Comparing Market Efficiency with Traditional and Non-Traditional Ratings Systems in ATP Tennis Dr Adrian Schembri Dr Anthony Bedford Bradley O’Bree Natalie Bressanutti RMIT Sports Statistics Research Group School of Mathematical and Geospatial Sciences RMIT University Melbourne, Australia www.rmit.edu.au/sportstats

RMIT Sports Statistics 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

RMIT Sports Statistics Background to ATP Tennis 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. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics ATP Tennis Rankings “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. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics ATP Tennis Rankings – Sept 12th, 2011 RMIT University©2011 RMIT Sports Statistics

Australian Hardcourt Titles Adelaide, Surface – Hardcourt How Predictive are Tennis Rankings? Case Study 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) RMIT University©2011 RMIT Sports Statistics

Chennai, Surface – Hardcourt How Predictive are Tennis Rankings? Case Study Aircel Chennai Open January 4 - 10, 2010 Chennai, Surface – Hardcourt Robby Ginepri Robin Soderling 6 - 4 7 - 5 Age 16 years 27 years Tourn Seed Unseeded 1 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Challenges Associated with Predicting Outcomes in ATP Tennis 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. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Recent Papers on Predicting ATP Tennis and Evaluating Market Efficiency 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). RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics 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

Elo Ratings and the SPARKS Model www.rmit.edu.au/sportstats

Introduction to Ratings Systems 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. Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Introduction to SPARKS 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). Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Introduction to SPARKS where Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Introduction to SPARKS Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics SPARKS: Case Study Robin Soderling (SWE) Ryan Harrison (USA) 6-2 6-4 Seeding 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 Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Longitudinal Examination of SPARKS Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Limitations of SPARKS: Case Study Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff) Player 1 7 21 + (3*6) 39 (21) Player 2 6 18 + (0*6) 18 (21) SPARKS 3 2 12 + (1*6) Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Limitations of SPARKS: Case Study Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff) Player 1 7 21 + (3*6) 39 (21) Player 2 6 18 + (0*6) 18 (21) SPARKS 3 2 12 + (1*6) Player 2 competitive in all three sets. Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Limitations of SPARKS: Case Study Player Set 1 Set 2 Set 3 Set 4 Calculation SPARKS (Diff) Player 1 7 21 + (3*6) 39 (21) Player 2 6 18 + (0*6) 18 (21) SPARKS 3 2 12 + (1*6) Player 2 competitive in all three sets. Change these to suit the current paper Player 2 competitive in 1 out of 4 sets. RMIT University©2011 RMIT Sports Statistics

Historical Results of the SPARKS Model The following table displays historical results of the raw SPARKS model over the past 8 years. Year Win Prediction in all ATP Matches 2003 .64 2004 2005 .69 2006 .67 2007 .66 2008 2009 2010 .72 Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Historical Results of the SPARKS Model The following table displays historical results of the raw SPARKS model over the past 8 years. Year Win Prediction in all ATP Matches 2003 .64 2004 2005 .69 2006 .67 2007 .66 2008 2009 2010 .72 Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Banding of Probabilities 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. Lower Band Upper Band Midpoint 0.00 0.05 0.025 0.10 0.075 0.15 0.125 0.20 0.175 0.25 0.225 0.30 0.275 0.35 0.325 0.40 0.375 0.45 0.425 0.50 0.475 Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Banding and the SPARKS Model Lower Band Upper Band Midpoint 0.00 0.05 0.025 0.10 0.075 0.15 0.125 0.20 0.175 0.25 0.225 0.30 0.275 0.35 0.325 0.40 0.375 0.45 0.425 0.50 0.475 Lower Band Upper Band Midpoint 0.50 0.55 0.525 0.60 0.575 0.65 0.625 0.70 0.675 0.75 0.725 0.80 0.775 0.85 0.825 0.90 0.875 0.95 0.925 1.00 0.975 Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Banding and the SPARKS Model Lower Band Upper Band Midpoint 0.00 0.05 0.025 0.10 0.075 0.15 0.125 0.20 0.175 0.25 0.225 0.30 0.275 0.35 0.325 0.40 0.375 0.45 0.425 0.50 0.475 Lower Band Upper Band Midpoint 0.50 0.55 0.525 0.60 0.575 0.65 0.625 0.70 0.675 0.75 0.725 0.80 0.775 0.85 0.825 0.90 0.875 0.95 0.925 1.00 0.975 Change these to suit the current paper Represent the underdog. Represent the favourite. RMIT University©2011 RMIT Sports Statistics

Banding and the SPARKS Model Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Banding and the SPARKS Model (2003-2010) Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Banding and the SPARKS Model (2003-2010) Over-estimates the probability of the favorite winning. Under-estimates the probability of the under-dog winning. Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Elo Ratings www.rmit.edu.au/sportstats

Introduction to Elo Ratings Elo ratings system developed by Árpád Élő to calculate relative skill levels of chess players where: RN = New rating RO = Old rating O = Observed Score E = Expected Score W = Multiplier (16 for masters, 32 for lesser players) Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2010) Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2006) Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings (2003-2006) High variability in the majority of probability bands during the burn-in period. Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings (2007-2010) Change these to suit the current paper + RMIT University©2011 RMIT Sports Statistics

Probability Bands: Elo Ratings (2007-2010) Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Advantages and Shortcomings of SPARKS and Elo Ratings 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. Change these to suit the current paper RMIT University©2011 RMIT Sports Statistics

Market Efficiency of ATP Tennis in Recent Years www.rmit.edu.au/sportstats

RMIT Sports Statistics ATP Betting Markets Used in the Current Analysis Market Abbreviation Bet 365 B365 Luxbet LB Expekt EX Stan James SJ Pinnacle Sports PS Elo ratings Elo SPARKS RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Overall Efficiency of Each Market between 2003 and 2010 Market 2003 2004 2005 2006 2007 2008 2009 2010 Overall B365 .71 .67 .70 .72 .703 LB .69 .68 .697 PS .65 .696 SJ .73 EX .698 Elo .59 .62 .66 .654 SPARKS .63 .64 .60 .667 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Overall Efficiency of Each Market between 2003 and 2010 Market 2003 2004 2005 2006 2007 2008 2009 2010 Overall B365 .71 .67 .70 .72 .703 LB .69 .68 .697 PS .65 .696 SJ .73 EX .698 Elo .59 .62 .66 .654 SPARKS .63 .64 .60 .667 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Overall Efficiency of Each Market between 2003 and 2010 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Overall Efficiency of Each Market between 2003 and 2010 Heightened stability and efficiency across markets and seasons since 2008. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Converting Market Odds into a Probability 2011 US Open Final Novak Djokovic Rafael Nadal Match Odds $1.63 $2.25 Conversion 1/1.63 1/2.25 Probability of Winning .61 .44 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round 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% RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round 2011 US Open Final 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% 6 – 2 6 – 4 6 – 7 6 – 1 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Comparison of Over-Round Across Markets + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Comparison of Over-Round Across Markets Kruskal-Wallis test with follow-up Mann-Whitney U tests: Significant difference between all betting markets aside from Pinnacle Sports and Stan James. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Over-Round for Bet 365 (2003-2010) RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round: Normalised Probabilities and Equal Distribution Novak Djokovic Rafael Nadal Match 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 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round: Normalised Probabilities and Equal Distribution Novak Djokovic Rafael Nadal Match 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 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round: Normalised Probabilities and Equal Distribution Roger Federer Bernard 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 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Accounting for the Over-Round: Normalised Probabilities and Equal Distribution Roger Federer Bernard 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 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis SPARKS significantly less efficient when compared with the betting markets for all bands aside from .50 - .55. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis - Raw + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis - Raw General inefficiency across bands, likely due to no correction for the over-round. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis - Normalised RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis – Equal Diff + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis – Equal Diff Relative consistency in efficiency and variability within each band across markets. + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis – Equal Diff Evidence of longshot bias for the .25 to .30 band. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis: Bet365 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Market Efficiency in ATP Tennis: Bet365 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Longitudinal Changes in Market Efficiency + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Longitudinal Changes in Market Efficiency Homogeneity of variance tests revealed significantly less variability across markets in recent years. Few significant differences emerged when comparing efficiency across the bands over the past 8 years. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Most Efficient Year: 2007 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Most Efficient Year: 2007 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Least Efficient Year: 2004 + RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Least Efficient Year: 2004 RMIT University©2011 RMIT Sports Statistics

Discussion of Findings www.rmit.edu.au/sportstats

RMIT Sports Statistics Psychological Player Considerations 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 RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Shortcomings of the Current Analysis 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. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Future Work 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) RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Conclusions 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. RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics Questions and Comments RMIT University©2011 RMIT Sports Statistics

RMIT Sports Statistics RMIT University©2011 RMIT Sports Statistics