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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.
⚫Served shot should land on service area
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
https://www.photo-ac.com/
Question:
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)
⚫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
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
service landing location [2020]
⚫Separation line is calculated by using Support
Vector Machine (SVM)
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
Near the sideline is

7. Background: Mathematical modeling of
service in tennis
PREVIOUS STUDIES AND THEIR LIMITATION
⚫Visualization of the boundary line 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)
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)
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)
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)
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/

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

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

23. Service scoring probability model: Data
DATA ANALYSIS
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
⚫Service shots landed more around the
sideline/centerline
⚫Different distribution between Deuce
⚫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
⚫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
⚫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
⚫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
⚫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
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST

30. Result: 1st service/equal strength
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
⚫Asymmetric
protrudes from outside to
inside
service line

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

32. Result: 1st service/equal strength
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
⚫Asymmetric ✓

protrudes from outside to
inside
service line

33. Result: 1st service/equal strength
MATHSPORTINTERNATIONAL CONFERENCE 2023@BUDAPEST
⚫Asymmetric ✓

protrudes from outside to
inside ✓
service line

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

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

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

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

45. Demonstration:
Implementation on Website
lhttps://www-ie.meijo-
u.ac.jp/~konaka/tennisServiceProb_Eng.html
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
⚫[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

48. 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)