Tennis competition winning rate prediction method based on GP-LDS and momentum model
By applying GP-LDS and momentum models in the prediction of tennis competition, the problems that are difficult to accurately predict the results of the tennis game in existing technologies, and achieve more accurate and real-time prediction results.
Patent Information
- Application Number
- CN202410870160.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-01
- Publication Date
- 2025-01-24
AI Technical Summary
The prior art is difficult to predict the results of tennis matches accurately and in real time, due to the combined influence of a variety of factors and the uncertainty of the match.
Adopting the Tennis competitive winning rate prediction method based on the Gaussian process-linear dynamic system (GP-LDS) and momentum models, the GPR model with GPC, tennis momentum models and relative momentum is constructed, combined with real-time data and historical performance.
A more accurate and real -time competition results forecast can be achieved, which can effectively handle the noise and complexity in the competition data, and provide an estimate of the uncertainty of prediction.
Smart Images
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of sports prediction, and in particular to a tennis competition winning rate prediction method based on GP-LDS and momentum model. Background Art
[0002] Tennis is a global sport that is highly competitive and entertaining. The results of a match are affected by many factors, including the players' skills, tactics, physical fitness, psychological state, and environmental conditions on the day of the match. The combined effect of these factors makes the results of tennis matches somewhat uncertain. Therefore, accurately predicting the results of a match is of great significance in improving game strategies, optimizing training plans, and enhancing the enjoyment of the match. Summary of the invention
[0003] 1. Technical issues to be resolved
[0004] In view of the shortcomings of the prior art, the present invention provides a tennis competitive winning rate prediction method based on GP-LDS and momentum model. By comprehensively analyzing factors such as players' historical performance, real-time data and competition environment, the GP-LDS and momentum model are constructed to provide more accurate and real-time prediction of competition results.
[0005] (II) Technical solution
[0006] To achieve the above objectives, the present invention is implemented by the following technical solutions: A tennis competitive winning rate prediction method based on GP-LDS and momentum model, comprising the following steps:
[0007] S1. Propose model assumptions;
[0008] S2, preprocessing the data, including data cleaning and replacement and feature index synthesis;
[0009] S3, probability prediction based on Gaussian process, construction of GPC and player performance analysis;
[0010] S4, constructing a tennis ball momentum model and correcting it by establishing a corresponding linear Gaussian dynamic system;
[0011] S5. Construct a GPR model of relative momentum difference, perform parameter optimization and model evaluation, and establish a Shapely calculation framework to interpret the model.
[0012] Preferably, the model assumptions include:
[0013] Assumption 1: A player's performance is reflected in the win rate; the higher the win rate, the more favorable the game is for the player. This assumption can well reflect the fluctuations during the game. The score is a sign of good performance.
[0014] Assumption 2: There is no force majeure during the game. In addition, no players are sick because we use data from additional data files. We ignore other factors such as force majeure or illness. This may cause drastic fluctuations in the data.
[0015] Assumption 3: Players’ win rate and momentum are continuous data. This assumption leads to more accurate modeling. It allows for more precise analysis. It makes our processing of data more comprehensive and diverse.
[0016] Preferably, the feature indicators in S2 are divided into dense features and sparse features, and the features are refined into win-loss performance indicators, physical performance indicators, technical performance indicators and serve performance indicators.
[0017] Preferably, the correlation analysis in S3 is measured using Spearman, and the basic idea of the probability prediction based on Gaussian process is to link the random variables before GP with the observed values to obtain the likelihood, then calculate the posterior based on the prior and the likelihood, and finally make a prediction based on the posterior probability.
[0018] Preferably, the GPC is constructed in S4 using two schemes:
[0019] In the first, the serve factor is modeled independently, and the probability of serving a point or winning is calculated using the naive Bayes method.
[0020]
[0021] Consider the winning rate for factors excluding serving as a binary classification problem, and assume that y is modeled by a Bernoulli distribution, that is, y|x~Bernoulli(p), where p is the winning probability independent of serving that needs to be estimated, then P when the modeled player wins yi=+1 is a random variable π(xi):
[0022] Where: π(x) is the response function of f(x), and Respectively represent the mean and covariance of the potential performance score, and finally define the Gaussian process of the potential performance score as,
[0023] First, calculate the distribution of the corresponding potential performance scores:
[0024]
[0025] Given a test set X* of size N*×D, predict the possible performance score output π*=[π(x1),...,π(xN*)]:
[0026] p(f * ||X,y,X *)=∫p(f * |X,X * , f X )p(f X |X,y)df X
[0027] Then calculate the final test performance score θ*=π(X*):
[0028] p(X,y,X * )=∫σ(f * )p(f * |X,y,X * )df *
[0029] On this basis, add the effect of serving and calculate the final winning probability:
[0030]
[0031] The indicator function It means that P should be considered only when serving. A ;
[0032] The second method is to construct the serve factor model using the data containing the serve factor directly, and then establish the GPC model. The final test performance score is θ * =π(X * ) is the winning probability. When performing parameter estimation and optimization, square exponential kernel, periodic kernel, rational quadratic kernel and white noise kernel are used as basic kernels.
[0033] Preferably, the tennis ball momentum model in S4 is:
[0034] v t =αv t-1 +βg t ,
[0035] Where v represents the momentum rate, {α, β} represents the coefficient, and g t It is the rate of change of the performance score P at time t. Then, by establishing the corresponding linear Gaussian dynamic system, we simulate the change of P over time and estimate g to correct P.
[0036] Preferably, the GPR model for constructing the relative momentum difference in S5 first constructs the relative momentum difference:
[0037] ΔM=M1-M2.
[0038] M=mv,
[0039] m=σ1W1+σ2W2+σ3W3,
[0040] Among them, ΔM is represented by the momentum of player 1 minus the momentum of player 2, and M is represented by the momentum of the player, W1 is the environmental index, W2 is the psychological index, W3 is the physical index, and (σ1, σ2, σ3) is the parameter combination;
[0041] Then, the Gaussian linear transformation rule is applied to define ΔM as a multivariate Gaussian distribution with mean g X , the covariance is K X,X +σ 2 I 334 , the marginal likelihood function is
[0042]
[0043] When the test sample set X is needed * The momentum difference ΔM * When making an estimate or prediction, we perform a posteriori
[0044]
[0045] Preferably, the Shapely calculation framework in S5 is
[0046]
[0047] Where S is the subset of features used in the established model, D is the feature dimension, D = 15 in the model, x is the vector of eigenvalues of the instance to be explained, and j is the feature vector, {x1,...,x D}\{x j} represents the feature set except j. Overall, the Shapely value of each feature calculated is the contribution to the prediction of each result distribution, which is the weighted sum of all possible feature value combinations.
[0048] (III) Beneficial effects
[0049] The present invention provides a tennis competitive winning rate prediction method based on GP-LDS and momentum model, which has the following beneficial effects:
[0050] 1. Establish a Gaussian process classification (GPC) model to estimate the player's win rate. The GPC model can adapt to this complex game data and make good predictions. We model the win rate as a continuous variable, that is, the response output of the joint Gaussian distribution. This is conducive to observing the entire game process from a continuous numerical perspective and evaluating the performance of players in different time periods.
[0051] 2. Establish a linear Gaussian dynamic system and model the winning rate as a short-term linear relationship. This is conducive to obtaining the optimal estimation result and can effectively deal with the noise in the system. We introduced the concept of momentum rate in LGDS, which accumulates the historical changes in winning rate and also depends on the current local mutation. This provides information of different historical ranges for momentum modeling.
[0052] 3. Build a multivariate Gaussian process regression (GPR) model that can provide uncertainty estimates for predictions. In addition, this model is highly adaptable and has shown high predictive performance in the analysis and prediction of other games. DETAILED DESCRIPTION
[0053] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0054] Example:
[0055] The embodiment of the present invention provides a tennis competitive winning rate prediction method based on GP-LDS and momentum model, comprising the following steps:
[0056] S1. Propose model assumptions, including:
[0057] Assumption 1: A player's performance is reflected in the win rate; the higher the win rate, the more favorable the game is for the player. This assumption can well reflect the fluctuations during the game. The score is a sign of good performance.
[0058] Assumption 2: There is no force majeure during the game. In addition, no players are sick because we use data from additional data files. We ignore other factors such as force majeure or illness. This may cause drastic fluctuations in the data.
[0059] Assumption 3: Players’ win rate and momentum are continuous data. This assumption leads to more accurate modeling. It allows for more precise analysis. It makes our processing of data more comprehensive and diverse.
[0060] S2. Preprocessing the data, including cleaning and replacing the data and synthesizing feature indicators. The feature indicators in S2 are divided into dense features and sparse features, and the features are refined into win-loss performance indicators, physical performance indicators, technical performance indicators and serve performance indicators.
[0061] Calculation and processing instructions for some indicators:
[0062] Continuous score: the number of points scored before a certain time. Take player A as an example. At the beginning, V 4A = 0. If player A wins the next point, then V 4A ←V 4A +1. On the contrary, V 4A = 0. By analogy, we can get V at each point 4A value,
[0063] Single / Secondary Serve Score Percentage: The percentage of a player's single / secondary serve scores to all valid serves in the time window. For a short time window, when a player does not serve in the time window, the serve score will be 0, which just indicates the non-serving state.
[0064] Return score ratio: The ratio of a player's return score to all valid serves in the time window. For a short time window, when a player serves in this time period, the return score will be 0, which just represents the serve status.
[0065] Normalization: We use maximum and minimum normalization to scale the data of each dimension feature to [0, 1] to eliminate the impact of dimension.
[0066] S3, index screening for correlation analysis based on the player's performance in the game, probability prediction based on Gaussian process, construction of GPC and player performance analysis. The correlation analysis in S3 is measured by Spearman. The basic idea of the probability prediction based on Gaussian process is to link the random variables before GP with the observed values to obtain the likelihood, then calculate the posterior based on the prior and likelihood, and finally make a prediction based on the posterior probability.
[0067] S4, constructing a tennis ball momentum model, and correcting it by establishing a corresponding linear Gaussian dynamic system. In S4, two schemes are used to construct the GPC:
[0068] In the first, the serve factor is modeled independently, and the probability of serving a point or winning is calculated using the naive Bayes method.
[0069]
[0070] Consider the winning rate for factors excluding serving as a binary classification problem, and assume that y is modeled by a Bernoulli distribution, that is, y|x~Bernoulli(p), where p is the winning probability independent of serving that needs to be estimated, then P when the modeled player wins yi=+1 is a random variable π(xi):
[0071] Where: π(x) is the response function of f(x), and Respectively represent the mean and covariance of the potential performance score, and finally define the Gaussian process of the potential performance score as,
[0072] First, calculate the distribution of the corresponding potential performance scores:
[0073]
[0074] Given a test set X* of size N*×D, predict the possible performance score output π*=[π(x1),...,π(xN*)]:
[0075] p(f * |X,y,X * )=∫p(f * |X,X * , f X )p(f X |X,y)df X
[0076] Then calculate the final test performance score θ*=π(X*):
[0077] p(X,y,X * )=∫σ(f * )p(f * |X,y,X * )df *
[0078] On this basis, add the effect of serving and calculate the final winning probability:
[0079]
[0080] The indicator function It means that P should be considered only when serving. A ;
[0081] The second method is to construct the serve factor model using the data containing the serve factor directly, and then establish the GPC model. The final test performance score is θ * =π(X * ) is the winning probability. When performing parameter estimation and optimization, square exponential kernel, periodic kernel, rational quadratic kernel and white noise kernel are used as basic kernels.
[0082] Preferably, the tennis ball momentum model in S4 is:
[0083] v t =αv t-1 +βg t ,
[0084] Where v represents the momentum rate, {α, β} represents the coefficient, and gt It is the rate of change of the performance score P at time t. Then, by establishing the corresponding linear Gaussian dynamic system, we simulate the change of P over time and estimate g to correct P.
[0085] S5. Construct a GPR model of relative momentum difference, perform parameter optimization and model evaluation, and establish a Shapely computing framework to interpret the model. Constructing the GPR model of relative momentum difference in S5 first requires constructing the relative momentum difference:
[0086] ΔM=M1-M2.
[0087] M=mv,
[0088] m=σ1W1+σ2W2+σ3W3,
[0089] Where ΔM is the momentum of player 1 minus the momentum of player 2, and M is the momentum of the player, W1 is the environmental index, W2 is the psychological index, and W3 is the physical index. (σ1, σ2, σ 3) is a parameter combination; Table 1 shows the momentum changes of the two players during the game. The distribution of momentum is consistent with the game situation to a large extent, and can clearly reflect some strong fluctuations during the game.
[0090]
[0091] Table 1 Momentum changes during the game
[0092] Then, the Gaussian linear transformation rule is applied to define ΔM as a multivariate Gaussian distribution with mean g X , the covariance is K X,X +σ 2 I 334 , the marginal likelihood function is
[0093]
[0094] When the test sample set X is needed * The momentum difference ΔM * When making an estimate or prediction, we perform a posteriori
[0095]
[0096] The Shapely computing framework in S5 is
[0097]
[0098] Where S is the subset of features used in the established model, D is the feature dimension, D = 15 in the model, x is the vector of eigenvalues of the instance to be explained, and j is the feature vector, {x1,...,xD}\{x j} represents the feature set except j. Overall, the Shapely value calculated for each feature is the contribution to the prediction of each result distribution, which is the weighted sum of all possible feature value combinations.
[0099] Table 2 shows the (partial) results of the SHAP values we calculated on different features. It can be seen that physical performance W3 is the factor that has the greatest impact on the change of ΔM. The second is the historical information under the 6-point time unit, including score difference, movement distance difference, untouchable serve score, etc. It also includes historical continuous score information. In addition, the factors corresponding to the 6-point time scale will have a higher SHAP value, which means that they occupy a more important position in the influencing factors of ΔM.
[0100]
[0101] Table 2 SHAP values calculated based on different features
[0102] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A tennis competitive winning rate prediction method based on GP-LDS and momentum model, characterized in that: The following steps are involved: S1. Propose model assumptions; S2, preprocessing the data, including data cleaning and replacement and feature index synthesis; S3, probability prediction based on Gaussian process, construction of GPC and player performance analysis; S4, constructing a tennis ball momentum model and correcting it by establishing a corresponding linear Gaussian dynamic system; S5. Construct a GPR model of relative momentum difference, perform parameter optimization and model evaluation, and establish a Shapely computational framework to interpret the model.
2. A tennis competitive winning rate prediction method based on GP-LDS and momentum model according to claim 1, characterized in that: The model assumptions include: Assumption 1: Players’ performance is reflected in their winning percentage; Assumption 2: There is no force majeure during the competition; Assumption 3. Players’ win percentage and momentum are continuous data.
3. The tennis competitive winning rate prediction method based on GP-LDS and momentum model according to claim 1, characterized in that: The feature indicators in S2 are divided into dense features and sparse features, and the features are refined into win-loss performance indicators, physical performance indicators, technical performance indicators and serve performance indicators.
4. The method for predicting tennis competitive winning rate based on GP-LDS and momentum model according to claim 1, characterized in that: The correlation analysis in S3 is measured by Spearman. The basic idea of the probability prediction based on Gaussian process is to link the random variables before GP with the observed values to obtain the likelihood, then calculate the posterior based on the prior and the likelihood, and finally make a prediction based on the posterior probability.
5. A tennis competitive winning rate prediction method based on GP-LDS and momentum model according to claim 1, characterized in that: There are two schemes for constructing GPC in S4: In the first, the serve factor is modeled independently, and the probability of serving a point or winning is calculated using the naive Bayes method. Consider the winning rate for factors excluding serving as a binary classification problem, and assume that y is modeled by a Bernoulli distribution, that is, y|x~Bernoulli(p), where p is the winning probability independent of serving that needs to be estimated, then P when the modeled player wins yi=+1 is a random variable π(xi): Where: π(x) is the response function of f(x), Respectively represent the mean and covariance of the potential performance score, and finally define the Gaussian process of the potential performance score as, First, calculate the distribution of the corresponding potential performance scores: Given a test set X* of size N*×D, predict the possible performance score output π*=[π(x1),...,π(xN*)]: p(f * |X,y,X * )=∫p(f * |X,X * ,f X )p(f X |X,y)df X Then calculate the final test performance score θ*=π(X*): p(X,y,X * )=∫σ(f * |X,y,X * )df * On this basis, add the effect of serving and calculate the final winning probability: The indicator function It means that P should be considered only when serving. A ; The second method is to construct the serve factor model using the data containing the serve factor directly, and then establish the GPC model. The final test performance score is θ * =π(X * ) is the winning probability. When performing parameter estimation and optimization, square exponential kernel, periodic kernel, rational quadratic kernel and white noise kernel are used as basic kernels.
6. The method for predicting tennis competitive winning rate based on GP-LDS and momentum model according to claim 1, characterized in that: The tennis ball momentum model in S4 is: v t =αv t-1 +βg t , Where v represents the momentum rate, {α, β} represents the coefficient, and g t It is the rate of change of the performance score P at time t. Then, by establishing the corresponding linear Gaussian dynamic system, we simulate the change of P over time and estimate g to correct P.
7. The method for predicting tennis competitive winning rate based on GP-LDS and momentum model according to claim 1, characterized in that: The GPR model for constructing relative momentum difference in S5 first needs to construct relative momentum difference: ΔM=M1-M2 M=mv, m=σ1W1+σ2W2+σ3W3, Among them, ΔM is represented by the momentum of player 1 minus the momentum of player 2, and M is represented by the momentum of the player, W1 is the environmental index, W2 is the psychological index, W3 is the physical index, and (σ1, σ2, σ3) is the parameter combination; Then, the Gaussian linear transformation rule is applied to define ΔM as a multivariate Gaussian distribution with mean g X , the covariance is K X,X +σ 2 I 334 , the marginal likelihood function is When the test sample set X is needed * The momentum difference ΔM * When making an estimate or prediction, we perform a posteriori 8. The tennis competitive winning rate prediction method based on GP-LDS and momentum model according to claim 1, characterized in that: The Shapely calculation framework in S5 is Where S is the subset of features used in the established model, D is the feature dimension, D = 15 in the model, x is the vector of eigenvalues of the instance to be explained, and j is the feature vector, {x1,...,x D }\{x j } represents the feature set except j. Overall, the Shapely value calculated for each feature is the contribution to the prediction of each result distribution, which is the weighted sum of all possible feature value combinations.