The Eagle Rating is a measure of perceived individual rugby player performance. This paper discusses
the underlying assumptions that are evident in its creation. The issue of non-performance by an
individual is explored and the potential impact of non-performance on statistical results examined

Bracewell, Paul

English

The Eagle Rating is a measure of perceived individual rugby player performance. This paper discusses the underlying assumptions that are evident in its creation. The issue of non-performance by an individual is explored and the potential impact of non-performance on statistical results examined

Paul Bracewell

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Perception of Individual Rugby Player Performance and the Impact of Non-Performance on Statistical Analyses

Massey Research Online

Res. Lett. Inf. Math. Sci,  (2001) 2,  19-22Available online at http://www.massey.ac.nz/wwiims/~rlimsPerception of Individual Rugby Player Performance and the Impact ofNon-Performance on Statistical AnalysesPaul BracewellI.I.M.S., Massey University Albany Campus, Auckland, N.Z.p.j.bracewell@massey.ac.nzAbstractThe Eagle Rating is a measure of perceived individual rugby player performance. This paper discussesthe underlying assumptions that are evident in its creation.  The issue of non-performance by anindividual is explored and the potential impact of non-performance on statistical results examined.IntroductionSport statistics are an addition to the entertainment package provided by the media.  The primary purposeof these statistics is to give an impression of the ability or performance level of competing individuals.To use these statistics effectively the underlying assumptions must be understood so that any potentiallimitations can be identified. This paper focuses on the Eagle Rating, an objective rating system extractedvia statistical analyses for individual rugby players in first class rugby.  The exact details of how theEagle Rating is calculated is inconsequential for this paper.  However, the methods and assumptions thatprovide the framework are important. These are discussed in part through the body of this paper.Essentially the Eagle Rating is based on the following premise: ability is inferred from performance,which is inferred from the combination of the successful and unsuccessful completion of physical tasks.It is for this reason that the effect of non-performance by a player in a single match needs careful study.The first section of this paper looks at the justification of a statistical performance barometer in rugby.The underlying assumptions are examined before the potential effect of non-performance is discussed.Finally an exponentially weighted moving average is suggested as the best method of estimating playerability as it reduces the susceptibility of the performance measure to match volatility.The Eagle Rating as a Sport StatisticThe theme of the Eagle Rating is no different to any other sport rating system, such as Cricket’sPricewaterhouse Coopers Rating (Formerly known as the Deloitte Rating, Coopers and Lybrand Rating)(Berkmann, 1990) and Baseball’s PGP (Player Game Percentage) (Bennet, 1992).  All are designed toindicate how well an individual has performed in a match situation.  This then enables a competitor’sability or their worth to the team to be assessed.  However, this assumes that the occurrences on fieldrelate directly to the individual’s ability.  Whilst this discussion focuses on rugby, parallels can be drawnto other sports.  Unlike cricket or baseball, rugby has few defined outcomes that represent successfulcontribution in a match context.  That is from a competitive team perspective, batsmen have played wellif they have scored runs, but a winger in rugby can have played extremely well, yet not scored any points.Rugby performance must therefore be measured on successfully completed tasks such as the number ofplayers beaten or the number of metres run on attack.Instead of quantifying ability through structured tests, the search for rugby ability must focus onunstructured rugby match participation, with the assumption that over time the nature of an individual’sability will be imposed on collated statistics.  Each time an individual participates in a game of rugby, thiscan be viewed as a sampling opportunity.  Essentially the game becomes a forum by which individualsexpress their inherent ability.In sport, skill must be perceived as sporting performance which tends to increase the probability ofsuccess (Thomas, 1970).  Further, sports skill can be defined as “any behaviour which tends to improveperformance in sport (Thomas, 1970, p.126)”.  According to the Oxford Senior Dictionary (Hawkins,1990), the combination of skills gives rise to ability.   This definition fits nicely with rugby terminologyand the continual reference to a player’s skill set by coaching staff determining player value (Stewart,1987; de Lacy & Fox, 2000).  Thus sporting ability is defined as the combination of skills that tend to20 R.L.I.M.S. Vol. 2,  May 2001improve the performance in sport and it is possible to measure these skills as outlined in the definition ofability.  However, it must be noted that there is a difference between what is measured, and what isinferred from this measurement.  This is an important distinction and a critical assumption thatunderwrites the development of the Eagle Rating.  Skill is inferred from performed tasks.  Tasks aredirectly measurable (countable) and to complete the task successfully, the skill to perform such a taskmust exist.  Mental and physiological tasks that contribute to the performance of a physical task, such aspassing the ball, are not directly measurable from a game and are inferred from the performance onphysical tasks.  Thus skill also comprises the set of mental, physical and physiological tasks that arerequired to increase the probability of success.  To successfully perform a physical task, such as kickingthe ball in a game situation, the other factors that comprise skill must also be successfully performed.Therefore by measuring physical tasks, skill can be inferred as the physical task cannot be completedunless the full set of tasks that comprise the skill (physiological, physical and psychological) arecompleted.  Consequently, quantified skill is inferred from quantified tasks.  As ability is the combinationof skills, by combining the measurement on tasks, ability is quantified.  Therefore to measure sportingability, we need to measure quantitatively the sporting skills of an individual. By measuring theperformance on physical tasks one can infer the level of an individual’s skill from the univariate datarelating to physical tasks in our possession.  The skill set of an individual to tackle, catch, kick, and evadedefenders is evident within the data set.  This provides the justification for calculating a value such as theEagle Rating.  Figure 1 is a schematic representation of the discussion presented, incorporating mmeasurable physical tasks that can be explained by n skills from which ability is inferred.  A note ofcaution must be included at this point: It would be naive to assume that an individual’s ability to playrugby could be completely described by a set of numerical measures.  However, a large portion of anindividual’s talent is expressed, exemplified by the desire for such statistics in the media.Figure 1. Schematic Representation of Ability Incorporating Physical TasksCollection of match data referring to individual physical tasks is a primary starting point for quantifyingperformance leading to the inference of ability.  Multivariate analyses provide the techniques to reveal thestructure of ability via the typical multivariate profile that is expressed from many match situations.  Thegreater an individual’s ability to play the game, the greater their capacity, and therefore the greater theirpotential involvement in the game.  Every time a task is performed a statistic is recorded from a matchtype situation, the existence of some associated skill can be supported.  Work rate is especially obvious inthe statistics that are generated.  The more often a player is involved, the higher their work rate.Obviously, the higher the successful involvement, the greater the individual’s inferred ability.Fitness and mental skills are core components of rugby ability.  Whilst not directly measurable from arugby match, existence can implied.  When a skill cannot be replicated in a game environment due toeither a lack of mental application or fitness, the absence of such data will suggest potential weakness.Specifically, what is the point of a player being able to wrestle the ball of any opposition player if thatP. Bracewell,  Perception of Individual Rugby Player Performance 21individual can never get to a situation where that skill is required due to lack of physiological attributessuch as fitness and mobility?  This example acknowledges that confounding variables such as fitness andmental attributes do not pose a problem. The mediating effects will influence task performance which ismanifested in the displayed skill-set recorded in a match situation.  However, as our perception ofindividual performance is based upon the occurrence of events and the measurement of physical tasks in amatch situation, we must also consider factors that restrict an individual from performing to the levelexpected.  This leads us into the area of non-performance.Non-PerformanceWe will define non-performance as a performance by an individual that is much less than expected by agiven individual in a specified position.  The handling and interpretation of non-performance data iscrucial in how the information generated by a rating system is generalised and used in statisticalinference.  Importantly, non-performance does not always relate to an individual’s ability.  Three keyareas can be isolated: 1) player inferior, 2) player superior  (over-targeted), and 3) game structure.  Thefirst situation is of no concern as it is expected that the successful contribution of inferior individuals tothe on-field performance of a team will be minimal.  However, the two remaining areas are of concern asboth are related to match volatility due to the dynamic and chaotic structure imposed by all participatingindividuals.A superior player may find that they are targeted or over marked in a match context.  From a teamperspective this can be favourable by creating space and opportunities for other team members.  However,from an individual perspective, the individual’s involvement will appear less than expected.  Thus ifability is inferred from a solitary match based solely on the individual perspective, the ability or overallperformance of that individual will be deemed to be less.  This brings into question any inferenceregarding player ability from a solitary match.  Similarly the structure of the game may not allow anindividual to become involved to the extent expected.  This may be due to tactics, weather or even theperformances of other co-operating or competing individuals.However, by considering many sampling situations, it is expected that an individual will haveencountered many different rugby situations enabling true ability to be determined in the longer term.Further, overtime, a player will develop strategies that enable appropriate involvement.  This may involvethe development of skills such as the ‘chip and chase’ a ‘side-step’ or ‘swerve’, a ‘dive pass’ and so forth.Also teams will be encountered who are of insufficient ability to “remove” the superior individual fromthe game.  Thus to have an accurate perception of individual performance several matches must beconsidered.This is contrary to the adage “You are only as good as your last game”, which implies assessing matchperformance purely on a match by match basis.  However, due to the potential impact of non-performance, variable match conditions and the differing standard of opposition presented at eachsampling situation, past performance must be included to produce reliability.  This can be achieved byimplementing an exponentially weighted moving average.  This is not a novel approach, thePricewaterhouse Coopers algorithm for rating cricket players incorporates a weighted average allowingpast performance to have some impact on the current perception of ability (Berkmann, 1990).  Due to thephysicality of rugby an exponentially weighted moving average is more suitable than a simple movingaverage.Impact on Statistical AnalysesThe most applicable arena for statistics such as the Eagle Rating is ranking and selection.  From astatistical perspective this involves the comparison of numerical measures.  These numerical measures areestimates of the attributes of interest, such as ability.  Means and variances can be obtained andimplemented quickly.  However, to be of most use time series of these measures must be examined.Ability cannot be assumed to be static, thus data must be observed sequentially allowing any change inability to be identified.22 R.L.I.M.S. Vol. 2,  May 2001It is inappropriate to compare individuals on the basis of one-off match observations due to the reasonsoutlined previously relating to match volatility. Whilst it is tempting to compare individual’s participatingin the same match, this must be approached with caution, due to the influence of game structure.However, a weighted rating of perceived ability over several matches provides an ideal comparison as itconsiders ability as an evolving entity.  Utilising a weighted average, comparisons can be made withinand between individuals from season to season, before and after interventions such as injury, technicalcorrections and the influence of coaching regimes.It must also be remembered that the data collected is happenstance, bringing about it’s own set ofcautions detailed by Roberts (1992) as follows.  Firstly, caution must be exhibited when attempting toinfer causation.  For example excessive tackle counts by an openside flanker inferring high defensiveinvolvement may not be the cause of an abnormally large number of turnovers by the inside backs of theopposition.  Secondly, overreaction to extreme individual observations must be tempered.  For example,an apparent excess of handling errors may be due to environmental conditions, not a deterioration inhandling skills.  As discussed with reference to non-performance, this can achieved via a dampeningprocess such as an exponentially weighted moving average.ConclusionHolistic individual rugby player performance is inferred from the performance on physical tasks thatoccur in matches.  However, the involvement of an individual on certain tasks can be restricted by anumber of factors, thus giving a reduced impression of that individual’s ability.  By taking anexponentially weighted moving average, past performance is considered, reducing an individual'svulnerability to match volatility.  This provides a more stable approximation of an individual’s ability inthe game of rugby.AcknowledgementsThis study is part of a larger body of work “Quantification of Individual Rugby Player Ability ThroughMultivariate Analysis and Data Mining”, a PhD thesis funded by Eagle Sports, a division of the EagleTechnology Group, and a Graduate Research in Industry Fellowship from Technology New Zealand.  Theresearch is supervised by Dr Denny Meyer and Dr Siva Ganesh.References[1] Berkmann, J. (1990). The Complete Guide To Test Cricket In The Eighties. Partridge Press:    London.[2] De Lacy, H. & Fox, G. (2000). Think and Play Winning Rugby.  Harper Sports: Auckland.[3] Hawkins, J.M. (1990).  Oxford Senior Dictionary. (7th ed.).  Oxford University Press: London.[4] Roberts, H.V. (1992). Can TQM Improve Athletic Performance? Proceedings of the Section on   Statistics in sports of the American Statistical Association.[5] Stewart, J.J. (1987). Rugby: A Tactical Appreciation. Rugby Press: Auckland.[6] Thomas, V. (1970). Science and Sport: The measurement and Improvement of Performance. Faber   & Faber: London.

Perception of individual rugby player performance and the impact of non-performance on statistical analyses

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Perception of individual rugby player performance and the impact of non-performance on statistical analyses

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