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Boğaziçi UniversityDepartment of Management Information Systems
MIS 463 Decision Support Systems for Business
PROJECT FINAL-REPORT
GOAL PREDICTION IN FOOTBALL GAMES
Project Team No: 5
Yerzhan BERDIMBETSezgin DEGİRMENCİ
Yakup Can KARADENİZNeslişah KOCADEMİR
Instructor : Aslı Sencer
İstanbul - December, 2015
I. INTRODUCTION
In our global world, with gradually developing technology and huge flow of
information, people who bet should make right estimations for scores of football games,
but still people betting in football games make wrong estimations. As a result, many of
them lose huge amount of money. To decrease the chance of wrong estimation, we
created a decision support system, which helps people to prevent from further money
loss in their bets by correct prediction.
I.1 The Decision Environment
The main decision is about the goal prediction of the teams, in other words, to know
whether a team will score on the game or not and, this way, users indirectly may
facilitate from this decision to estimate the results of their teams’ game. Also,
bookmakers give an option where one can bet if one team scores or not, which would be
perfect for our system.
Actually, we can say that everybody who uses the system can be described as
decision makers and so users who want to estimate the scores of their teams in terms of
the information that they provided before running the system are the main decision
makers.
The system makes the decision about whether a team scores to another team or not.
The system does not predict the exact game result. The user can use the system before a
particular game starts.
There are many independent variables that affect the game result. But there is not
enough information about some of them before the game starts. The squad of a team
also plays big role and one can’t know it many days before, so best prediction would be
just before the start of a game.
Even if we have every independent variable that affects the game result, we cannot
predict the sudden events that may occur during the game such as injury of famous
player in first 15 minutes. Also, it would be harder to predict if a team scores or not
because data might be inaccurate for teams that recently joined the main league by
winning or qualifying from lower league.
There is a lot of information about factors that make a team to score or not to score.
However, it is difficult to specify these factors and this process spends too much time to
gather all this information.
In every estimation that we make, there will be very little amount of risk that we
cannot control. For example, one can receive a red card in a game and team might play
defensive way and not score at all. Mainly the cost of erroneous estimation is the
amount invested or betted.
Betting is an enormous sector around the world that people invest in and gain/lose
huge amount of money. Experts developed advanced statistical structures. Our system is
created to support the truth of users’ decisions.
I.2 Mission of ProjectThe mission of the project is to provide the goal estimation of the football games
with a high probability of occurrence. Despite the hardships in the estimation of results
of football games, we will implement a scientific approach to provide accurate
estimations to the people who bet and people who are interested in this kind of
information. This way, as a mission, we can protect people from further huge amounts
of money loss.
When it comes to sub-goals, we cannot only prevent people from money loss, also
we can try to increase their profits from bets as a sub-goal. Moreover, later on, by
developing this system and project further, we will be able to expand to other type of
sports.
I.3 Scope of ProjectOur goal prediction system is focusing on Turkish Superlig. We are predicting if one
team from this league scores or not scores in the upcoming game. Data have been
gathered from previous 4 years’ matches of teams.
I.4 Methodology We implemented data mining approach with decision tree classification in this
project. Decision Trees are commonly used in data mining with the objective of creating
a model that predicts the value of a target (in our case it is 1 if a team will score or 0 if a
team will not score) or dependent variable based on the values of several input (or
independent variables).
After creating a database of the system, we used IBM SPSS in order to develop a
model, actually a decision tree based on which we wrote our code and made user
interface.
Football game scores from former seasons, cost of the team, league points of a team,
and bet rates from websites were collected and manually entered into database. After
filtering and processing the data and also by normalizing data, we applied decision tree
approach, which helps us to decide whether a team scores or not in an upcoming game.
Then, we designed and developed a user-friendly graphical interface, which makes
able users to select the teams from Turkish Superlig and makes able users to see the
estimation by clicking the button.
II. LITERATURE SURVEY
In this literature survey, we made a research on the former studies about football
match prediction and similar statistical studies. In our internet age, betting companies
became widespread with the effect of the internet and so many people use internet to bet
on different games from football to basketball and even to ice-hockey. However, most
people do wild guesses on these games and they don’t think properly over the
possibilities, so they lose money and decrease their chance of profit unfortunately.
Therefore, as Gomes, Portela, and Santos (2015) aimed to support users to increase
their profits on bets related to football matches, and give them advice which bet they
should choose, we are also, in this study, mainly aiming to help people who bet and lose
money on games unfortunately because of limited information, we want to give them
better choices to minimize their losses and increase their profits. Moreover, in another
similar study, stanford graduates Cheng, Dade, Lipman, and Mills (2013) researched to
predict the NBA game outcomes more accurately than the experts who decide on the
betting lines, this way they tried to help people with better prediction than professional
analysts and basketball experts.
In the part of data collection, we can say that taking the data of the previous years
from websites is a popular and important way of data collection. As we collect the data
from www.canliskor.com, the other researchers in this topic mostly took their data from
sports websites like Liu and Lai (2010) received the data from www.cfbstats.com which
is a american college football statistics repository. Not only for american football but
also for football (soccer) and basketball, previous researchers almost always looked to
sports websites for match scores and statistical records like Haghigat, Rastegari, and
Nourafza (2013) collected from the valid websites which is related to that specific
sports and also Langseth (2013) collected the data of UK’s premier league from
www.football-data.co.uk for her study.
When it comes to the variables of our study, it can easily be said that all of them can
be supported by previous studies. Former researchers in this area used all or some part
of our variables in their own studies. First and major mutuality is that all the researchers
took the match result records of previous years of football teams or basketball teams etc.
In our study, we collected data records of spor toto super league of Turkey, which
consists of 4 seasons’ data records as Gomes et al. (2013) and Langseth (2013) collected
records of English premier league.
The first and the most important variable in our study is the goals scored by the home
team and away team of a game. This variable is an inevitable part of our study and
collected by almost all of the previous researchers in this area because the scores of
teams in previous years is an important source for prediction of scores of future games
to decide whether a team will win or lose. Not only for football but also even for
basketball and NHL (National Hockey League), the researchers collected the scores of
teams in previous years as Cheng et al. (2013) collected basketball game scores of
previous years and Pischedda (2014) took the data of previous NHL (National Hockey
League) scores of teams in previous seasons.
The second variable of our study is the position of the team in the league because we
think that position reflects the performance of the team in that season. As we consider
that as a variable in our study, Joseph, Fenton, and Neil (2006) take position of a team
in the league into consideration for predicting football game results and also Pischedda
(2014) paid attention to position of the teams within the NHL.
Thirdly, we added bet rates into our research because bookmakers who decide on bet
rates considers some data which we cannot reach and evaluate easily such as current
injuries of important players, banned players due to red or yellow cards, resignation of
coach and transfer of a player in the middle of the season. For example, Gomes et al.
(2013) took betting rates not only from one betting source, even from several betting
sources as a variable in their study of decision support system for predicting football
game result.
Fourth and the last one is team value. Team value is total of team’s players’ values.
Player’s value composed of players’ abilities, performance, scores etc. so that if a team
has more valuable players than the other team, the chance of winning and scoring will
be high. Joseph et al. (2006) used team quality in his project, even though this variable
is not as same as we used, it is similar because they take the value of team, players’
quality and performances as an indication for team quality.
Also, it is not a must for this part but we would like to mention about methodologies
and our own methodology which will be used in this study. In this study, we will use
decision tree because of the format our topic. Decision trees can handle both nominal
and numeric input attributes. Also, decision tree representation is rich enough to
represent any discrete-value classifier. In the overview chart below, you will see that
decision tree is one of the most popular methods in these type of studies and it was used
by most of the researchers in previous studies. For example, Gomes et al. (2013) used
decision tree for their football prediction studies and also, Pischedda, G. (2014) used
decision tree even for NHL which consists more complex game rules and principles
compared to football. These are just a few examples and these examples can be
increased with our other referenced articles. You can see the chart below to see more
clearly.
An Overview Chart of Variables Used in Former Studiesand For Mutual Ones Used in Our Study
Former Studies Methods Variables Mutual
Decision Support System for
Predicting Football Game Result
Gomes, J. Portela, F. Santos, M.F. (2013)
Naïve Bayes,
Decision Tree,
Support Vector Machine
Date, Home/away team, Full time home goals, full time
away goals, half time home goals and half time away team goals, home team
shoots and away team shoots, fauls, corners, red and yellow
cards, betting odds…
Full time home score and away score (simply final score of the match)
Betting odds
Predicting the Betting Line in
NBA Games
Cheng, B. Dade, K. Lipman, M. & Mills,
C. (2013)
Support Vector Machine
Home team score, away team score, Fouls, blocks,
rebounds, attendance…
Home team score Away team score
NHL Match Outcomes with ML
Models
Pischedda, G. (2014)
Decision Tree
And
Multi-Layer Artificial Neural
Networks
Goals for, goals against, goals differential, power play
success rate, power kill success rate, shoot%, save%,
winning streak, league position…
Goals for(equivalent of home score)
Goals against(equivalent of away score)
League position
Predicting football Results using
Bayesian nets and other machine
learning techniquesA.Joseph, N.E. Fenton, M.Neil
(2006)
Bayesian Nets
And
Decision Trees
Final league position, average performance, home
or away, representative quality of attacking
force(high, medium, low), team quality…
League position Team quality (can be
considered similar to value of the team
Beating the Bookie: A look at statistical
models for prediction of
football matches
Langseth, H. (2013)
Maher model and Gaussian model in a combination with
the aggressive Markovitz strategy.
The number of goal saved, fired shoots, shoots on
target, away teams defensive ability, attacking strength of
home team, home advantage…
Attacking strength of team (which is extracted from the number of goal scored in previous games, so closely similar to our home and away team scores of teams)
Predicting Sports Events from Past
ResultsBuursma, D. (2011)
Classification via Regression
Goals scored by home teamGoals scored by away teamGoals conceded by home
teamGoals conceded by away
teamAvg. number of points
gained by home and away teams
Goals scored by home team Goals scored by away team Goals conceded by home
team Goals conceded by away
team Number of points gained by
teams in the league
III. DEVELOPMENT OF THE DSS
III.1 DSS Architecture
First, a user selects the team that he
wants to estimate if it will score or not.
Then the user decides if the team plays at home or away. Then the user selects the
rival team.
Then, according to the inputs from the user, the system evaluates the possibility of scoring of the team, which is selected by the user and the possibility of the rival team to concede.
And, the system returns the result to the screen whether the selected team will score or not.
III.2 Technical Issues
In order to develop a model, we used decision tree classification with data mining
approach in IBM SPSS and then by using our model we wrote a code on JavaScript. By
using a template we developed a user-friendly interface.
Yes, we made a web-based application. As the database, we have used Excel file
with variables and we are updating them if necessary.
III.3 Data Source and Flow Mechanisms
The inputs for independent variables are obtained from www.canliskor2.com and
www.mackolik.com websites, calculated and entered manually.
Basically, most of the data are collected from www.canliskor2.com
Game scores, bet rates, rank of the teams, team points, and etc. Also, normalized
variables are acquired using these data.
On this screenshot, you can see how the data looks like on the website.
If you click on any game, there is a section “Oran Karşılaştırması”, from where you
can obtain bet rates.
From www.mackolik.com we have obtained team costs. If you click on a team, its
market value of players is shown as “P. Değeri”. In order to find market values of
player of different seasons, you need to select related seaon on top-right corner.
The bet rates for upcoming games are entered by a user in our website, because bet
rates are changing and not announced several days before the game.
Our database is on Excel file, here is the screenshot of part of it
III.4 Model and Algorithms
In our project we use data mining classification with decision tree technique in IBM
SPSS. A decision tree is a structure that includes a root node, branches, and leaf nodes.
Each internal node denotes a test on an attribute, each branch denotes the outcome of a
test, and each leaf node holds a class label. The topmost node in the tree is the root
node. Tree models where the target variable can take a finite set of values are
called classification trees. Decision tree classifies cases into groups or predicts values of
a dependent (target) variable based on values of independent (predictor) variables. The
procedure provides validation tools for exploratory and confirmatory classification
analysis.
We use two decision trees. The first one estimates if a home team scores, and the
second one estimates if an away team scores. We have two decision trees because we
have two different dependent variables to estimate. The first decision tree’s dependent
variable is “if a home team scores or not”, where 1 stands for scores, and 0 stands for
does not score and the second decision tree’s dependent variable is “if an away team
scores or not”, where 1 stands for scores, and 0 stands for does not score. For both
decision trees there are 15 same independent variables that we used. The independent
variables are:
1. Team 1 (home team)
2. Team 2 (away team)
3. Bet 1 (bet rate for win of home team)
4. Bet X (bet rate for draw)
5. Bet 2 (bet rate for win of away team)
6. Team 1 cost (market cost of home team players)
7. Team 2 cost (market cost of away team players)
8. Team 1 rank (rank of home team in the league)
9. Team 2 rank (rank of away team in the league)
10. Team 1 points / played games (how many points on average home team gains)
11. Team 2 points / played games (how many points on average away team gains)
12. Home goal scored ave / game (how many goals on average home team scores)
13. Home goal conceded ave / game (how many goals on average home team
concedes)
14. Away goals scored ave / game (how many goals on average away team scores)
15. Away goals conceded ave / game (how many goals on average away team
concedes)
The first decision tree’s dependent variable is Team1Scoredbinary (home team
scored or not).
The second decision tree’s dependent variable is Team2Scoredbinary (away team
scored or not).
By using this model and later by summing up estimations form both decision trees,
we will give more accurate information on if the team will score or not.
The following decision trees are for the concept “team scores or not” that indicates
whether a team from Turkish Superlig is likely to score a goal or not. Each internal node
represents a test on an attribute. Each leaf node represents a class.
Classification Tree for Home Team (Team 1)
Model Summary
Specifications
Growing Method CHAID
Dependent Variable Team1Scoredbinary
Independent Variables
Team1, Team2, Bet1, BetX, Bet2, Team1Cost,
Team2Cost, Team1Rank, Team2Rank,
Team1Pointsplayedgamesintheseason,
Team2Pointsplayedgamesintheseason,
Homegoalscoredavegame,
Homegoalconcededavegame,
Awaygoalsscoredavegame,
Awaygoalsconcededavegame
Validation None
Maximum Tree Depth 3
Minimum Cases in Parent Node 30
Minimum Cases in Child Node 10
Results
Independent Variables Included
Homegoalscoredavegame,
Team2Pointsplayedgamesintheseason,
Awaygoalsconcededavegame,
Awaygoalsscoredavegame, BetX, Bet2
Number of Nodes 23
Number of Terminal Nodes 16
Depth 3
Risk
Estimate Std. Error
.213 .011
Growing Method: CHAID
Dependent Variable:
Team1Scoredbinary
Classification
Observed Predicted
.0 1.0 Percent Correct
.0 103 208 33.1%
1.0 71 930 92.9%
Overall Percentage 13.3% 86.7% 78.7%
Growing Method: CHAID
Dependent Variable: Team1Scoredbinary
Here, the decision tree first divided the first node “Team1scoredornot” into 4 nodes
that are based on “Homegoalscoredavegame” that is how many goals home team scored
per game on average.
a) The first of 4 nodes has condition “Homegoalscoredavegame <=0.88”, it has on
total 117 samples, where “Team1scoredornot=1” percentage is 50.4, that is 59
samples.
b) The second of 4 nodes has condition “Homegoalscoredavegame >0.88 and
Homegoalscoredavegame <=1.24”, it has on total 293 samples, where
“Team1scoredornot=1” percentage is 69.3, that is 203 samples.
c) The third of 4 nodes has condition “Homegoalscoredavegame >1.24 and
Homegoalscoredavegame <=1.71”, it has on total 490 samples, where
“Team1scoredornot=1” percentage is 77.1, that is 378 samples.
d) The forth of 4 nodes has condition “Homegoalscoredavegame >1.71”, it has on
total 412 samples, where “Team1scoredornot=1” percentage is 87.6, that is 361
samples.
The same logic is applied for the rest nodes.
For example, we want to estimate if a home team will score or not. Let’s say that
home team scores 2 goals per home game on average.
So, by following tree model, we find out that the percentage of occurring 0 (the
team does not score) is 12.4 and the percentage of occurring 1 (the team scores) is 87.6.
And the P-value=0.000, which is quite good. Thus, we say that the team will score with
around 87.6% of probability.
Classification Tree for Away Team (Team 2)
Model Summary
Specifications
Growing Method CHAID
Dependent Variable Team2Scoredbinary
Independent Variables
Team1, Team2, Bet1, BetX, Bet2, Team1Cost,
Team2Cost, Team1Rank, Team2Rank,
Team1Pointsplayedgamesintheseason,
Team2Pointsplayedgamesintheseason,
Homegoalscoredavegame,
Homegoalconcededavegame,
Awaygoalsscoredavegame,
Awaygoalsconcededavegame
Validation None
Maximum Tree Depth 3
Minimum Cases in Parent Node 30
Minimum Cases in Child Node 10
Results
Independent Variables IncludedAwaygoalsscoredavegame,
Homegoalconcededavegame, BetX
Number of Nodes 16
Number of Terminal Nodes 10
Depth 3
Risk
Estimate Std. Error
.293 .013
Growing Method: CHAID
Dependent Variable:
Team2Scoredbinary
Classification
Observed Predicted
.0 1.0 Percent Correct
.0 57 356 13.8%
1.0 28 871 96.9%
Overall Percentage 6.5% 93.5% 70.7%
Growing Method: CHAID
Dependent Variable: Team2Scoredbinary
The logic of analyzing and getting probability is the same as for “Classification Tree
for Home Team”, but only decision tree is different.
III.5 User Interface and Reports
This is our homepage, it has “HOW IT WORKS?” button that redirects you to related
part.
This part explains how the site, making a prediction works. Firstly, you select home
and away teams, then you enter bet rates for an upcoming game in order to make
prediction more accurate, and then you get results with their probabilities of occurrence.
When you click “START!” button, you will be redirected to prediction part of the
site.
This is a prediction part, here you select home and away teams, and you also should
enter bet rates of a game according to selected teams. After Bet 1 (bet rate for win of the
home team), Bet X (bet rate for draw), and Bet 2 (bet rate for win of the away team) are
entered, you click “SHOW RESULT” button and the prediction will be shown.
Let’s make an example, Besiktas vs. Mersin, Bet 1 is 1.50, Bet X is 2.40, Bet 2 is
4.70
Now you can see results. For this example, the probability that Besiktas will score is
84.8%, and the probability that Mersin will score is 55.8%. The calculations are based
on the decision tree models we have developed and they are working in our codes.
We have 4 team members who are listed in this part of the site. Also, the fields that we worked on are written.
IV. ASSESSMENT
Firstly, we created a team and discussed project topics we could choose for this
course. After deciding on project topic we made a project plan and master plan, which
we were updating periodically.
We have chosen a project topic, which required a methodology that had not been
used before in this course. So, we couldn’t consult the former 463 students of previous
years. That is why it was challenging for our team to be the first group that used data
mining approach with decision tree classification. After meeting the professor with
related field of study, we started to investigate on our project. Another challenge of our
project can be seen as the number of members of our team. We worked on project with
just 3 members and we did it as web-based project which required for teams with 5
members.
We were thinking that the coding part would be really hard for our team, But by
studying hard, combining and using the fields that we are best on, we could follow
master plan and finish our project on time. Also, we are so thankful to our coding
instructors because we consulted them so much and they provide us so critical
information when we couldn’t find out any answer our problems especially to the
instructor of our web based application programming course.
V. PROJECT PLAN
We are meeting twice a week. Generally we have met on Fridays and Wednesdays.
Since we have almost the same courses, we have a chance to see each other and talk
about our project every day. In weekends, we are using online co-working tools.
We use Decision Tree methodology. Since there is no available database, we had to
create our database manually. We decided to work on database that consists of 3 leagues
but Aslı Sencer advised us to narrow the scope of the project and work on 1 league. So,
we decided to work on Spor Toto Süper Lig. Creating database manually has taken very
long time. We changed our task allocation and all of the group members entered data to
our database. We entered all match scores and bet rates from 2011-2012 to 2015-2016
seasons. We developed classifying decision tree model on IBM SPSS and used it in our
website as a background.
Meeting Place: Hisar Campus
Meeting Time: Fridays, 13:00 – Wednesdays, 14:00
Coordinator: Yerzhan Berdimbet
Task Allocation:
Development: Neslişah Kocademir, Sezgin Değirmenci, Yakup Can Karadeniz,
Yerzhan Berdimbet
Design: Yakup Can Karadeniz
Creating algorithms: Yerzhan Berdimbet
Database: Sezgin Değirmenci, Yakup Can Karadeniz, Neslişah Kocademir, Yerzhan
Berdimbet
Documentation: Neslişah Kocademir
Data Collection: Sezgin Değirmenci
MASTER PLAN
Project Code Group 5Project Title Goal Prediction in football games
Team Members Yerzhan Berdimbet, Neslisah Kocademir, Sezgin Degirmenci, Yakup Can Karadeniz
Phase Planned Actual Complete% ProblemsStart Finish Start Finish
Team Formation 29 Sept. 9 Oct. 29 Sept 5 Oct. 100
Project Proposal 10 Oct. 25 Oct. 10 Oct. 25 Oct. 100
We had a problem about writing decision-tree solutions on Excel cell, but we handled this problem via IBM SPSS.
Presentation 15 Oct. 26 Oct. 20 Oct. 26 Oct 100Literature Review (Library, Web, former studies) 6 Oct. 26 Oct. 6 Oct. 26 Oct. 100Interviews with experts, decision makers in the related area 6 Oct. 26 Oct. 6 Oct. 24 Oct. 100
Development of the model 10 Oct. 26 Oct. 6 Oct. 26 Oct. 100
Midreport 29 Oct. 22 Nov. 29 Oct. 22 Nov. 100
Presentation 19 Nov. 22 Nov. 19 Nov. 22 Nov. 100
Data Collection and Organization 10 Nov. 15 Nov. 10 Nov. 18 Nov. 100
Coding interfaces 20 Nov. 10 Dec. 20 Nov. 19 Dec. 100
Validation (Optional)
Final Report 10 Dec. 15 Dec. 20 Dec. 21 Dec. 100
Presentation 15 Dec. 20 Dec. 21 Dec.
VI. CONCLUSION
We created “Goal prediction in football games” Decision Support System and on
general, it works as we planned.
There was no delay in project. We had to spend more time on creating our database
but we have completed tasks on schedule. In order to use our limited time, we specified
new deadlines for next steps. Planned and actual dates of previous and next steps of our
project are stated in master plan.
The weakness of our DSS is that we have to enter data manually in order to make it
up to date. In the future, we could connect them with required database, so we could
pull bet rates and game scores in order to make variables up to date. Also, for this
project, 15 independent variables are very good, but we can use more to be more
accurate.
Another weakness of this DSS is that at the beginning of the season, there are low
amount of data, so we need to wait until several games are played and then to make a
prediction. Also, when a new team that qualified from lower league to the upper league
and has not played in the main league for years, it is harder to make correct prediction.
However, it is not the only problem of this DSS, it is a problem for every DSS projects
on this field that we previously researched in the literature review part.
On the other hand, the main positive sides of this DSS are its current results and user-
friendly interface. When we consider former studies in this field, we see that most of
them only depends on the data of previous years. However, our project has current bet
rate variables. If any important player of a team is injured or got red card in a few days
ago of the next game, it will affect the bet rates of the team. And, we use these current
bet rates to get more current results, but former studies depend on only previous years
data. Another difference of our project is its user friendly interface which can be
understood even by a child, it is so easy, understandable and well designed. The reason
why we focus on interface is the bad and complicated design of similar websites which
cannot be understood by everyone because they consist so much symbols and jargons as
we represented you in class presentation.
REFERENCES------------Journal paper--------------------
[1] Gomes, J. Portela, F. and Santos, M. F. (2016) “Real-Time Data Mining Models to Predict Football 2-Way Result.” Jurnal Teknologi, Penerbit UTM Press. (accepted for publication)
[2] Haghighat. M. Rastegari, H. and Nourafza, N. (2013) “A Review of Data Mining Techniques for Result Prediction in Sports”, ACSIJ Advances in Computer Science: an International Journal, Vol. 2, Issue 5, No.6, pp.1-6.
[3] Joseph, A. Fenton, N.E. and Neil, M. (2006) “Predicting Football Results Using Bayesian Nets and Other Machine Learning Techniques”, Knowledge Based Systems, vol.19, no.7, pp.544-553.
[4] Pischedda, G. (2014) “Predicting NHL Match Outcomes with ML Models”, International Journal of Computer Applications, vol.101, no.9, pp.15-22.
----------Conference Proceedings---------
[5] Buursma, D. (2011) “Predicting Sports Events from Past Results”, 14th Twente Student Conference on IT, Enschede, Netherlands
[6] Langseth, H. (2013) “Beating the Bookie: A Look at Statistical Models for Prediction of Football Matches”, Presented at the 12th Scandinavian AI conference, Aalborg, Denmark
-----------Web sources-----------------------
[7] Cheng, B. Dade, K. Lipman, M. & Mills, C. (2013). “Predicting the betting line in NBA games”. Retrieved from Stanford University, Program on Computer Science Web Site: http://cs229.stanford.edu/proj2013/ChengDadeLipmanMills-PredictingTheBettingLineInNBAGames.pdf
[8] Liu, B. and Lai, P. (2010). “Beating the NCAA Football Point Spread”. Retrieved from Stanford University, Program on Computer Science Web Site:
http://cs229.stanford.edu/proj2010/LiuLai-BeatingTheNCAAFootballPointSpread.pdf