# Analysis and Parameterization of Sports Performance: A Case Study of Soccer
## 4 Dataset and Parameterization
In [40], the CIES Football Observatory was also used for the comparison. It presents forecasts for the 2021/22 season for the five major European leagues. The statistical model used for this season includes player experience, investments in transfers to build the squads, as well as the performance of each team over the last 365 days. Considering the predictions made by the tools proposed (Table 11), the prediction of the classification of this type of data cannot be accurate. The models used for this purpose are often fed back based on the performance of the teams; however, physical and psychological parameters such as those established in the present work are not taken into account. In all predictions, including those made with the proposed ES, teams remain in the actual quartiles; however, there are different outliers that either climb or move to the lower part of the ranking. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **ES Ranking** & & & **Actual Ranking** & \\ \hline
**Rank** & **Team** & **Average** & **Rank** & **Team** & **Score** \\ \hline
6 & Villarreal CF & 67.64 & 6 & Real Sociedad & 62 \\
7 & Rayo Vallecano & 67.12 & 7 & Villarreal CF & 59 \\
8 & Atl. de Madrid & 66.87 & 8 & Ath. de Bilbao & 55 \\
9 & Real Sociedad & 66.22 & 9 & Valencia CF & 48 \\
10 & RCD Espanyol & 65.18 & 10 & CA Osasuna & 47 \\
11 & Ath. de Bilbao & 64.41 & 11 & RC Celta de Vigo & 46 \\
12 & CA Osasuna & 64.38 & 12 & Rayo Vallecano & 42 \\
13 & Getafe CF & 64.07 & 13 & Elche CF & 42 \\
14 & Granada CF & 64.04 & 14 & RCD Espanyol & 42 \\
15 & Cadiz CF & 63.89 & 15 & Getze CF & 39 \\
16 & Elche CF & 63.43 & 16 & RCD Mallorca & 39 \\
17 & Valencia CF & 63.30 & 17 & Cadiz CF & 39 \\
18 & Levante UD & 61.88 & 18 & Granada CF & 38 \\
19 & RCD Mallorca & 61.09 & 19 & Levante UD & 35 \\
20 & Deportivo Alavés & 60.92 & 20 & Deportivo Alavés & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **FiveThirtyEight [39]** & \multicolumn{2}{c}{**CIES Football**} & \multicolumn{2}{c}{**Actual Rank**} \\ \hline
**Rank** & **Team** & **Rank** & **Team** & **Rank** & **Team** \\ \hline
1 & Real Madrid CF & 1 & Real Madrid CF & 1 & Real Madrid CF \\
2 & FC Barcelona & 2 & Atl. de Madrid & 2 & FC Barcelona \\
3 & Atl. de Madrid & 3 & FC Barcelona & 3 & Atl. de Madrid \\
4 & Sevilla FC & 4 & Sevilla FC & 4 & Sevilla FC \\
5 & Real Sociedad & 5 & Real Sociedad & 5 & Real Betis \\
6 & Villarreal CF & 6 & Valencia CF & 6 & Real Sociedad \\
7 & Real Betis & 7 & Villarreal CF & 7 & Villarreal CF \\
8 & Ath. de Bilbao & 8 & Ath. de Bilbao & 8 & Ath. de Bilbao \\
9 & Valencia CF & 9 & Real Betis & 9 & Valencia CF \\
10 & Rayo Vallecano & 10 & CA Osasuna & 10 & CA Osasuna \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Predictions based on other tools. In the model developed in this work, there are two clear cases such as Atl. de Madrid, which is positioned in a clearly lower place, as well as RC Centa de Vigo, which is attributed to a position much higher than the real one. It should be noted that the proposed ES only has data on individual players, but the collective capabilities of the team and those of the coaching staff have not been used. We consider that this additional information could be very useful to determine the final classification and obtain a better model fit so that these parameters will be taken into account for future research. ## 8 Conclusions

In the present work, we have carried out the implementation of an ES that allows us to make estimations about the players of a soccer team and their respective teams. For this purpose, a previous parameterization of each player was carried out, considering data about his physical condition, skills, psychological state, and certain characteristics of his game. Based on this data and the application of different fuzzy logic functions, a series of scores were established, both for each player and for the teams, so that a comparison can be established and an estimate of the result of a match can be made.