soccer/world football data collection and … · soccer/world football david r. brillinger...

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Cochran eorms0791.tex V1 - April 29, 2010 3:56 P.M. P. 1

SOCCER/WORLD FOOTBALL

DAVID R. BRILLINGER

Statistics Department, Universityof California, Berkeley,California

Soccer/world football, also known as asso-ciation, is a sport involving two teams ofplayers kicking and heading a medium-sizedball about on a large rectangular field. Eachteam has a goal that is quite wide and highand seeks to shoot the ball into the otherteam’s goal. The basic objective is to see whichteam of the two can score the most goals andthereby win the game. The sport is subjectto laws set down by the Federation Interna-tionale de Football Association (FIFA). Typ-ically, there is a group of teams playingagainst each other in a league or tourna-ment, with a formal schedule of games. Ateam’s intention then is to win a tourna-ment or championship by scoring the mostpoints, where 3 points are awarded for a win,1 for a tie, and 0 for a loss.

The sport of soccer has a long and full his-tory possibly going back to 2500 BC [1]. In thepresent time, the teams each have 11 players.One, the goalie, may handle the ball but onlywithin a restricted area in front of his goal.There is a neutral referee whose decisions arefinal. The grandest tournament, the WorldCup, moves amongst different countries andoccurs nominally every 4 years. The pastworld champions are Uruguay, Argentina,Brazil, England, France, Germany, and Italy.The sport has become a multibillion dollarbusiness.

Tactics are basic to the games, with manystyles and plating formations available. Ateam’s choice has been based, in part, onstudies of match statistics. The pioneer inthe field of match performance analysis isCharles Reep [2–4].

Wiley Encyclopedia of Operations Research and Management Science, edited by James J. CochranCopyright © 2010 John Wiley & Sons, Inc.

DATA COLLECTION AND DESCRIPTIVEANALYSES

Data collection and analysis have been basicto soccer for many years. The most commonstatistics are a game’s result and the numberof goals scored by each team. Outputs of thedata analyses include reports, tables, graphs,talks, images, and videos.

Many things go on during a game. A basicquestion is what is to be recorded for theanalysis and how to do so. Charles Reep[2,3] developed solutions starting in the early1950s. The study of basic events in a gamehas been called both as match performanceanalysis and match analysis [2,5–7].

A recent addition to the type of infor-mation available for individual games isnear-continuous high frequency digitalspatial-temporal data. Companies cometo stadium and set up an array of videocameras. By signal processing, they thendevelop the spatial-temporal coordinates ofthe changing locations of the players on thefield, the ball, and the referee. Companiesdoing this include Match Analysis, ProzoneHoldings, and Sport-Universal SA. Di Salvoet al. [8] have validated one such system.The basic quantities that may now be tableddirectly include counts of tackles, crosses,distances covered, key moments and actions,possessions, passes, interceptions, runswith the ball, incorrect referee decisions,fouls, penalty kicks, challenges, entries intothe opponent’s area, ball touches, blocks,forward passes, long balls, high intensityrunning, ball velocity and accuracy, and ballsreceived. Individual player’s performancesmay be evaluated directly. The data canlead to changes in tactics during a game[9,10]. Substantial soccer databases havebeen available for many years. Websitesinclude www.uefa.com, www.fifa.com [11,12], Q1www.soccerbase.com, www.soccerway.com,and www.soccerpunter.com.

1

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2 SOCCER/WORLD FOOTBALL

One early investigation of basic data isthat of Moroney ([13], pp. 101–103). He stud-ied the numbers of goals scored in 480 gamesand prepared a histogram of the counts. Inanother early study, the number of successfulpasses in passing movements were studiedfor the English First Division during theyears 1957–1958 and 1961–1962 [14]. Theresults were presented in tabular form. Reepand Benjamin found a stable correspondencebetween shots on goal and goals scored ofabout 10 to 1. Distances traveled by individ-ual players during a game are graphed byplayer position in Ref. 5. Hughes and Franks[15] present scatter and time series plots.One early discovery was the existence of ahome advantage. Schedules are often set upso that the two teams meet both, at homeand away to deal with this. Jochems [16,17],while addressing the question of whether theDutch football pools were breaking the gam-bling laws, found the percentages to be 46.6for a home win, 31.0 for a visitor win, and22.4 for a draw/tie. Managers make use ofsuch data in their decision-making, more soevery year. Stochastic models are importantin this connection.

STOCHASTIC MODELING

Stochastic models are pertinent to soccerstatistics, because there is much uncertaintyin what happens and what may happen. Dur-ing the preceding 50 years, stochastic modelshave been constructed to address soccer ques-tions.

Between Game Modeling

Some models may be distinguished as to con-cerning goals, win–tie–loss, or points. Spe-cific distributions and models that have beenemployed include bivariate Poisson, expo-nential, extreme value, GARCH, generalizedlinear, logistic, Markov, negative binomial,ordinal, regression, prior, point process, andstate space. Many analyses are based on thePoisson distribution whose probability func-tion is given by

Prob{Y = y} = μye−y/y! for y = 0, 1, 2, . . . .

Here Y might represent the number ofgoals a team scores in a future game. Inan early work, Moroney [13], using the datamentioned above, compared the number ofgoals scored by a team in a game to theirestimated expected frequency assuming thata Poisson distribution held. On examiningthe result, he was led to seek to improveit and fit a negative binomial distribution.This is a generalization of the Poisson. Thisfit was satisfactory. However, Greenhoughet al. [18] found that when data from 169countries were pooled, extreme value distri-butions were needed.

Reep et al. [14,19] work on the numberof passes in successful passing movements.They fit the negative binomial and found itwas good when 0-length cases were excluded.

Suppose next that team i at home isplaying against team j visiting. Denote thefinal score by (Xij, Yij). Various authors haveassumed that Xij and Yij are independentPoissons with respective means,

αiβj, γiδj Ref. 20

exp{α + η + γi + δj},exp{α + γj + δi}

Refs 21 and 22

αiβjη, αjβi Ref. 23

exp{α + η + γi − δj − φ

(εi − εj)}, exp{α + γj − δi+ φ(εi − εj)}

Ref. 24

here η is the home advantage, φ the psycho-logical effect, and εi = γi + δi. In their fitting,Dixon and Coles modify the low score modelprobabilities. The probability that team iwins the game may be estimated having esti-mated the model parameters.

Maher [20] estimates α, β, γ , δ by max-imum likelihood and mentions fitting thebivariate Poisson. Karlis and Ntzoufras [25]give details of fitting a bivariate Poisson,studying the data for 24 leagues. They findthat the assumption of independence is notrejected in 15 out of the 24 cases. They alsoconsider the negative binomial distributionand the inclusion of interaction terms.

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SOCCER/WORLD FOOTBALL 3

The goal difference Xij − Yij is also impor-tant. It determines whether a game result iswin, tie or loss (W, T, or L) and is used toresolve conflicts when the points are equal.Stefani [26] considers the model

Xij − Yij = η + ρi − ρj + random error

with η the home advantage and ρi the rank-ings. Karlis and Ntzoufras [27] fit the Poissondifference distribution to observed goal differ-ences including a home effect, attacking, anddefensive parameters.

Fahrmeir and Tutz [28] employ a logisticlatent variable-cutpoint setup to model anordinal-valued variable. Their model is

Prob{Yij = r} = F(θr + αi − αj)

−F(θr−1 + αi − αj)

for r = W, T, L,

with F the logistic and αi the ability of team i.In contrast, Brillinger [29–33] employs anextreme value variable-cutpoint approach. Itleads to the model

Prob{ i wins at home playing j}= 1 − exp{− exp{βi + γj + θ2}},

Prob{ i ties at home against j}= exp{− exp{βi + γj + θ2}}

× − exp{− exp{βi + γj + θ1}},Prob{ i loses at home against j}

= exp{− exp{βi + γj + θ1}},

with θ2 >θ1 cutpoints and the standardiza-tions

∑βi,

∑γi = 0. The parameters βi and

γi represent home and away effects of team i.The extreme value distribution employed islonger tailed to the right. The result of thepreceding game and the distances betweenthe cities involved were considered asexplanatories. The βi − γi can be interpretedas the advantage of team i when playingat home. These values were also consideredin Ref. 34. These authors model the goaldifferences as

Xij − Yij = η + αi + βj + random error,

calling the αi and βj ‘‘forces.’’ Least squaresestimation is employed. Including pastresults did not improve things. Goodard [35]fits an ordered probit model, that is, F aboverelates to the normal, with explanatories.

In a linear regression analysis, Panaretos[36] studies the number of points collectedin the course of a double round robin tour-nament and the effect of the explanatoriesgoals scored, goals conceded, and time of ballpossession. The regression model

points = α

+βlog(goals scored/goals conceded)

+ γ ball possession + random noise

is fitted and a proportion of varianceexplained of 0.971 is found.

Barnett and Hilditch [37] study whetherthe field being artificial turf affects the gameresult. They find that the home team’s advan-tage was increased. The use of artificial turfwas abandoned.

Attention now turns to the case wheretime or round, t, plays an essential role inthe modeling. Jochems [16,17] defines, as ameasure of strength of team i at home andj visiting, λij = Wi − Wj, with Wi the averagepoints of team i in its preceding games. Theprediction of the result for team i is

i wins if λij > 0,

i wins if λij = 0 home advantage,

i loses if λij < 0.

Jochem’s study had been commissioned bythe Netherlands Lottery Commission to see ifany skill was involved on the part of tipsters.

The models listed above can be turned intoforecasting procedures by simply adding a t tothe subscripts of the parameters and estimat-ing them by using the data up to time t. Onethen uses the schedule of remaining games todevelop forecasts. For example, Stefani [26]considers the model

Xijt − Yijt = ηijt + ρi − ρj + random error,

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with ρi a rating based on i’s past games andηijt = ±η represents a home advantage. Thequantity ρi represents team i’s ability. The fitis by conditional least squares.

Dixon and Coles [23] employ indepen-dent Poissons and introduce an exponentiallydecaying time function to damp out the effectsof previous rounds. The Poisson means areαi(t)βj(t)η and αj(t)βi(t), respectively. The vari-able t is time or round number and η standsfor home advantage. Estimation is by maxi-mizing the likelihood.

Fahrmeir and Tutz [28] work with a latentvariable-motivated ordinal model,

Prob {Rtij = r} = F(θtr − αti − αtj)

−F(θtr−1 − αti − αtj),

with R the result, r = 0, 1, 2 is a win–tie–lossindicator. Further F is the logistic, and αti arerandom walks in t. The computations involvea Kalman filter and simulation. Rue andSalvesen [24] employ a Bayesian dynamicgeneralised linear model with independentnormals having conditional means given thepast

exp {α + η + γ ti − δt

j − φ(εti − εt

j )},exp {α + γ t

j − δti + φ(εt

i − εtj )},

to predict next weekend’s results. Theyemploy a directed graph to describe thecausal structure of the model as a function oftime.

Brillinger [32,33], for each round, t,uses previous round results. He fits alatent variable-based model and then usessimulation to make projections of the finalpoints and standings of the teams using theknowledge of the remaining games in theschedule. Estimates are then available forfuture rounds.

Harvey and Fernandes [38] study theseries of goals scored by England againstScotland in a biyearly match. In a state spaceapproach, they assume a negative binomialmodel with mean an exponentially decayingfunction of past values.

Within Game Modeling

Next, consider modeling the progress of asingle game. One approach breaks the course

of a game into states corresponding to thezones in the field. Pollard and Reep [39]carry out a logistic regression analysis tomodel the probability of scoring from variouspositions on the field. In a series of papers[40–42], Markov chains with a finite numberof states are employed. Hirotsu and Wright[40] use a four-state model to determine theoptimal timing of substitution and tacticaldecisions. The expected number of points tobe gained from a change in tactics is consid-ered an objective, and dynamic programmingis employed. The model includes transitionrates of scoring and conceding, and ratesof gaining and losing possession. Hirotsuand Wright found evidence for replacing adefender with an attacker when losing.

A common problem is to look for changetaking place. Croucher [43] studied the effectof changing the points awarded. The objectof this change is to generate more attackingplay. Ridder et al. [44] study the effect of ared card in game. They infer that the scoring Q2rate does change after the ejection, and has anegative effect on the team with fewer play-ers. Other studies that deal with the effectare given in Refs 45–47. The latter take apoint process approach. When team i is play-ing team j, the times of goals are modeled byPoisson processes with log rates

νij(t) = λi(t) exp {αj + βzij(t)} and

νji(t) = λj(t) exp {αi + βzji(t)},

respectively, t being time. The function, λi(t),is referred to as the attack intensity for teami and αi as the defense parameter. The zij arethe explanatories

zij1(t) = 1 when rival player off with red

card, 0 otherwise;zij2(t) = 1 if actual score positive;zij3(t) = 1 if actual score negative;

where t is time, β and zij are the 3 vectors.The parameters are estimated using datafrom the 2006 World Cup. The fitted modelmay be employed to generate simulations.Dixon and Robinson [48] also take a point

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process approach, employing a birth process,to model the scoring.

The match video data being collectedthese days may be processed to determinetrajectories of players and the ball. Thenmodels can be developed. Xie et al. [49] takea video of a game, break it into segments,for example, ‘‘play’’ or ‘‘break.’’ They dealwith camera pans and zooms using thegreen grass ratio and motion intensity.Their analysis uses dynamic programmingand spatial-temporal hidden Markov pro-cesses. Min et al. [50] work on the sameproblem making use of rule-based reason-ing, Bayesian inference, simulation, andexpert systems. Palavi et al. [51] developsa graph-based multiplayer detection andtracking system. In the simplest case of anoteable goal scoring movement in one game,Brillinger [31] develops a potential functionapproach to obtain a stochastic model.

Berument et al. [52] look for evidence ofsoccer results affecting the Turkish stockmarket. They do find an effect for one teamas well as a day of the week effect.

Garvia [53] asks, ‘‘Is soccer dying?’’ Heuses a Markov switching model to look fora break in the series of yearly average goalsper game. He finds a drop for England, Italy,and Spain around 1965.

RANKING

Rankings/ratings/seedings are numericalvalues meant to describe the relativeperformances of teams in a league. Theyare used for a variety of specific purposes.One is the preparation of schedules forknock-out tournaments. Another is for themaximization of the probability that the bestcompetitors meet in a tournament’s laterstages. If there are N teams the collectionof ranking values might be the sequenceof integers 1 to N. A famous exampleis the FIFA/Coca-Cola world ranking[www.fifa.com.worldfootball/ranking/procedure/men.html [54]], where the values derivefrom a formula involving major games duringthe previous 4 years, strength of opponent,W–T–L points, and several other items. Itorders the teams of all the countries that are

members of the FIFA and is updated steadilyas more game results become available.

Jochems [16,17] employed the differencesof average game scores and compared this totipsters’ predictions. Hill [55] uses Kendall’stau to compare tipster results with the endof season standings and finds association.Stefani [26] suggests the model

Xij − Yij = η + ρi − ρj + random error,

with the ρi’s rankings. Stefani [56] surveyedthe major world sports rating systems. Bas-sett [57] suggests improving the estimatesby employing a robust estimation methodto handle long tails. Forrest and Simmons[58,59] investigate the predictive quality ofnewspaper tipsters match results. Stefaniand Pollard [60] provide a critical survey ofranking procedures. Gelade and Dobson [61]relate the international standing of a coun-try’s team to various social factors includingnumber playing regularly, wealth, and cli-mate. McHale and Davies [62] focus on theFIFA rankings.

There are papers on ratings for othersports; for example, Refs 63–65.

TOURNAMENTS AND SCHEDULING

Scheduling is a basic step involved whengames need to be organized amongst themembers of a group of teams. Two basictypes of tournament design are the roundrobin and the knock-out. In the round robin,each pair of teams plays against each otherthe same number of times, equally at homeand away. The champion of the group is theteam with the most points at the end of allthe games. In the knock-out case, there isa seeding order and the first round is basedon it. The tournament progresses with twoteams playing in pair setup by the seedingorder and the winner going on to the follow-ing round. This continues until only one teamis left, the champion.

Sometimes there are numerical-valuedobjective functions that can be employedin developing schedules. Their forms caninclude distance traveled, total expenses,numbers of consecutive home or away

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games, and referees’ time. There are oftenconstraints that need to be taken noteof in the scheduling. For example, theremay be multiple venues, television sched-ules, desired dates for two teams fromthe same city. Analytic tools employed inan optimization include integer program-ming, maximization, knapsack algorithms,simulation and stochastic models.

Kuonen [21,66] employs a logistic regres-sion model and shows how output can beused to estimate probabilities of interest for aknock-out tournament. Unlike a round robin,future opponents for the following rounds areonly known probabilistically. Kuonen workswith European Cup Winners Cup data. Heinvestigates three methods for calculatingseeding coefficients based on the data for 3preceding years.

Urban and Russell [67] consider schedul-ing competitions on multiple venues, venuesnot associated with any of the participants.Della Croce and Oliveri [68] present aninteger linear programming approach forscheduling the Italian League. They had todeal with cable TV and with games betweenteams in the same city.

Scheduling the Chilean League has alsoposed special problems. As described in Refs69 and 70, these were dealt with via usingmathematical programming, recognizedexisting weaknesses, stadiums availability,international requirements, and reducingtravel distance.

Objectives may be described probabilisti-cally and then stochastic models are involved.When the goal is to determine a champion,it is natural to ask questions like: what isthe probability that the ‘‘best’’ team actuallywins the tournament, or how much better isthe first team than the second? Appleton [71]provides definitions and reviews many tour-nament structures. He employs simulations.

Scarf et al. [72] provide an extensivereview including discussion of: tournamentmetrics, how the design influences outcomeuncertainty, the use of simulation, robust-ness (to teams dropping out), effects of rulechanges, and probability model employed.

He defines the parameter

PqR = Prob{team in top 100q

pretournament rank percentile progresses};

here R is round achieved and 0 < q < 1. Tounderstand the PqR values, he graphs themagainst q.

It is necessary to schedule the refereesalso. Yavuz et al. [73] provide an extensivereview. The topics covered include leaguesin different countries requiring differentobjective functions and constraints, tensionbetween referees and clubs caused by pastincidents, reducing frequent assignment ofthe same referee to a team’s games. In ama-teur leagues, there may be several gamesthe same day for same referee, perhaps atdifferent places even.

GAME THEORY

The expression ‘‘game theory’’ has both a gen-eral and a technical meaning. The ‘‘technical’’comes from the classic [74] setup. The ‘‘gen-eral’’ refers to others, particularly tactics.Both meanings provide general frameworkswith which to study soccer. A difficulty aris-ing in the theories’ applications to soccer isthat the game is highly dynamic. Jones andTrantner’s [75] book is unusual in that, itstarts by emphasizing the defensive forma-tions. Wilkinson’s [76] book is devoted to thetopic of tactics.

The formation selected would be controlledby the coach. The 2-3-5 was very common formany years. In it, there are two defensive spe-cialists, five attacking, and three midfieldersin between. Newer formations include 3-5-2, 5-4-1, 4-5-1, 4-3-3, and even 4-1-4-1 withan extra row. The formation 4-4-2 is favoredby various famous teams. The two attackerscan drop back to assist in obtaining the ball.When the team has possession of the ball, thetwo outside midfielders can move forward toincrease pressure on the opponent. Wilson[77] provides a review and insightful anal-ysis of many of the formations employed ingames dating from 1878 to 2008.

Pollard and Reep [39] seek to quantify theeffectiveness of different playing strategies.

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They break the action of a game down intodiscrete events, for example, pass, center,shoot. They define the ‘‘yield’’ as the probabil-ity a goal is scored minus the probability oneis conceded. This quantity is used to evaluatethe expected outcome of a team possession.

The book, The Science of Soccer, has achapter on ‘‘game theory’’ [78]. It discusseshow the strength and deployment of the teammoderates the apparent random motion anddiscusses the fact that low scoring benefitsthe weaker team.

One of the momentous occasions in a soc-cer game is the awarding of a penalty shot.There have been a number of formal studies.Greenless et al. [79] study how the penaltytakers’ uniform color and prepenalty gazeaffect the impressions formed by the goal-keeper. When penalties take place to breaka tie, McGarry and Franks [80] identify anoptimal order for a team to take the shots in.Their conclusion is to begin by ranking theplayers 1 (best) to 11 (worst). Then use theorder: 5, 4, 3, 2, 1, and if necessary after that6, 7, 8, 9, 10, and 11. Jordet et al. [81] consid-ers the roles of stress, skill, and fatigue foranswering why the English are poor at penal-ties. He analyzed 200 shots from World Cupand European Championship. In an analysisof many penaltues, Franks et al. [82] learnedthat in 80% of the cases studied, if the non-kicking foot points to the left, the ball willbe shot to the left. They developed a trainingprogram to test this discovery.

Larsen [2] describes the arrival of Reep’sideas in Norway and the success that teamsadopting it enjoyed.

The theory of von Neumann and Morgen-stern provides general definitions and leadsto random strategies. Haigh [83] provides thefollowing intuitive example. The table showsestimated percentages of successful penaltyshots based on 1876 attempts.

KickerGoalie Left Center Right

Left 60 90 93

Center 100 30 100

Right 94 85 60

The situation can be considered is a two-person zero-sum game. If the kicker wins byscoring, the goalie loses. If the goalie winsby saving, the kicker loses. Haigh finds thatNash equilibrium theory leads to the goalie’schosing to move left, center or right withthe respective probabilities of 0.44, 0.13, and0.43. For the kicker, they are 0.37, 0.29, and0.34, respectively. If either player uses theirstrategy, 80% of the shots would be scored inthe long run. This turns out to be close to theactual percentage.

Other references to applications of the for-mal theory include Refs 84–86. Hirotsu andWright [85] consider a zero-sum game focus-ing on who wins the game, while Hirotsu et al.[87] focus on points gained and where one hasa nonzero-sum game. Bennett et al. [88] usehypergame analysis, involving the rankingof various forms of hooligans’ actions andauthorities’ reactions followed by hooligan’sreactions and so on, followed by exploring theimplications of such scenarios.

ECONOMICS AND MANAGEMENT

Reilly and Williams [89] write, ‘‘In the 1980sit became apparent that the football (soccer)industry and professionals in the game couldno longer rely on the traditional methodsof previous decades. Methods of managementscience were applied to organizing the big soc-cer clubs and the training of players could beformulated on a systematic basis.’’ Desbordes[90, Chapter 10] advocates the introductionof modern management tools into soccer. Thismakes sense if for no other reason than thefact that billions of dollars are now involvedin the sport. One does need to remember thatat the youth and amateur levels, the amountof money involved is little. Really, all that isneeded for a game is a ‘‘ball’’ and a field or abeach. This is the charm of the game.

Management refers to a sport’s structure,owners, sponsors, marketers, financiers,schedulers, and others with some form ofcontrol. Management provides the super-structure. The fans expect both their team’splayers and its management to be successfulin acquiring players, providing facilities,and hiring the coach. Management assists

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by supporting the enterprise generally. Itprovides the infrastructure. Other thingsthat management is responsible for includecash inflows–outflows, advertising, man-power planning and hiring, planning newand keeping up old stadiums, and sign-ing players. The stadium owners providefacilities for security, ticket collection, food,souvenirs, and parking. Management studiesthe performance of their players and others[10,91].

Sometimes, there is a numerical-valuedobjective function for the management towork with. Then optimization methods maybe employed to good advantage. Other con-cerns are loss functions, earnings/revenue,prestige/honor, recruitment, salary negotia-tion, scouting, referees, merchandise, com-mercialism, productivity, profitability, travel,and television rights.

There is a common wish to improve indi-vidual player’s and a team’s performance. Anaccompanying question is how to assess per-formance and efficiency. One paper on thetopic for English soccer is Ref. 92. Others areRefs 93 and 94. The latter concerns the Span-ish Soccer League. There have been analyses.Audas et al. [95] study the impact of man-agerial change on team performance usingthe data of English football match resultssince the 1970s, while Partovi and Corre-doira [96] investigate models for prioritizingand designing rule changes.

In a study of competitive balance in theDutch League, Koning [97] employs the val-ues Cij, corresponding to W, T, L, generatedvia

Dij = ϕi − ϕj + εij with the ε’s mean 0,

common variance normals,

Cij = 1 if Dij > c2

= 0 if Dij = 0

= −1 if Dij < c1.

It is used to study changes in competitivebalance in Holland.

A novel application of programming the-ory is presented in Ref. 98. He applies aninteger program to the generalized knapsack

problem to find a ‘‘Dream Team.’’ Player val-ues were established by a public poll withthe participants given a budget of 2.5 milliondollars each. A knapsack algorithm was thenemployed to establish the best team at thelowest price.

Calster et al. [99] study an unwanted hap-pening in soccer, the scoreless draw. Theoccurrence is related to indices of a team’soffensive performance including total goalsand earned points per game.

SOME REMAINING TOPICS

The book, The Inner Game of Soccer, pro-vides details of the game from a referee’sstandpoint [100]. It discusses the laws andthe mechanics and talks of the characteris-tics of the best referees and the ones who canturn benign games into ugly unsportsman-like confrontations.

Reference 78 lays out some of the physicsof soccer. For example, the section titled Q3‘‘Tournaments and Scheduling’’ analyzes themovement of a ball spinning in flight and howplayers can make it bend. Hall [101] elabo-rates on that describing the physical forces atwork in a double banana shot, which curvesin one direction then swerves in another.Such a shot is very difficult for the goalie tohandle.

Sports biomechanics concerns physicalactions that occur in sport that can beobserved and improved, for example, toreduce injuries. The Refs 102 and 103 areon the topic of biomechanics in soccer. Grim-pampi et al. [104] concern computationalbiomechanics. Bradley et al.’s study [105] isa human biology study. It refers to results onhigh-intensity running using data collectedvia an array of television cameras.

There are many articles on employingstochastic models in evaluating bets. Mostof the articles referred above go on to studythe efficiency of various gambling strategies.

What is ahead for the game? Wright [106]writes on 50 years of operations research insport to provide a background. The futureis discussed in Ref. 107 and by the sportswriter Garner [108] in World Soccer. Hesuggests the following changes: bigger goals,

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smaller penalty area, a revised offside rule,fouls denoted contact or technical, red-cardedplayer punished but replacement allowed.Reviewing the literature and practice sug-gest that one can expect to see much more inthe way of the collection and analysis of thespatial-temporal data collected in a game.

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Abstract:

Keywords: association football; efficiency; FIFA; game theory; laws of the game; match anal-

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soccer/world football data collection and … · soccer/world football david r. brillinger...

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