using poisson distribution to predict a soccer betting winner

7/23/2019 Using Poisson Distribution to predict a Soccer Betting Winner

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Using PoissonDistribution to

predict a SoccerBetting Winner

SYED AHMER RIZVI

1511060 – Section A

Quantitative Methods - I

By



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APPLICATION OF DESCRIPTIVE STATISTICS AND PROBABILITY IN SOCCER

Concept

This article was published by the popular sports bookmaker Pinnacle Sports. It details the use of Poisson

distribution to work with data sets from past events i.e. Average Number of goals scored in a match by a team

during the past and current English Premier League Seasons to calculate the likely number of goals that will bescored by the same team in the upcoming matches. This concept forms the basic model behind the football

sportsbook rates offered by online betting giants such as 365.com and wbx.com.

For example Manchester United might average 1.7 goals per game in the last season. Entering this data as

Expected Value/Mean into a Poisson formula would show that this average equates to Manchester United

scoring 0 goals 18.3% of the time, 1 goal 31% of the time, 2 goals 26.4% of the time and 3 goals 15% of the

time.

Application methodology

Let’s assume Team 1 is playing the match at its home stadium

The method used to come up with the likely number of goals for a particular game is as follows:

For Team 1

Team 1’s Goals = {Team 1’s Offence} X {Team 2’s Defense} X { Average Goals/Game by any club}

For Team 2

Team 2’s Goals = {Team 2’s Offence) X {Team 1’s Defense} X { Average Goals/Game by any club}

Where

Team 1’s Offence = {Number of Goals Scored at Home Last Season / (Number of Home Matches Last

Season) X (Average Goals scored/Game at Home last Season by any club)}

Team 2’s Offence = {Number of Goals Scored Away Last Season / (Number of Away Matches Last

Season) X (Average Goals scored/Game Away last Season by any club)}

Team 1’s Defense = {Number of Goals conceded at Home Last Season / (Number of Home Matches

Last Season) X (Average Goals conceded/Game at Home last Season by any club)}

Team 2’s Defense = {Number of Goals conceded Away Last Season / (Number of Away Matches Last

Season) X (Average Goals conceded/Game at Home last Season by any club)}

The Last Step is to use the Poisson distribution Formula to calculate the Betting/Goals Table.

P(x; μ) = (e-μ) (μx) / x!

Where μ = Average Goals / Game

X = Different goals outcomes (0-5) in the Random Variable (x) category



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Let’s assume Team 1’s (Expected Value) = 1.654 Goals/Game and Team 2’s Goals (Expected value) = 1.278

Goals/Game.

The below embedded excel sheet can be used to find the Probability of the number of goals scored by each

team.

For example, we want to look at chances of the match being a 2 – 2 Draw, we can do that as:

Probability (2 – 2 Draw) = Probability (Team 1’s Goals = 2) X Probability (Team 2’s Goals = 2)

Since we are assuming Team 1’s Goals and Team 2’s Goals are independent events

= 0.2616 X 0.2275

= 5.95 %

This also implies that in-case you place a bet on the final score line being 2-2, you have a probability of 5.95%of winning the bet.

Similarly probabilities of all possible score-lines can be calculated.

Goals 0 1 2 3 4 5

Team 1 19.13% 31.64% 26.16% 14.43% 5.96% 1.97%

Team 2 27.86% 35.60% 22.75% 9.69% 3.10% 0.79%

Please click on the excel sheet to check the formulas.

Note: The values of Mean 1 and Mean 2 can be changed in respective cells.

Goal Likelihood TableTeam 1's Goals 1.654

Team 2's Goals 1.278



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CHOICE OF TOPIC

The two main reasons for choosing the topic “Using Poisson Distribution to predict Soccer Betting Winner” are:

Personal Interest

Being a football fanatic and having followed the English Premier League religiously for the past 8 or 9 years,

I was always aware that statistics plays a major part in the opinions shared by football pundits, but had never

looked into the topic in detail. Therefore it was quite interesting for me to look into the nuances of how

Poisson’s Distribution can be used to predict matches on the basis of a single parameter μ.

Non Routine Application of Probability/Statistics

The concepts used to demonstrate probability in undergraduate / school level courses usually involve dices,

cards and colored balls. Although these ideas help in developing a basic grasp of the concepts, the

application of Probability to real life situations/industries is a new concept for most of the PGP I students at

IIM Bangalore.

In the recent case study discussions in QM – I classes, we have looked at several sectors such as

manufacturing, healthcare and others to understand the role of descriptive statistics in business. One such

sector that is usually cordoned off and not brought up for discussion because of its gray nature is “Betting”,

although the illegal betting/gambling industry in India is worth 60 Billion USD and is growing exponentially.

One major subdivision of this industry is Sports betting. It involves prediction of sports results and placing

wagers on the outcome with the bookmaker. This activity is legal in most parts of the western world with

places in Asia such as Macau and Hong Kong following the trend. We also often read about the scale of

gambling involved in IPL i.e. India’s richest sports league.

CRITIQUE OF THE METHODOLOGY & ALTERNATIVE METHOD

The model fails to recognize the relation often seen between Score Line and Extraneous Factors such as Pitch

Effect or the ‘X Factor’ of the new manager . These factors play a major part in the score line and the model

would be not accurate without their inclusion. For example, a densely water soaked pitch prevents many goal

scoring opportunities and hence brings down the average score line.

To include the effect of these factors, I would recommend the use of Conditional Probability.

Let’s take the case of rain. A rainy weather condition is unfavorable for long through ball strategy i.e the most

utilized tactic in offense in English football and therefore hinders the attacking capabilities of a team.

Let Event R represent “Heavy Rain”.

Let Event A represent Team 1’s Goals = 2

Let Event B represent Team 2’s Goals = 2

Let us assume that Rain decreases the chances of a team scoring N goals by 20N%



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Therefore using the original data let us look at the probability of a 2-2 draw in case there is rain.

Probability (2-2|”Rain”) = Probability (Team 1’s Goals = 2|”Rain”) X Probability (Team 2’s Goals = 2|”Rain”)

= P (A|R) X P (B|R)

Now based on our assumption we can say N = 2 and therefore,

P (A|R) = P(A) X [1 – {(20 * 2)/100}] & P (B|R) = P(B) X [1 – {(20 * 2)/100}]

P (A|R) = 0.2616 * 0.6 = 0.1569 & P (B|R) = 0.2275 * 0.6 = 0.1365

Probability (2-2|”Rain”) = Probability (Team 1’s Goals = 2|”Rain”) X Probability (Team 2’s Goals = 2|”Rain”)

= 0.1569 * 0.1365

= 2.14 %

As we can see by taking external factors into consideration, the probability of a 2-2 score-line reducesconsiderably. This has an important implication in soccer betting. When the number of external factors in

consideration are large, it is very difficult to come up with a predication of an exact score-line with any level of

confidence. Therefore keep your MONEY SAFE and AVOID GAMBLING.

APPENDIX 1 – ARTICLE

http://www.pinnaclesports.com/en/betting-articles/soccer/how-to-calculate-poisson-distribution

Poisson Distribution, coupled with historical data, can provide a method for calculating the likely number

of goals that will be scored in a soccer match. Bettors will find this simple method of how to calculate

the likely outcome of a soccer match using Poisson Distribution very useful.

Poisson Distribution explained

Poisson Distribution is a mathematical concept for translating mean averages into a probability for variable

outcomes. For example, Chelsea might average 1.7 goals per game. Entering this information into a Poisson

formula would show that this average equates to Chelsea scoring 0 goals 18.3% of the time, 1 goal 31% of the

time, 2 goals 26.4% of the time and 3 goals 15% of the time.

How to calculate soccer outcomes with Poisson Distribution

Before we can use Poisson to calculate the likely outcome of a match, we need to calculate the average number

of goals each team is likely to score in that match. This can be calculated determining an “Attack” and “Defence

Strength” for each team and comparing them.

Selecting a representative data range is vital when calculating Attack and Defence strengths – too long and the

data will not be relevant for the teams current strength, while too short may allow outliers to skew the data. For

this analysis we’re using the 38 games played by each team in the 2013/14 EPL season.






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Calculating Attack and Defence strengths

Calculate the average goals scored at home and away

The first step in calculating Attack and Defence strengths based upon last season’s results is to determine the

average number of goals scored per team, per home game, and per away games.

Calculate this by taking the total number of goals scored last season and dividing it by the number of gamesplayed:

Season Goals Scored at Home / Number of Games (in season)

Season Goals Scored Away / Number of Games (in season)

In 2013/14, that was 598/380 at home and 454/380 away, equalling an average of 1.574 goals per game at

home and 1.195 away.

Average number of goals scored at home: 1.574

Average number of goals scored away from home: 1.195

The difference from the above average is what constitutes a team’s “Attack Strength”.

We’ll also need the average number of goals an average team concedes. This is simply the inverse of the above

numbers (as the number of goals a home team scores will equal the same number that an away team concedes):

Average number of goals conceded at home: 1.195

Average number of goals conceded away from home: 1.574

We can now use the numbers above to calculate the Attack and Defence Strength of both Manchester United

and Swansea City for their match on August 16th, 2014.

Predicting Man United’s Goals

Calculate Man United’s Attack Strength:

1. Take the number of goals scored at home last season by the home team (Man United: 29) and divide

by the number of home games (29/19): 1.526

2. Divide this value by the season’s average home goals scored per game (1.526/1.574), to get the “Attack

Strength”: 0.970. This shows that Man United scored 3.05% fewer goals at home than a hypothetical

“average” Premier League side last season.

Calculate Swansea’s Defence Strength:

1. Take the number of goals conceded away last season by the away team (Swansea: 28) and divide by

the number of away games (28/19): 1.474.

2. Divide this by the season’s average goals conceded by an away team per game (1.474/1.574) to get the

“Defence Strength”: 0.936. This therefore highlights Swansea conceded 6.35% fewer goals than an

“average” Premier League side on the road.

We can now use the following formula to calculate the likely number of goals the home team might score:



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Man United’s Goals = Man United’s Attack x Swansea’s Defence x Average No. Goals

In this case, that’s 0.970* 0.936 * 1.574, which equates to United scoring 1.429 goals.

Predicting Swansea’s Goals

Calculate Swansea’s Attack Strength:

1. Take the number of goals scored away last season by the away team (Swansea: 21) and divide by the

number of away games (21/19): 1.105

2. Divide this value by the season’s average away goals scored per game (1.105/1.195), to get the “Attack

Strength”: 0.925. This shows that Swansea scored 7.53% fewer away goals than a hypothetical “average”

Premier League side.

Calculate Man United’s Defence Strength:

1. Take the number of goals conceded at home last season by the home team (Man United: 21) and divide

by the number of home games (21/19): 1.105.

2. Divide this by the season’s average goals conceded by a home team per game (1.105/1.195) to get the“Defence Strength”: 0.925. Man United conceded 7.53% more goals than an “average” Premier League

side at home.

We can now use the following formula to calculate the likely number of goals the away team might score:

Swansea’s Goals = Swansea’s Attack x Man United’s Defence x Average No. Goals

In this case, that’s 0.925* 0.925 * 1.195, which equates to Swansea scoring 1.022 goals.

Poisson Distribution betting – Predicting multiple match outcomes

Of course, no game ends 1.429 vs. 1.022 – this is simply the average. Poisson Distribution, a formula created

by French mathematician Simeon Denis Poisson, allows us to use these figures to distribute 100% of probability

across a range of goal outcomes for each side. The results are shown in the table below:

The formula itself looks like this: P(x; μ) = (e-μ) (μx) / x!, however, we can use online tools such as this Poisson

Distribution Calculator to do most of the equation for us.

All we need to do is enter the different goals outcomes (0-5) in the Random Variable (x) category, and the

likelihood of a team scoring (for instance, Swansea at 1.022) in the average rate of success, and the calculator

will output the probability of that score.

Poisson Distribution for Man United vs. Swansea

Goals 0 1 2 3 4 5

Man United 23.95% 34.23% 24.46% 11.65% 4.16% 1.19%

Swansea 35.99% 36.78% 18.79% 6.40% 1.64% 0.33%

This example shows that there is a 23.95% chance that Man Utd will not score, but a 34.23% chance they will

get a single goal and a 24.46% chance they’ll score two.

http://stattrek.com/online-calculator/poisson.aspx








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Swansea, on the other hand, are at 35.99% not to score, 36.78% to score one and 18.79% to score two.

Hoping for a side to score five? The probability is 1.19% if United are the scorers, or 0.33% for Swansea to do

it.

As both scores are independent (mathematically-speaking), you can see that the expected score is 1 – 1. If you

multiply the two probabilities together, you’ll get the probability of the 1-1 outcome – 0.125 or 12.59%.

Now you know how to calculate outcomes, you should compare your result to a bookmaker’s odds to help see

how they differentiate.

Example: comparing the draw

The above example showed us that a 1-1 draw has a 12.59% chance of occurring, according to our model. But

what if you wanted to bet on the “draw”, rather than on individual score outcomes? You’d need to calculate the

probability for all of the different draw scorelines – 0-0, 1-1, 2-2, 3-3, 4-4, 5-5 etc.

To do this, simply calculate the probability of all possible draw combinations and add them together. This will

give you the chance of a draw occurring, regardless of the score.

Of course, there are actually an infinite number of draw possibilities (both sides could score 10 goals each, for

example), but the chances of a draw above 5-5 are so small that it’s safe to disregard them for this model.

For the United – Swansea game, combining all of the draws gives a probability of 0.266 or 26.6%. Pinnacle

Sports’ odds were 5.530 (an 18.08% implied probability).

Therefore if last season’s form was a perfect indicator of this season’s results, there would appear to be value

in backing the draw, as the model shows that it more likely to happen than the Pinnacle Sports odds suggest.

Unfortunately it isn’t as simple as that, which is why pure Poisson analysis has limitations.

The limits of Poisson Distribution

Poisson Distribution is a simple predictive model that doesn’t allow for a lot of factors. Situational factors – suchas club circumstances, game status etc. – and subjective evaluation of the change of each team during the

transfer window are completely ignored.

In this case, it means the huge x-factor of Manchester United’s first Premier League game with new manager

Louis Van Gaal is entirely ignored.

Correlations are also ignored; such as the widely recognised pitch affect that shows certain matches have a

tendency to be either high or low scoring.

These are particularly important areas in lower league games, which can give punters an edge against

bookmakers, while it’s harder to gain an edge in major leagues, given the expertise that modern bookmakers

like Pinnacle Sports possess.

using poisson distribution to predict a soccer betting winner

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