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Comparing Market Efficiency with Traditional and Non-Traditional Ratings Systems in ATP Tennis
Dr Adrian Schembri Dr Anthony Bedford Bradley O’BreeNatalie Bressanutti
RMIT Sports Statistics Research GroupSchool of Mathematical andGeospatial SciencesRMIT UniversityMelbourne, Australia
www.rmit.edu.au/sportstats
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 2
Background to ATP Tennis
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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.
ATP Tennis Rankings
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“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.
ATP Tennis Rankings – Sept 12th, 2011
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How Predictive are Tennis Rankings? Case Study
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Australian Hardcourt Titles January, 1998
Adelaide, Surface – Hardcourt
Lleyton Hewitt (AUS) Andre Agassi (USA)
Age 16 years 27 years
ATP Ranking 550 86 (6th in Jan, 1999)
How Predictive are Tennis Rankings? Case Study
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Robby Ginepri Robin Soderling
6 - 4 7 - 5Age 16 years 27 years
Tourn Seed Unseeded 1
Aircel Chennai OpenJanuary 4 - 10, 2010
Chennai, Surface – Hardcourt
Challenges Associated with Predicting Outcomes in ATP Tennis
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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.
Recent Papers on Predicting ATP Tennis and Evaluating Market Efficiency
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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).
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 10
www.rmit.edu.au/sportstats
Elo Ratings and the SPARKS
Model
Introduction to Ratings Systems
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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.
Introduction to SPARKS
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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).
Introduction to SPARKS
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• where
• where
Introduction to SPARKS
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oldoldppoldnew
oldoldppoldnew
PPSSPP
PPSSPP
where
ts
winsxf
processonOptimisati
1212
2121
10022
10011
.10000
.1000
.100
..
)(max
SPARKS: Case Study
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Robin Soderling (SWE) Ryan Harrison (USA)
6-2 6-4Seeding 1 Qualifier
Pre-Match Rating 2986.3 978.4
Expected Outcome 20.1 -20.1
Observed Outcome Win Loss
SPARKS 24 6
SPARKS Difference 18 -18
Residuals -2.1 2.1
Post-Match Rating 2975.9 988.8
Longitudinal Examination of SPARKS
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0
500
1000
1500
2000
2500
3000
3500
4000
4500
13000 18000 23000 28000 33000 38000 43000
Limitations of SPARKS: Case Study
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Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff)
Player 1 7 7 7 21 + (3*6) 39 (21)
Player 2 6 6 6 18 + (0*6) 18 (21)
Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS
Player 1 6 3 6 6 21 + (3*6) 39 (21)
Player 2 2 6 2 2 12 + (1*6) 18 (21)
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Limitations of SPARKS: Case Study
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Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff)
Player 1 7 7 7 21 + (3*6) 39 (21)
Player 2 6 6 6 18 + (0*6) 18 (21)
Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS
Player 1 6 3 6 6 21 + (3*6) 39 (21)
Player 2 2 6 2 2 12 + (1*6) 18 (21)
Player 2 competitive in all three sets.
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Limitations of SPARKS: Case Study
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Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff)
Player 1 7 7 7 21 + (3*6) 39 (21)
Player 2 6 6 6 18 + (0*6) 18 (21)
Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS
Player 1 6 3 6 6 21 + (3*6) 39 (21)
Player 2 2 6 2 2 12 + (1*6) 18 (21)
Player 2 competitive in all three sets.
Player 2 competitive in 1 out of 4 sets.
Historical Results of the SPARKS Model
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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.
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Historical Results of the SPARKS Model
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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.
Banding of Probabilities
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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.
Banding and the SPARKS Model
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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
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Banding and the SPARKS Model
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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.
Banding and the SPARKS Model
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Banding and the SPARKS Model (2003-2010)
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Banding and the SPARKS Model (2003-2010)
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Under-estimates the probability of the under-dog winning.
Over-estimates the probability of the favorite winning.
www.rmit.edu.au/sportstats
Elo Ratings
Introduction to Elo Ratings
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Elo ratings system developed by Árpád Élő to calculate relative skill levels of chess players
EOWRR ON
400/)(101
1BA RRE
5.0
0
1
Owhere: RN = New rating
RO = Old ratingO = Observed ScoreE = Expected ScoreW = Multiplier (16 for masters, 32 for lesser
players)
Probability Bands: Elo Ratings
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Probability Bands: Elo Ratings
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Probability Bands: Elo Ratings (2003-2010)
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Probability Bands: Elo Ratings (2003-2006)
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Probability Bands: Elo Ratings (2003-2006)
High variability in the majority of probability bands during the burn-in period.
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Probability Bands: Elo Ratings (2007-2010)
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Probability Bands: Elo Ratings (2007-2010)
Advantages and Shortcomings of SPARKS and Elo Ratings
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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.
www.rmit.edu.au/sportstats
Market Efficiency of ATP Tennis in Recent Years
ATP Betting Markets Used in the Current Analysis
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Market Abbreviation
Bet 365 B365
Luxbet LB
Expekt EX
Stan James SJ
Pinnacle Sports PS
Elo ratings Elo
SPARKS SPARKS
Overall Efficiency of Each Market between 2003 and 2010
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Market 2003 2004 2005 2006 2007 2008 2009 2010 Overall
B365 .71 .67 .70 .71 .72 .71 .70 .70 .703
LB .70 .69 .68 .69 .70 .71 .70 .70 .697
PS .71 .65 .70 .68 .72 .70 .70 .70 .696
SJ .69 .69 .70 .67 .73 .69 .70 .71 .696
EX .72 .65 .72 .69 .73 .70 .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 .70 .69
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Overall Efficiency of Each Market between 2003 and 2010
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Market 2003 2004 2005 2006 2007 2008 2009 2010 Overall
B365 .71 .67 .70 .71 .72 .71 .70 .70 .703
LB .70 .69 .68 .69 .70 .71 .70 .70 .697
PS .71 .65 .70 .68 .72 .70 .70 .70 .696
SJ .69 .69 .70 .67 .73 .69 .70 .71 .696
EX .72 .65 .72 .69 .73 .70 .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 .70 .69
Overall Efficiency of Each Market between 2003 and 2010
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Overall Efficiency of Each Market between 2003 and 2010
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Heightened stability and efficiency across markets and seasons since 2008.
Converting Market Odds into a Probability
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Novak Djokovic Rafael Nadal
Match Odds $1.63 $2.25
Conversion 1/1.63 1/2.25
Probability of Winning .61 .44
2011 US Open Final
Accounting for the Over-Round
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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%
Accounting for the Over-Round
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Novak Djokovic Rafael Nadal
Match Odds $1.63 $2.25
Conversion 1/1.63 1/2.25
Probability of Winning .61 .44
Sum of Probabilities 1.05
Over-Round 5%
2011 US Open Final
6 – 2 6 – 4 6 – 7 6 – 1
Comparison of Over-Round Across Markets
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Comparison of Over-Round Across Markets
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Kruskal-Wallis test with follow-up Mann-Whitney U tests:Significant difference between all betting markets aside from Pinnacle Sports and Stan James.
Over-Round for Bet 365 (2003-2010)
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Accounting for the Over-Round: Normalised Probabilities and Equal Distribution
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Novak Djokovic Rafael Nadal
Match Odds $1.63 $2.25
Raw Probability of Winning .61 .44
Over-round .05 .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
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Accounting for the Over-Round: Normalised Probabilities and Equal Distribution
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Novak Djokovic Rafael Nadal
Match Odds $1.63 $2.25
Raw Probability of Winning .61 .44
Over-round .05 .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
Accounting for the Over-Round: Normalised Probabilities and Equal Distribution
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Roger Federer Bernard Tomic
Match Odds $1.07 $6.60
Raw Probability of Winning .93 .15
Over-round .08 .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
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Accounting for the Over-Round: Normalised Probabilities and Equal Distribution
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Roger Federer Bernard Tomic
Match Odds $1.07 $6.60
Raw Probability of Winning .93 .15
Over-round .08 .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
Market Efficiency in ATP Tennis
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Market Efficiency in ATP Tennis
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SPARKS significantly less efficient when compared with the betting markets for all bands aside from .50 - .55.
Market Efficiency in ATP Tennis - Raw
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Market Efficiency in ATP Tennis - Raw
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General inefficiency across bands, likely due to no correction for the over-round.
Market Efficiency in ATP Tennis - Normalised
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Market Efficiency in ATP Tennis – Equal Diff
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Market Efficiency in ATP Tennis – Equal Diff
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Relative consistency in efficiency and variability within each band across markets.
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Market Efficiency in ATP Tennis – Equal Diff
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Evidence of longshot bias for the .25 to .30 band.
Market Efficiency in ATP Tennis: Bet365
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Market Efficiency in ATP Tennis: Bet365
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Longitudinal Changes in Market Efficiency
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Longitudinal Changes in Market Efficiency
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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.
Most Efficient Year: 2007
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Most Efficient Year: 2007
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Least Efficient Year: 2004
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Least Efficient Year: 2004
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www.rmit.edu.au/sportstats
Discussion of Findings
Psychological Player Considerations
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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 violations
Shortcomings of the Current Analysis
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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.
Future Work
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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)
Conclusions
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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.
Questions and Comments
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