British scientists have found that the dynamics of the location of the teams in the standings of the English football divisions obeys the power law. For this they used the final and intermediate results of the four highest leagues of England for 1995-2017 year. On what the team is after 10, 20 and 30 rounds, can be with different degree of confidence to predict the probability with which she will be the winner, write the scientists in PLoS One.
Prediction results of football matches and tournaments (and other sports) seems not a very simple task: mainly because there are so many external factors to take into account the real probability and the contribution which the as by variables is very difficult. Such factors can be sudden injuries, the weather or the unpredictable decisions of the judges. In addition, it is difficult in advance to predict the strategy chosen by the coach and team leader, she easily might not be the same that was used before.
However, the data during the football tournaments are a lot, and use them later for predictions of results. Moreover, these can be very different from the results of all previous matches of the team in a particular tournament and outside it, to the individual performance of specific players.
Ben Jones (Ben Jones) from the City University of Leeds and his colleagues found that the results of football tournaments are the easiest to predict when they have started — for example, the location of teams in the standings at the beginning or the middle. As an example, they led the standings of the Championship of England football for the 2016/2017 season: winning the team of club “Chelsea” came in first place in the table is 10 round of 36, “Liverpool”, which in the end, fourth place, took it all the last 10 rounds.
Scientists have collected data from four divisions of English football: the Premier League, the Championship, League 1 and League 2 (the last three are part of the English football League). In dataset hit the tables with results for all rounds of these divisions for the period from 1995 to 2017. The data for each season in each division is easiest to imagine in the form of matrix m×n where m is a separate command, n is a single round, but the elements inside — the points scored by the team in this round.
Based on the data, the researchers calculated two coefficients of rank correlation (the Spearman’s coefficient and Kendall), which allow to evaluate the Association between two given indices in the given case, the outcome of competitions and the results after 10, 20 and 30 rounds.
Regardless of the division, year, and which teams took part, the clubs in the final standings were correlated with how they settled it during the season: indicators of Spearman’s correlation and Kendall were equal to 0.8 and 0.87, respectively). The probability that the place in the standings will coincide with the total, however, increased from 10 round to 30: for example, in the Premier League after 10 rounds — 76.9%, after 20 — 87%, and after 30 93.9%. Thus, according to the researchers, to predict the winner of the division with a fairly high precision for a few matches before the final race: in the case of the Premier League — six.
The resulting Kendall coefficient indicates that the standings in English football obey the power law, and a change in one quantity leads to a proportional change in the other. In other words, a strong command in the list to quickly go to the top ranks and stay there to the end, and the team is weaker — on the contrary.
In General, one of the most reliable ways of predicting the results of football matches are considered to be quotations of the bookmakers, but they do not have one hundred percent efficiency. For example, the Austrian mathematics based on the bookmakers predicted a victory in last year’s soccer world Cup Brazil or Germany, but the real winner of France — in their table of probabilities only got fourth place.