$30 off During Our Annual Pro Sale. View Details »

Scoring probability model based on service landing location and ranking points in men’s professional tennis matches

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.

konakalab

June 28, 2023
Tweet

More Decks by konakalab

Other Decks in Science

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