How many points for CL qualification?

One of the perennial discussions we hear near the end of the Premier League season is “What is the point threshold that guarantees a team is safe from relegation”. Right now, as we already know two of the three teams to compete in the Championship next year (well, ok, Middlesbrough still have a mathematical chance), it is the battle for a CL spot that is way more interesting. Chelsea is assured a top four spot as practically are Spurs (97.5% chance even if they lose all remaining matches), leaving two places for the challengers Liverpool, Man City, Man United, and Arsenal.

Before we go on to answer the question “How many points secure a CL spot”, we need to make clear that, theoretically, the answer is different after every match day is played. In a more balanced season, where teams closer to the top lose often to teams lower, we expect a lower threshold. In a season where five or six teams win more often, the point threshold for CL qualification is expected to be higher. That is, if at the beginning of a season we can make the statement “70 points send you to next season’s CL with 70% probability” it doesn’t mean that the same is true after half of the matches are already played.

First of all we take a look at the number of points of the top four teams since 95/96 (first PL season with 20 participants).

We see that there is an upwards trend in the points of the top four teams over time. This suggests that the gap between stronger and weaker teams is growing. In order to have a more rigorous analysis we should take this trend into account.

Now to the main question: What is the probability of qualifying for the CL for a given amount of points earned?

We will use two different methods to estimate the probabilities in question. The first is based on the final tables of the past 21 PL seasons. We don’t want to go deep into technical details, but just briefly, for a given amount of points X, we look at how often a team with X points made it into the top four. If there is more than one team with X points and not all of those teams either succeeded or failed, we count the season as partially successful (for an X-point team). If there are no teams with X points, we look at where an X-point team would have finished in the final table. Here’s what we get.

So, it looks like, based on the past, with 66 points a team has about 48% chance to qualify for next season’s CL. If we take into account the trend seen in the first plot, we tend to believe that the chances are at most that much. 79 points almost certainly guarantee a CL spot. But even with as little as 61 points there seems to be a realistic chance (17%).

The other method to tackle this, the parametric method, is based on simulating PL seasons using a model which associates different strengths to different teams.  The way to do this is to take the team strengths and, allowing for some fluctuation of them along the season, simulate full PL seasons of matches. Then we can treat the simulated seasons like we treated the past seasons in the previous method and estimate the conditional probabilities in question. This second method has some advantages and some disadvantages: One of the disadvantages is that it is parametric, i.e. it assumes that the PL match results are generated according the underlying model. This is always an assumption in statistics and it can deviate from the truth. A big advantage is that it allows us to simulate only a part of the season, i.e. we can take the PL table as it stands right now and simulate only the remaining matches. Additionally it allows us to avoid the trend problem of the other approach, if the team strength estimates are current.  In the chart below you can see what were the CL qualification chances (given points earned at the end of season) before the season started, and what these chances are now (again, given points earned at the end of the season).

First of all we see that the CL qualification chances at the start of the season (blue line) look a bit different in this plot compared to the previous one. One of the main reasons that drives the differences is that the previous plot is a blend of the sets of team strengths at the start of the previous 20 seasons, whereas the last plot is based solely on the strengths of the 20 teams of the current PL season. Interesting is also the difference between the blue and red lines in the plot above. As the current season is nearly over, there is a much smaller range of final points that can take a team to next season’s CL, compared to the situation at the start of the season.  We also learn that this season the bar is higher than we would have expected.  At the start of the season 70 points would have got you more than a 50% chance of CL qualification.  Now, 70 points only has a 5% chance of being enough.

So, how many points do you need to make it to the CL?  It depends when you ask.  At this moment 73 points gets you a 51% chance, and 76 points a more than 95% chance.

Attendance in the Premier League

Is poor performance by a team punished by low attendance by fans? Attendance figures have just been released by the BBC from the past season, prompting us to look into whether or not football supporters are emotional consumers or rational ones who chose to go to games based upon the quality of football available? At a first glance it would appear to be so with Stoke, Man City and Chelsea all down on the previous season’s average attendance and all three teams having been perceived to have had weak seasons.

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Is Fergie time over for United?

As we wave goodbye to one of the most successful managers in British football it’s also a time to focus on the ways that he has changed the football lexicon, whether it be through terms he coined himself (squeaky bum time) or phrases that were used about him (the hairdryer treatment). Probably the most statistically interesting is “Fergie time” the idea that Alex Ferguson through sheer force of personality gets more added time than other managers would when Man United are down.

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A new German dawn for European Football?

After the thrashing of Barcelona and Real Madrid there’s been a lot of discussion about the ascendancy of German football and the decline of Spanish football. But how surprising were these results and is there any chance the Spanish teams will be able to strike back?

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.

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A match of two legs?

It feels like it’s been a long two months without European football. With the Spanish, English and German title competitions looking pretty much wrapped up at the moment and a disappointing Africa Cup of Nations, it’s exciting to welcome back the Champions league and Europa league.  So after the first round of of first legs for the Champions league and the first legs of the Europa league we wanted to see how things stood.

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Africa Cup of Nations: Update

We’re now half way through the Africa Cup of Nations and it has gone relatively to plan so far. The big 4, Ivory Coast, Nigeria, Ghana and South Africa are all through to the quarter -finals with only Nigeria unable to top their group. The North African teams have been something of a disappointment with Morocco, Tunisia and Algeria all knocked out.

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Preview: Africa Cup of Nations 2013

It may feel like the Africa Cup of Nations has just finished but due to the rescheduling of the tournament it is yet again that time of year. Below is a brief preview of what’s to come.

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%.

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Europa: The other competition

The Champions League knockout stage might have the glamour of Manchester United v Real Madrid, but what of its little brother (whatever AVB might say), the Europa League? We decided to look at our predictions for the Europa League knockout draw.

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?

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