Based on results, the German Bundesliga is currently the most competitive among Europe’s top leagues this season.
A study evaluated La Liga, Serie A, Ligue 1, the Premier League, and the Bundesliga, assessing the points gap in each competition. The figure computed was the standard deviation of points earned, the square root of the average of summed squared differences between each team’s points and the league average.
In simpler terms, each value is computed by finding the difference between a certain team’s points earned and the average points for all teams in the league. These differences are found for all teams within a league, and averaged.
A high standard deviation value means a broader points gap, and thus a less competitive league: for example, one in which one or two teams are running away with the title, and a few teams are hopelessly caught in the relegation battle.
By contrast, a low standard deviation means a tighter table, suggesting less of a gap between the elite and lower teams, and tighter competition.
In the Premier League, there now are only two teams realistically in contention for the title: leaders Manchester City and runners-up United. There is a narrow points range between eighth-placed Stoke and the 15th-placed West Brom, but on either end, the next few teams are significantly separated from the pack. And the gap between first and last is a whopping 39 points, with the average higher than all but seven of the league's 20 teams. By standard deviation, the Premier League is the least competitive in Europe.
The standard deviation of points in La Liga is significantly smaller than that in the Premier League, but still greater than that of any of Europe’s other top leagues. The mid-table range is quite tight: a gap of just 10 points separates Espanyol (5th) from Sporting Gijon (19th). In Spain, the race for a fourth Champions League spot is still far from decided, and the Europa League berths are completely up for grabs: the average is right in the middle, between ninth-placed Sevilla and 10th-positioned Malaga. But the league’s extremes are so far from the mean that, even with an otherwise tight pack, the standard deviation is still higher than most. Real Madrid and Barcelona are a whopping 14 and nine points clear respectively of third-placed Valencia, who are a further four ahead of Levante. At the bottom, Zaragoza are six points behind Gijon, making the difference between first and last nearly as great as that in England: 37 points.
Serie A has seen a contraction at the top in recent weeks, as Inter have stormed up the table to a position where they can once more be considered title contenders. And as in England and Spain, there is a tight pack in the centre of the table, with just five points separating Palermo (eighth) from Siena (17th). Novara and Lecce appear almost without a hope in the relegation zone, however, with Cesena dangerously close to a similar position. This, coupled with the five-point drop from Napoli (eighth) to Palermo (ninth) augments the data, splitting the league table effectively into three tiers that are separately competitive, if hard to break away from.
In France, the difference between first and last is lesser still than any of the aforementioned. From ninth place down, starting just below the mean, just eight points separate the remaining 12 teams, which offsets what is a considerably higher gap of 16.10 points to leaders PSG. In all of France, only two teams are more than nine points from the rounded mean.
In Germany, the title race is more open than in any other league: Bayern Munich, Borussia Dortmund and Schalke are all tied on points for first place, while dark horses Borussia Monchengladbach are just a point off the pace. Werder Bremen and Bayer Leverkusen round off the top six, with 30 and 29 points apiece, beyond which there is a big drop to Hannover, and a steady decrease in points down the table. Rounding the mean, the leaders are just 12 points above, while basement side Augsburg are 10 below, making a first-to-last gap smaller than that of any other league.
It is important to note that the standard deviation is to some degree influenced by number of games played: with more matchdays having passed, there is a slightly greater likelihood of a gap - and deviation - growing. And surely enough, the league with the most games played (the Premier League) has the greatest standard deviation, while that of the which has completed the fewest (the Bundesliga) has the smallest.
Many fans have often asserted that when the lower half of one league is stronger than that of another, that one league is tougher to win than the rest. And without the chance for real, objective comparison, the debate can rage endlessly with no conclusion. There is no objective way to definitively compare competition between leagues, especially those at different stages in the season that are comprised of an unequal number of teams.
However, standard deviation is the best way to measure how tight a table is, and accordingly, how strong the lower teams are relative to the higher. And in the case of the German Bundesliga, based on results, the gap in quality between the higher and lower teams is significantly less than that in any of Europe's other top leagues.