This table also reports the number of times each of the efficient teams acted as referent in the assessment of the inefficient ones, which is determined as the number of times the corresponding ��j in model (2) is non-zero in the assessment of the different teams. Table 1 Efficient teams: Contributions to the efficiency selleck chemical Nutlin-3a and number of times acting as referent The benchmarking analysis provided by DEA is reported in Table 2. For each inefficient team, in this table we have its actual data (in the first row of each team) and the corresponding efficient targets (in the second row). The third row records the difference between the target and the actual data in relation to the actual data. Large values of these percentages may suggest the need of the team under assessment for improvement in the corresponding aspect of the game.

Table 2 also reports which efficient teams compose the benchmark used in the assessments, together with their contributions as efficient referents in such benchmark, i.e., the ��j��s provided by model (2). Table 2 Benchmarking analysis: Actual data and efficient targets (inefficient teams) Table 3 records the cross-efficiencies (3) and the cross-efficiency scores (4). We note that in our analysis we used a variant of the standard cross-efficiency evaluation that assesses the teams by only using the weights of those that have been rated as efficient in the DEA self-evaluation (Ram��n et al., 2011). Thus, the rows of this table correspond to each of the teams participating in the championship, and in each of them we have the evaluations of their game (the cross-efficiencies) with the weights of each of the efficient teams (under the corresponding column).

The last column of the table shows the cross-efficiency scores and in brackets their corresponding rankings. We can see, for instance, that France ranks 1st followed by Spain, Denmark and Slovakia, in this order. The teams in the rows of the table appear in order of the final classification of the world championship, so we can make comparisons between the two rankings. Table 3 Cross-efficiency evaluation. Discussion On many occasions, tactics are validated on the basis of the achievement of victory, the winning team being rated as the best. However, we should not close the door to the analysis of other teams whose performance can serve as a model of efficiency for the game.

For example, Table 1 shows that the 9 efficient teams achieved the efficiency with different patterns of game. We can see that France used a pattern of game in which all of the factors considered have the same importance. This shows a good performance of France in all of the aspects of the game. Denmark and Spain needed to put more weight in some of the game factors Drug_discovery in order to be rated as efficient. Table 1 reveals that Denmark exploited to some extent its relative strength in G6m, Gwing and G9m in the achievement of the efficiency (with a contribution to the efficiency of 22.