Scoring probability model based on service landing location and ranking points in men’s professional tennis matches MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Fumiya SHIMIZU, *Eiji KONAKA (Meijo University)

Today’s presentation Shimizu and Konaka. “Scoring probability model based on service landing location and ranking points in men’s professional tennis matches” MathSportInternational Conference 2023@Budapest ⚫Background ⚫Objective ⚫Data collection ⚫Hawk-Eye, Data in official website ⚫ATP Ranking ⚫Model construction ⚫Method ⚫Result and discussion ⚫Web implementation MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Background: Service in tennis ⚫Service shot in tennis ⚫All plays begin with service ⚫Only shot without being influenced by opponent. ⚫Server has clear advantage. ⚫Served shot should land on service area MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.photo-ac.com/ Question: ”Where is advantageous service landing location?”

Rule of service in tennis ⚫Service is shot from outside the baseline. ⚫Directly land the service on the service area once ⚫Deuce side (green) ⚫Ad side (blue) ⚫Alternate Deuce/Ad sides. ⚫Second chance ⚫1st/2nd service MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST (Based on [ITF RULES OF TENNIS 2022], edited by the authors)

(Area definition in the following slides) ⚫In the following slides, the service area (red box) will be depicted. ⚫Left, green: Deuce side ⚫Right, blue: Ad side MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST (Based on [ITF RULES OF TENNIS 2022], edited by the authors)

Background: Mathematical modeling of service in tennis PREVIOUS STUDIES ⚫Visualization of the boundary line of the advantageous/disadvantageous area of the service landing location [2020] ⚫Separation line is calculated by using Support Vector Machine (SVM) MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Near the sideline is advantageous

Background: Mathematical modeling of service in tennis PREVIOUS STUDIES AND THEIR LIMITATION ⚫Visualization of the boundary line of the advantageous/disadvantageous area of the service landing location [2020] ⚫Prediction model of ace by using k-nearest neighbor(NN) method. [Whiteside et al, 2017] ⚫Prediction model from service/stroke landing location sequence. Court is partitioned into large rectangles.[Born et al, 2021] MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Background: Previous studies and their limitation (summary) Input Input resolution Objective Output tyｐe [2020] Service landing location Continuous (Hawk- Eye) Prediction Advantageous or not (Binary, SVM) [Whiteside et al, 2017] Service impact and landing location, speed, score, … Continuous (Hawk- Eye) Prediction Ace or not (Binary, k-NN) [Born et al, 2021] Service to 4th stroke landing locations Partitioned Analysis between player level (WTA/ITF) - MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Background: Previous studies and their limitation (summary) Input Input resolution Objective Output tyｐe [2020] Service landing location Continuous (Hawk- Eye) Prediction Advantageous or not (Binary, SVM) [Whiteside et al, 2017] Service impact and landing location, speed, score, … Continuous (Hawk- Eye) Prediction Ace or not (Binary, k-NN) [Born et al, 2021] Service to 4th stroke landing locations Partitioned Analysis between player level (WTA/ITF) - MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Red text: limitation of each method Blue text: advance of each method

Proposed method: Overcome limitations of previous studies Input Input resolution Objective Output tyｐe [Shimizu and Konaka, 2023] Service landing location, player strength Continuous (Hawk- Eye) Prediction Score probability (Continuous, GLM) [2020] Service landing location Continuous (Hawk- Eye) Prediction Advantageous or not (Binary, SVM) [Whiteside et al, 2017] Service impact and landing location, speed, score, … Continuous (Hawk- Eye) Prediction Ace or not (Binary, k-NN) [Born et al, 2021] Service to 4th stroke landing locations Partitioned Analysis between player level (WTA/ITF) - MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Proposed method: Overcome limitations of previous studies Input Input resolution Objective Output tyｐe [Shimizu and Konaka, 2023] Service landing location, player strength Continuous (Hawk- Eye) Prediction Score probability (Continuous, GLM) [2020] Service landing location Continuous (Hawk- Eye) Prediction Advantageous or not (Binary, SVM) [Whiteside et al, 2017] Service impact and landing location, speed, score, … Continuous (Hawk- Eye) Prediction Ace or not (Binary, k-NN) [Born et al, 2021] Service to 4th stroke landing locations Partitioned Analysis between player level (WTA/ITF) - MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Player strength is used High-resolution Hawk-Eye data is used Output continuous score probability

Objective of proposed method OBJECTIVE ⚫Construct a mathematical prediction model of scoring in tennis ⚫Input variables ⚫Service landing location ⚫Player strength metric ⚫Method: Generalized Linear Model Regression PROS OF PROPOSED METHOD MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Large amount, high-resolution Hawk- Eye data ⚫Over 100,000 services. ⚫Four models: Deuce/Ad sides, 1st /2nd services ⚫Continuous probability output ⚫Web-based implementation

Today’s presentation Shimizu and Konaka. “Scoring probability model based on service landing location and ranking points in men’s professional tennis matches” MathSportInternational Conference 2023@Budapest ⚫Background✓ ⚫Objective✓ ⚫Data collection ⚫Hawk-Eye, Data in official website ⚫ATP Ranking ⚫Model construction ⚫Method ⚫Result and discussion ⚫Web implementation MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

About ATP / Hawk-Eye system ATP ⚫Association of Tennis Professionals ⚫Official governing body of men’s professional tennis ⚫Management of data acquisition system (Hawk-Eye) and collected data publication ⚫Management of official ranking point system Hawk-Eye ⚫Measure three-dimensional trajectory of ball using multiple camera ⚫Support of umpires ⚫“Challenge” system ⚫Many ATP Tour tournaments accepts the system MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

About ATP / Hawk-Eye system Hawk-Eye ⚫Measure three-dimensional trajectory of ball using multiple camera ⚫Support of umpires ⚫“Challenge” system ⚫Many ATP Tour tournaments accepts the system MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Y.Baodong, “Hawkeye technology using tennis match,” (2014)

About ATP / Hawk-Eye system Hawk-Eye ⚫Measure three-dimensional trajectory of ball using multiple camera ⚫Support of umpires ⚫“Challenge” system ⚫Many ATP Tour tournaments accepts the system MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.sony.com/ja/SonyInfo/technology/stories/Hawk-Eye/

Data publication on official website MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.atptour.com/en/stats/second-screen/archive/2019/339/MS003

Data publication on official website MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.atptour.com/en/stats/second-screen/archive/2019/339/MS003 Relation between service landing location and its point have been published (NOT all tournaments)

ATP Ranking ⚫Official world ranking of men’s professional tennis players ⚫Based on the tournament final standings of the latest 52 weeks ⚫One Win→Awarded point multiplies 5/3 to 2 times ⚫Top players should participate in mandatory tournaments MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.atptour.com/en/rankings/singles?ra nkRange=0-100&rankDate=2023-05-29

Strength difference measured by ATP Ranking ⚫Axes: Ranking point ratio (horizontal), Win probability (vertical) ⚫ATP ranking is good strength metric ⚫Predicted win probability=Logistic regression whose variable is logarithm of ranking point ratio. ⚫Ex. 6815/(6815+3100)=0.687 MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Strength difference =Log of ranking point ratio

Today’s presentation Shimizu and Konaka. “Scoring probability model based on service landing location and ranking points in men’s professional tennis matches” MathSportInternational Conference 2023@Budapest ⚫Background✓ ⚫Objective✓ ⚫Data collection ✓ ⚫Hawk-Eye, Data in official website ✓ ⚫ATP Ranking ✓ ⚫Model construction ⚫Method ⚫Result and discussion ⚫Web implementation MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Service scoring probability model: Data COLLECTED DATA ⚫ATP Tour, 2019, 30 Tournaments, 897 Matches, 111473 Services ⚫Deta definition ⚫位置 ⚫得点 ⚫サーバー，レシーバー名 ⚫ランキングポイント ⚫Data distribution (right figure) MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST Variable Meaning 𝑠, 𝑟 Index of server and receiver 𝑥, 𝑦 Service landing location 𝑃𝑠 , 𝑃𝑟 ATP Ranking point 𝑡 Score (1:Server, 0:Receiver)

Service scoring probability model: Data DATA ANALYSIS MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Service shots landed more around the sideline/centerline ⚫Different distribution between Deuce and Ad sides ⚫Biased dominant arm. Right:Left=167：21 ⚫Few shots landed on the front side (near the net)

Service scoring probability model: Data DATA ANALYSIS MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Service shots landed more around the sideline/centerline✓ ⚫Different distribution between Deuce and Ad sides ⚫Biased dominant arm. Right:Left=167：21 ⚫Few shots landed on the front side (near the net)

Service scoring probability model: Data DATA ANALYSIS MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Service shots landed more around the sideline/centerline ✓ ⚫Different distribution between Deuce and Ad sides ✓ ⚫Unbalanced dominant arm. Right:Left=167：21 ⚫Few shots landed on the front side (near the net)

Service scoring probability model: Data DATA ANALYSIS MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Service shots landed more around the sideline/centerline ✓ ⚫Different distribution between Deuce and Ad sides ✓ ⚫Unbalanced dominant arm. Right:Left=167：21 ⚫Few shots landed on the front side (near the net) ✓

Service scoring probability model: Stepwise regression ⚫Preprocess ⚫Each service shot→(𝑥, 𝑦, 𝑃𝑠 , 𝑃𝑟 , 𝑡) ⚫𝐿𝑠,𝑟 ≡ log 𝑃𝑠 𝑃𝑟 ⚫Predictor variables:(𝑥, 𝑦, 𝐿𝑠,𝑟 ) ⚫Response variable :𝑡 ∈ {0,1} ⚫Add dummy data on the front side ⚫Method: Stepwise regression ⚫Predictor terms: 4th polynomial ⚫Link function: logit ⚫Use stepwiseglm in MATLAB ⚫Four models (1st/2nd , Ad/Deuce) are constructed. MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST 𝑡~ 1 1 + exp(−𝑋) 𝑋: (Up to) 4th order polynomial of predictor variables

Today’s presentation Shimizu and Konaka. “Scoring probability model based on service landing location and ranking points in men’s professional tennis matches” MathSportInternational Conference 2023@Budapest ⚫Background✓ ⚫Objective✓ ⚫Data collection ✓ ⚫Hawk-Eye, Data in official website ✓ ⚫ATP Ranking ✓ ⚫Model construction ✓ ⚫Method ✓ ⚫Result and discussion ⚫Web implementation MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result 1ST/DEUCE SIDE ⚫ 𝑥1 , 𝑥2 , 𝑥3 = 𝑥, 𝑦, 𝐿𝑠,𝑟 ⚫Stepwise regression ⚫Add/remove term based on p-value MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Asymmetric ⚫Advantageous on sidelines ⚫Advantageous area protrudes from outside to inside ⚫Disadvantageous on service line

Result: 1st service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Asymmetric✓ ⚫Advantageous on sidelines ⚫Advantageous area protrudes from outside to inside ⚫Disadvantageous on service line

Result: 1st service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Asymmetric ✓ ⚫Advantageous on sidelines ✓ ⚫Advantageous area protrudes from outside to inside ⚫Disadvantageous on service line

Result: 1st service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Asymmetric ✓ ⚫Advantageous on sidelines ✓ ⚫Advantageous area protrudes from outside to inside ✓ ⚫Disadvantageous on service line

Result: 2nd service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Almost symmetric ⚫Decreased scoring probability ← Reduced service speed ⚫Disadvantageous on service line

Result: 2nd service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Almost symmetric ✓ ⚫Decreased scoring probability ← Reduced service speed ⚫Disadvantageous on service line

Result: 2nd service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Almost symmetric ✓ ⚫Decreased scoring probability ← Reduced service speed ⚫Disadvantageous on service line

Result: 2nd service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Almost symmetric ✓ ⚫Decreased scoring probability ← Reduced service speed ✓ ⚫Disadvantageous on service line

Result: 1st /Deuce side/Not equal strength ⚫In case Ranking Point Ratio =5 ⚫Server is higher-ranked ⚫On sidelines, less difference ⚫Large difference near center service line MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫In case Ranking Point Ratio =5 ⚫Server is higher-ranked ⚫On sidelines, less difference ⚫Large difference near center service line MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫In case Ranking Point Ratio =5 ⚫Server is higher-ranked ⚫On sidelines, less difference ⚫Large difference near center service line MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫In case Ranking Point Ratio =5 ⚫Server is higher-ranked ⚫On sidelines, less difference ⚫Large difference near center service line ⚫Higher-ranked players can score even if his service land on easier location MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫Higher-ranked players can score even if his service land on easier location ⚫Higher-ranked players can land his service on difficult location more frequently MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫Higher-ranked players can score even if his service land on easier location ⚫Higher-ranked players can land his service on difficult location more frequently MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Result: 1st /Deuce side/Not equal strength ⚫Higher-ranked players can score even if his service land on easier location ⚫Higher-ranked players can land his service on difficult location more frequently MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Demonstration: Implementation on Website lhttps://www-ie.meijo- u.ac.jp/~konaka/tennisServiceProb_Eng.html MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Summary WHAT WE COULD ACHIEVE ⚫Construct a mathematical prediction model of scoring in tennis ⚫Input variables ⚫Service landing location ⚫Player strength metric ⚫Output variable ⚫Scoring probability ⚫Method: Generalized Linear Model Regression FUTURE WORKS ⚫Include service speed ⚫(We wish we could have found service data with speed.) ⚫Player evaluation ⚫Match analysis ⚫Analysis by court surface MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

References Shimizu and Konaka. “Scoring probability model based on service landing location and ranking points in men’s professional tennis matches” MathSportInternational Conference 2023@Budapest ⚫[2020] https://logmi.jp/tech/articles/324033 (written in Japanese. Non-academic presentation) ⚫[Whiteside et al, 2017] Spatial characteristics of professional tennis serves with implications for serving aces: A machine learning approach. Journal of Sports Sciences, 35(7) ⚫[Born et al, 2021] Stroke placement in women's professional tennis: What's after the serve? Sport Science, 3 MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

Hawk-Eye system MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST https://www.sony.com/ja/SonyInfo/technology/stories/Hawk-Eye/ Y.Baodong, “Hawkeye technology using tennis match,” (2014)