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.

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)
   

   View Slide

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
   

   View Slide

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?”
   

   View Slide

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)
   

   View Slide

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)
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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)
    

    View Slide

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/
    

    View Slide

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

    View Slide

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)
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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)
    

    View Slide

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)
    

    View Slide

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)
    

    View Slide

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)
    

    View Slide

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) ✓
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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

    View Slide

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

    View Slide

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

    View Slide

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

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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

    View Slide

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
    

    View Slide

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
    

    View Slide

48. MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
    

    View Slide

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)
    

    View Slide