Measuring efficiency and productivity in professional football teams: evidence from the English Premier League

Professional football clubs are unusual businesses, their performance judged on and off the field of play. This study is concerned with measuring the efficiency of clubs in the English Premier League. Information from clubs’ financial statements is used as a measure of corporate performance. To measure changes in efficiency and productivity the Malmquist non-parametric technique has been used. This is derived from the Data Envelopment Analysis (DEA) linear programming approach, with Canonical Correlation Analysis (CCA) being used to ensure the cohesion of the input–output variables. The study concludes that while clubs operate close to efficient levels for the assessed models, there is limited technological advance in their performance in terms of the displacement of the technological frontier. The research was supported by the Investigation Program of the Technical University of Cartagena (Spain) and by the Department of Sports Studies at the University of Stirling (Scotland, UK).     

Selecting non-zero weights to evaluate effectiveness of basketball players with DEA

In this paper, we show how DEA may be used to identify component profiles as well as overall indices of performance in the context of an application to assessments of basketball players. We go beyond the usual uses of DEA to provide only overall indexes of performance. Our focus is, instead, on the multiplier values for the efficiently rated players. For this purpose we use a procedure that we recently developed that guarantees a full profile of non-zero weights, or “multipliers.” We demonstrate how these values can be used to identify relative strengths and weaknesses in individual players. Here we also utilize the flexibility of DEA by introducing bounds on the allowable values to reflect the views of coaches, trainers and other experts on the basketball team for which evaluations are being conducted. Finally we show how these combinations can be extended by taking account of team as well as individual considerations.     

Measuring overall efficiency and effectiveness using DEA

This paper presents a framework where data envelopment analysis (DEA) is used to measure overall efficiency and show how to apply this framework to assess effectiveness for more general behavioral goals. The relationships between various cone-ratio DEA models and models to measure overall efficiency are clarified. Specifically it is shown that as multiplier cones tighten, the cone-ratio DEA models converge to measures of overall efficiency. Furthermore, it is argued that multiplier cone and cone-ratio model selection must be consistent with the behavioral goals assigned or assumed for purposes of analysis. Consistent with this reasoning, two new models are introduced to measure effectiveness when value measures are represented by separable or linked cones, where the latter can be used to analyze profit-maximizing effectiveness.     

Efficiency assessment of primary care providers: A conditional nonparametric approach

This paper uses a fully nonparametric approach to estimate efficiency measures for primary care units incorporating the effect of (exogenous) environmental factors. This methodology allows us to account for different types of variables (continuous and discrete) describing the main characteristics of patients served by those providers. In addition, we use an extension of this nonparametric approach to deal with the presence of undesirable outputs in data, represented by the rates of hospitalization for ambulatory care sensitive condition (ACSC). The empirical results show that all the exogenous variables considered have a significant and negative effect on efficiency estimates.     

Sensitivity analysis of efficiency and Malmquist productivity indices: An application to Spanish savings banks

Hypothesis testing and statistical precision in the context of non-parametric efficiency and productivity measurement have been investigated since the early 1990s. Recent contributions focus on this matter through the use of resampling methods—i.e., bootstrapping techniques. However, empirical evidence is still practically non-existent. This gap is more noticeable in the case of banking efficiency studies, where the literature is immense. In this work, we explore productivity growth and productive efficiency for Spanish savings banks over the (initial) post-deregulation period 1992–1998 using Data Envelopment Analysis (DEA) and bootstrapping techniques. Results show that productivity growth has occurred, mainly due to improvement in production possibilities, and that mean efficiency has remained fairly constant over time. The bootstrap analysis yields further evidence, as for many firms productivity growth, or decline, is not statistically significant. With regard to efficiency measurement, the bootstrap reveals that the disparities in the original efficiency scores of some firms are lessened to a great extent.     

Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan

The efficiency of decision processes which can be divided into two stages has been measured for the whole process as well as for each stage independently by using the conventional data envelopment analysis (DEA) methodology in order to identify the causes of inefficiency. This paper modifies the conventional DEA model by taking into account the series relationship of the two sub-processes within the whole process. Under this framework, the efficiency of the whole process can be decomposed into the product of the efficiencies of the two sub-processes. In addition to this sound mathematical property, the case of Taiwanese non-life insurance companies shows that some unusual results which have appeared in the independent model do not exist in the relational model. In other words, the relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately. Based on the structure of the model, the idea of efficiency decomposition can be extended to systems composed of multiple stages connected in series.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

Efficiency measurement for parallel production systems

In the real world there are systems which are composed of independent production units. The conventional data envelopment analysis (DEA) model uses the sum of the respective inputs and outputs of all component units of a system to calculate its efficiency. This paper develops a parallel DEA model which takes the operation of individual components into account in calculating the efficiency of the system. A property owned by this parallel model is that the inefficiency slack of the system can be decomposed into the inefficiency slacks of its component units. This helps the decision maker identify inefficient components and make subsequent improvements. Another property is that the efficiency calculated from this model is smaller than that calculated from the conventional DEA model. Few systems will have perfect efficiency score; consequently, a stronger discrimination power is gained. In addition to theoretical derivations, a case of the national forests of Taiwan is used as an example to illustrate the whole idea.     

Organizational capability,efficiency, and effectiveness in Major League Baseball: 1901–2002

Effective organizations need capabilities relevant to their missions and must manage those capabilities efficiently. We anticipate capability is more important in industries in which labor is highly paid, while efficiency is more important in industries in which labor is inexpensive. We explore the contributions of capability and efficiency to effectiveness for Major League Baseball teams from 1901 through 2002. Our analysis measures team capability using offensive and defensive statistics and uses Network Data Envelopment Analysis to derive efficiency scores to capture managerial performance. We define effectiveness as the team’s winning percentage. Both capability and efficiency are significant contributors to regular season effectiveness. Capability is more important. Finally, we examine the post-season performance of post-season teams between 1903 and 2002. Our analysis measures post-season performance based on the team’s winning percentage and that of its opponent. Post-season performance is unrelated to capability and managerial performance, accounting for about 1% of post-season success.     

The impact of tourist destination on hotel efficiency: A data envelopment analysis approach

This paper evaluates the impact of location on hotel efficiency using a sample of 400 Spanish hotels, the novel aspect being that location is considered at the tourist destination level. Moreover, for the first time, the location variables are based on the main theoretical models concerning location in the hotel sector, namely geographical positioning models, agglomeration and urbanization economic models and competitive environment models. The methodology consists of a four-stage data envelopment analysis (DEA) model that decomposes super-efficiency in the portion attributable to the tourist destination and the portion attributable to hotel management. Then, managerial efficiency is regressed against hotel characteristics, while tourist destination efficiency is explained by the characteristic of each location. The findings highlight the importance of tourist destinations, providing novel empirical support for the propositions of the main location models. Indeed, the tourist destination is the main cause of differences in the level of efficiency among hotels. The occupancy level, degree of seasonality and market concentration are the variables with the greater impact on efficiency.     

Network data envelopment analysis: A review

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional black-box approach, where the operations of the component processes are ignored. This paper reviews studies on network DEA by examining the models used and the structures of the network system of the problem being studied. This review highlights some directions for future studies from the methodological point of view, and is inspirational for exploring new areas of application from the empirical point of view.     

Efficiency decomposition in network data envelopment analysis: A relational model

Traditional studies in data envelopment analysis (DEA) view systems as a whole when measuring the efficiency, ignoring the operation of individual processes within a system. This paper builds a relational network DEA model, taking into account the interrelationship of the processes within the system, to measure the efficiency of the system and those of the processes at the same time. The system efficiency thus measured more properly represents the aggregate performance of the component processes. By introducing dummy processes, the original network system can be transformed into a series system where each stage in the series is of a parallel structure. Based on these series and parallel structures, the efficiency of the system is decomposed into the product of the efficiencies of the stages in the series and the inefficiency slack of each stage into the sum of the inefficiency slacks of its component processes connected in parallel. With efficiency decomposition, the process which causes the inefficient operation of the system can be identified for future improvement. An example of the non-life insurance industry in Taiwan illustrates the whole idea.     

Efficiency decomposition for general multi-stage systems in data envelopment analysis

Conventional data envelopment analysis (DEA) models only consider the inputs supplied to the system and the outputs produced from the system in measuring efficiency, ignoring the operations of the internal processes. The results thus obtained sometimes are misleading. This paper discusses the efficiency measurement and decomposition of general multi-stage systems, where each stage consumes exogenous inputs and intermediate products (produced from the preceding stage) to produce exogenous outputs and intermediate products (for the succeeding stage to use). A relational model is developed to measure the system and stage efficiencies at the same time. By transforming the system into a series of parallel structures, the system efficiency is decomposed into the product of a modification of the stage efficiencies. Efficiency decomposition enables decision makers to identify the stages that cause the inefficiency of the system, and to effectively improve the performance of the system. An example of an electricity service system is used to explain the idea of efficiency decomposition.     

Distribution of cost and profit efficiency: Evidence from Indian banking

This paper uses the nonparametric DEA methodology to estimate cost and profit efficiency of Indian banks during the post-reform period. The results show considerable variation in average levels of profit efficiency across various ownership categories of banks. In general, state owned banks are found to be more efficient than their private counter parts. Further, efficiency tends to be low among the small banks (assets up to Rs. 50 billion), indicating that at the existing scale of operations, these banks are operating far below the efficient frontier. We also examine the distribution of efficiency using nonparametric kernel density estimates. The analysis reveals a rightward-shift of the efficiency distribution over the years. A major part of this shift comes from the state owned banks. Based on the conditional distribution, the study finds strong evidence of ownership explaining the efficiency differential of banks. Additionally, bank size and product-mix are also found to be important, although to a lesser extent.     

On the relative efficiency of alternative modes of producing a public sector output: The case of the developmentally disabled

This paper examines the relative efficiency of alternative methods of producing care for the developmentally disabled. A linear programming framework is used to construct a production frontier which allows measurement of relative efficiency among institutions in the sample. Tests are performed to detect influential observations in the data which might result from measurement error which could distort the efficiency measures. Different types of institutions are compared in terms of average efficiency. Policy implications of the analysis are discussed in the concluding section.     

Ranking efficient DMUs using the Tchebycheff norm

One problem that has been discussed frequently in data envelopment analysis (DEA) literature has been lack of discrimination in DEA applications, in particular when there are insufficient DMUs or the number of inputs and outputs is too high relative to the number of units. This is an additional reason for the growing interest in complete ranking techniques. In this paper a method for ranking extreme efficient decision making units (DMUs) is proposed. The method uses L_∞(or Tchebycheff) Norm, and it seems to have some superiority over other existing methods, because this method is able to remove the existing difficulties in some methods, such as Andersen and Petersen [2] (AP) that it is sometimes infeasible. The suggested model is always feasible.     

A comment on “An extended assignment problem considering multiple inputs and outputs”

This note shows that the data envelopment analysis (DEA) models formulated by Chen and Lu [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Modell. 31 (2007) 2239–2248] are not correct. The enveloping form of the Chen and Lu formulation is studied and a simple example is presented to demonstrate the differences between the efficiency scores resulted of the Chen and Lu formulation, and the true ones.     

Dynamic data envelopment analysis: A relational analysis

This paper proposes a dynamic data envelopment analysis (DEA) model to measure the system and period efficiencies at the same time for multi-period systems, where quasi-fixed inputs or intermediate products are the source of inter-temporal dependence between consecutive periods. A mathematical relationship is derived in which the complement of the system efficiency is a linear combination of those of the period efficiencies. The proposed model is also more discriminative than the existing ones in identifying the systems with better performance. Taiwanese forests, where the forest stock plays the role of quasi-fixed input, are used to illustrate this approach. The results show that the method for calculating the system efficiency in the literature produces over-estimated scores when the dynamic nature is ignored. This makes it necessary to conduct a dynamic analysis whenever data is available.