Calculating Odds in Probability

Introduction

Since the betting industry went online in the 1990's, there has been a tremendous growth

in all areas. More and more bookmakers emerge, now with a total of several hundred

providers. As the turnover grows, and the competition increases, the betting market is

constantly evolving and many attempts are made towards lowering costs and maximizing

the profit (James & Franklin : 280).

Motivation

The concept of gambling has been around for centennials, evolving from chance games

with dice to modern day casinos. In the late 19th century the preliminaries to present

day bookmakers saw the light of day, being the first step on the way to the multi billion

dollar industry that the betting industry is today. For the remainder of this report,

the term betting industry refers to the market of bookmakers with focus on gambling

on sporting events, while the term betting is sports gambling.

Sports Betting

The goal of this project is primarily to create a prediction model which can assess the probabilities of the number of goals in a soccer match as well as the bookmakers. Secon- darily the goal is to devise a betting strategy, which in the long run can minimally break even when betting at bookmakers. In order to create such a model and strategy, one must fully understand the mathematics behind sports betting odds and the mechanisms which in uence them (Tom , & Mitchell: 41). In this chapter the basic theoretical background for understand- ing sports betting is presented, and various concepts related to this are accounted for. Finally previous works in the subject of odds assessment and betting are discussed, with regards to their possible utilization in this project.

Calculating Odds

A given sporting event has a finite number of outcomes. For a soccer match, for instance,

the number of possible outcomes is three, and can be one of home, draw or away. For

any given sporting event with n possible outcomes, outcome = 1…. n, the probability of

the outcome i is P(outcome = i). The outcomes are mutually exclusive, since a match

can not have two winners for example. So the following holds:

European Odds

When speaking of odds, there are several odds formats used on the market. In America moneyline odds are used, while some British bookmakers use fractional odds. Both types differ from the decimal type, which is most commonly used format in Europe. A decimal odds of 1.80 means, that if you place a wager with a stake s, your winnings will be s.1:80, and you net winnings will be (s -1:80) s = s . 0:80. The decimal odds type, will be the type used for the remainder of this report (Keeping: 51).

Bookmakers are basically companies trying to make money through sports wagers.

Therefore they operate with a theoretical payback percentage when oering odds to their customers. The theoretical payback is set by the bookmaker and is the percentage of the turnover on a betting event which is expected to be paid back to the customers. The payback is less than 100%, normally around 90-95%. The higher the percentage, the lower the margin of ...