On the development of decision rules for bar quiz handicapping

Some competitions involve teams comprising different numbers of players. For informal games, such as the popular ‘pub quiz’, we argue that teams with fewer players are at a disadvantage. This paper investigates the properties of these games and develops several methods for allocating handicaps within such competitions, so that the competitions may be considered fair, based on a simple Bernoulli model for correctly answering questions and assuming exchangeability of participants. We recommend a natural conjugate prior subjective handicapping rule; with this rule handicaps may be set beforehand given the judgement of the quiz setter regarding the difficulty of the questions. We also describe a posterior rule that provides improved accuracy but is calculated after the quiz is complete. Finally, the paper considers modifications of the proposed rules to cope with multiple-choice questions and progressive quizzes.     

Rating players in test match cricket

In general, the evaluation of player performance in test cricket is based on measures such as batting and bowling averages. These measures have a number of limitations, among which is that they fail to take into account the context in which runs are made or conceded and wickets are taken or given away. Furthermore, batting and bowling averages do not allow the comparison of performances in these two disciplines; this is because batting and bowling performances are measured using different metrics. With these issues in mind, we develop a new player rating system for test cricket. We use multinomial logistic regression to model match outcome probabilities session by session. We then use these probabilities to measure the overall contribution of players to the match outcome based on their individual batting, bowling and fielding contributions during each session. Our measure of contribution has the potential for rating players over time and for determining the ‘best’ player in a match, a series or a calendar year. We use results from 104 matches (2010–2012) to illustrate the method.     

Test sets for integer programs

In this paper I discuss various properties of the simplicial complex of maximal lattice free bodies associated with a matrixA. If the matrix satisfies some mild conditions, and isgeneric, the edges of the complex form the minimal test set for the family of integer programs obtained by selecting a particular row ofA as the objective function, and using the remaining rows to impose constraints on the integer variables.     

Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a₁,a₂,...,a_n ∈ ℤ^d$, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z) = ∑_{b ∈ G}z_b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in ℤ_n. In the generic case, this follows from algebraic results of Bayer and Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.     

On the application of a model of condition-based maintenance

In this paper the modelling of condition monitoring information for three critical water pumps at a large soft-drinks manufacturing plant is described. The purpose of the model is to predict the distribution of the residual lifetimes of the individual pumps. This information is used to aid maintenance management decision-making, principally relating to overhaul. We describe a simple decision rule to determine whether maintenance action is necessary given monitoring information to date.     

An analysis of strategy in the first three innings in test cricket: declaration and the follow-on

This paper analyses declaration and the follow-on decisions in test cricket. We model the match outcome given the end of first, second and third innings positions; data on 391 test matches, from the period 1997 to 2007, are used to fit the models. We then investigate how declaration strategy should vary from innings to innings, and how the nature and strength of the covariate effects vary. As the match progresses, the explanatory power of the covariates increases (from 44% at the end of the first innings to 80% at the end of the third). Home advantage and the effects of team strengths decrease. Overs-remaining, or equivalently overs used, and the number of runs by which the reference team lead their opponents remain important throughout. The follow-on decision problem is also briefly considered, and surprisingly, we find that the decision to enforce the follow-on or otherwise has no effect on match outcome.     

Asset replacement for an urban railway using a modified two-cycle replacement model

This paper considers the application of capital replacement models at Mass Transit Railway Corporation Limited (MTRCL), Hong Kong. A particular characteristic of the replacement problems considered is that costs relating to existing equipment are generally constant or increasing only slowly. Consequently, replacement is often driven by technical obsolescence, but other criteria are used for informing decisions. The applicability of traditional OR models of replacement is then problematic. We recommend the use of a modified two-cycle replacement model and compare this model to existing capital replacement models. Issues relating to the estimation of delay costs and failure consequences and their influence on the replacement decision are also considered—this is done using a fixed horizon model, which is a special case of the modified two-cycle model. Track points and escalators are used as particular examples. In addition to modelling recommendations, we discuss the management of asset replacement with emphasis on the procedures necessary to ensure that asset replacement requirements are considered appropriately and effectively. The paper treats, in particular, the procedural issues of asset replacement, and the discussion of asset replacement system methodology reflects the current practise at MTRCL, Hong Kong, and developments within that organization through collaboration with academia. The modified two-cycle replacement model is recommended by us for general replacement applications. The asset replacement procedure is presented as an exemplar for business and industry.     

On the limiting joint distribution of the extreme order statistics

The connection between extreme values and record-low values is exploited to derive simply the limiting joint distribution of the r largest order statistics. The use of this distribution in the modelling of corrosion phenomena is considered, and the extrapolation of maxima in space and time is described in this context. There has been recent emphasis on movement away from classical extreme value theory to more efficient estimation procedures. This shift is continued with the illustration of the extra precision of predicted maxima obtained from a model based on extreme order statistics over the classical extreme value approach.     

Modelling match outcomes and decision support for setting a final innings target in test cricket

^** E-mail: p.a.scarf{at}salford.ac.uk This paper considers the problem of timing the declaration ofthe third innings in test cricket. Data on the outcomes of recenttest matches are analysed in order to develop simple decisionsupport tools. The first of these tools presents match outcomeprobabilities given the position of the match at a potentialdeclaration point. These probabilities are determined usinga multinomial logistic regression model that is fitted to thetest match data. This idea is then extended to consider progresstowards a declaration—match outcome probabilities areconsidered as a function of target aimed for and run-rate. Thedecision tools have been implemented on a spreadsheet and examplecalculations are presented. The modelling described has thepotential for practical use in test matches.     

Maintenance scheduling of a protection system subject to imperfect inspection and replacement

An inspection and replacement policy for a protection system is described in which the inspection process is subject to error, and false positives (false alarms) and false negatives are possible. We develop two models: one in which a false positive implies renewal of the protection system; the other not. These models are motivated by inspection of a protection system on the production line of a beverage manufacturer. False negatives reduce the efficiency of inspection. Another notion of imperfect maintenance is also modelled: that of poor installation of a component at replacement. These different aspects of maintenance quality interact: false alarms can, in a worst case scenario, lead to the systematic and unnecessary replacement of good components by poor components, thus reducing the availability of the system. The models also allow situations in which maintenance quality differs between alternative maintainers to be investigated.