Case Study On Tennis

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Mathematical Exploration

“Calculating the impact of change in probability of winning a point on the probability of winning the match.”

Candidate Name: Rohan Ketan Dhamsania
Candidate number: 003436-0017
Session: November 2014
School: The Galaxy School
Mathematics SL

INTRODUCTION

Tennis is a game, which rewards skill and technique. The roll of ‘winning by chance’ is minimized in tennis, in fact Pete Sampras, a tennis legend, had said, “The difference of great players is at a certain point in a match they raise their level of play and maintain it.” - it is the probability of the point that matters the most. I have been playing tennis since a tender age of 10 years and have experienced it first hand that
However, initially I was not sure as to how would the probability of winning a point be applied to that of match. After exploring and trying various methods like tree diagrams and binomial distribution, I found out that Binomial distribution was the most accurate and effective
Let us assume the probability to win a point to be 0.60 and calculate the probability of winning the match:

Table – 1 showing the calculations for player A winning a game: p = Probability of player A to win a point q = Probability of player A to lose a point (or player B to win a point) n = The number of points in which the player A can lose the required number of points (remember the last point has to be won by player A to win the game) r = The number of points lost by player A

HOW IS THE GAME WON p q n r nCr “a”[ ] WINNING CALCULATIONS (the values are substituted into the formula derived for P(winning a game to x points) “a” WIN
Game to 0 0.60 0.40 4 0 4C0 = 1 1(0.60)^4 (0.40)^0 0.129600

Game to 15 0.60 0.40 4 1 4C1= 4 4(0.60)^4 (0.40)^1 0.207360

Game to 30 0.60 0.40 5 2 5C2= 10 10(0.60)^4 (0.40)^2 0.207360

Game after deuce 0.60 0.40 6 3 6C3= 20 20〖(0.60)〗^5 〖(0.40)〗^3 {1/(1-2(0.60)(0.40))} 0.191409

Total probability of winning the game is the summation of above all solutions 0.735609

Table – 2 showing the calculations for the server winning a set:

a = Probability of winning n number of games for player A b = Probability of losing n number of games for player A (or winning n number of games for player

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