By Daniel Geey, Haim Levi and Beri Pardo
This blog began after a twitter conversation with Michael Cox better known for his excellent ‘Zonal Marking’ tactics website. The conversation followed on from a guardian quiz and article from Paul Wilson about the Liverpool Everton derby matches which included the following paragraph:
“So keenly anticipated is the Merseyside derby that for the last 10 years, alone in the Premier League, it has been governed by special rules. The first fixture will now always be at Goodison and the second, after Christmas, at Anfield. This prevents supporters having to wait more than a year for what they always used to consider their most important home fixture and avoids the situation that cropped up 50 years ago, whereby Goodison Park did not see a derby game during the whole of 1963.”
The Predictability of the Derby
The reason why this debate is of significance is because for the last eleven years (from 2003-4 onwards), Everton have played the first derby of the season at Goodison and Anfield has hosted the second derby. After chatting with Michael at Zonal Marking my first reaction was to believe that no such agreement could exist. From an ‘integrity of competition perspective’, the fixture list, bar police resourcing issues, should be drawn/calculated at random. An agreement between two clubs on their home and away fixtures potentially distorts the competitive dynamic in the league, especially if a number of clubs enter into similar arrangements. Premier League head of communications Dan Johnson clarified (via twitter) that no such arrangement exits.
We asked Birkbeck Sports Management programme student Beri Pardo to crunch the numbers to see the statistical possibility of such an occurrence eleven years in a row. Beri calculated that each team has the same chance of being the home side first each season which meant that the probability of this happening i.e. Everton hosting the first derby in each of the last eleven seasons was 0.00048828125 or one in two thousand.
Beri explained that the reason the ‘binomial distribution’ is the exact solution to this problem is because the following criteria were satisfied:
- There has to be a repetition of trials/events.
- There can only be 2 outcomes (i.e. either Everton or Liverpool will host first).
- The events should be independent (i.e. if Everton host Liverpool last year it has nothing to do with who will host first this year).
- The success rate should be constant (i.e. every year the probability of Everton hosting first is 0.5).
The perfect example of a binomial experiment is a series of coin tosses. Naturally, this satisfies the four criteria. If we toss a coin 11 times, the probability of getting exactly 0 heads is 0.00048828125.
A small sample of other derbies from across various European leagues were compared to ascertain their home/away split and a relatively even split was discovered. The results are set out in the below table.
|Manchester City v Manchester United||Manchester City at home 5 out of 11|
|Arsenal v Spurs||Arsenal at home 7 out of 11|
|Roma v Lazio||Roma at home 6 out of 11|
|Milan v Inter||Milan at home 6 out of 11|
|Galatasaray v Fenerbahce||Galatasaray at home 6 out of 11|
|Panathinaikos v Olympiakos||Panathinaikos at home 6 out of 11|
|Atletico Madrid v Real Madrid||Atletico Madrid at home 4 out of 11|
|Sparta Prague v Slavia Prague||Sparta Prague at home 5 out of 11|
It will be interesting to see whether the fixture list continues with the Everton Liverpool fixture anomaly for the twelfth consecutive year. If Goodison again hosts the first derby match of the season and the run goes to twelve, the binomial of twelve trials without success (i.e. Liverpool hosting first) is 0.000244140625 or one in five thousand.
Due to lack of statistical resources, the authors believe a more objective test of whether the Liverpool derby is really the ‘outlier’ of the fixture computer could be assessed by reviewing the fixture list over the last eleven years in the Premier League for clubs that have been members during that time frame to assess whether there are any other examples of a run of eleven home games for a particular club pairing. The authors would welcome any input or comments on the above blog.