How Worried Should Real Madrid, Bayern Munich, And Barcelona Be?

The article is written by Michael Caley in 2018 to presents an overview of the soccer. In the article, the writer has discussed the previous and current performances of the famous soccer players. In the article main emphasis is on the three main players of the game the Barcelona, Real Madrid and Bayern Munich. In the article, previous scores of the super players are discussed through presenting the information in the numerical way [1].

In the article, graphs are used for the presentation of the information used in the article. In the article statistical analysis are made and expected performance of the players is calculated from 2010 to 2019. In accordance with the article, the European leagues are reporting the records in winning soccer game competitions [1].

In the six seasons duration, the winning records by the Bayern Munich are incredible. He won the German Bundesliga during the year. While the expectation towards the performance of the super players is increasing with the time rather than decreasing. In the past few years, it was considered that their performance will not improve but now the current statistics are showing quite different results.

Basically, the main purpose of the article is to cover the differences in the expected goals and the actual scores of the super players as through this information readers can identify the potential for their favorite players in the upcoming sessions of the soccer. In accordance with the views of the Michael (article writer) the situation for the Barcelona is not too bad in comparison to the Real and Bayern. He also claims that problems for the Barcelona are flexible that can be managed and tackled easily. The reason according to him is the difference in the start of the career. As Barcelona is at the top level while they do not stat at the top.

In the article writer put value in the content by providing the information regarding the previously occurred events in the soccer game. Examples of other great players as Lionel Messi and Ronaldo are also discussed to elaborate the views towards the future of the game’s players [1]. The writer concluded the article by claiming that Catalan (another player) is also in the same trouble and may face problems in the near future.        

Statistical Analysis of Real Madrid, Bayern Munich, And Barcelona

At the beginning of the session (soccer game sessions) and at the end of the session, there was a clear difference in the favorites also. For instance, the article presented the example of the super player's decrease in the favorites and increase in the favorites because of their differences in the performance. In the beginning and end of the favorites are mentioned below in the table form.

Figure 1Comparitive differences

In accordance with this table favorites for Real Munich and Bayern was decreased but the favorites for Bayern are increased that represents his high performance in the session.

The article also provides a comprehensive overview of the difference in goals and expected goals of the super players through the use of scatter plot. Scatter plot can efficiently represent the distribution and variance of the data [1]. In the article scatter plot is describing how much difference there was found in the expectation and the goals achievement. A cigar shaped scatter plot presents that the data has less variance.

The graph presented in the article is presenting the cigar shape that presents that performance of the super players Bayern, Barcelona and Real Madrid are relatively same. While the numerical data discussed in the article presents that the variance is minor in the performance of three super players because expected and actual performance of the Barcelona and Real Madrid is decreasing, while at the same time performance of the super player of the Europe Bayern is increasing and improving [1]. However, the tendency towards the expected and actual goals is between 10 to 20 goals.    

In accordance with the Michal (the writer of the article) since 2010, even the performance of the Bayern is improving but his goals differences are still in the 2^nd worst club. The article elaborates that Real Madrid is in trouble because of the decrease in his performance standards. In the article expected goals are based on the probability and prediction estimated through the means and variance values of the previous performance. In the analysis section future of the Real Madrid performance and expected goals is elaborated to help readers understand the problems for Real Madrid in the future.     

Normal Distribution _ Statistical Technique

The normal distribution is a statistical technique that is also known as the Gaussian Curve and Bell curve. The normal distribution as the statistical technique is used to presents continues probability of an event occurrence. Normal distribution values can be found through the normal equation and normal distribution formula. The most common use of the Normal distribution is to provide the standard reference for the problems of probability. The normal distribution has the quality to represents the central limit theorem for the selected data.

Normal distribution formula

The normal distribution of the data is calculated through the use of formula mentioned below:

In this formula, the standard deviation and mean is used for the calculation of the normal distribution scores and the cumulative probability for the data.

Normal Distribution Calculation  

The writer has also presented the previous 9 to 10 years expected goals of the Real Madrid in the article that are used for the calculation of the normal distribution. In accordance with the calculation of the mean, the average scored value during the last ten years performance is 26.7 for Real Madrid. While the standard deviation for the last 10 years is 3.75. That shows that the variance in the 10 years expected goals is very minor. However, on the other hand, the normal distribution is calculated by considering the mean 0, and the standard deviation as 1. While the cumulative was taken as the true value more and equals the 0.

The table mentioned below represents the normal distribution for the expected goals in the range of 20 to 0.

Figure 2Normal Distribution of the data

In accordance with the calculated values, the probability for the goals 0 is 0.3 that relatively equals to the 0. The values less than the 1 are showing that there are very minor chances for such values. However, the highest value of 7.6 and 5.5 is presented that these values have greater chances to be proved as true. A normal distribution curve usually represents the bell-shaped curve. The negative and positive values of the data shown in the normal distribution graph present the two different modes of the data.

 In the graph, positive values are presented at the right side of the graph and the negative values are presented at the left side of the graph. Balance in right and left side values are causing to produce a bell shape with the peak point of 7.6 at the 10 expected goals. The graph is developed with the values of the normal distribution table. The graph clearly illustrates that there is more probability that Real Madrid will have 10 or more than 20 expected goals. While the probability of below 10 is very minor.        

References of Real Madrid, Bayern Munich, And Barcelona