This paper represents an analysis on the momentum of tennis match. And due to
Generalization performance of it, it can be helpful in constructing a system to
predict the result of sports game and analyze the performance of player based
on the Technical statistics. We First use hidden markov models to predict the
momentum which is defined as the performance of players. Then we use Xgboost to
prove the significance of momentum. Finally we use LightGBM to evaluate the
performance of our model and use SHAP feature importance ranking and weight
analysis to find the key points that affect the performance of players.

本文分析了网球比赛的势头，并且基于技术统计数据构建了一个系统来预测体育比赛结果和分析选手的表现。使用隐马尔可夫模型预测势头，使用 Xgboost 验证其重要性，最后使用 LightGBM 评估模型性能，并利用 SHAP 特征重要性排名和权重分析找出影响选手表现的关键因素。

捕捉动量：运用机器学习与时间序列理论进行网球比赛分析

Capturing Momentum: Tennis Match Analysis Using Machine Learning and  Time Series Theory

Wordle is a popular, online word game offered by the New York Times
(nytimes.com). Currently there are some 2 million players of the English
version worldwide. Players have 6 attempts to guess the daily word (target
word) and after each attempt, the player receives color-coded information about
the correctness and position of each letter in the guess. After either a
successful completion of the puzzle or the final unsuccessful attempt, software
can assess the player's luck and skill using Information Theory and can display
data for the first, second, ..., sixth guesses of a random sample of all
players. Recently, I discovered that the latter data is presented in a format
that can easily be copied and pasted into a spreadsheet. I compiled data on
Wordle players' first guesses from May 2023 - August 2023 and inferred some
interesting information about Wordle players. A) Every day, about 0.2-0.5% of
players solve the puzzle in one attempt. Because the odds of guessing the one
of 2,315 possible target words at random is 0.043%, this implies that 4,000 -
10,000 players cheat by obtaining the target word outside of playing the game!
B) At least 1/3 of the players have a favorite starting word, or cycle through
several. And even though players should be aware that target words are never
repeated, most players appear to remain loyal to their starting word even after
its appearance as a target word. C) On August 15, 2023, about 30,000 players
abruptly changed their starting word, presumably based on a crossword puzzle
clue! Wordle players can be influenced! This study goes beyond social media
postings, surveys, and Google Trends to provide solid, quantitative evidence
about cheating in Wordle.

Wordle 玩家的猜测、作弊和影响的研究提供了有力的定量证据。

Wordle：生活的微观世界。运气、技巧、作弊、忠诚和影响力！

Wordle: A Microcosm of Life. Luck, Skill, Cheating, Loyalty, and  Influence!

We study stochastic multi-armed bandits with many players. The players do not
know the number of players, cannot communicate with each other and if multiple
players select a common arm they collide and none of them receive any reward.
We consider the static scenario, where the number of players remains fixed, and
the dynamic scenario, where the players enter and leave at any time. We provide
algorithms based on a novel `trekking approach' that guarantees constant regret
for the static case and sub-linear regret for the dynamic case with high
probability. The trekking approach eliminates the need to estimate the number
of players resulting in fewer collisions and improved regret performance
compared to the state-of-the-art algorithms. We also develop an epoch-less
algorithm that eliminates any requirement of time synchronization across the
players provided each player can detect the presence of other players on an
arm. We validate our theoretical guarantees using simulation based and real
test-bed based experiments.

本文研究了具有许多玩家的随机多臂老虎机。结果表明我们提出的一种新的 “徒步旅行策略” 不需要估计玩家的数量，同时保证了静态情况下常数风险和动态情况下高概率的子线性风险表现。我们还证明了我们的算法的有效性。