Notational Analysisa Math Perspective

7/31/2019 Notational Analysisa Math Perspective

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ModellingModelling FeedbackFeedback

AnalysisAnalysis

ImprovementImprovement

ObservationObservation

PerformancePerformance

Notational analysisNotational analysis a mathematicala mathematical

perspectiveperspective

Mike Hughes, Benn Blackburn and Nic James


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7th Australasian Conference on Mathematics7th Australasian Conference on Mathematicsand Computers in Sportand Computers in Sport

Linear relationships in data gathering and feedback

Research

Data

Performance

Analyst

Coach/Athlete


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The role of the performance analyst using early analogue video

and computer systems

Performance Analyst

DATA

Coach/Athlete

DATA DATA

Motor ControlNotational AnalystBiomechanist

Motor ControlNotational AnalystBiomechanist

Gathering

systems

Gathering

systems

Gathering

systems

Processing

systems

Processing

systems

Processing

systems


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A digital systems approach to the data sharing that the interactive commercial

systems have enabled for performance analysts working with coaches and athletes

(apologies to Popper).

Coach

Athletes

Motor

Control

Notational

Analyst

Coach

Athletes

Biomechanist

Performance

Data

Coach

Athletes

Performance Analysis Team


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ANALYST

The answer to the mystery of the universe?


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ANALYST

PERFORMANCE

INDICATORS


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Performance IndicatorsPerformance Indicators


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IntroductionIntroduction

Performance Indicators arePerformance Indicators are

a selection or combination ofa selection or combination of

action variable(s) that aim toaction variable(s) that aim todefine some aspect, or all, ofdefine some aspect, or all, of

a performance.a performance.

hat are:-

ERFORMANCE INDICATORS?

Hughes and Bartlett, 2002)


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IntroductionIntroduction

Performance Indicators are usedPerformance Indicators are used

to assess performance eitherto assess performance either

comparatively, with previouscomparatively, with previous

performances, or absolutely.performances, or absolutely.

Why use:Why use:--

PERFORMANCE INDICATORS?PERFORMANCE INDICATORS?


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Notational AnalysisNotational Analysis -- Performance IndicatorsPerformance Indicators

CRICKETCRICKET : Strike rate, Dismissal rate, Fielding Efficiency: Strike rate, Dismissal rate, Fielding Efficiency

Examples:Examples:--

SOCCERSOCCER : Shots, Passes, Passing Accuracy: Shots, Passes, Passing Accuracy

RUGBYRUGBY : Turnovers, Tackles, Passes/Possession: Turnovers, Tackles, Passes/Possession

BADMINTONBADMINTON : W/E ratio, shots/rally, Quality serve/return: W/E ratio, shots/rally, Quality serve/return


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Performance Indicators?Performance Indicators?

How do we choose the performance indicators?


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Definition of Success:Definition of Success:--

It could be defined byIt could be defined by

winning (scoring more goalswinning (scoring more goals

than the opposition) but itthan the opposition) but it

may not.may not.


Or a coach may be lookingOr a coach may be looking

for a qualitative improvementfor a qualitative improvement

in performancein performance -- whichwhich

could be assessed by acould be assessed by a

performance indicator.performance indicator.


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Definition of Success:Definition of Success:--

Success then is relativeSuccess then is relative --

either to your opposition,either to your opposition,

racket sportsracket sports --

more winners; less errors,more winners; less errors,

invasive gamesinvasive games --

more points or goals than themore points or goals than theoppositionopposition


or to previousor to previous

performancesperformances

of your own team, orof your own team, or

individual player,individual player,

or to aggregated meansor to aggregated means

of peer performancesof peer performances


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POSITIVE or NEGATIVEPOSITIVE or NEGATIVE

Types of Performance Indicators:Types of Performance Indicators:--

SCORING :SCORING : Goals etc., W, E, W/E, Goals/Shots, DismissalGoals etc., W, E, W/E, Goals/Shots, Dismissal

rate, etc.rate, etc.

QUALITY :QUALITY : Turnovers, Tackles, Passes/Possession,Turnovers, Tackles, Passes/Possession,shots/rally, Strike rate, etc.shots/rally, Strike rate, etc.


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Dangers of Performance Indicators:Dangers of Performance Indicators:--

In other areas of science,In other areas of science,

performance indicatorsperformance indicators

tend to be ratios oftend to be ratios of

variables, orvariables, or

combinations ofcombinations of

variables, that thenvariables, that then

render the final P.I.render the final P.I.dimensionless:dimensionless:--


=density=density

Reynolds No. =Reynolds No. = UdUd U=velocityU=velocity

=viscosity=viscosity

d=size of objectd=size of object

E.g.E.g.

In aerodynamics,In aerodynamics,

Mach No. =Mach No. = Velocity of aircraftVelocity of aircraft

Velocity of soundVelocity of sound

In fluid dynamics,In fluid dynamics,


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MMaattcchh

CCllaassssiiffiiccaattiioonn

TTeecchhnniiccaall TTaaccttiiccaall

Performance IndicatorsPerformance Indicators -- GENERICGENERIC

Data for bothData for both

teamsteams (T(TVV))NN/ (T/ (TVV)TOTAL)TOTAL

Means of peerMeans of peer

performancesperformances

oror

(T(TVV))NN/ (/ (POSSPOSSnn)) TOTALTOTAL


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Dangers of Performance Indicators:Dangers of Performance Indicators:--

Performance Indicators should bePerformance Indicators should be normalisednormalised oror

standardisedstandardised in some way to the respectivein some way to the respective

performance variables, and should also be usedperformance variables, and should also be used

comparatively with either your opponentscomparatively with either your opponents data,data,

previous data of your own performances, orprevious data of your own performances, or

with aggregated data of performances of yourwith aggregated data of performances of your

own level.own level.



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To differentiate between important dataTo differentiate between important data

and DIRTY WASHING:and DIRTY WASHING:--

*Choose parameters*Choose parameters

that relate strongly tothat relate strongly to

outcome or quality ofoutcome or quality of

performance.performance.


*What are the units of your*What are the units of your

Performance Indicator?Performance Indicator?

*Can these be related to*Can these be related to

other variables or previouslyother variables or previously

calculated means?calculated means?

*Are there ways of*Are there ways of

combining variables incombining variables in

a group that will saya group that will say

more about thismore about this

performance?performance?


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Dangers of Performance Indicators:-

A single action variable, taken in isolation, can givedistorted impression of a performance because of other

variables, more or less important.

E.g. TEAM A: 12 Turnovers; TEAM B: 8 Turnovers

TEAM B playing better than TEAM A?


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TEAM B playing better than TEAM A?


E.g. TEAM A: 12 Turnovers; TEAM B: 8 Turnovers

This will depend upon the possession of both the teams

- if TEAM A have had twice as many possessions (48) as

TEAM B (24) then their relative performance w.r.t.TURNOVERS/POSSESSION (T/P)

will be better than that of TEAM B

(T/P)A = 1/4; (T/P)B = 1/3

Notational Analysis - Performance Indicators


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Let us consider a more complex example

One of the most quoted

research studies in

notation is that of

Reep and Benjamin (1968).


Most frightening is the

effect that this study

has had on British soccer

and its coaching.


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They found:-

80% of goals resulted from

a sequence of three passes or

less,

60% of all goals came from

possession gained in the final

attacking third of the pitch,and

a goal is scored every 10

shots (approximately).


Hughes, C. (1985,1990)

reinforced these ideas and,

as he was the Director of

coaching for the English

Football Association (F.A.),

his influence in the game

was considerable. So much

so, that these tenets were

included in the coaching

literature produced by the F.A.


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Patterns of goal scoring with respect to the different

lengths of possessions in the 1990 and 1994 world cups

for soccer.


0

5

10

15

20

25

30

35

Goals

0 1 2 3 4 5 6 7 8 >

Touches/Possession

1990

1994


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Frequency of each possession string in the two

tournaments.


0100020003000

400050006000700080009000

Frequency

0 1 2 3 4 5 6 7 8 >

Touches/Possession

1990

1994


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Analysis of the number of goals scored

per 1000 possessions for the 2 world cups.


0

2

4

6

8

10

1214

0 1 2 3 4 5 6 7 8 >

Touches/Possession

(G/P)*1000

1990

1994

Mean


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Frequency of shots per 1000 possessions

for the 1990 and 1994 World Cups.


0

20

40

60

80

100

120140

0 1 2 3 4 5 6 7 8 >

Touches/Possession

(S/P)*1000

1990

1994

Mean


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They found:-

80% of goals resulted from

a sequence of three passes or

less,

60% of all goals came from

possession gained in the final

attacking third of the pitch,and

a goal is scored every 10

shots (approximately).


NOT

SO

SIMPLE


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7th Australasian Conference on Mathematics7th Australasian Conference on Mathematics

and Computers in Sportand Computers in Sport

ANALYST

PERFORMANCE

INDICATORS


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ANALYST

PERFORMANCE

INDICATORS

WHICH ARE

MOST

IMPORTANT?


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Multivariate StatisticsMultivariate Statistics

Multiple Linear RegressionMultiple Linear Regression

Discriminant Function AnalysisDiscriminant Function Analysis

Binary Logistic RegressionBinary Logistic Regression


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Multiple Linear RegressionMultiple Linear Regression

Linear Regression produces an equation inLinear Regression produces an equation inthe formthe form Y = a + b.XY = a + b.X

Multiple Linear Regression produces anMultiple Linear Regression produces anequation in the formequation in the form

Y = bY = b00 + b+ b11.X.X11 + b+ b22.X.X22 + b+ b33.X.X33 ++ ++ bbnn.X.Xnn By using databases from tournaments,By using databases from tournaments,

European Championships, WorldEuropean Championships, WorldChampionships, etc., we can assess theChampionships, etc., we can assess therelative importance of the PIrelative importance of the PIs selected. Thats selected. Thatis we are predicting Y (a known outcome)is we are predicting Y (a known outcome)using several PIusing several PIss -- XX11 toto XXnn


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Assumptions of MLRAssumptions of MLR

((NtoumanisNtoumanis, 2001), 2001) Ratio of cases to independent (X) variables should be atRatio of cases to independent (X) variables should be at

least 5 : 1 and ideally 20 : 1least 5 : 1 and ideally 20 : 1

All outliers should be excluded or transformedAll outliers should be excluded or transformed Save standardised residuals and explore theseSave standardised residuals and explore these

ResidualsResiduals

Should be normally distributedShould be normally distributed There should be no relationship between anyThere should be no relationship between any

independent (X) variables and residualsindependent (X) variables and residuals

There should be no relationship between residuals andThere should be no relationship between residuals andpredicted valuespredicted values which can be savedwhich can be saved

Any relationship between the residuals and dependentAny relationship between the residuals and dependent(Y) variable should be linear(Y) variable should be linear

The residuals should be independent,The residuals should be independent, ieie no relationshipno relationshipbetween order of observation (timebetween order of observation (time--order) and residualorder) and residual


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ANALYST

PERFORMANCE

INDICATORS

WHICH ARE

MOST

IMPORTANT?


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ANALYST

PERFORMANCE

INDICATORS

PERFORMANCERELIABILITYWHICH ARE

MOST

IMPORTANT?


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ReliabilityReliability

A guide to some ideas about

some of the issues and problems

associated with reliability.

Analysis procedures for non-parametric data from performance analysis

MIKE HUGHES, STEVE-MARK COOPER AND ALAN NEVILL

(2001, eIJPAS, 2)


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ANALYST

PERFORMANCE

INDICATORS


MOST

IMPORTANT?


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ANALYST

PERFORMANCE

INDICATORS


MOST

IMPORTANT?

HOW MUCH

DATA?

PERFORMANCE

PROFILE


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ANALYST

PERFORMANCE

INDICATORS

PERFORMANCERELIABILITY

WHICH ARE

MOST

IMPORTANT?

HOW MUCH

DATA?

EMPIRICALMETHODS

PERFORMANCE

PROFILE


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Normative Profiles

Some examples of sample sizes for profiling in sport.

Research

Reep & Benjamin (1969)

Eniseler et al., (2000)

Larsen et al., (2000)

Hughes et al., (1988)

Tyryaky et al., (2000)

Hughes (1986)

Hughes & Knight (1993)

Hughes & Williams (1987)

Smyth et al., (2001)

Blomqvist et al., (1998)

O'Donoghue (2001)

Hughes & Clarke (1995)

O'Donoghue & Ingram (2001)

SportSoccer

Soccer

Soccer

Soccer

SoccerSquash

Squash

Rugby Union

Rugby Union

Badminton

Badminton

Tennis

Tennis

N(matches for profile)

3,216

4

4

8 (16 teams)

4 and 3 (2 groups)12, 9 & 6 3 groups

400 rallies

5

5 and 5

5

16, 17, 17, 16, 15

400 rallies

1328


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Performance ProfilesPerformance profiling of an elite male badminton player (Hughes, Evans and Wells, 2001)Search for a normative profile

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of a data set

Cumulative

meanofdatavalue

Series1


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Performance ProfilesPerformance profiling of an elite male badminton player

The cumulative means of each variable were examined over a series of

matches/games.At the first point, the number of matches, N(E), where the cumulative mean

consistently lay within set limits of error was recorded as the establishment of a

normative template of play. These limits of error are a percentage deviation (+/- 1%;

+/- 5%; +/- 10%) of the overall data mean about the overall mean.

Let n = the variable number of matchesg = the variable number of games

N(E) = value of n to reach limits of error

N(T) = total number of matches

Cumulative mean = (Sum of the frequencies of n) / n

Limits of error (10%) = Mean N(T) (Mean N(T) x 0.1)




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Performance ProfilesStudy 2:- Performance profiling of an elite male badminton player

M e a n n u m b e r o f s h o t s p e r r a l l y b y m a t c h

4 . 0

5 . 0

6 . 0

7 . 0

8 . 0

9 . 0

1 0 . 0

1 1 . 0

1 2 3 4 5 6 7 8 9 1 1 1

N u m b e r o f m a t c h e s

C u m u l a t i v e m e a n P l u s 1 0 %

L e s s 1 0 % P l u s 5 %

l e s s 5 %


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Performance ProfilesStudy 2:- Performance profiling of an elite male badminton playerF i g u r e 4 . 5 M e a n n u mb e r o f s h o t s b y g a me

300.0

350.0

400.0

450.0

500.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Number of games

Cumulative mean '+10% '-10% '+5% '-5% '+1% '-1%


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European

0.00

25.00

50.00

75.00

100.00

125.00150.00

175.00

200.00

225.00

250.00

275.00

300.00

325.00

350.00375.00

400.00

425.00

450.00

475.00

500.00

525.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Number of matches

Meanscore

Pass

Runs

Dribbles

Crosses

Header

Shots

Number of matches needed to achieve a normative profile for attacking variables for

European teams


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ANALYST

PERFORMANCE

INDICATORS

PERFORMANCERELIABILITY WHICH ARE

MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICALMETHODS

PERFORMANCE

PROFILE


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ANALYST

PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICALMETHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE


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James et al. (2004, JSS, in press)James et al. (2004, JSS, in press)

James et al. (2004) suggested an alternative approach whereby thJames et al. (2004) suggested an alternative approach whereby thee

specific estimates of population means are calculated from thespecific estimates of population means are calculated from thesample data through confidence limits (CLsample data through confidence limits (CLs).s).

CLCLs represent upper and lower values between which thes represent upper and lower values between which thetrue (population) mean is likely to fall based on the observedtrue (population) mean is likely to fall based on the observedvalues collected.values collected.

Calculated CLCalculated CLs naturally change as more data is collected,s naturally change as more data is collected,typically resulting in the confidence interval (CItypically resulting in the confidence interval (CI -- upper CLupper CL

minus lower CL) decreasing.minus lower CL) decreasing.

Confidence intervals (CIConfidence intervals (CIs) were therefore suggested to bes) were therefore suggested to bemore appropriate as performance guides compared to usingmore appropriate as performance guides compared to using

mean values.mean values. Using a fixed value appears to be too constrained due toUsing a fixed value appears to be too constrained due to

potential confounding variables that typically affectpotential confounding variables that typically affectperformance, making prescriptive targets untenable.performance, making prescriptive targets untenable.


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James et al. (2004, JSS, in press)James et al. (2004, JSS, in press)

From a theoretical perspective, James et al. argued that theFrom a theoretical perspective, James et al. argued that theuse of CIuse of CIs can also add significance to the judgement of thes can also add significance to the judgement of thepredictive potential of a data set, i.e. whether enough data haspredictive potential of a data set, i.e. whether enough data has

been collected to allow a reasonable estimation.been collected to allow a reasonable estimation.

For their investigation a criterion was formulated to test theFor their investigation a criterion was formulated to test therate of change of the CI for stability.rate of change of the CI for stability.

Initially 95% CIInitially 95% CIs were calculated for each performances were calculated for each performanceindicator as soon as enough match data had been collected (indicator as soon as enough match data had been collected (NN= 2) and each time more data was added the new CI was= 2) and each time more data was added the new CI wascalculated.calculated.

This meant that CIThis meant that CIs could be constructed for eachs could be constructed for eachperformance indicator after 2, 3 andperformance indicator after 2, 3 and..NNmatchesmatchesrespectively.respectively.


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ANALYST

PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICALMETHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE


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ANALYST

PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICALMETHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES


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Comparing profilesComparing profiles

Many research papers have used parametric tests in the past thesehave been found to be slightly less sensitive than the non-parametric

tests, and they did not respond to large differences within the data.

The results of performance analysis are very often recorded asdiscrete events. Clearly, investigating categorical differences in

discrete data using traditional parametric tests of significance (e.g.

ANOVA, based on the continuous symmetric normal distribution) is

inappropriate.

More appropriate statistical methods are promoted based on twokey discrete probability distributions, the Poisson and binomial

distributions.

Nevill, A., Atkinson, G., Hughes, M. and Cooper, S-M. (2002).

Journal of Sports Science, 20, 829 - 844.


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When carrying out tests of significance on continuous data using

regression and analysis of variance (ANOVA), the observed randomvariation is assumed to have a normal distribution.

Clearly, the frequency distribution of discrete events, such as thenumber of shots per rally in tennis or squash, do not follow a normal

distribution.

For example, the frequency distribution of shots per rally of an elitesquash player over a three-game match (total number of rallies = 104)

is discrete, positively skewed and not normally distributed.

Two key distributions for such discrete data are the Poisson andbinomial distributions.


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Two approaches are proposed and compared using examples

from notational analysis:-

The first approach is based on the classic chi-square test of

significance (both the goodness-of-fit test and the test ofindependence).

The second approach adopts a more contemporary method

based on log-linear and logit models fitted using the statisticalsoftware GLIM.


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Comparing profilesComparing profilesProvided relatively simple one-way and two-waycomparisons in categorical data are required, both of these

approaches result in very similar conclusions.

However, as soon as more complex models or higher-ordercomparisons are required, the approach based on log-linear and

logit models is shown to be more effective.

Indeed, when investigating those factors and categoricaldifferences associated with binomial or binary response

variables, such as the proportion of winners when attemptingdecisive shots in squash or the proportion of goals scored from

all shots in association football, logit models become the only

realistic method available.


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FurtherFurther ?? WeWe needneed teststests ofofdifferencedifference

thatthat areare farfar moremore sensitivesensitive..

TheThe winnerwinner ofofthethe womenwomenss

400m400m OlympicOlympic GoldGold inin

SydneySydney performedperformed 11 -- 2%2%

betterbetter thanthan thethe personperson whowho

waswas 8th8th -- oneone isis aa millionairemillionaire

-- thethe otherother??


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ANALYST

PERFORMANCE

INDICATORS

PERFORMANCE

RELIABILITY WHICH ARE

MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICAL

METHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES


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ANALYST

PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICAL

METHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES

MODELLING

PERFORMANCE


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Empirical ModellingEmpirical Modelling

Stochastic ModellingStochastic Modelling

PerturbationsPerturbations

Artificial IntelligenceArtificial Intelligence

Expert SystemsExpert Systems

Neural NetworksNeural Networks

Modelling


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M d lliM d lli P b bilitP b bilit


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ModellingModelling -- ProbabilityProbability

Sport and Chance

Reep and Benjamin (1968)

Ladany and Machol (1977)

Alexander et al (1988)

McGarry and Franks (1996)

Stochastic Modelling



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Stoc ast c ode gg

Problems:-

too few data

antecedent shot is a naive predictor of the

next shot to be selected

memory-limiting nature of stochastic(Markov) processes, where the future is

predicted only from the present, might be an

insufficient descriptor of sports behaviours



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gg

Problems:-

Sports analysts have tended to record all the

data from a sports contest and to search thosedata for patterns. Implicit in this method of

analysis are two assumptions.

The first assumption is that if the data areto have information value then they are

likely to be repeated under similar future

circumstances.

The second assumption is that the data

are of equal importance, at least in the long

run.



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World Congress of Notational Analysis of Sport,Burton Manor, 1992

Downey talked of rhythms in badminton rackets, co-

operation, until there was a dislocation of therhythm a perturbation sometimes

resulting in a rally end situation ( a critical

incident), sometimes not.



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Harmonic Motion

Fig. 3.1. A schematic example of Simple Harmonic Motion (SHM) from

Weinstein (2004).



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Figure 1.2. Distance Time Graph for Pilot study 1

0

2

4

6

8

10

12

14

0.0 1.0 2.0 4.0 5.2 7.2 8.4 9.6 11.0 13.0 14.2 15.4 17.0

Time (s)

Server Receiver

Distance (m) Rally 21

0

1

2

3

4

5

6

00:14:13:01

00:14:21:12

00:14:29:23

00:14:38:09

00:14:46:20

00:14:55:06

00:15:03:17

00:15:12:03

00:15:20:14

00:15:29:00

00:15:37:11

00:15:45:22

00:15:54:08

00:16:02:19

00:16:11:05

Time (s)

D

istance(m)

Series1



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If we study a system only in the linear range of its

operation where change is smooth, its difficult if not

impossible to determine which variables are essential andwhich are not.

Most scientists know about nonlinearity and usually try

to avoid it.

Here we exploit qualitative change, a nonlinear

instability, to identify collective variables, the implication

being that because these variables change abruptly, it is

likely that they are also the key variables when the systemoperates in the linear range.

Scott Kelso, 1999



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SQUASH

McGarry, Khan & Franks, 1999

SOCCER

Hughes, Dawkins, Davids & Mills, 1998


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Artificial IntelligenceArtificial Intelligence

- Roger Bartlett

.and Jurgen Perl!

The Decision Making Scope of AIThe Decision Making Scope of AI


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g pg p

Expert systems :Expert systems :

RuleRule--based.based.

Fuzzy.Fuzzy.

FrameFrame--based.based.

Artificial neural networks :Artificial neural networks :

Biological and artificial neural networks.Biological and artificial neural networks.

TheThe PerceptronPerceptron..

MultiMulti--layer neural networks.layer neural networks.

Recurrent neural networks.Recurrent neural networks.

SelfSelf--organising neural networks.organising neural networks.

Expert SystemsExpert Systems


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AdvantagesAdvantages


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Separate knowledge from processing, unlike conventionalSeparate knowledge from processing, unlike conventional

programs.programs.

Provide an explanation facility.Provide an explanation facility.

Can deal with incomplete and vague data.Can deal with incomplete and vague data.

Can model fuzzy human decisionCan model fuzzy human decision--making.making.

Are good for diagnosis.Are good for diagnosis.

ShellsShells for development of expert systems are widelyfor development of expert systems are widely

available (e.g. addavailable (e.g. add--ons to MATLAB).ons to MATLAB).

DisadvantagesDisadvantages


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gg

Need to acquire knowledge from experts; this is a majorNeed to acquire knowledge from experts; this is a majorproblem.problem.

Very domainVery domain--specific; fast bowling one could not be used forspecific; fast bowling one could not be used forjavelin throwing.javelin throwing.

Opaque relationships between rules.Opaque relationships between rules.

In general, do not have an ability toIn general, do not have an ability to learnlearn..

Have to manage conflicts between rules.Have to manage conflicts between rules.

Ineffective rules searchingIneffective rules searching trawl through all rules in eachtrawl through all rules in each

cycle.cycle.

Expert SystemsExpert Systems -- Performance AnalysisPerformance Analysis


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Given that they are good diagnostic tools and thatGiven that they are good diagnostic tools and that

systemsystem shellsshells easily available, how widespread is theeasily available, how widespread is the

use of them in PA?use of them in PA?

Not very!Not very!

The reality conflicts with the positive view of theirThe reality conflicts with the positive view of their

utility byutility by LaphamLapham and Bartlett in 1995and Bartlett in 1995(3)(3)..

Artificial Neural NetworksArtificial Neural Networks


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Allow computers to learn from experience and byAllow computers to learn from experience and by

anologyanology(1)(1)..

A computer program that tries to create a mathematicalA computer program that tries to create a mathematical

model of neurons in the brainmodel of neurons in the brain(2)(2)..

An interconnection of simple adaptable processingAn interconnection of simple adaptable processing

elements or nodeselements or nodes(2)(2)::

Nodes simplified models of brain neurons.Nodes simplified models of brain neurons.

Store experiential knowledge as pattern of connectedStore experiential knowledge as pattern of connected

nodes and synaptic weightings between them.nodes and synaptic weightings between them.

NonNon--linear programs that represent nonlinear programs that represent non--linear systems,linear systems,such as the human movement system and games.such as the human movement system and games.

Originally developed to exploit the power of parallelOriginally developed to exploit the power of parallel

processing, now mostly PC based.processing, now mostly PC based.

AdvantagesAdvantages


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Learn by experience; in the case of selfLearn by experience; in the case of self--organisingorganising ANNsANNs,,

without a teacher!without a teacher!

Are good for classification, clustering and predictionAre good for classification, clustering and prediction

tasks.tasks.

Can be adapted for inexact or incomplete data throughCan be adapted for inexact or incomplete data through

fuzzyfuzzy ANNsANNs..

Are widely available, e.g. the MATLAB Neural NetworkAre widely available, e.g. the MATLAB Neural NetworkToolbox, and relatively simple programs.Toolbox, and relatively simple programs.

Seem to mimic brain processes.Seem to mimic brain processes.

Provide link to dynamic systems theory as nonProvide link to dynamic systems theory as non--linearlinearprogram representations of nonprogram representations of non--linear biological systems.linear biological systems.

DisadvantagesDisadvantages


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They are opaqueThey are opaque black boxesblack boxes with no explanation of thewith no explanation of the

reasoning process.reasoning process.

TheThe rulesrules within the nonwithin the non--linear network are not welllinear network are not well

understood; the nonunderstood; the non--linear characteristics may prohibitlinear characteristics may prohibitsimple and understandable rulessimple and understandable rules(1)(1)..

To validate their output, they need test cases for whichTo validate their output, they need test cases for which

output is known.output is known.

They often do not work well for inputs outside the rangeThey often do not work well for inputs outside the range

used for learning.used for learning.

Back propagation is very slow, although widely used forBack propagation is very slow, although widely used for

pattern recognition.pattern recognition.

KohonenKohonen SOMsSOMs need lots of learning data and aren'tneed lots of learning data and aren't

dynamic.dynamic.

ANNS in Performance AnalysisANNS in Performance Analysis


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As their main function is for classification,As their main function is for classification,

clustering and prediction, and that they are nowclustering and prediction, and that they are now

easily available (but only recently)easily available (but only recently) -- howhow

widespread is their use in PA?widespread is their use in PA?

NOT VERYNOT VERY

They have been used in PA, both in techniqueThey have been used in PA, both in technique

analysis and notational analysis, and in otheranalysis and notational analysis, and in otherbranches of sport and exercise science.branches of sport and exercise science.

ANALYST


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PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICAL

METHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES

MODELLING

PERFORMANCE

ANALYST


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PERFORMANCE

INDICATORS


MOSTIMPORTANT?

HOW MUCH

DATA?

EMPIRICAL

METHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES

MODELLING

PERFORMANCE

PREDICTION


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Performance PredictionPerformance Prediction

Multiple Linear RegressionMultiple Linear RegressionDiscriminant Function AnalysisDiscriminant Function Analysis

Binary Logistic RegressionBinary Logistic Regression

Neural NetworkNeural Network

ExampleExample 2003 Rugby World Cup2003 Rugby World CupPeterPeter O'DonoghueO'Donoghue and Jason Williamsand Jason Williams


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Individual Human PredictionsIndividual Human Predictions

Expert focus groupExpert focus group

MLRMLR

BLRBLR

ANNANN

Simulation packageSimulation package



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Points difference between higher and lower ranked teamsPoints difference between higher and lower ranked teamsis the Y variableis the Y variable

The X variables areThe X variables are

Difference in ranking pointsDifference in ranking points

Difference in distance travelled to tournamentDifference in distance travelled to tournament

Difference in recovery days since last matchDifference in recovery days since last match

Used 137 cases from 1987 to 1999 to do the linearUsed 137 cases from 1987 to 1999 to do the linear

regression model in SPSSregression model in SPSS

Used 40 group matches to see predictions in ExcelUsed 40 group matches to see predictions in Excel



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Rugby union is an easier sport than soccer to predict theRugby union is an easier sport than soccer to predict theoutcome for because there is a greater amount of scoring inoutcome for because there is a greater amount of scoring inrugby union and currently less strength in depth in therugby union and currently less strength in depth in the

international game.international game. The most successful machine based method was theThe most successful machine based method was the

simulation package which produced a prediction thatsimulation package which produced a prediction thatrecognised the effect of combined conditional probabilitiesrecognised the effect of combined conditional probabilities

on the overall outcome of the tournament.on the overall outcome of the tournament. Quantitative and computerQuantitative and computer--based prediction methods werebased prediction methods were

more successful at predicting the results of the 2003 Rugbymore successful at predicting the results of the 2003 RugbyWorld Cup than most of the predictions made byWorld Cup than most of the predictions made by

individual humans which were based on qualitativeindividual humans which were based on qualitativeanalysis.analysis.

However, the expert focus group demonstrated thatHowever, the expert focus group demonstrated thathuman expertise still exceeds that of machine basedhuman expertise still exceeds that of machine based

methods.methods.

ANALYST


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Discriminate between PIs

Performance Indicators?

Predictive Profiling Methods?Comparing data

Modelling?Prediction?

Reliability

Empirical Profiling

PERFORMANCE

INDICATORS


MOST

IMPORTANT?

HOW MUCH

DATA?

EMPIRICAL

METHODS

PREDICTION

FROM

VARIANCE

PERFORMANCE

PROFILE COMPARING

PROFILES

MODELLING

PERFORMANCE

PREDICTION


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ANALYST

The answer to the mystery of the universe?


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ANALYST

42?To get the correct answers youhave to ask the right questions.


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International Society of Performance Analysis of Sport

Mike HughesInternational Society of Computers in Sport Science

Jurgen Perl

E-Journals-

International Journal ofPerformance Analysis of Sport

International Journal ofComputers in Sport Science

[email protected]

Notational analysisNotational analysis a mathematical perspective.a mathematical perspective.


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Mike Hughes,Mike Hughes,

Centre for Performance Analysis,Centre for Performance Analysis,

University of Wales Institute Cardiff.University of Wales Institute Cardiff.

THANKS for your attention.THANKS for your attention.

PP


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PapersPapers

Hughes, M.D. (2004). Performance AnalysisHughes, M.D. (2004). Performance Analysis

a mathematical perspective.a mathematical perspective. EIJPAS,EIJPAS,International Journal of PerformanceInternational Journal of PerformanceAnalysis Sport (Electronic)Analysis Sport (Electronic),, 44, 2, 97, 2, 97 --

139.139.

Hughes, M.D. and Bartlett, R.(2002). TheHughes, M.D. and Bartlett, R.(2002). Theuse of performance indicators inuse of performance indicators inperformance analysis.performance analysis. Journal of SportsJournal of SportsScience 20,Science 20, 739739 754.754.

Documents

Notational Analysisa Math Perspective