Source-linked AI summary
Forecasting the Winner of a Live Tennis Match
Charles Xie, Aneesh Muppidi
TL;DR
Live tennis forecasting must integrate changing score and performance information with pre-match player strength. This study compares five models combining those sources in different ways; Trace achieves the greatest accuracy among them in the primary evaluation, with 77.84% accuracy across all points.
Problem
Live tennis models must adapt to score and performance changes while balancing useful live statistics against the risk of incorporating them indiscriminately.
Source: §1 · p. 1, §3.4 · p. 3Method
The study evaluates five approaches, with Trace combining Markov predictions from pre-match and live serve information with score and other live features through an HGBM.
Source: §3.6 · p. 4, §6 · p. 8Results
Trace achieved the greatest accuracy among the five models, reaching 77.84% across all points.
Source: §6 · p. 8Takeaways & Limitations
The study demonstrates the practicality of developing a live-match tennis prediction model.
Source: §6 · p. 8The models mainly explore service points and features; return features and statistics remain possible additions.
Source: §5 · p. 7
Abstract
from arXiv · showhide
With the rise of live sports betting in recent years, tennis forecasting has expanded from pre-match prediction to models that update win probabilities as a match unfolds. A central challenge in creating such a model is the constant need for models to adapt to score and performance changes. This study examines how pre-match and live information can be most effectively integrated into a model to produce accurate win-probability estimates. The analysis uses 8,222 Grand Slam matches containing a total of 1,505,355 points. Five models were evaluated using a chronological split, with matches from 2011-2021 used for training, 2022 for validation, and 2023-2024 for testing. Trace, a hybrid model, achieved accuracies of 76.06%, 82.15%, and 88.34% at 25%, 50%, and 75% match progress, suggesting that hybrid modeling is a practical approach to live tennis forecasting.
1 Introduction
Live tennis forecasting must balance the influx of match information against the risk of incorporating it indiscriminately. This study compares approaches to integrating pre-match and live data within a shared chronological evaluation.
1 Introduction
- Live betting is substantial in tennis, where approximately 80% of wagered money has been reported to be placed in-play [2].The growth of real-time data collection and digital betting platforms has contributed to the expansion of live sports betting [1].Source: §1 · p. 1
- Live statistics can add predictive signals, but too little or too much live data can mislead a model, making balanced integration a central challenge [3–5].Technologies such as Hawk-Eye® expand the shot-level and contextual information available during matches [3].Source: §1 · p. 1
1.1 Related Work
- Prior live-tennis models include a hierarchical Markov model [6], a beta-binomial live update reaching 76.5% maximum accuracy [7], and DeepTennis, an LSTM reaching 79.5% test accuracy [8].DeepTennis used different test years and data, so it is a contextual rather than directly comparable benchmark [8].Source: §1.1 · p. 1
- Pre-match Elo ratings offer player-strength information before play begins, and prior work found career-history Elo achieved 70% overall accuracy, second only to market consensus odds [9, 10].Elo-based methods were reported to forecast current player performance more strongly than official rankings [9].Source: §1.1 · p. 1
- This study compares score structure, Elo, live-serve updates, and machine learning within the same chronological evaluation [1.1 Related Work].The supplied passage does not include a printed bibliography marker for this study’s comparison.Source: §1.1 · p. 1
2 Data
The study builds point-level match states from Grand Slam data and calculates pre-match Elo ratings from ATP and WTA results. It evaluates the models on a chronological train-validation-test split.
2 Data
- The dataset contains Grand Slam point-by-point information and ATP/WTA results for calculating pre-match Elo; after cleaning, it retained 8,222 matches and 1,505,355 point-level prediction states.Elo ratings were matched to 96.0% of prepared matches; the counts precede filtering for Elo availability.Source: §2.1 · p. 1, §2 · p. 1, Table 1 · p. 2
2.1 Data Preprocessing
- Each point-level row records the state before a point, including score, server, match format, and live features, with the eventual winner stored as the target.Point scores were numerically encoded, and derived cumulative features captured serve rates and game or set outcomes alongside raw point information.Source: §2.1 · p. 2, Table 2 · p. 2, Table 3 · p. 2
2.2 Elo
- Pre-match Elo ratings start at 1500 and update chronologically from historical ATP and WTA results, with update size decreasing as a player completes more matches.Ratings are recorded before the current match outcome to prevent that match from affecting its pre-match estimate.Source: §2.2 · p. 2
2.3 Evaluation Split
- The chronological split uses 2011–2021 matches for training, 2022 for validation and tuning, and 2023–2024 for testing.The split was chosen to prevent leakage and mirror real-time use.Source: §2.3 · p. 2
3 Methods
The methods compare five approaches that use tennis scoring, pre-match strength, live serve performance, and machine learning in different combinations. Trace combines Markov predictions and live match features through a histogram gradient-boosting model.
3 Methods
- The study evaluates five models: symmetric Markov, Elo-asymmetric Markov, serve-shrink Markov, histogram gradient boosting (HGBM), and Trace.Their progression enables comparison of different information sources and modeling approaches.Source: §3 · pp. 2–3
3.1 Markov Score Recursion
- Markov recursion uses point-level serve probabilities and tennis scoring rules to calculate the probability that player 1 eventually wins from the current score state.It forms the backbone of every model except the HGBM, recursively considering the possible outcomes of the next point.Source: §3.1 · p. 3
3.2 Symmetric Markov Baseline
- The symmetric Markov baseline assigns both players the same serve probability, so its prediction depends only on score and not player identity or strength.It was designed to isolate the predictive value of tennis scoring.Source: §3.2 · p. 3
3.3 Elo-asymmetric Markov Model
- The Elo-asymmetric Markov model converts pre-match Elo differences into distinct starting serve probabilities, avoiding a default 50–50 estimate when players differ in strength.Its serve-probability parameters are selected using validation data.Source: §3.3 · p. 3
3.4 Serve-shrink Markov Model
- The serve-shrink model blends observed in-match serve rates with pre-match estimates, weighting live evidence according to the number of observed serve points.The parameter κ controls shrinkage: larger values give more weight to the prior, while smaller values give more weight to recent serve performance.Source: §3.4 · pp. 3–4
3.5 Histogram Gradient-Boosting Baseline
- The HGBM baseline estimates live match-win probability directly from current score and live features, without a Markov prediction.Histogram gradient boosting was selected as the machine-learning baseline because it achieved the lowest validation log loss among the evaluated classifiers.Source: §3.5 · p. 4
3.6 Trace
- Trace passes Elo-asymmetric and serve-shrink Markov predictions, current score, and other live features to an HGBM for the final match-win probability.Its live features are constructed using only information available before the next point, preventing future information from entering a prediction.Source: §3.6 · p. 4
4 Results and Discussion
The models were evaluated at fixed match-progress checkpoints and across all points using accuracy, log loss, and calibration. Trace led the accuracy and log-loss comparisons; the discussion also examines changing model strengths, tour differences, and limits on comparison with prior work.
4.1 Accuracy
- Trace had the highest accuracy at every reported checkpoint and across all point-level predictions, with its largest advantage around 40%–70% match progress.Source: Table 4 · p. 5, §4.1 · p. 5, Figure 2 · p. 5
- Accuracy rose for all models as matches progressed, while their differences narrowed near the end, motivating evaluation of probability quality as well as winner accuracy.Source: §4.1 · p. 5
4.2 Log Loss and Calibration
- Trace had the lowest log loss at all three checkpoints and was reasonably well calibrated, especially at 25% and 50% match progress.Source: Table 5 · p. 6, §4.2 · p. 6, Figure 3 · p. 6
4.3 Tour-specific Performance
- Across ATP and WTA matches, Trace was almost always strongest, particularly in mid-match, while WTA predictions fluctuated more than ATP predictions.Source: Figure 4 · p. 6, §4.3 · pp. 6–7
4.4 Discussion
- HGBM was weak early but improved as matches unfolded, leading individual models in accuracy at 75% and beating all three Markov models in log loss at 50% and 75%.The authors suggest live features become more valuable than Markov score recursion as matches develop.Source: §4.4 · p. 7
- Serve-shrink consistently beat Elo-asymmetric in log loss despite small, inconsistent accuracy gains; Trace combines models whose relative strengths shift across match stages.Source: §4.4 · p. 7
- Under a non-chronological comparison split, multiple models matched or exceeded DeepTennis, but the authors caution that potential data leakage limits this comparison.The study's main evaluation instead uses a strictly chronological split.Source: §4.4 · p. 7
5 Limitations
The study identifies limits in its feature coverage and evaluation scope: it emphasizes service information, lacks surface-specific performance, omits several factors, and covers only Grand Slam matches.
5 Limitations
- The models mainly explore service points and features, while future models could add return features and statistics.The authors say return information could add insights into player performance.Source: §5 · p. 7
- The current Elo system does not directly account for surface differences, which could affect measures of player strength.The authors suggest surface-specific Elo ratings or performance statistics as possible additions.Source: §5 · p. 7
- Fatigue, injury, weather, handedness, and playing style are not represented as explicit features.The authors note some effects may be indirectly reflected in existing data; representing them more concretely may make them easier for models to incorporate.Source: §5 · pp. 7–8
- The analysis includes only Grand Slam matches, so its results may not generalize well to lower-level tour events.The authors suggest adding ATP and WTA tour-level events to expand model usefulness.Source: §5 · p. 8
6 Conclusion
The study concludes that Trace combines Markov score recursion with pre-match and live information and outperformed the other four models in its primary evaluation. It also presents live-match prediction as practical to develop.
6 Conclusion
- 77.84% across all points was Trace’s accuracy, the greatest among the five models in the primary evaluation.The authors say the other models’ results show value in different information sources.Source: §6 · p. 8
- Elo ratings provide player-strength information, live serve statistics improve probability estimates, and HGBM captures patterns not directly represented by the Markov models.These are the contributions of the information sources highlighted in the conclusion.Source: §6 · p. 8
- The study presents developing a live-match prediction model as practical, in contrast with tennis forecasting’s focus on pre-match prediction.Source: §6 · p. 8
7 Future Work
Future work proposes turning Trace into a real-time system that updates after each point. The authors also call for testing its accuracy and efficiency in real-time matches.
7 Future Work
- A proposed real-time Trace system would update score state and live features from point-by-point data, then provide a new match-win probability after every point.Source: §7 · p. 8
- More testing is needed to establish whether the model remains accurate and efficient in real-time tennis matches.Source: §7 · p. 8
8 Implementation Notes
The project reports the software used for statistical analysis and figure generation and provides a repository link for the full pipeline.