On the development of a soccer player performance rating system for the English premier league

The EA Sports Player Performance Index is a rating system for soccer players used in the top two tiers of soccer in England—the Premier League and the Championship. Its development was a collaboration among professional soccer leagues, a news media association, and academia. In this paper, we describe the index and its construction. The novelty of the index lies in its attempts to rate all players using a single score, regardless of their playing specialty, based on player contributions to winning performances. As one might expect, players from leading teams lead the index, although surprises happen

Determining optimal cadence for an individual road cyclist from field data

The cadence that maximises power output developed at the crank by an individual cyclist is conventionally determined using a laboratory test. The purpose of this study was two-fold: (i) to show that such a cadence, which we call the optimal cadence, can be determined using power output, heart-rate, and cadence measured in the field and (ii) to describe methodology to do so. For an individual cyclist's sessions, power output is related to cadence and the elicited heart-rate using a non-linear regression model. Optimal cadences are found for two riders (83 and 70 revolutions per minute, respectively); these cadences are similar to the riders’ preferred cadences (82–92?rpm and 65–75?rpm). Power output reduces by approximately 6% for cadences 20?rpm above or below optimum. Our methodology can be used by a rider to determine an optimal cadence without laboratory testing intervention: the rider will need to collect power output, heart-rate, and cadence measurements from training and racing sessions over an extended period (>6 months); ride at a range of cadences within those sessions; and calculate his/her optimal cadence using the methodology described or a software tool that implements it

Sequential regression measurement error models with application

Sequential regression approaches can be used to analyse processes in which covariates are revealed in stages. Such processes occur widely, with examples including medical intervention, sports contests, and political campaigns. The naïvenaive sequential approach involves fitting regression models using the covariates revealed by the end of the current stage, but this is only practical if the number of covariates is not too large. An alternative approach is to incorporate the score (linear predictor) from the model developed at the previous stage as a covariate at the current stage. This score takes into account the history of the process prior to the stage under consideration. However the score is a function of fitted parameter estimates and therefore contains measurement error. In this paper, we propose a novel technique to account for error in the score. The approach is demonstrated with application to the sprint event in track cycling, and is shown to reduce bias in the estimated effect of the score and avoid unrealistically extreme prediction

To lead or not to lead : analysis of the sprint in track cycling

This paper uses a statistical analysis of match sprint outcomes to guide tactical decisions in this highly tactical contest and to provide competitors and coaches with a potential, marginal gain. Logistic regression models are developed to predict the probability of the leading rider winning at different points of the race, based on how the race proceeds up to each point. Key tactics are successfully identified from the models, including how the leading rider might hold the lead and how the following rider might optimise overtaking

A general inspection and opportunistic replacement policy for one-component systems of variable quality

We model the influence of opportunities in a hybrid inspection and replacement policy. The base policy has two phases: an initial inspection phase in which the system is replaced if found defective; and a later wear-out phase that terminates with replacement and during which there is no inspection. The efficacy of inspection is modelled using the delay time concept. Onto this base model, we introduce events that arise at random and offer opportunities for cost-efficient replacement, and we investigate the efficacy of additional opportunistic replacements within the policy. Furthermore, replacements are considered to be heterogeneous and of variable quality. This is a natural policy for heterogeneous systems. Our analysis suggests that a policy extension that allows opportunities to be utilised offers benefit, in terms of cost-efficiency. This benefit is significant compared to those offered by age-based inspection or preventive replacement. In addition, opportunistic replacement may simplify maintenance planning

Imperfect inspection of a system with unrevealed failure and an unrevealed defective state

This paper proposes a model of inspection of a protection system in which the inspection outcome provides imperfect information of the state of the system. The system itself is required to operate on demand typically in emergency situations. The purpose of inspection is to determine the functional state of the system and consequently whether the system requires replacement. The system state is modeled using the delay time concept in which the failed state is preceded by a defective state. Imperfect inspection is quantified by a set of probabilities that relate the system state to the outcome of the inspection. The paper studies the effect of these probabilities on the efficacy of inspection. The analysis indicates that preventive replacement mitigates low quality inspection and that inspection is cost-effective provided the imperfect-inspection probabilities are not too large. Some derivative policies in which replacement is “postponed” following a positive inspection are also studied. An isolation valve in a utility network motivates the modeling

A study of postponed replacement in a delay time model

We develop a delay time model for a one component system with postponed replacement to analyze situations in which maintenance might not be executed immediately upon discovery of a defect in the system. Reasons for postponement are numerous: to avoid production disruption or unnecessary or ineffective replacement; to prepare for replacement; to extend component life; to wait for an opportunity. This paper explores conditions that make postponement cost-effective. We are interested in modelling the reality in which a maintainer either prioritizes functional continuity or is not confident of the inspection test indicating a defective state. In some cases more frequent inspection and a longer time limit for postponement are recommended to take advantage of maintenance opportunities, characterized by their low cost, arising after a positive inspection. However, when the cost of failure increases, a significant reduction in the time limit of postponement interval is observed. The examples reveal that both the time to defect arrival and delay time have a significant effect upon the cost-effectiveness of maintenance at the limit of postponement. Also, more simply, we find that opportunities must occur frequently enough and inspection should be a high quality procedure to risk postponement

Conditional inspection and maintenance of a system with two interacting components

In this paper we consider the inspection and maintenance of a two-component system with stochastic dependence. A failure of component 1 may induce the defective state in component 2 which in turn leads to its failure. A failure of component 1 and a defect in component 2 are detected by inspection. Our model considers a conditional inspection policy: when component 1 is found to have failed, inspection of component 2 is triggered. This opportunistic inspection policy is a natural one to use given this stochastic dependence between the components. The long-run cost per unit time (cost-rate) of the conditional inspection policy is determined generally. A real system that cuts rebar mesh motivates the model development. The numerical examples reveal that when the ratio of the cost of corrective system replacement, that is on failure, to the cost of preventive system replacement is large there exists a finite optimum policy in most cases. Moreover, for the studied system wherein inspections of component 2 are expensive relative to those of component 1, having a reliable indicator of the defective state in component 2 is a good strategy to avoid costly failures of component 2, particularly when its time to failure is short