than an average player. A positive selfishness index score for a player in a match indicates that in that match the player was more selfish than an average player. We were then able to fit a model for each outfield position predicting the performance level given the selfishness index.

Relationship between selfishness index and performance level

The graph shows that it is never beneficial for defenders to behave selfishly. For midfielders and forwards this relationship is more complicated. The peaks of both curves are to the left of the y-axis indicating that the optimum level of selfishness is below the average level of selfishness displayed by Premier league footballers. The peak for forwards is much higher than for that of midfielders, indicating that they get a better return on similarly selfish behaviour than midfielders do.

So finally we can return to our ball-hogging forwards and determine if some of them are playing too selfishly or selflessly. This can be found by looking at the residuals from the model for a player, i.e the difference between the level of performance the model predicts based upon their selfishness index and the observed level of performance.

Top ten most selfish players

Although Mario Balotelli is the third worst ball hogging forward, we think his level of selfishness is justified – i.e the return he gets on his ball hogging actions increases his Castrol Rankings such that we don’t view him as one of the top ten most selfish players. The same cannot be said for Jermain Defoe.

Similarly we can find the players that should be hogging the ball that bit more.

Top ten most selfless players

Ball-hogging is not necessarily a sin; it is entirely inadvisable for a defender, but a certain amount of ball-hogging or selfishness in a midfielder or forward is necessary to be a good player.

Maybe instead of shouting “Pass it!”, managers will start to shout “Keep it!” at some of their players.