2024年美赛35篇特等奖O奖论文-C-2418251.pdf

display of youthful exuberance over seasoned skill. The match’s dynamic ebb and flow highlighted

the intangible factor of momentum. To capture this phenomenon, our team crafted mathematical

with experience. Additionally, we created visualization charts to intuitively display the changes in

winning probability throughout the match.

tity related to five features: service points, break points, continuous scoring, unforced errors, and

distance run. We used Principal Component Analysis (PCA) on five features to extract three prin-

cipal component vectors as input features and built a momentum model based on Support Vector

Machines (MSVM). This model was used to obtain the single-game momentum and accumulated

set momentum for two players. We conducted a correlation analysis between the calculated single-

game momentum and the single-game winning probability obtained from Model 1, yielding corre-

lation values of 0.704 and 0.729. This indicates that a player’s success is not random but related to

converting break points.

pionships (match 1502). The model’s calculations of accumulated momentum closely matches the

match flow. We also provided general advice for modifying the model for different types of com-

petition. After conducting a sensitivity analysis, the results shows that the momentum calculation

model is highly sensitive to various input features.

role of momentum, and offers recommendations.

Keywords: Momentum; RNN; PCA; The MSVM Model; ARIMA

Contents

3 Establishment and Solution of Single Game Winning Probability Model 4

4 Establishment and Solution of the Momentum Model 8

6 Verification and Application of the Model 18

7 Sensitivity Analysis 19

8 Strengths and Weaknesses 20

Appendices 23

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1 Introduction

back spectator lounging on their sofa. So for coaches, comprehending precisely what momentum

is can be vital, as this understanding will aid them in directing the game.

1.2 Restatement of the Problem

statement, we need to solve the following problems:

Team # 2418251 Page 3 of 23

1.3 Ourwork

1.4 Assumptions and Justification