konakalab
June 28, 2023
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# Scoring probability model based on service landing location and ranking points in men’s professional tennis matches

Presentation at 10th Mathsport International Conference 2023 (https://sites.google.com/view/mathsportinternational10 )

The main objective of this research is to construct a mathematical model that expresses the scoring probability of service shots. The explanatory variables are the service landing location and the ranking points of the server and receiver. The model has been constructed using more than 110 thousand service shots from ATP Tour tourna-ments in 2019. The model produced reveals the following facts: In 1st service, advantageous locations for servers are not symmetric between the ad and deuce sides. The higher-ranked player can win more points than lower-ranked players even if his shot lands in an easy location, i.e., in the middle of the service court.

June 28, 2023

## Transcript

1. ### 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)
2. ### 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
3. ### 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?”
4. ### 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)
5. ### (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)
6. ### 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
7. ### 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
8. ### 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
9. ### 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
10. ### 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
11. ### 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
12. ### 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
13. ### 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
14. ### 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
15. ### 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)
16. ### 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/

18. ### 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)
19. ### 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
20. ### 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
21. ### 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
22. ### 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)
23. ### 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)
24. ### 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)
25. ### 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)
26. ### 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) ✓
27. ### 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
28. ### 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
29. ### Result 1ST/DEUCE SIDE ⚫ 𝑥1 , 𝑥2 , 𝑥3 =

𝑥, 𝑦, 𝐿𝑠,𝑟 ⚫Stepwise regression ⚫Add/remove term based on p-value MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
30. ### Result: 1st service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Asymmetric ⚫Advantageous on

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

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

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

on sidelines ✓ ⚫Advantageous area protrudes from outside to inside ✓ ⚫Disadvantageous on service line
34. ### Result: 2nd service/equal strength MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST ⚫Almost symmetric ⚫Decreased

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

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

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

⚫Decreased scoring probability ← Reduced service speed ✓ ⚫Disadvantageous on service line
38. ### 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
39. ### 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
40. ### 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
41. ### 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
42. ### 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
43. ### 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
44. ### 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

46. ### 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
47. ### 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

49. ### 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)