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Comparing Market Efficiency with Traditional and Non-Tradit - PPT Presentation

Dr Adrian Schembri Dr Anthony Bedford Bradley OBree Natalie Bressanutti RMIT Sports Statistics Research Group School of Mathematical and Geospatial Sciences RMIT University Melbourne Australia ID: 143656

2011 rmit statistics sports rmit 2011 sports statistics university

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Slide1

Comparing Market Efficiency with Traditional and Non-Traditional Ratings Systems in ATP Tennis

Dr Adrian Schembri

Dr Anthony Bedford Bradley O’BreeNatalie BressanuttiRMIT Sports Statistics Research GroupSchool of Mathematical andGeospatial SciencesRMIT UniversityMelbourne, Australia

www.rmit.edu.au/sportstatsSlide2

Aims of the Presentation

Structure of ATP tennis, rankings, and tournaments;

Challenges associated with predicting outcomes of tennis matches; Utilising the SPARKS and Elo ratings to predict ATP tennis; Evaluate changes in market efficiency in tennis over the past eight years.RMIT University©2011

RMIT Sports Statistics

2Slide3

Background to ATP Tennis

RMIT Sports Statistics3 ATP: Association of Tennis Professionals; Consists of 65 individual tournaments each year for men playing at the highest level;

Additional:178 tournaments played in the Challenger Tour;

534 tournaments played in Futures tennis.Slide4

ATP Tennis Rankings

RMIT Sports Statistics4 “Used to determine qualification for entry and seeding in all tournaments for both singles and doubles”; The rankings period is always the past 52 weeks prior to the current week.Slide5

ATP Tennis Rankings – Sept 12th, 2011

RMIT Sports Statistics5Slide6

How Predictive are Tennis Rankings? Case Study

RMIT Sports Statistics6Australian Hardcourt Titles January, 1998

Adelaide, Surface – Hardcourt

Lleyton

Hewitt

(AUS)

Andre Agassi (USA)

Age

16 years

27 years

ATP

Ranking

550

86 (6

in Jan, 1999)Slide7

How Predictive are Tennis Rankings? Case Study

RMIT Sports Statistics7Robby Ginepri

Robin Soderling

6 - 4

7 - 5

Age

16 years

27 years

Tourn

Seed

Unseeded

Aircel

Chennai

Open

January 4 - 10, 2010

Chennai, Surface –

HardcourtSlide8

Challenges Associated with Predicting Outcomes in ATP Tennis

RMIT Sports Statistics8 Individual sport and therefore natural variation due to individual differences prior to and during a match; Constant variations in the quality of different players:

Players climbing the rankings; Players dropping in the rankings; Players ranking remaining stagnant.

The importance of different tournaments varies for each individual players.Slide9

Recent Papers on Predicting ATP Tennis and Evaluating Market Efficiency

RMIT Sports Statistics9 Forrest and McHale (2007) reviewed the potential for long-shot bias in men’s tennis; Klaassen and Magnus (2003) developed a probability-based model to evaluate the likelihood of a player winning a match, whilst Easton and Uylangco (2010) extended this to a point-by-point model;

A range of probability-based models are available online, however these are typically volatile and reactive to events such as breaks in serve and each set result (e.g., www.strategicgames.com.au).Slide10

Aims of the Current Paper

Evaluate the efficiency of various tennis betting markets over the past eight years;

Compare the efficiency of these markets with traditional ratings systems such as Elo and a non-traditional ratings system such as SPARKS; Identify where inefficiencies in the market lie and the degree to which this has varied over time.RMIT University©2011

RMIT Sports Statistics

10Slide11

www.rmit.edu.au/sportstats

Elo Ratings and the SPARKS ModelSlide12

Introduction to Ratings Systems

RMIT Sports Statistics

Typically used to:

Monitor the relative ranking of players with other players in the same league;

Identify the probability of each team or player winning their next match.

Have been developed in the context of individual (chess, tennis) or group based sports (e.g., AFL football, NBA);

The initial ratings suggest which player is likely to win, with the difference between their old ratings being used to calculate a new rating after the match is played.Slide13

Introduction to SPARKS

RMIT Sports Statistics

Initially developed by Bedford and Clarke (2000) to provide an alternative to traditional ratings systems;

Differ from Elo-type ratings systems as SPARKS considers the margin of the result;

Has been recently utilised to evaluate other characteristics such as the travel effect in tennis (Bedford et al., 2011).Slide14

Introduction to SPARKS

RMIT Sports Statistics

where

whereSlide15

Introduction to SPARKS

RMIT Sports StatisticsSlide16

SPARKS: Case Study

RMIT Sports Statistics

Robin Soderling (SWE)

Ryan Harrison

(USA)

6-2 6-4

Seeding

Qualifier

Pre-Match Rating

2986.3

978.4

Expected Outcome

20.1

-20.1

Observed Outcome

Win

Loss

SPARKS

SPARKS Difference

-18

Residuals

-2.1

2.1

Post-Match Rating

2975.9

988.8Slide17

Longitudinal Examination of SPARKS

RMIT Sports StatisticsSlide18

Limitations of SPARKS: Case Study

RMIT Sports Statistics

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS (Diff)

Player 1

21 + (3*6)

39 (21)

Player 2

18 + (0*6)

18 (21)

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS

Player 1

21 + (3*6)

39 (21)

Player

12 + (1*6)

18 (21)

+Slide19

Limitations of SPARKS: Case Study

RMIT Sports Statistics

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS (Diff)

Player 1

21 + (3*6)

39 (21)

Player 2

18 + (0*6)

18 (21)

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS

Player 1

21 + (3*6)

39 (21)

Player

12 + (1*6)

18 (21)

Player 2 competitive in all three sets.

+Slide20

Limitations of SPARKS: Case Study

RMIT Sports Statistics

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS (Diff)

Player 1

21 + (3*6)

39 (21)

Player 2

18 + (0*6)

18 (21)

Player

Set 1

Set 2

Set 3

Set 4

Calculation

SPARKS

Player 1

21 + (3*6)

39 (21)

Player

12 + (1*6)

18 (21)

Player 2 competitive in all three sets.

Player 2 competitive in 1 out of 4 sets.Slide21

Historical Results of the SPARKS Model

RMIT Sports Statistics

Year

Win Prediction in

all

ATP Matches

2003

.64

2004

.64

2005

.69

2006

.67

2007

.66

2008

.67

2009

.69

2010

.72

The following table displays historical results of the raw SPARKS model over the past 8 years.

+Slide22

Historical Results of the SPARKS Model

RMIT Sports Statistics

Year

Win Prediction in

all

ATP Matches

2003

.64

2004

.64

2005

.69

2006

.67

2007

.66

2008

.67

2009

.69

2010

.72

The following table displays historical results of the raw SPARKS model over the past 8 years.Slide23

Banding of Probabilities

RMIT Sports Statistics

Lower Band

Upper Band

Midpoint

0.00

0.05

0.025

0.05

0.10

0.075

0.10

0.15

0.125

0.15

0.20

0.175

0.20

0.25

0.225

0.25

0.30

0.275

0.30

0.35

0.325

0.35

0.40

0.375

0.40

0.45

0.425

0.45

0.50

0.475

Probability banding is used primarily to determine whether a models predicted probability of a given result is accurate;

Enables an assessment of whether the probability attributed to a given result is appropriate based on reviewing all results within the band;

For example, if 200 matches within a given tennis season are within the .20 to .25 probability band, then between 20% and 25% (or approx 45 matches) of these matches should be won by the players in question.Slide24

Banding and the SPARKS Model

RMIT Sports Statistics

Lower Band

Upper Band

Midpoint

0.00

0.05

0.025

0.05

0.10

0.075

0.10

0.15

0.125

0.15

0.20

0.175

0.20

0.25

0.225

0.25

0.30

0.275

0.30

0.35

0.325

0.35

0.40

0.375

0.40

0.45

0.425

0.45

0.50

0.475

Lower Band

Upper Band

Midpoint

0.50

0.55

0.525

0.55

0.60

0.575

0.60

0.65

0.625

0.65

0.70

0.675

0.70

0.75

0.725

0.75

0.80

0.775

0.80

0.85

0.825

0.85

0.90

0.875

0.90

0.95

0.925

0.95

1.00

0.975

+Slide25

Banding and the SPARKS Model

RMIT Sports Statistics

Lower Band

Upper Band

Midpoint

0.00

0.05

0.025

0.05

0.10

0.075

0.10

0.15

0.125

0.15

0.20

0.175

0.20

0.25

0.225

0.25

0.30

0.275

0.30

0.35

0.325

0.35

0.40

0.375

0.40

0.45

0.425

0.45

0.50

0.475

Lower Band

Upper Band

Midpoint

0.50

0.55

0.525

0.55

0.60

0.575

0.60

0.65

0.625

0.65

0.70

0.675

0.70

0.75

0.725

0.75

0.80

0.775

0.80

0.85

0.825

0.85

0.90

0.875

0.90

0.95

0.925

0.95

1.00

0.975

Represent the underdog.

Represent the favourite.Slide26

Banding and the SPARKS Model

RMIT Sports StatisticsSlide27

Banding and the SPARKS Model (2003-2010)

RMIT Sports Statistics

+Slide28

Banding and the SPARKS Model (2003-2010)

RMIT Sports Statistics

Under-estimates the probability of the under-dog winning.

Over-estimates the probability of the favorite winning.Slide29

www.rmit.edu.au/sportstats

Elo RatingsSlide30

Introduction to Elo Ratings

RMIT Sports Statistics

Elo ratings system developed by

Árpád

Élő

calculate relative skill levels of chess players

where:

= New rating

= Old rating

O =

Observed Score

E =

Expected Score

= Multiplier

(

for masters, 32 for lesser players

)Slide31

Probability Bands: Elo Ratings

RMIT Sports Statistics

+Slide32

Probability Bands: Elo Ratings

RMIT Sports StatisticsSlide33

RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2010)Slide34

RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2006)

+Slide35

RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2006)

High variability in the majority of probability bands during the burn-in period.Slide36

RMIT Sports Statistics

Probability Bands: Elo Ratings (2007-2010)

+Slide37

RMIT Sports Statistics

Probability Bands: Elo Ratings (2007-2010)Slide38

Advantages and Shortcomings of SPARKS and Elo Ratings

RMIT Sports Statistics

SPARKS considers the margin of the result, often a difficult task in the context of tennis;

Elo is only concerned with whether the player wins or loses, not the margin of victory in terms of the number of games or sets won;

Elo provides a more efficient model in terms of probability banding, suggesting that evaluating the margin of matches may be misleading at times.Slide39

www.rmit.edu.au/sportstats

Market Efficiency of ATP Tennis in

Recent YearsSlide40

ATP Betting Markets Used in the Current Analysis

RMIT Sports Statistics40MarketAbbreviationBet 365

B365LuxbetLB

ExpektEX

Stan JamesSJ

Pinnacle Sports

Elo

ratings

Elo

SPARKS

SPARKSSlide41

Overall Efficiency of Each Market between 2003 and 2010

RMIT Sports Statistics41Market2003

20042005

20062007

2008

2009

2010

Overall

B365

.71

.67

.70

.71

.72

.71

.70

.703

.70

.69

.68

.69

.70

.71

.70

.697

.71

.65

.70

.68

.72

.70

.696

.69

.70

.67

.73

.69

.70

.71

.696

.72

.65

.72

.69

.73

.70

.69

.698

Elo

.59

.62

.66

.65

.70

.66

.68

.67

.654

SPARKS

.63

.64

.69

.67

.66

.60

.69

.72

.667

Overall

.68

.66

.69

.68

.71

.68

.70

.69

+Slide42

Overall Efficiency of Each Market between 2003 and 2010

RMIT Sports Statistics42Market2003

20042005

20062007

2008

2009

2010

Overall

B365

.71

.67

.70

.71

.72

.71

.70

.703

.70

.69

.68

.69

.70

.71

.70

.697

.71

.65

.70

.68

.72

.70

.696

.69

.70

.67

.73

.69

.70

.71

.696

.72

.65

.72

.69

.73

.70

.69

.698

Elo

.59

.62

.66

.65

.70

.66

.68

.67

.654

SPARKS

.63

.64

.69

.67

.66

.60

.69

.72

.667

Overall

.68

.66

.69

.68

.71

.68

.70

.69Slide43

Overall Efficiency of Each Market between 2003 and 2010

RMIT Sports Statistics43+Slide44

Overall Efficiency of Each Market between 2003 and 2010

RMIT Sports Statistics44

Heightened stability and efficiency across markets and seasons since 2008.Slide45

Converting Market Odds into a Probability

RMIT Sports Statistics45Novak DjokovicRafael Nadal

Match Odds$1.63

$2.25Conversion1/1.63

1/2.25Probability of Winning

.61

.44

2011 US Open FinalSlide46

Accounting for the Over-Round

RMIT Sports Statistics46 The sum of the probability-odds in any given sporting contest typically exceeds 1, to allow for the bookmaker to make a profit; The amount that this probability exceeds 1 is referred to as the over-round;

For example, if the sum of probabilities for a given match is equal to 1.084, the over-round is equal to .084 or 8.4%Slide47

Accounting for the Over-Round

RMIT Sports Statistics47Novak DjokovicRafael Nadal

Match Odds$1.63

$2.25Conversion1/1.63

1/2.25Probability of Winning

.61

.44

Sum of Probabilities

1.05

Over-Round

2011 US Open Final

6 – 2 6 – 4 6 – 7 6 – 1 Slide48

Comparison of Over-Round Across Markets

RMIT Sports Statistics48+Slide49

Comparison of Over-Round Across Markets

RMIT Sports Statistics49Kruskal-Wallis test with follow-up Mann-Whitney U tests:Significant difference between all betting markets aside from Pinnacle Sports and Stan James.Slide50

Over-Round for Bet 365 (2003-2010)

RMIT Sports Statistics50Slide51

Accounting for the Over-Round: Normalised Probabilities and Equal Distribution

RMIT Sports Statistics51Novak Djokovic

Rafael NadalMatch Odds$1.63

$2.25

Raw Probability of Winning.61

.44

Over-round

.05

Normalisation

.61/1.05

.44/1.05

Normalised Probability of Winning

.58

.42

Equal Distribution

.61 – (.05/2)

.44 – (.05/2)

Equalised Probability of Winning

.585

.415

+Slide52

Accounting for the Over-Round: Normalised Probabilities and Equal Distribution

RMIT Sports Statistics52Novak Djokovic

Rafael NadalMatch Odds$1.63

$2.25

Raw Probability of Winning.61

.44

Over-round

.05

Normalisation

.61/1.05

.44/1.05

Normalised Probability of Winning

.58

.42

Equal Distribution

.61 – (.05/2)

.44 – (.05/2)

Equalised Probability of Winning

.585

.415Slide53

Accounting for the Over-Round: Normalised Probabilities and Equal Distribution

RMIT Sports Statistics53Roger FedererBernard Tomic

Match Odds$1.07$6.60

Raw Probability of Winning

.93

.15

Over-round

.08

Normalisation

.93/1.08

.15/1.08

Normalised Probability of Winning

.86

.14

Equal Distribution

.93 – (.08/2)

.15 – (.08/2)

Equalised Probability of Winning

.89

.11

+Slide54

Accounting for the Over-Round: Normalised Probabilities and Equal Distribution

RMIT Sports Statistics54Roger FedererBernard Tomic

Match Odds$1.07$6.60

Raw Probability of Winning

.93

.15

Over-round

.08

Normalisation

.93/1.08

.15/1.08

Normalised Probability of Winning

.86

.14

Equal Distribution

.93 – (.08/2)

.15 – (.08/2)

Equalised Probability of Winning

.89

.11Slide55

Market Efficiency in ATP Tennis

RMIT Sports Statistics55+Slide56

Market Efficiency in ATP Tennis

RMIT Sports Statistics56

SPARKS significantly less efficient when compared with the betting markets for all bands aside from .50 - .55.Slide57

Market Efficiency in ATP Tennis - Raw

RMIT Sports Statistics57+Slide58

Market Efficiency in ATP Tennis - Raw

RMIT Sports Statistics58

General inefficiency across bands, likely due to no correction for the over-round.Slide59

Market Efficiency in ATP Tennis - Normalised

RMIT Sports Statistics59Slide60

Market Efficiency in ATP Tennis – Equal Diff

RMIT Sports Statistics60+Slide61

Market Efficiency in ATP Tennis – Equal Diff

RMIT Sports Statistics61

Relative consistency in efficiency and variability within each band across markets.

+Slide62

Market Efficiency in ATP Tennis – Equal Diff

RMIT Sports Statistics62

Evidence of

longshot

bias for the .25 to .30 band.Slide63

Market Efficiency in ATP Tennis: Bet365

RMIT Sports Statistics63+Slide64

Market Efficiency in ATP Tennis: Bet365

RMIT Sports Statistics64Slide65

Longitudinal Changes in Market Efficiency

RMIT Sports Statistics65+Slide66

Longitudinal Changes in Market Efficiency

RMIT Sports Statistics66

Few significant differences emerged when comparing efficiency across the bands over the past 8 years.

Homogeneity of variance tests revealed significantly less variability across markets in recent years. Slide67

Most Efficient Year: 2007

RMIT Sports Statistics67+Slide68

Most Efficient Year: 2007

RMIT Sports Statistics68Slide69

Least Efficient Year: 2004

RMIT Sports Statistics69+Slide70

Least Efficient Year: 2004

RMIT Sports Statistics70Slide71

www.rmit.edu.au/sportstats

Discussion of FindingsSlide72

Psychological Player Considerations

RMIT Sports Statistics72 Form of an individual player will affect the context and potential outcome of the entire match, as opposed to a team-based sport where individual players have less impact or can be substituted off if out of form.

Micro-events within a match, at times, have an impact on the outcome of the match. Examples: Rain delays

Injury Time outs Code violationsSlide73

Shortcomings of the Current Analysis

RMIT Sports Statistics73 A set multiplier of ‘6’ was used for the SPARKS model based on the original SPARKS model published in 2000; Only a limited number of betting markets were incorporated, and therefore it was not possible to utilise Betfair

data into the analysis; Differences in market efficiency and inefficiency were not evaluated at the surface level. This would be particularly interesting if evaluated for clay, given the volatility of player performance on clay when compared with other surfaces.Slide74

Future Work

74 Optimise the set multiplier of the SPARKS model; Develop a model that combines SPARKS and Elo ratings;

Extend the current findings to incorporate women’s tennis given that evidence has shown greater volatility in the women’s game.

Incorporate data on other potential predictors of tennis outcomes. Examples include: The set sequence of the match

Surface Importance of the tournament (e.g., Grand slams)Slide75

Conclusions

75 Whilst considerable variability was evident during the 2003 – 2007 seasons, an increase in consistency across markets since 2008. Following a lengthy burn-in period of four years, the Elo model outperformed SPARKS and most betting markets across the majority of probability bands;

Whilst not efficient in terms of probability banding, the SPARKS model was able to predict an equivalent proportion of winners to the betting markets, and outperformed some markets in recent years;

A model that combines both Elo and SPARKS may yield the most efficient model.Slide76

Questions and Comments

RMIT Sports Statistics76Slide77