Last week, after the victory over Hull City, Morinho the Chelsea Manager claimed that his team has 90% chance to win the league championship this season. Now, Chelsea is leading the second place Manchester City with 6 points and played one less game than Manchester City. We can say that Manchester City has small chance to win the championship this season, but if they can win all the way down to the end of the season, which are eight games in total, they can still remain their hope for the championship. This time, we are going to estimate their chance to challenge Chelsea in the rest of the season.
First of all, let us use simple K-means Clustering to view their recent performance. Based on Cattell scree test, we choose 7 clusters in this case. Let us take a look at the visualization of clustering assignment,
and here is partial result of each cluster centroid,
As we can see in the cluster centroids, none of the centroids has a negative result, which indicates the team is not likely to lose in any situation. As we can see in the partial result, the clusters with the worst results are cluster 0, cluster 4, and cluster 5.
In the next step, we run the multi-factors ANOVA based on the formula between the game results and cluster assignments, and here is the result,
we can see in the result above, the p-values of cluster 0(Intercept), cluster 4, and cluster 5, are small, which means that statistically these so-called “bad games” of Manchester City happens randomly, and these bad games would not last long and affect the team consistently for the game result.
However, we did the same test on the formula between the goal scored and the cluster assignment, and got rather different result,
we can see that cluster 0 is radically different from the other two clusters; Manchester City in cluster 0 tends to score much more goals that they do in the other two clusters. Also, we can see that even though the p-values of cluster 4 and cluster 5 are still larger than the average, but the difference is not as significant as we see in the one with game results.
Therefore, we run the same test on the formula between the goal being scored and the cluster assignment, to see what happen on the defense side,
we can see in the result above, the p-values of cluster 0 and cluster 5 are large enough to convince us that it will make changes. We can see that even though the team play relatively badly, they can’t balance themselves between offense and defense. As a sophisticate team, this problem would just exist temporarily in one or two games, and that is the reason why we held the conclusion
Let us take a look at the cluster assignment again. Neither cluster 0 or cluster 5 took place in row. However, we need to know that the home attribute of cluster 0 and cluster 5 are 0, which means that the team plays badly in their away games, and in fact for games in cluster 0, the last three games actually happened in row of away games. As another cluster (cluster 6) consisted of away games, which the team performs well, is confirmed with a large p-value as we see above. However, all of the games in cluster 6 locate in the beginning of the season, so it proves that the team is able to perform well in away games but does not prove the team to be able to perform regularly as they did in the beginning of the season.
To prove whether the cluster 0 can last in row or not, we did some simulation whether the three home games locate within last three games of cluster 0. In this simulation, we would assume that the three home games took place in away field and see if they would move to cluster 0.
Here is the new clustering assignment,
Here is the new partial results of the cluster centroids,
we can see in the new assignment graph, two games of cluster 0 happened in row, and the three games are equally distributed from cluster 2 and 3 to cluster 0, cluster 5, and cluster 6. Therefore, we can see that the problem of the games does not last long.
As we can see in the new assignment, the recent two games locate in cluster 2 and cluster 5, which is an improvement compared to the previous games. We can be sure that the team will play rather strongly in the coming future, and resolve the problems within the team. We can’t guarantee Manchester City will make a comeback and defend their championship, but we can be sure that the competition is far from over as Mourinho has said in the press:”Chelsea has 90% chance to get the championship”.