Modelling Probabilities in Games of Tennis

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Math HL Portfolio Type II:

Modelling Probabilities in Games of Tennis

May 2009

In this portfolio we will look at the probability involved in playing tennis. Our calculations will be based on the estimated probability a player has of scoring a point. We will develop models for different kinds of tennis games and use Excel to explore up to what extent we can exploit the two probabilities with which we start. Furthermore, we will differentiate between probability and odds, comparing them and analyzing how they can affect the way we look at the same numbers. In my conclusion I will mention the possibility of involving other kinds of distribution in this portfolio, such as Poisson.

Part 1: Club Practice.

1. Games to 10 points.

a) Since we know that Adam wins about twice as many points as Ben does, we can say that the probability of Adam winning a point is, and the probability of Ben winning a point is. So, given that P(A) is the probability of Adam winning a point and P(B) is the probability of Ben winning a point, we have that:

P(A)=

P(B)=