text:
\section{Introduction}\label{sec1}

Due to the worldwide appeal of football, the football industry has occupied an unassailable position in the sports business since its inception. The popularity of the sport is continuing to increase and increasing sports fans are becoming involved in the football industry. At the same time, betting on sporting events, including football, has become a growth industry. The number of legal sports betting organisers and participants worldwide is increasing every year.

Meanwhile, the pre-match predictability of the sport is fairly low with some attribution placed on the sheer length of the matches as well as the number of players involved  \cite{hucaljuk2011predicting}. Others \cite{bunker2022application} have argued that the lower predictability of football can be explained by its low-scoring natures as well as the higher competitiveness relative to other sports and the fact that football can have more outcomes than merely wins and losses, but also draws, which contribute to the uncertainty of predicting the outcome of the matches\cite{wunderlich2018betting}. Other reasons have also been suggested such as power struggles within the leadership of football clubs\cite{huggins2018match}, match-fixing\cite{huggins2018match}, referees with low ethical standards\cite{carpenter2012match} and tacit understandings between teams on both sides of the game simultaneously reduce the predictability of football matches. The limited ability to counter match-fixing of local football leagues\cite{park2019should} and illegal internet gambling\cite{hill2010critical} are contributing components to the uncertainty of match outcomes.

The drive for increasing the predictability of football matches and profitability in gambling contexts,  has encouraged researchers to work on devising effective strategies. These approaches have taken the form of statistical\cite{baio2010bayesian}, machine learning\cite{baboota2019predictive}, \cite{fialho2019predicting}, natural language processing of football forums\cite{beal2021combining} as well as in-play image processing from camera footage of players\cite{lopes2014predicting} have been used in the attempt to  create more accurate predictive systems of football matches. However, even in recent years, research efforts have realised limited and incremental successes at predicting the outcome of pre-match football matches.

In contrast to other sports, such as horse racing, there is no significant difference in the predictive accuracy between the opinions of the general public on internet forums, or the judgement of football experts and that of sophisticated machine learning methods\cite{brown2019wisdom} which underscores the challenge of the task.
Even with access to rich sources of raw data and information, as well as the expert judgement of pundits,  the accuracy of the best predictions from literature after converting odds set by bookies into probabilities of events reaches  $\sim$55\%.

\subsubsection*{Contribution}

This study joins the growing body of literature that is attempting to improve the predictive accuracy of football matches using machine learning techniques, demonstrating the proposed methods on three seasons of Premier League matches in Europe sourced from publicly available datasets. In this work, we use a range of new features and algorithms that have not yet been used on this problem domain, and we employ tools from the explainable AI field in order to infuse the predictive models with interpretability and the ability to expose their reasoning behind the predictions. This study ultimately proposes a novel strategy for maximising the return on investment which relies on the Kelly Index in order to first categorise matches into levels of confidence with respect to their outcomes that are calculated on betting odds. We show how the decomposition of the problem with the aid of the Kelly Index and subsequent machine learning can indeed form an investment strategy that returns a profit.

\section{Related work}

This review divides previous studies in predicting the outcome of football matches into the target type of outcome (win/loss/draw) and those that have attempted at predicting the final scores of matches. However, because of the emergence of new betting options on betting platforms, predictions have emerged about whether or not both teams in the match will score goals\cite{da2022forecasting} \cite{inan2021using}. In fact, researchers now rarely predict the score of a match, as the uncertainty of the score and the existence of draws make score prediction  approach challenging and the prediction accuracy low, even with the inclusion of betting odds data\cite{reade2021evaluating}. The methods used for predicting the result of football matches fall into 3 categories. In the literature, statistical models, machine learning algorithms and rating systems have been explored.

\subsection*{Statistical and rating-system approaches}

\citet{inan2021using} fitted the team's offensive and defensive capabilities calculated from the goals made and conceded by teams each week to a Poisson distribution in his study while also taking  the home advantage into account. After fitting the team's offensive and defensive capabilities, home team advantage and betting parameters into a Poisson model, \citet{egidi2018combining} has developed a method of testing the prediction results to obtain more accurate predictions.

\citet{robberechts2018forecasting} used ELO ratings in predicting the result of FIFA World Cup matches. this approach considers the team's earlier result (whether it won or not) as the team's performance, and then gradually adjusts for subsequent results to obtain the final team performance rating. In order to identify and adjust a team's score, \citet{beal2021combining} used goals  by the team. They also considered the strength of the opponent of the match which is the source of the data to correct the team performance scores. In addition, \citet{constantinou2019dolores} used a hybrid Bayesian network to develop a dynamic rating system. The system corrects the team performance ratings by assigning greater weight to data on the results of the most recent matches that occurred. The researchers found that the study that uses scoring systems to predict the results of a football match usually uses databases with less content. These approaches need a small amount of data to extract features that can be used for prediction.

\citet{koopman2019forecasting} used both a bivariate Poisson distribution model and a team performance rating system in their research. They held home team advantage constant when predicting National League outcomes but varied the team's offensive and defensive capabilities over time. The results proved that there was no major difference in prediction between the two methods and that both could make good predictions. However, the team performance rating system was ineffective at predicting draws. Most of the above research on the use of rating systems noted the near absence of ties in the predicted results.
\citet{berrar2019incorporating} used team performance scores as a predictive feature for machine learning.

\subsection*{Machine learning approaches}

Efforts to improve the predictability of football have focused on two aspects. They have either attempted to use more sophisticated machine learning algorithms, or on feature engineering in order to develop more descriptive variables. Sometimes both aspects have been pursued. Table \ref{Prediction accuracy of different studies} summarises all the key studies and their attributes.

\subsubsection*{Algorithms}

A mixture of more simplistic approaches like Linear Regression\cite{prasetio2016predictingLR}, K-nearest neighbors\cite{brooks2016usingKNN} and Decision Trees\cite{yildiz2020applyingDT} have been explored. Subsequently, the algorithms have increased in their sophistication with the use of Random Forests\cite{groll2019hybridRF}, Support Vector Machines\cite{oluwayomi2022evaluationSVM},  Artificial Neural Networks\cite{bunker2019machineANN} and boosting Boosting\cite{hubavcek2019learningBoosting}. More recently, Deep learning methods have emerged with the use of
Convolutional Neural Networks \cite{hsu2021usingCNN} and LSTM \citet{zhang2021sports,malini2022deep} where the authors concluded that the LSTM model displayed superior characteristics to traditional machine learning algorithms and artificial neural networks in predicting the results of matches \cite{malini2022deep}.

\subsubsection*{Features}

Literature has shown that some of the effective features so far are half-time goal data as used by \citet{yekhande2582predicting}, first goal team data and individual technical behaviour data used by \citet{parim2021prediction}, ball possession and passing over data used by \citet{bilek2019predicting}, key player position data used by \citet{joseph2006predicting}.

 Kınalıoğlu and Coskun\cite{kinaliouglu2020prediction} compared predictive models of six machine learning algorithms and evaluated models with different hyperparameters settings using a large number of model evaluation methods. \citet{beal2021combining} improved prediction accuracy by $\sim$7\% by extracting expert and personal opinions published on self-published media and combining environmental, player sentiment, competition, and external factors in their predictions.

Overall, studies using machine learning methods mention the need to use richer predictive features and validate them more robustly in future works. However, even newer studies have a tendency to reuse existing features and limited proposals have been made for innovating with novel features.
Moreover, suggestions for new predictive features have primarily focused on ones that are not available in public datasets \cite{wunderlich2018betting} such as player transfer data, injuries, expert advice, and psychological data.

Direct prediction of odds are rarely researched in this context, this is because the calculation of the odds itself contains the bookmaker's prediction of the results of the matches\cite{zeileis2018probabilistic}. Using odds to predict the outcome of a match requires a combination of machine learning or statistical methods. \citet{zeileis2018probabilistic} and \citet{wunderlich2018betting} both reverse the odds into the probability of a team winning and fit it into the ELO team performance scoring system to predict the outcome of the match. \citet{vstrumbelj2014determining} used traditional linear regression models and Shin models to predict the probability of winning directly from the odds, with the aim of inverting the bookmaker's method of calculating odds based on the betting.

\begin{sidewaystable}[]\tiny
\caption{\label{Prediction accuracy of different studies}Prediction accuracy of different studies}
\resizebox{\textwidth}{30mm}{
\begin{tabular}{lllllllll}
\hline
Study &
  Competition &
  Features &
  Non-pre-match features &
  Best Algorithm &
  Accuracy &
  Test set duration &
  Matches &
  Class \\ \hline
\citet{joseph2006predicting}\citeyear{joseph2006predicting} &
  Tottenham Hotspur Football Club &
  7 &
  None &
  Bayesian networks &
  58\% &
  1995-1997(2 years) &
  76 &
  3 \\
\citet{constantinou2019dolores} \citeyear{constantinou2019dolores} &
  52 football leagues &
  4 &
  None &
  Hybrid bayesian networks &
  - &
  2000-2017(17 years) &
  216,743 &
  3 \\
\citet{hubacek2019score}\citeyear{hubacek2019score} &
  52 football leagues &
  2 &
  None &
  Double Poisson &
  48.97\% &
  2000-2017(17 years) &
  218,916 &
  3 \\
\citet{mendes2020comparing}\citeyear{mendes2020comparing} &

  6 Leagues &
  28 &
  None &
  Bagging &
  51.31\% &
  2016-2019(3 years) &
  1,656 &
  3 \\
\citet{danisik2018football}\citeyear{danisik2018football} &

  5 Leagues &
  139 &
  None &
  LSTM regression &
  52.5\% &
  2011-2016 &
  1520 &
  3 \\
\citet{berrar2019incorporating}\citeyear{berrar2019incorporating} &

  52 football leagues &
  8 &
  None &
  KNN &
  53.88\% &
  2000-2017(17 years) &
  216,743 &
  3 \\
\citet{herbinet2018predicting}\citeyear{herbinet2018predicting} &

  5 leagues &
  6 &
  None &
  XGBoost &
  54\% &
  2014-2016(2 years) &
  3,800 &
  3 \\
\citet{carloni2021machine}\citeyear{carloni2021machine} &

  12 countries &
  47 &
  None &
  SVM &
  57\% &
  2008-2020(12 years) &
  49,319 &
  3 \\
\citet{baboota2019predictive}\citeyear{baboota2019predictive} &

  English Premier League &
  12 &
  None &
  Random Forest &
  57\% &
  2017-2018(1 year) &
  380 &
  3 \\
\citet{chen2019neural}\citeyear{chen2019neural} &

  La Liga &
  34 &
  None &
  Convolution neural network &
  57\% &
  2016-2017(1 year) &
  380 &
  3 \\
\citet{esme2018prediction}{}\citeyear{esme2018prediction} &

  Super League of Turkey &
  17 &
  None &
  KNN &
  57.52\% &
  2015-2016(half year) &
  153 &
  3 \\
\cite{rodrigues2022prediction}\citeyear{rodrigues2022prediction} &

  English Premier League &
  31 &
  None &
  SVM &
  61.32\% &
  2018-2019(1 years) &
  380 &
  3 \\
\citet{alfredo2019football}\citeyear{alfredo2019football} &

  English Premier League &
  14 &
  Half-time results &
  Random Forest &
  68,16\% &
  2007-2017(10 years) &
  3,800 &
  3 \\
\citet{pathak2016applications}\citeyear{pathak2016applications}&

  English Premier League &
  4 &
  None &
  Logistic Regression &
  69.5\% &
  2001-2015(14 years) &
  2280 &
  2 \\
\citet{prasetio2016predictingLR}\citeyear{prasetio2016predictingLR}&

  English Premier League &
  13 &
  Ball possession, Distance run &
  Logistic Regression &
  69.51\% &
  2015-2016(1 year) &
  380 &
  3 \\
\citet{danisik2018football}\citeyear{danisik2018football} &

  5 leagues &
  139 &
  None &
  LSTM regression &
  70.2\% &
  2011-2016 &
  1520 &
  2 \\
\citet{ievoli2021use}\citeyear{ievoli2021use} &

  UEFA Champions League &
  29 &
  Number of passes and other features &
  BLR &
  81\% &
  2016-2017(1 year) &
  75 &
  3 \\
\citet{azeman2021prediction}\citeyear{azeman2021prediction} &

  English Premier League &
  11 &
  Shooting, fouls and other 8 features &
  Multiclass decision forest &
  88\% &
  2005-2006(1 year) &
  380 &
  3 \\ \hline
\end{tabular}
}
\end{sidewaystable}

\subsection*{Summary of literature}

The reported accuracies by existing studies as summarised in Table~\ref{Prediction accuracy of different studies} are chiefly determined first by the nature of the features used, and specifically if these are generated in real-time during in-play match outcome predictions. Features generated in-play are more deterministic and thus result in considerably higher accuracies than more static pre-match features when predicting outcomes. Therefore these kinds of studies are different in nature than those that simply rely on pre-match prediction.

Next, the accuracy is strongly affected by the nature of the predictive problem in the manner in which it is formulated. Models that attempt to predict a simple win or loss scenario are more accurate than those that also attempt to predict draws. This is expected since all predictive problems become more complex as the number of categories being predicted increases. For this reason, a number of researchers have opted for eliminating the prediction of tied matches.

In addition, the size of the datasets also affects the overall capability of the models, however, the number of features used in football match prediction has a small effect on prediction accuracy (Figure~\ref{fig:Feature-Acc}). The figure highlights that the accuracy of pre-match prediction is consistently below 60\%. However, when predicting pre-match results over multiple seasons, the prediction accuracy was almost always below 55\%. The researchers were unable to break the bottleneck in predicting football matches with more advanced algorithms and scoring systems.

When predictions are made over a large time span, for example, predicting the results of a game over 10 seasons, then these models will be less accurate than those predicting the results of a game over 1 season.
Furthermore, the choice of machine learning method does not seem to have a significant impact on the accuracy of the model.

\begin{figure}[h]
\centering
\includegraphics[width=0.9\textwidth]{Feature-Acc.png}
\caption{The plot of the number of features against prediction accuracy for all types of literature}
\label{fig:Feature-Acc}
\end{figure}

\subsubsection*{Research question}

In light of the literature, this study poses the following research questions:

\begin{enumerate}
    \item Is it possible to use public data to find out which matches are difficult to predict and which results are already certain before the match?
    \item Can prediction accuracy be improved by training models using hard-to-predict matches or easy-to-predict matches?
    \item Which machine learning predictions perform best for hard-to-predict matches and easy-to-predict matches?
    \item Is it possible to increase returns by applying different weights to hard-to-predict matches and easy-to-predict matches when investing?
\end{enumerate}

\section{Methodology}

\subsection{Machine learning algorithms}
The machine learning methods used  are drawn from open-source machine learning libraries. These include Scikit-learn\cite{pedregosa2011scikit}, XGboost and CatBoost.

\paragraph*{Logistic regression} Logistic regression predicts the probability on the basis of linear regression. It converts predictions to probabilities and then implements classification.
The algorithm demonstrates a strong ability to deal with data with a strong linear relationship between features and labels. Logistic regression also has the advantage of being noise-resistant and performs well on small data sets. \citet{prasetio2016predictingLR} used logistic regression in predicting the English Premier League. Using in-play features, the authors obtained a prediction accuracy of 69\%.

\paragraph*{Decision Tree}  This algorithm builds a Decision Tree \cite{quinlan1986induction} by choosing features that have the greatest information gain. The advantage is that it does not require any domain knowledge or parameter assumptions and is suitable for high-dimensional data. However, this algorithm is prone to overfitting and tends to ignore correlations between attributes. The use of a small number of features in the Decision Tree methods can prevent overfitting when predicting the results of football matches. The Decision Tree approach may therefore produce a more explanatory and thus informative model.

\paragraph*{Random Forest} This is an ensemble-based method  which combines  multiple Decision Trees. The Random Forest approach integrates multiple Decision Trees and builds each one using a non-backtracking approach. Each of these Decision Trees relies on independent sampling and has the same randomness in data selection as the other trees. When classifying the data, each tree is polled to return the category with the most votes, giving a score for the importance of each variable and assessing the importance of each variable in the classification. Random Forests tend to perform better than Decision Trees in preventing overfitting.

The correlation between the model features and the test predictions in the Random Forest approach is not strong. For poorly predicted football match results, this may be an advantage of the Random Forest approach. Using a training set containing a large number of features can result in a generated model with strong predictive power on a small number of them and weak predictive power on others. The classification criteria are different for each Decision Tree in the Random Forest model. This can also be a good way to reduce the correlation between Decision Trees.

\paragraph*{k-Nearest Neighbor} The k-Nearest Neighbor(KNN) method classifies samples by comparing a particular sample with its \textit{k} closest data points in a given dataset and therefore does not generate a classifier or a model  \cite{peterson2009k}.

KNN methods have an excellent performance when using data from in-play contexts to predict the results of contests\cite{esme2018prediction}. However, the method needs to consider all the data in the sample when generating the prediction model. Such an approach creates a strong risk of overfitting in the prediction of pre-match results in competitive sports. Nevertheless, it is still not known how well the KNN method can perform for hard-to-predict matches.

\paragraph*{Gradient Boosting} The idea behind gradient boosting is to iteratively generate multiple weak models and then add up the predictions of each weak model. Each residual calculation increases the weight of the wrongly split samples, while the weights of the split pairs converge to zero, so the generalisation performance is better. The importance of the features of the trained model can be extracted.

In previous studies\cite{alfredo2019football} of match prediction gradient boost methods have often failed to produce the best models. However, the predictive power of the method in hard-to-predict matches cannot be denied outright.

\paragraph*{XGBoost} XGBoost extends and improves upon the Gradient Boosting. The XGBoost algorithm is faster. It takes advantage of the multi-threading of the CPU based on traditional Boosting and introduces regularisation to control the complexity of the model. Prior to the iteration, the features are pre-ranked for the nodes and by traversing them the best segmentation points are selected, which results in lower complexity of data segmentation.

The XGBoost method is popular amongst machine learning researchers. However, the method does not perform well in capturing high-dimensional data, such as images, audio, text, etc. For predicting football matches with based on lower-dimensional data, XGBoost may produce promising models.

\paragraph*{CatBoost}
CatBoost algorithm is a type of gradient boosting algorithm. In contrast to the gradient boosting algorithm, this algorithm can also achieve excellent results using data that has not been feature engineered. It does better than gradient boosting in preventing overfitting. The CatBoost method has not been explored in previous studies of football match result prediction.

\paragraph*{Voting and Stacking} The voting classifier can vote on the results of different models, with the majority deciding the outcome. The Voting classifier is divided into Hard and Soft implementation. The Hard voting is votes on the results obtained using multiple machine learning methods, with the majority getting the result. Soft voting is the process of calculating the mean of the classification probabilities of the different methods, and finally selecting the one with the highest mean as the prediction result.

The stacking algorithm refers to a hybrid estimator approach in which a number of estimators are fitted separately on training data, while the final estimator is trained using the stacked predictions of these basic estimators. However, the stacking method uses cross-validation which is not favoured in the field of football result prediction when training the model.

Voting and stacking methods have produced the best prediction models in other studies of athletic match result prediction\cite{li2019high}. However, in football these two methods are rarely used. This study uses both methods in an attempt to find the most suitable model for prediction in difficult-to-predict matches.

\subsection{Dataset characteristics and feature engineering}

The Premier League data used in this study was sourced from the website https://www. footballdata.co.uk/englandm.php. The results from the 2001 to 2018 seasons were used to develop features based on ELO ratings, attack and defence ratings and home-team and away-team winning percentages. Data from the 2019 to 2021 seasons were used for testing. The raw data was recorded using a total of 107 columns of data for the 2019 to 2021 seasons.

The Premier League system divides the season into 38 rounds and guarantees that each of the 20 teams will play once in each of the 10 matches in each round. After 380 matches per season, each team plays 19 times in the home position and 19 times in the away position. This study predicts the results of 3 seasons, implying a total of 1140 predicted matches.

The Premier League is based on a points system, with the winning team gaining three points after the match and the two drawing teams gaining one point each. 24 teams are entered for the 2019-2021 season, all of which appeared in the 2001-2018 season. However, due to differences in the raw data on each season on bookmaker odds records, in fact, only 21 of the 83 columns of data were used in the 2019-2021 season predictions. The records are for the six European bookmakers and the European average odds respectively.

The premise of this study for feature engineering is the assumption that all matches occur continuously.

A total of 52 features were generated and explored in this project. Their names and descriptions are given in Table~\ref{Table 1. Description of features}.

\begin{table}[]
\centering
\caption{\label{Table 1. Description of features}Description of features}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}ll@{}}
\toprule
Feature Name  & Description                                                                         \\ \midrule
AvgGoalDiff   & Average goal difference between the two teams in the previous six games             \\
TotalGoalDiff & Goal difference between the two teams in the previous six games                     \\
HomeELO       & ELO ratings for the home team                                                       \\
AwayELO       & ELO ratings for away teams                                                          \\
ELOsta        & Standard deviation of the ELO ratings of the two teams                              \\
ELOHomeW      & Probability of home team winning converted by ELO ratings                           \\
ELOAwayW      & Probability of away team winning converted by ELO ratings                           \\
ELODraw       & Probability of a draw occurring converted by ELO ratings                            \\
one\_ELO      & Probability of conversion from ELO ratings after PCA dimensionality reduction       \\
HomeHELO      & ELO ratings for the home team's half-time result                                    \\
AwayHELO      & ELO ratings for the away team's half-time result                                    \\
HELOSta       & Standard deviation of the half-time ELO ratings of the two teams                    \\
ELOHHomeW     & Probability of home team winning converted by half-time ELO ratings                 \\
ELOHAwayW     & Probability of away team winning converted by half-time ELO ratings                 \\
ELOHDrawW     & Probability of a draw occurring converted by half-time ELO ratings                  \\
one\_HELO    & Probability of conversion from half-time ELO ratings after PCA dimensionality reduction                                                    \\
HomeTeamPoint & Current home team points in the season                                              \\
AwayTeamPoint & Current away team points in the season                                              \\
PointDiff     & Current point difference between home and away teams in the season                  \\
AvgHOddPro    & Average of pre-match home team odds offered by all bookmakers in the available data \\
AvgAOddPro    & Average of pre-match away team odds offered by all bookmakers in the available data \\
AvgDOddPro    & Average of pre-match draw odds offered by all bookmakers in the available data      \\
one\_Odd\_Pro & Average odds after PCA dimensionality reduction                                     \\
HomeOff       & Rating of the home team's offensive capabilities                                    \\
HomeDef       & Rating of the home team's defensive capabilities                                    \\
AwayOff       & Rating of the away team's offensive capabilities                                    \\
AwayDef       & Rating of the away team's defensive capabilities                                    \\
Offsta        & Difference in offensive capability rating                                           \\
Defsta        & Difference in defensive capability rating                                           \\
AvgShotSta   &  Standard deviation of shots on goal for both sides in six matches          \\
AvgTargetSta & Standard deviation of shots on target for both sides in six matches \\
ShotAccSta    & Standard deviation of shot accuracy between the home team and the away team         \\
AvgCornerSta & Standard deviation of corners for both sides in six matches         \\
AvgFoulSta   & Standard deviation of fouls for both sides in six matches          \\
HomeHWin      & Home team's winning percentage in home games                                        \\
HomeHDraw     & Home team's draw percentage in home games                                           \\
AwayAWin      & Away team's winning percentage in away games                                        \\
AwayADraw     & Away team's draw percentage in away games                                           \\
HomeWin       & Home team's win percentage in all previous matches                                  \\
HomeDraw      & Home team's draw percentage in all previous matches                                 \\
AwayWin       & Away team's win percentage in all previous matches                                  \\
AwayDraw      & Away team's draw percentage in all previous matches                                 \\
LSHW          & Home team win percentage last season                                                \\
LSHD          & Home team draw percentage last season                                               \\
LSAW          & Away team win percentage last season                                                \\
LSAD          & Away team draw percentage last season                                               \\
Ysta          & Difference in the number of yellow cards between the home team and the away team    \\
Rsta          & Difference in the number of red cards between the home team and the away team       \\
StreakH       & Home team winning streak index                                                      \\
StreakA       & Away team winning streak index                                                      \\
WStreakH      & Home team weighted winning streak index                                             \\
WStreakA      & Away team weighted winning streak index
                                        \\
\midrule
\end{tabular}
\end{table}

\subsubsection*{ELO Rating}

The ELO rating was first introduced by ELO\cite{ELO1978} to assess the ability of players in chess competitions and has been extended to the assessment of the performance of players or teams in many sports. The rationale is to achieve a dynamic evaluation of a particular player's ability by comparing the ability of the player in a recent match with that player's past performance. The time-series nature of football matches makes the  ELO model suitable for scoring the performance of football teams\cite{jain2021sports}.

The score of the participating teams in a football match is determined by their performance in past matches (Eq~\ref{Eq.1}) and the rating of their performance in the current match of the competition (Eq`\ref{Eq.2}) are as follows:

\begin{align}\label{Eq.1}
    E_{}^{H} & = \cfrac{1}{1 + \cfrac{c^{R^{H} -R^{A}} }{d}}  \quad\quad\quad E_{}^{A}  = 1-E_{}^{H}
\end{align}

\begin{align}\label{Eq.2}
S_{}^{H} & = \left\{\begin{matrix}
  1 \qquad  Home\quad team\quad win\\
  0.5 \qquad  Draw\\
  0\qquad  Away\quad team\quad win
\end{matrix}\right. \qquad
\end{align}

\begin{align}\label{Eq.3}
S_{}^{A} = 1 -S_{}^{H}
\end{align}

where $E^H$ and $E^A$ are the performance ratings that teams are supposed to have in that match, $S^H$ and $S^A$ are the actual performance ratings of two teams. $R^H$ and $R^A$ are the ratings that the two teams have constantly revised to represent their own team's ability, and $c$ and $d$are two constants based on the scale of scoring. In this study $c$ was set to 10 and $d$ to 400 to ensure that the effect of the new matches' results on the previous ELO ratings was kept in a balanced range.. The scoring of the two teams is appropriately corrected by the error between the ability of the two teams during the newly occurring match and previously assessed performance, using the following:

\begin{align}
R^{'H} = R^{H} +k(S^{H}-S^{E})
\end{align}

where $k$ indicates the magnitude of the correction. $k$ is used to determine the effect of the results of the new competition on the scoring. $k$ is calculated as follows:

\begin{align}
k = k_0(1+\delta)^{\gamma }
\end{align}

where $\delta$ is the absolute goal difference and $k_0$ and $\gamma$ are set to 10 and 1.

The performance ability of teams was first assessed in this study using match results from the 2001-2005 English Premier League season. Teams were ranked and assigned ratings by comparing the total scores and wins of teams in the 2001-2002 season. The team ratings were corrected using match data from the 2002-2017 season. 2018-2019 season was formally characterised using the ratings generated by the ELO model, and each team's rating was subsequently corrected for the previous match results.

In a subsequent study on ELO ratings, a regression model was generated to predict wins and losses by the ELO rating profile of the teams from both sides before the match\cite{hvattum2010using}. The model has a high degree of confidence among those involved in football gambling. The probability of different match outcomes occurring can be simply predicted using the ELO scores of the teams on both sides of the match using the following formula:

\begin{align}
P_{H} & = 0.448+(0.0053*(E^{H} -E^{A} ))
\end{align}
\begin{align}
P_{A} & = 0.245+(0.0039*(E^{A} -E^{H} ))
\end{align}
\begin{align}
P_{D} = 1- (P_{H}+P_{A})
\end{align}

where $P^H$ indicates the probability of the home team victory, $P^A$ indicates the probability of the away team victory occurring and $P^D$ indicates the probability of a draw situation occurring.

\subsubsection*{Offensive and defensive capabilities}

The Offensive and Defensive Model (ODM) \cite{govan2009offense} is used to generate a team's offensive and defensive abilities. The calculation formula (Eq~\ref{Eq.9}) for scoring given in the introduction of the ODM model by \citet{govan2009offense} is as follows:

\begin{align}\label{Eq.9}
o_j = \sum_{i = 1}^{n} \frac{{A_i}_j}{d_i}  \qquad dj = \sum_{i = 1}^{n} \frac{{A_j}_i}{o_i}
\end{align}

where ${A_i}_j$ is a goal scored by team $j$ in a match between teams from both sides of the match, $o_j$ is the offensive rating and $d_j$ is the defence rating. The equation shows that the two ratings affect each other.  We directly assess the offensive and defensive ratings of a team one season and apply them to the next season. A team with high goal-scoring has a high offensive rating. Likewise, a team with a high number of goals conceded has an inefficient defensive rating.

For teams new to the season, we extrapolate their offensive and defensive ratings based on that team's ranking in goals scored and goals against during the season. This is calculated as follows:

\begin{align}
o_j = \frac{XG_2+X_2G_1-X_1G_1-X_1G_2}{X_2-X_1}
\end{align}

where $O_j$ represents the new team's offensive score. $G$ is the goals scored by the new team during the season. $G1$ and $R1$ are the goals scored and offensive rankings of the teams that are one place above the new team in the season goal rankings. $G2$ and $R2$ are the goals scored and rankings of the teams that are one place below. The defensive rating is calculated in the same way.

\subsubsection*{Streak Index}

The Streak Index represents a team's capacity to go on a winning streak which captures a team's most recent form. The index was generated by \citet{baboota2019predictive}  in predicting the results of the Premier League for the two seasons 2014-2016. the Streak Index is further divided into two categories, the first of which directly measures the team's form over the previous $k$ games, with the following formula:

\begin{align}
S = (\sum_{p=j-k}^{j-1} res_{p} )/3k
\end{align}

where $j$ indicates the number of matches to be predicted and $res_p$ indicates the team's score in a particular match, where a win and a draw correspond to 3 points and 1 point respectively. No points are awarded for losses. In the second category, the Streak Index, is weighted and normalised based on the first category. Relatively low weights are given to matches that occur further back in time. The formula for this is as follows:
\begin{align}
\omega _{S} = \sum_{p=j-k}^{j-1} 2\frac{p-(j-k-1)res_{p} }{3k(k-1)}
\end{align}

The Streak Index is logically problematic when calculating across seasons. This means that when calculating the Streak Index for the first few games of a season, the data used is from the last season's end. The changes in team form that occur during the intervening season can compromise the effectiveness of the Streak Index.

\subsubsection*{Principal Component Analysis}

As the outcome of a football match includes a draw, bookmakers also offer odds in the event of a draw. This requires a feature reduction method to turn three-dimensional data into one-dimensional data.

This study uses the Principal Component Analysis (PCA) \cite{wold1987principal}  to reduce the dimensionality of the data. This function linearly reduces the dimensionality on the original data by projecting the original data to an alternative dimension where the data loss is minimised.
PCA is generally used to process and compress high-dimensional data sets. The main objective is to reduce the dimensionality of a large feature set into one that is most essential with the tradeoff that the new features lose interpretability.

\subsubsection*{Kelly Index}

The Kelly index\cite{thorp1975portfolio} was used as a tool to classify the matches in  the dataset into categories that define different levels of predictability.
In literature, the Kelly Index was originally used to calculate the flow-through rate of electronic bits\cite{kelly1996synchronization}. However, due to its probabilistic nature and its similarity to the nature of betting, the Kelly Index is also widely used by bettors.

Each bookmaker calculates the Kelly Index before a match and makes it available to members who gamble.
The Kelly Index can be calculated from the available data using the following formula:

\begin{align}
K_{H}=(O_{H}/avgO_{H} )F_{99}   &\\K_{A}= (O_{A}/avgO_{A} ) F_{99} &\\K_{D}=(O_{D}/avgO_{D} )F_{99}
\end{align}

where $K_{H}$, $K_{A}$, and $K_{D}$ indicate the three results of matches in terms of the Kelly Index. $avgO_{H}$, $avgO_{A}$, and $avgO_{D}$ indicate in our dataset the average European betting market odds for each of the three results of the matches. $F_{99}$ indicates the return rate of the European average odds, which is calculated by the following formula:

\begin{align}
F_{99} =\frac{1}{\frac{1}{avgO_{H}}+ \frac{1}{avgO_{A}}+\frac{1}{avgO_{D}}}
\end{align}

If a bookmaker has set lower odds on an event occurring than any other bookmaker,  this means that the bookmaker is confident enough to believe that a particular outcome will occur. This confidence may come from the bookmaker's perception of possessing more effective prediction models, having access to more extensive sources of information, or illegal black market trading. The bookmaker as a dealer is willing to set the lowest odds on a more likely event to maximise profits. Therefore a bookmaker's Kelly Index is the most likely event to occur. At the same time, if there is a low Kelly Index at one bookmaker, there will be a high Kelly Index for other events accordingly. However, there is no guaranteed correlation between the level of the Kelly Index and the result of a match as this is just a technique for understanding what odds have been determined to be in the best interest of the bookmaker for maximising their returns.

\begin{figure}[h]
\centering
\includegraphics[width=0.9\textwidth]{boxplot01.png}
\caption{The distribution of the Kelly Index of the six European bookmakers for the 2019-2021 season.}
\label{fig:The distribution of the Kelly Index of the six European bookmakers for the 2019-2021 season}
\end{figure}

As shown in Figure ~\ref{fig:The distribution of the Kelly Index of the six European bookmakers for the 2019-2021 season}, the Kelly Indexes of these six bookmakers are mainly concentrated in the range of 0.9-1.0. In the setup of the predictive problem, the matches for the 2005-2021 season were divided into 3 categories with each one reflecting the confidence levels of their predictability. These were, matches with Kelly indexes greater than 1 (Type 1), matches with only one Kelly index greater than 1 (Type 2), and matches with no Kelly Index greater than 1 (Type 3).

\subsection{Model Optimisation}

\subsubsection*{Hyperparameter tuning}

This study used the RandomizedSearchCV method from the scikit-learn library to select the most effective parameter values. All the parameter tuning values for the machine learning algorithms used in this study are shown in Table~\ref{Values for parameter tuning}.

\begin{table}[hbt]
\centering
\caption{\label{Values for parameter tuning}
Values for parameter tuning
}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}lll@{}}
\midrule
Algorithm                                                       & Parameter                  & Range of values                           \\
\midrule
\vcell{CatBoost}                                                & \vcell{learning\_rate}     & \vcell{0.01,0.02,0.03,0.04}               \\[-\rowheight]
\printcelltop                                                   & \printcellmiddle           & \printcellmiddle                          \\
                                                                & iterations                 & 10,20,30,40,50,60,70,80,90                \\
                                                                & depth                      & 4,5,6,7,8,9,10                            \\
\vcell{Decision Tree}                                           & \vcell{criterion}          & \vcell{'gini', 'entropy'}                 \\[-\rowheight]
\printcelltop                                                   & \printcellmiddle           & \printcellmiddle                          \\
                                                                & max\_depth                 & 2,4,6,8,10,12                             \\
\vcell{Gradient boost}                                          & \vcell{min\_samples\_leaf} & \vcell{2,5,8}                             \\[-\rowheight]
\printcelltop                                                   & \printcellmiddle           & \printcellmiddle                          \\
                                                                & min\_samples\_split        & 3,5,7,9                                   \\
                                                                & max\_features              & Based on number of filtered features  \\
                                                                & max\_depth                 & 2,5,7,10                                  \\
                                                                & learning\_rate             & 0.1,1.0,2.0                               \\
                                                                & subsample                  & 0.5,0.8,1                                 \\
\textcolor[rgb]{0.125,0.129,0.141}{k-Nearest Neighbor}          & n\_neighbors               & Based on sample size                      \\
\vcell{\textcolor[rgb]{0.071,0.071,0.071}{Logistic regression}} & \vcell{solver}             & \vcell{liblinear}                         \\[-\rowheight]
\printcelltop                                                   & \printcellmiddle           & \printcellmiddle                          \\
                                                                & penalty                    & 'l1','l2'                                 \\
                                                                & class\_weight              & 1:2:1,3:3:4,4:3:3                         \\
\vcell{Random Forest}                                           & \vcell{min\_samples\_leaf} & \vcell{2,5,8}                             \\[-\rowheight]
\printcelltop                                                   & \printcellmiddle           & \printcellmiddle                          \\
                                                                & max\_features              & Based on number of filtered features  \\
                                                                & max\_depth                 & 2,5,7,10                                  \\
Stacking                                                        & Same as above algorithm    & Same as above algorithm                   \\
Voting                                                          & Same as above algorithm    & Same as above algorithm               \\
\hline
\end{tabular}
\end{table}

\subsubsection*{Feature selection}
Models developed with feature selection tend to have greater explanatory power, run faster, and have a decreased risk of over-fitting. In some cases, feature selection will improve the predictive power of models. With the exception of the two ensemble algorithms Voting classifier and Stacking, feature selection was used to enhance the models.

Feature selection decisions were made using Shapley Additive exPlanations\cite{lundberg2017unified} (SHAP). SHAP is based on the Shapley value\cite{winter2002shapley}, a concept derived from cooperative games, and is a common metric for quantitatively assessing the marginal contribution of users in an equitable manner. SHAP has been implemented as a visualisation tool for model interpretation that is able to score every feature in terms of its effects on the final outcome. Efficient feature selection can be achieved by removing features that are indicated to have low impacts on predictions. For multiclassification gradient boosting models where the SHAP explainer is not available, the Recursive Feature Elimination method in the scikit-learn library was used to remove the least important features recursively selected in the dataset.

In the feature selection process, after generating a model that has been modelled using all features and tuned with hyperparameters, the features in the validation set with an average SHAP value of less than zero were removed and the dataset was remodelled after the low-impact features were. This loop continues until the number of features is less than 2 or no features with a SHAP value less than zero appear. After the iterative process is completed, the model with the highest prediction accuracy in the validation set is selected as the prediction model for the test set.

\subsection{Model training and testing framework}

\subsubsection{Modelling process}

This study uses an extended window approach to test the models in order to avoid the mistake of using information from future matches to predict past matches which is in contrast to a number of other studies on sports outcome prediction. \citet{bunker2019machineANN} outline in detail why  standard cross-validation is not suitable for evaluation of prediction models in this domain. The pattern of the training and testing sequences comprising windows of division is shown in Figure  ~\ref{fig:Window extension strategies for predictive models} while the modelling process is shown in Figure ~\ref{fig:modelling process}.

Training sets from the immediately preceding season are used to make predictions for the next season. This strategy was followed since it has been shown that it is more informative to choose the most recent matches for predictions of upcoming matches. The reason for this is that the game of football, being a high-intensity competitive sport, advances over time in terms of its macro tactics and the detail of the players' actions\cite{smith2007nature}. As the number of different types of matches varies from season to season, the size of the test set is set at 20 to 30 matches depending on the number of matches of a particular type in the current season.

\begin{figure}[h]
\centering
\includegraphics[width=0.9\textwidth]{Windowapproach.png}
\caption{Window extension strategies for predictive models}
\label{fig:Window extension strategies for predictive models}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=0.5\textwidth]{Step.png}
\caption{Modelling process}
\label{fig:modelling process}
\end{figure}

The validation set is used in order to select the best model during parameter tuning. When using models where parameter tuning has little impact on model quality (e.g. Voting Classifier) the validation set is not used and the part of the model that would otherwise be part of the validation set is merged with  the training set. The validation set is usually set to the same size as the test set for that window.

\subsubsection{Model evaluation}

This study evaluates the predictive ability of each classifier by using four metrics. These four reported metrics are accuracy, precision, recall and F1 Score.
Accuracy is used as a primary metric for ranking the performances of the algorithms which the remaining metrics are used as a reference for completion.
These evaluation metrics are calculated as follows:

\begin{align}
Accuracy = \frac{TP+TN}{TP+FN+FP+TN}
\end{align}

where the denominator part indicates the number of all samples and the numerator part indicates the number of all correctly predicted samples.

\begin{align}
Precision = \frac{TP}{TP+FP}
\end{align}

where the denominator part indicates the number of samples for a particular result and the numerator part indicates the number of correctly predicted samples for that result species. The precision of the three classification questions is weighted by the proportion of each result in the sample using the precision of the three results.

\begin{align}
Recall = \frac{TP}{TP+FN}
\end{align}

Theoretically, the three classification problems have the same recall and accuracy on a given result. The recall in this study uses macro-Recall without considering the weights of each result.

\begin{align}
F_{1} = \frac{2\times Precision \times Recall}{Precison + Recall}
\end{align}

To evaluate the relative capability of the models, two baseline models were added for comparison. Both models are referenced from the Dummy Classifier class in the scikit-learn library. Both models ignore the data in the training set and make random predictions on the test set. Baseline model 1 is a random selection of one result from three results of matches as the predicted result. Baseline model 2 has a similar prediction process to baseline model 1, but predictions follow the distribution of each result in the test set.

\section{Result and discussion}\label{sec2}

\subsection{Match classification}\label{fm}

This study classified 1,140 matches in the English Premier League for the three seasons of 2019-2021 into three possible categories, namely win, loss, draw. Matches with multiple bookmakers having a Kelly Index greater than 1 were categorised as Type 1. Matches with only one bookmaker having a Kelly Index greater than 1 were categorised as Type 2. Matches with no bookmaker having a Kelly Index greater than 1 were categorised as Type 3. Their precise numbers in each season are shown in Table~\ref{Number of matches divided into different types}. The number of Type 1 matches decreases yearly, while the number of Type 2 matches increases yearly. This may indicate that bookmakers are generally becoming progressively more conservative in setting their odds.

\begin{table}
\centering
\caption{\label{Number of matches divided into different types}Number of matches according to different types and categories}
\label{Number of matches divided into different types}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{lcccccc}
\hline
\multirow{2}{*}{Category}  & \multirow{2}{*}{Season} & \multicolumn{4}{c}{Result Number}            & \multirow{2}{*}{Draw proportion}  \\
                           &                         & Home & Away & Draw & \multicolumn{1}{l}{All} &                                   \\
\hline
\multicolumn{1}{c}{Type 1} & 2019                    & 61   & 28   & 17   & 106                     & 16.0\%                           \\
                           & 2020                    & 50   & 43   & 18   & 111                     & 16.2\%                           \\
                           & 2021                    & 42   & 18   & 16   & 76                      & 21.1\%                           \\
\multicolumn{1}{c}{Type 2} & 2019                    & 35   & 28   & 18   & 81                      & 22.2\%                           \\
                           & 2020                    & 36   & 29   & 22   & 87                      & 25.3\%                           \\
                           & 2021                    & 55   & 42   & 27   & 124                     & 21.8\%                           \\
\multicolumn{1}{c}{Type 3} & 2019                    & 76   & 60   & 57   & 193                     & 29.5\%                           \\
                           & 2020                    & 58   & 81   & 43   & 182                     & 23.6\%                           \\
                           & 2021                    & 66   & 69   & 45   & 180                     & 25.0\%                           \\
\multicolumn{1}{c}{All}    & 2019                    & 172  & 116  & 92   & 380                     & 24.2\%                           \\
                           & 2020                    & 144  & 153  & 83   & 380                     & 21.9\%                           \\
                           & 2021                    & 163  & 129  & 88   & 380                     & 23.2\%
                           \\
                           \hline
\end{tabular}
\end{table}

Nearly half of all 1140 matches belonged to the Type 3. In these matches, the bookmakers were not confident in setting odds that constituted an increased liability for them.
Ultimately, Type 3 matches produced the highest percentage of draws, while Type 1 matches had the lowest percentage of draws confirming the efficacy of the Kelly Index to reduce uncertainty to some degree. Although draws are difficult to predict, they do not account for more than a third of matches in any category. In addition, home-team wins in Type 1 matches were much higher than the number of away-team wins. However, away-team wins were higher in the Type 3 matches. Bookmakers consider both draws and home team advantages when formulating their predictions.  Bookmakers are more likely to reduce the odds of a home win when considering setting odds or home teams.

Although bookmakers can adjust the odds based on their own predictions, upsets often happen in football matches. It is not always straightforward to precisely define which matches are upsets based on the available data. This study identifies matches as an upset when the study's prediction was correct and the bookmaker not only predicted incorrectly, but also set the highest odds on the actual outcome of the match. See the next sub-section for the predicted results. The percentage of upsets for each type is shown in Figure~\ref{fig:Percentage of upset in each type of match}.

\begin{figure}[h]
\centering
\includegraphics[width=1.0\textwidth]{coldGame.png}
\caption{Percentage of upset in each type of match}
\label{fig:Percentage of upset in each type of match}
\end{figure}

Betting agencies are poor predictors of Type 3 matches compared to the other two types. Upsets are very unlikely in the Type 1 matches, but they become a regular occurrence in the Type 3 matches. Figure~\ref{fig:Distribution of odds set by the six bookmakers on the predicted results of this study} aggregates the spread of the odds across all six betting agencies in this study. According to this figure, on average, bookmakers set significantly lower odds on results in Type 1 matches than in the other two categories.

\begin{figure}[htb]
\centering
\includegraphics[width=0.6\textwidth]{avg_odd_range.png}
\caption{Distribution of odds set by the six bookmakers on the predicted results of this study}
\label{fig:Distribution of odds set by the six bookmakers on the predicted results of this study}
\end{figure}

\subsection{Result prediction}
The prediction accuracy, precision, recall and average ranking of each algorithm across the prediction process for Type 1, Type 2 and Type 3 matches are all shown in Table~\ref{Prediction results from various machine learning algorithms in the Type 1 match}, Table~\ref{Prediction results from various machine learning algorithms in the Type 2 match} and Table~\ref{Prediction results from various machine learning algorithms in the Type 3 match} respectively. The algorithms are rank-ordered from best-performing onwards. The average ranking is likewise calculated by the accuracy of each algorithm across all different forecasting windows. Meanwhile, the accuracies of all the algorithms across the different Types are contrasted with the accuracies attained across all matches without taking the Kelly Index into account. These results can be seen in Table~\ref{Prediction results from various machine learning algorithms in the Type all matches}.

\begin{table}[]
\centering
\caption{\label{Prediction results from various machine learning algorithms in the Type 1 match}Prediction results from various machine learning algorithms in the Type 1 match}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}
>{\columncolor[HTML]{FFFFFF}}l
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c @{}}
\toprule
\textbf{Algorithm} & \textbf{Accuracy} & \textbf{Precision} & \textbf{Recall} & \textbf{F1\_Score} & \textbf{Rank} \\ \midrule
CatBoost           & 70.0\% & 66.6\% & 54.8\% & 63.6\% & 1.1 \\
Logistic Regression & 67.9\% & 64.8\% & 53.6\% & 62.3\% & 3.1 \\
Random Forest       & 68.9\% & 64.3\% & 54.9\% & 63.4\% & 3.2 \\
Voting              & 66.6\% & 59.4\% & 52.4\% & 61.7\% & 4.3 \\
KNN                 & 62.1\% & 60.6\% & 52.8\% & 61.3\% & 4.5 \\
Gradient Boosting   & 62.5\% & 59.6\% & 51.7\% & 60.8\% & 4.8 \\
Stacking            & 65.5\% & 54.1\% & 50.9\% & 59.1\% & 5.0 \\
Decision Tree       & 60.4\% & 56.7\% & 48.9\% & 58.2\% & 5.1 \\
XGBoost            & 63.8\% & 57.1\% & 51.0\% & 59.6\% & 5.3 \\
Baseline 1               & 47.1\% & 33.5\% & 31.5\% & 37.4\% & 8.8 \\
Baseline 2        & 30.4\% & 36.9\% & 29.9\% & 32.1\% & 9.8 \\ \bottomrule
\end{tabular}
\end{table}

\begin{table}[]
\centering
\caption{\label{Prediction results from various machine learning algorithms in the Type 2 match}Prediction results from various machine learning algorithms in the Type 2 match}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}
>{\columncolor[HTML]{FFFFFF}}l
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c @{}}
\toprule
\textbf{Algorithm} & \textbf{Accuracy} & \textbf{Precision} & \textbf{Recall} & \textbf{F1\_Score} & \textbf{Rank} \\ \midrule
CatBoost           & 49.7\% & 38.8\% & 42.0\% & 43.3\% & 2.8 \\
Logistic Regression & 51.0\% & 49.3\% & 45.4\% & 48.8\% & 3.1 \\
Random Forest       & 52.7\% & 50.9\% & 46.5\% & 49.2\% & 3.4 \\
Decision Tree       & 45.9\% & 45.3\% & 42.6\% & 45.6\% & 3.7 \\
Stacking            & 49.3\% & 44.5\% & 42.1\% & 43.8\% & 4.3 \\
Voting              & 47.9\% & 44.5\% & 42.7\% & 45.7\% & 4.9 \\
XGBoost            & 48.6\% & 46.0\% & 43.6\% & 46.7\% & 5.0 \\
KNN                 & 39.7\% & 40.1\% & 37.5\% & 39.9\% & 5.9 \\
Gradient Boosting   & 40.8\% & 39.7\% & 37.6\% & 40.0\% & 6.2 \\
Baseline 1               & 40.1\% & 29.0\% & 32.3\% & 31.7\% & 6.9 \\
Baseline 2        & 31.5\% & 33.5\% & 31.3\% & 32.1\% & 8.7 \\ \bottomrule
\end{tabular}
\end{table}

\begin{table}[]
\centering
\caption{\label{Prediction results from various machine learning algorithms in the Type 3 match}Prediction results from various machine learning algorithms in the Type 3 match}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}
>{\columncolor[HTML]{FFFFFF}}l
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c @{}}
\toprule
\textbf{Algorithm} & \textbf{Accuracy} & \textbf{Precision} & \textbf{Recall} & \textbf{F1\_Score} & \textbf{Rank} \\ \midrule
Decision Tree       & 40.0\% & 38.5\% & 37.5\% & 38.5\% & 3.9 \\
CatBoost           & 40.0\% & 37.6\% & 36.3\% & 35.2\% & 4.0 \\
Random Forest       & 41.1\% & 39.4\% & 38.4\% & 39.1\% & 4.2 \\
Logistic Regression & 40.7\% & 38.8\% & 38.2\% & 39.1\% & 4.5 \\
Voting              & 40.0\% & 39.1\% & 37.7\% & 38.5\% & 4.6 \\
Gradient Boosting   & 37.7\% & 38.0\% & 37.0\% & 37.8\% & 5.0 \\
Stacking            & 39.1\% & 35.5\% & 35.9\% & 36.2\% & 5.2 \\
XGBoost            & 39.6\% & 38.8\% & 37.9\% & 39.0\% & 5.4 \\
KNN                 & 35.3\% & 34.9\% & 33.9\% & 34.8\% & 5.8 \\
Baseline 2        & 37.3\% & 38.3\% & 37.0\% & 37.6\% & 6.2 \\
Baseline 1               & 36.4\% & 26.3\% & 33.4\% & 26.4\% & 6.4 \\ \bottomrule
\end{tabular}
\end{table}

\begin{table}[]
\centering
\caption{\label{Prediction results from various machine learning algorithms in the Type all matches}Prediction results from various machine learning algorithms in the all matches}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}
>{\columncolor[HTML]{FFFFFF}}l
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
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\toprule
\textbf{Algorithm} & \textbf{Accuracy} & \textbf{Precision} & \textbf{Recall} & \textbf{F1\_Score} & \textbf{Rank} \\ \midrule
CatBoost           & 51.9\% & 45.7\% & 44.7\% & 45.3\% & 2.6 \\
Logistic Regression & 50.6\% & 44.0\% & 43.5\% & 45.2\% & 3.2 \\
Random Forest       & 52.0\% & 47.7\% & 44.7\% & 45.7\% & 3.4 \\
Stacking            & 51.3\% & 46.7\% & 44.5\% & 45.9\% & 3.6 \\
Decision Tree       & 50.2\% & 46.6\% & 44.6\% & 46.2\% & 3.8 \\
Voting              & 49.9\% & 46.7\% & 44.5\% & 47.0\% & 4.6 \\
Gradient Boosting   & 47.1\% & 45.8\% & 43.3\% & 46.3\% & 5.0 \\
XGBoost            & 48.4\% & 45.7\% & 43.5\% & 46.5\% & 5.7 \\
KNN                 & 45.4\% & 44.4\% & 42.0\% & 44.8\% & 5.7 \\
Baseline 1               & 40.5\% & 28.4\% & 32.8\% & 29.7\% & 8.0 \\
Baseline 2        & 31.9\% & 33.2\% & 32.1\% & 32.2\% & 9.2 \\ \bottomrule
\end{tabular}
\end{table}

The model offering the greatest predictive performance for the Type 1 matches across all forecasting windows was produced by  CatBoost, with an accuracy of 70\%. This performance was significantly better than that of the baseline methods which scored well below 50\%.

The best model in the Type 2 matches was generated by Random Forest, although Catboost ranked as the winner across all the forecasted windows. Random Forest achieved 53\% which represents a significant reduction in accuracy compared to Type 1 models. However, the best-performing models under the Type 2 setting still clearly outperformed baseline predictions.

The accuracy of Type 3 accuracies continued the decrease down to 41\%, which was the best accuracy registered by  Random Forest. Though overall, both the Decision Tree and CatBoost performed more consistently across all the forecasting windows. While the best-performing models' efficacy significantly reduced for Type 3 matches, they still marginally contributed more value than baseline models.
Unexpectedly, stacking and voting methods were consistently outperformed by other algorithms which is in contrast to the performance of these algorithms in other studies covering competitive sports.

The results from the previous tables are depicted in Figure~\ref{fig:As the extended window progresses, the trend in prediction accuracy of the algorithms with the best predictive ability for different types of matches} highlighting the accuracy of each of the best-performing algorithms across time for each season, and Type of matches. The dashed lines in the figure represent interpolations in cases where no matches were predicted for a given Type when matches meeting the Kelly Index criteria did not exist. The figure demonstrates that Type 1 predictions consistently outperformed other Types.
.
Taken altogether, the results demonstrate the  efficacy of the Kelly Index to reduce an element of uncertainty from the predictive problem and thereby increase the overall predictive accuracy.

\begin{figure}[hbt]
\centering
\includegraphics[width=1.0\textwidth]{United.png}
\caption{As the extended window progresses, the trend in prediction accuracy of the algorithms with the best predictive ability for different types of matches.}
\label{fig:As the extended window progresses, the trend in prediction accuracy of the algorithms with the best predictive ability for different types of matches}
\end{figure}

The next analysis considers the internals of the predictive moedls and uses SHAP in order to understand the impact of the key features on the best-performing algorithms based on their ranks, across each of the Types of matches. The feature importances and their effects are shown in Figure~\ref{fig:Scatterplot of SHAP values for the top 10 features of importance when being predicted for the three different types of matches and for all matches.}.

For Type 1 matches, the top most influential features are based on the team's historical match statistics based on their home-win record. These are matches where the home team's advantage exists and it is easier to determine whether the match will be one-sided based on the features of the home team. The rarety of draw results of such matches also leads to a higher prediction accuracy.

In the cases of Type 2 matches, we can see that as the prediction becomes more difficult, historical data on both teams becomes less important in and is replaced by odds data provided by bookmakers before the match.

Meanwhile, in predicting the Type 3 matches, historical data appears to be inconsequential. The features based on bookmakers' prediction estimates  still have the advantage in predicting these matches. The already low accuracy accuracy of the Type 3 matches still depends on the results of the bookmakers' forecasts. The odds in this case  have an almost direct influence on the prediction of uncategorised matches.

\begin{figure}[H]
\centering
\includegraphics[width=1.0\textwidth]{new_united_shap.png}
\caption{Scatterplot of SHAP values for the top 10 features of importance when being predicted for the three different types of matches and for all matches.}
\label{fig:Scatterplot of SHAP values for the top 10 features of importance when being predicted for the three different types of matches and for all matches.}
\end{figure}

\subsection{Betting returns}
This section compares traditional betting methods in football betting with the returns of classified matches betting to examine if there is a way to maximise returns or minimise risk. We first begin by highlighting the distribution in confidence probabilities of the machine learning algorithms across different Types as this will form a key factor when comparing betting strategies.

Table \ref{The distribution of confidence in the predicted results of each type across seasons in different ranges} shows the distribution of confidence in the predicted outcomes for the three types of matches. Even for the most predictable matches, machine learning has difficulty predicting a match's result with confidence. Surprisingly, the proportion of these predictions that machine learning considered extremely confident was similar for the easy-to-predict matches and the hard-to-predict matches, and these matches were rarely present in both types of matches.

\begin{table}
\centering
\caption{\label{The distribution of confidence in the predicted results of each type across seasons in different ranges}The distribution of confidence in the predicted results of each type across seasons in different ranges}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{lccccccc}
\toprule
\multirow{2}{*}{Type}  & \multicolumn{1}{l}{\multirow{2}{*}{Season}} & \multicolumn{5}{c}{Range of confidence}                                                      & \multicolumn{1}{l}{\multirow{2}{*}{Match number}}  \\
                       & \multicolumn{1}{l}{}                        & 0.7-1.0          & 0.6-0.7          & 0.5-0.6          & 0.4-0.5          & 0.33-0.4         & \multicolumn{1}{l}{}                               \\\midrule
\multirow{3}{*}{Type1} & \vcell{2019}                                & \vcell{8.5\%}    & \vcell{10.4\%}   & \vcell{15.09\%}  & \vcell{55.7\%}   & \vcell{10.4\%}   & \vcell{106}                                        \\[-\rowheight]
                       & \printcellmiddle                            & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle                                   \\
                       & 2020                                        & 0.0\%            & 0.0\%            & 4.50\%           & 42.3\%           & 53.2\%           & 111                                                \\
                       & 2021                                        & 2.6\%            & 25.0\%           & 27.63\%          & 36.8\%           & 7.9\%            & 76                                                 \\
\multirow{3}{*}{Type2} & \vcell{2019}                                & \vcell{17.3\%}   & \vcell{28.4\%}   & \vcell{13.58\%}  & \vcell{25.9\%}   & \vcell{14.8\%}   & \vcell{81}                                         \\[-\rowheight]
                       & \printcellmiddle                            & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle                                   \\
                       & 2020                                        & 5.8\%            & 10.3\%           & 33.33\%          & 41.4\%           & 9.2\%            & 87                                                 \\
                       & 2021                                        & 11.3\%           & 33.1\%           & 18.55\%          & 24.2\%           & 12.9\%           & 124                                                \\
\multirow{3}{*}{Type3} & \vcell{2019}                                & \vcell{6.2\%}    & \vcell{6.2\%}    & \vcell{19.69\%}  & \vcell{48.7\%}   & \vcell{19.2\%}   & \vcell{193}                                        \\[-\rowheight]
                       & \printcellmiddle                            & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle & \printcellmiddle                                   \\
                       & 2020                                        & 2.2\%            & 8.2\%            & 21.98\%          & 47.8\%           & 19.8\%           & 182                                                \\
                       & 2021                                        & 2.8\%            & 8.9\%            & 21.11\%          & 47.2\%           & 20.0\%           & 180              \\
                       \midrule
\end{tabular}
\end{table}

We next construct a simulated betting scenario in order to determine the return on investment(ROI) based on several strategies. We hypothetically invest \$1 on each match and receive corresponding profits according to the odds for a correct prediction, and a loss of the investment of \$1 for a wrong prediction. The ROI is calculated by dividing the investment profit by the total amount invested. A positive or negative ROI is used to determine whether an investment strategy is profitable or not.

Firstly, a set of benchmark ROIs are prepared for this study and are shown in Table~\ref{All invested in one type of return}. These are returns based on the model with the highest prediction accuracy across each of the Kelly index categories as well as the baseline which includes all matches, investing in the six bookmakers. A naive approach indicates marginal returns on two cases only, with higher losses across all other scenarios.

\begin{table}[]
\centering
\caption{\label{All invested in one type of return}Return on total investment by type of competition}
\fontsize{7pt}{9pt}
\selectfont
\begin{tabular}{@{}
>{\columncolor[HTML]{FFFFFF}}l
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c
>{\columncolor[HTML]{FFFFFF}}c @{}}
\toprule
\textbf{}             & \textbf{Type1} & \textbf{Type2} & \textbf{Type3} & \textbf{Baseline} \\ \midrule
\textbf{Match number}   & 292            & 293            & 555            & 1140            \\ \hline
\textbf{Bet365}       & -1.1\%         & -5.9\%         & -3.8\%         & -6.7\%            \\
\textbf{Interwetten}  & 0.9\%          & -4.8\%         & -3.4\%         & -5.4\%            \\
\textbf{Bet\&Win}     & -0.2\%         & -5.5\%         & -3.8\%         & -6.2\%            \\
\textbf{Pinnacle}     & 1.4\%          & -3.5\%         & -1.1\%         & -4.1\%            \\
\textbf{VC Bet}       & -0.7\%         & -6.0\%         & -3.3\%         & -6.3\%            \\
\textbf{William Hill} & -0.5\%         & -5.6\%         & -3.6\%         & -6.1\%            \\ \bottomrule
\end{tabular}
\end{table}

The next step in the experiments was to calibrate the investment strategy based on the confidence level of the predictive model in the outcome of each match. Thus, a bet would be placed only if the predictive model's confidence level met or exceeded a predefined threshold. Several Thresholds were chosen and examined for returns. For each Type level, the best-performing model was selected. Odds from Pinnacle were chosen.

The results of the experiments are shown in Figure \ref{fig:Trend in returns} highlighting the ROI across time and seasons. Over time, all strategies based both on Type and models' confidence level conclude with a negative ROI. The exception to this is found in a single strategy based on Type 1 matches and a confidence threshold of 70\%. The final ROI using this strategy is ~17\%.

\begin{figure}[H]
\centering
\includegraphics[width=1.0\textwidth]{Return_1117.png}
\caption{A graph of the return on investment as the match progresses, based on how confident the machine learning method is in predicting the result to determine whether to invest in the match.}
\label{fig:Trend in returns}
\end{figure}

\section{Conclusions and future work}\label{sec13}

This study has considered the problem of predicting the outcomes of football matches using the Premier League match data from 2019-2021 seasons.  The proposed strategy used the Kelly Index to first categorise the matches into three groups, with each one representing different levels of uncertainty, or predictability. A range of machine learning algorithms were explored for predicting the outcomes of the matches from each category in order to determine the utility of the process of decomposing the predictive problem into sub-tasks. This paper devised a range of new features previously unexplored as well as machine learning algorithms not investigated in this domain. The study found that ensemble-based algorithms outperformed all other approaches including the benchmark approaches, while the models produced competitive results with prior works.

The paper also validates the proposed approaches by benchmarking them against bookmaker odds in order to determine with strategies are able to return a profit on investment. A method was developed that combines both the Kelly Index together with predictive confidence thresholds and investigated. The findings indicate that a strategy comprised of a combination of focusing on easy-to-predict matches that have a high predictive confidence level from machine learning models can return a profit over the long term.  is a non-negligible part of the match data for machine learning. Moreover, the available features cannot explain the reasons for the match result.

redpajama_set_name: RedPajamaArXiv


Oh the good old days, running around in your Superman pajamas, velcro cape included, running around daydreaming of being the man of steel. Your Superman days aren't over, you just happen to wear a different superhero suit these days. Be faster than a locomotive and leap tall boardrooms in a single bound in style with the Superman Cape Cufflinks. Accept no imitations, the Superman Hero Cape hails from the officially licensed DC Comics Cufflinks Collection. The cufflinks are constructed in a shiny, gold-plated setting, featuring the iconic red cape in brilliant red enamel. The cufflinks feature a one-piece, fixed DC Comics logo backing. Officially Licensed by DC Comics.


Q: As a woman, is it preferable for me to Daven at the Kotel where it is difficult for me to concentrate or at home where it is quiet?
A: At home where it is quiet.
Q: How should we relate to the soccer team from Argentina canceling their game (which was supposed to take place in Yerushalayim) on account of threats they received?
A: Competitive sports are nonsense. B. It was supposed to take place with severe desecration of Shabbat.
Q: Is it permissible to look in a mirror during the Shemoneh Esrei to make sure that my head Tefillin are in the correct spot?
A: No. 1. One fulfills the Mitzvah of putting on Tefillin if it is in the correct spot on one's head for the amount of time it takes to walk 4 Amot (6 feet). 2. Even if it moves a little to the side, one still fulfills his obligation. 3. One should not be involed in other activities in the middle of the Shemoneh Esrei.


There are a few things that people don't realize when they shop around for a new water heater install. Many people just call to get the lowest price but with the lowest price the Orlando plumber may cut corners and you will not know unless you know what you are looking at. One of the things that new Orlando water heaters need are either an expansion valve like the Watts 530 or an expansion tank. These are to be installed on the cold side and are now code. These little devices do cost money to install so you should ask if the lowest Orlando plumbers quote is going to include this. A lot of cities in Central Florida are now installing double check valves at the meter and when they install this device it keeps anything from going from your water supply into the city. In return when your Orlando water heater heats up at night and no one is using the water and the water expands because of the heat, there is nowhere for the pressure to go, so it leaks water out of your T&P valve wasting water or worse if it is in your home flooding your house. Expansion valves or tanks are a must when installing a water heater in Orlando. If you need a water heater installed or repaired please call Drain Genie Plumbing at 407-490-1230. We are Orlando's #1 plumber.


This client knows exactly what she wants and what she wants is quite different from what most people I have worked for request. A banking executive, born in the Middle East, and traveling all over the world most of the time, she enjoys staying at fine old hotels furnished in the sumptuous royal Louis the XIV, XV, and XVI style. After we chose an investment quality carpet that determined the main colors I would use for planning the room, I brought her rich tapestries, golden fleur-de-lis woven patterns, damask blue silks with sheen and coordinating tassels and fringes. She loved them all and from that starting point, we began to fashion a small baroque palace on the corner of 57th St and Sutton Place.
This may sound heavy and and busy looking for a New York City apartment, but it is not. Though the rooms are far from Versailles size, the ceilings are high and the spaces retain a light airy look because of the sheen of butter colored eggshell finish walls and that same shade repeated in the wall to wall carpeting under the area rugs. As a focal point for the main sitting area, I was able to install a gas burning fireplace with an elegant old granite surround, on the wall that abuts the kitchen, conveniently allowing for the contractor to hook up to the existing incoming gas piping.
Everything had to be highlighted by gold- gold leaf wood finishes on the chairs, a gilded metal low round side table, golden fringes and tassels hanging from the draperies and the four antique gold finished brass, three light sconces. The client and her husband found antique painted mirrored side tables and a coffee table that they bought at auction, adding further shimmer to the living room.
Three floor to ceiling windows, facing Sutton, have been given curved cornices from which hang balloon swags, tails, and drapes festooned to the sides by ornate brass rosettes. Ivory sheers against the windows allow for light in the daytime and privacy at night.
The other seating area of the living room invites intimate, less formal gatherings on a flowing curved sofa, upholstered with golden damask fabric. I can only imagine the entertaining and the informal meetings that take place in this room where the baronial atmosphere contributes to closing important global deals.


The clinical study report is written according to the data obtained from the data management and analysis procedures defined in the study protocol. At this step, project manager of the study and the medical advisor of OPTIMUM cooperate in the formation of the report ensuring that obtained data is correctly and fully reflected in the report.
Two different methods are applied for these trials. Distant Monitorization For both of the above cases, Optimum ensures that LEC approval from coordinator is obtained and forwarded to MoH for its review.
OPTIMUM CRO takes part in organization of laboratories (both central and local) that will be included in the study to perform protocol-defined examinations.
OPTIMUM CRO was established in September 2000 as one of the first CROs in Turkey. Beginning from this date, many projects have been conducted, varying from international phase III and local phase II studies to post-marketing trials. More than 20 employees (including CRAs, PMs, QC and data management units) are located in the main office based in Ankara, the capital city of Turkey.
OPTIMUM CRO organizes investigator meetings at the start of the study, during the study and/or at the end of the study.
This service includes design of study CRFs by project coordinators according to the study protocol and final review is performed by QC unit.


text:
The Reject's Revenge: Was Major Manasa Tagicakibau bursting with jealousy for playing second-fiddle to Pita Driti and Ului Mara at RFMF?
RFMF Chief of Staff and Bainimarama crony AZIZ will not be investigated by Police for drawing up plan for Driti and Mara to exile Bainimarama to Sudan
"You will be aware, that the thrust of the prosecution case comes from the evidence of Lieutenant Colonel Manasa Tagicakibau who at all relevant times was based at the Queen Elizabeth Barracks and was of the rank of Major in charge of the Logistical Support Unit ("LSU") .
I mean no disrespect to the officer or his rank but in this summing up I will refer to him as Manasa. The defendant, Pita Driti was then his superior and held the very high rank of Brigadier General and was in 2010 Commander of Land Forces. Manasa had in 2010 been in the Forces for some 20 years. In those 20 years he had known Mr. Driti , serving with him in Lebanon: they were known to each other both professionally and personally.
In 2010 Manasa had been away on a year's study leave and he returned to take up his previous posting as OC Logistics, but he was unhappy because most of the duties and responsibilities of the post had been assumed in his absence by the then Chief of Staff, Ratu Mara. Manasa spoke to Mara twice about it but there was no result so in early February 2010 Manasa went to see the defendant who was one of the most senior officers as Commander Land Forces and therefore everybody's superior. He wasn't helped there either but told to just accept the "status quo" and put up with it.
Manasa the witness was concerned because Chief of Staff Mara was holding three important posts: he was Chief of Staff, Land Forces Command (that is deputy to the Brigadier General). He was Commanding Officer 3 F.I.R. (an operational unit of about 500 people). he was effectively the OC Logistics handling all resources of the Force (which was in effect PW1's job).
Manasa thought that this was a highly unusual situation and he presumed that there were underlying currents happening that he was not aware of; because of the great position of power that Mara had arrogated to himself.
[19] PW1 Manasa then took it upon himself to use his own little private intelligence cell because he was disturbed and a little suspicious of what was going on. The members of his intelligence gathering cell were tasked to listen and observe within the military, outside in the public sphere and in the markets to find information that might contradict anything that the RFMF stands for. Over time intelligence started rolling in reaching a crescendo about the end of February 2010.
This information concerned the disaffected utterances of Ratu Mara, and the undocumented movement of arms and ammunition between Q.E. Barracks and the G.P. Hotel, which was the temporary residence of part of the 3FIR troops. The intelligence gathered was relayed through intermediaries to Commander Land Forces (Driti) and to the Commander RFMF, the P.M. Manasa was told that the intelligence had been passed on and had been received. He was very concerned that there was no feed back from the intelligence passed on.
As a precaution he made sure that the main armoury was following proper security regulations with regard to the moment [amount] of weapons. In April 2010 it was confirmed that all weapons were safe and accounted for but the members of the cell group reported that their military sources had "dried up." PW Manasa asked his cell group members to keep a low profile and to try and get close to to the Chief of Staff and try to learn his state of mind.
In April/May 2010 Manasa learned on some occasions talking to Chief of Staff Mara over a cup of tea that he was still voicing discontent with the Government. On those occasions other officers would be present and on one or two occasions the defendant Driti himself was present. Remarks such as: we hope the Government will take us out of these economic doldrums were made. The defendant would say nothing but just laugh it off.
[20] In July 2010 Manasa went to South Korea with Chief of Staff Mara for a one week buying trip for the Army. Manasa's impression of Mara during the trip was that he was dissatisfied and discontented with the Government in Fiji. In particular he was of the view that the Government should stand down. Manasa advised him that the best course of action would be to have dialogue with the Commander (P.M.) but Mara did not agree with his advice. They returned from Korea in July 2010 and at the end of that month, Ratu Mara was told to go on leave and use all his leave before a decision would be made on his future. Manasa didn't speak to anybody about the conversations that he and Ratu Mara had in Korea but he noted that in the two weeks between returning and Ratu Mara going on leave the intelligence was streaming in of Mara's utterances. When Mara went on leave Manasa got his full job back as officer in charge of Logistics...He (Driti) said that the allegations from the Major came from somebody who was "striving for promotion", and acting in his own interests,; and you will note that this allegation was never put to the Major in cross-examination." Justice Paul Madigan in his Summing Up.
JUDAS? Manasa Tagicakibau - consumed with bitterness and turned key star State witness against Pita Driti?
Ratu Ului Mara had lions share of responsibilities over Manasa Tagicakibau
Manasa Tagicakibau hated living in Driti's shadow
Manasa Tagicakibau says Mara foul-mouthed regime on trip to South Korea in 2010
On way to be locked up until December 10 for sentencing - on evidence of sole disgruntled prosecution witness Manasa Tagicakibau
Note from Fijileaks Editor:
Pita Driti was unhappy with Aiyaz Khaiyum and Frank Bainimarama and so was Mohammed Aziz but they couldn't talk to each other about it. They always brought this up when Ratu Ului Mara met them separately so he (Ratu Ului) told them individually to go and talk to each other, which they did and the rest is history now.
About the weapons at GPH, there was a Company strength of 120 men at GPH at any one time so they had their personal weapons with them all the time. Unaccounted weapons from where? Only weapons left in Fiji now are at QEB.
So this is the same scenario that Bainimarama was going through in 2004-2006 before he decided to overthrow the legal Qarase government because they were going to charge him for the same charges that Driti faced and has now been convicted and locked away, waiting sentencing on 10 December.
Bainimarama: "Dou cakava vakatotolo na plan de dou qai kidacala au sa liu sobu i ra." ("You people carry out the plan quickly, or I'll surprise you by doing it ahead of you".)
Pita Driti: "Io, vinaka me caka ni sa rui levu na butako." ("Yes, good do it as there is too much stealing (corruption)".
Fugitive still on the run from sedition and murder charges!
Fijian Revoltonary
And here we go, still blaming Indo-Fijians and Aiyaz Khaiyum for our plight. Isa! Kaviti politics and li muri lot.
Fijian army liumuri fijian people is a norm by military dictatorship.
Aziz and Khaiyum are in power bec of fijian army .
Fijian army have destroyed fijians culture/lotu,vanua .madua na sotia.
Fiji's dictatorship is hated by all!
Ahahaha.....just love the cartoon - my thoughts precisely! hihihi....
Sotia Liu Muri
Isa - same old story,,,,,,coup, then liu muri then watch as these soldiers start shooting each other .......while the general i Taukei population go on the rampage burning and robbing indians chinese etc,,,,,,,,
worse now as kai dia supporting the side which will be targetted soon....
YEP THE SAME CYCLE OF EVENTS AGAIN...........WORSE THIS TIME AS KAI VITI ANGER HAS BEEN BOILING NOW FOR 6 YRS AND WATCH IT EXPLODE SOON,,,,WILL START WITH SOLDIERS SHOOTING EACH OTHER
SOTIA
kai vitis are ALWAYS F'ING ANGRY....CHILL BRO ,YOU MIGHT GET HIGH BLOOD PRESSURE AND DIE YOUNG ...THAT WOULD BE A TRAGEDY !!!
Chodo
yeah bro.....you not even sure why they angry ,,,,,good for you cause you will never know what hit you,,,,,,,yep keep on relaxing bro
KAIVITINDIA
keep angry ,sounds like ultimate christian love coming from people not sure of the reason for their anger.
If you are refering to Indians ,then you all have only yourselves to blame ...for not planting sugar cane for your white masters which necessitated the Indian slavery,for which the indigenous will pay compensation handsomely very soon.The Indians are more angry than Kaiviti for being uprooted from their motherland and brought to this third world shithole.Now its too late to go back cause we are born here...too bad, blame the chiefs for agreeing with the white masters.

redpajama_set_name: RedPajamaCommonCrawl


From the beautiful range for the Advent and Christmas season featuring the artwork of the Benedictine Sisters of Turvey Abbey.
This designs will make a colourful and thought provoking addition to the interior of a school, church or home.
A3L/A4L - Printed on gloss coated paper and encapsulated laminated.
Artwork also available as a wall hanging banner (order ref: BAN19).


On 1 June 1829 Stirling and his party arrived at Garden Island and erected the necessary buildings to protect the stores. On 18 June, Stirling and others landed on the mainland at Rous Head and formally published, both on the mainland and at Garden Island, this Proclamation constituting His Majesty's Settlement in Western Australia. In the Proclamation Stirling indicated that His Majesty's Authority now applied over the Colony and hence 'all persons whom it may concern should obey all Legal Commands and regulations, as I may see fit from time to time to enact ...'.
The Proclamation was the last of a number of initial steps necessary to establish the Colony, including the original Instructions to the Admiralty, the formal appointment of Stirling as Lieutenant-Governor and the issuing of his detailed Instructions, and the passage of the 1829 Act formally establishing the Colony.
In the weeks that followed Stirling took steps to found the town of Fremantle at the mouth of the Swan River and the capital, Perth, further upstream at the foot of Mount Eliza. At a formal ceremony on 12 August, the King's birthday, a tree was cut down to mark the foundation of Perth.
Battye, JS, Western Australia: A History from its Discovery to the Inauguration of the Commonwealth, Oxford, Clarendon Press, 1924.
Colebatch, H, A Story of a Hundred Years, Western Australia 1829–1929, Government Printer, Perth, 1929.
Crowley, FK, Australia's Western Third: A History of Western Australia From the First Settlements to Modern Times, Macmillan, London, 1960.
This document was written on lightweight paper. Although it is fairly brittle and fragile, with some light damage, it is nevertheless clearly legible.
Detail from the title page of Lieutenant-Governor Stirling's Proclamation of the Colony of Western Australia.
Long Title: Proclamation by Lieutenant-Governor Stirling of His Majesty's settlement in Western Australia thus effecting the settlement of the Colony, 18 June 1829.


bonus program being introduced by Champion Tire of Ringoes, NJ, this season.
racer bonuses will be distributed in victory lane on the two dates.
Race fans are also on the receiving end of Unfried's big bonus program.
the grandstands with regular giveaways, like logo T-shirts and hats.
addition to retail customers, from its location on Old York Road.
Don't miss the first night of competition on the newly-expanded raceway!
Adult admission is $13, children 7-12 are $4 and kids 6 and under are free.
For more information, call the speedway office at (609) 758-1900.


Kwesi Abakah and Distilled Harmony perform an acapella version of "Feeling Good" by Nina Simone at the Dr Martin Luther King Jr. Convocation at Northeastern University on January 16, 2014.
Conférence co-organisée par le master Management du sport et la Bibliothèque universitaire sciences-STAPS, le 12 décembre 2013.
Lindsey Hilsum, International Editor, Channel 4, gives a talk for the Business and Practice of Journalism Seminar Series. Introduction by Richard Sambrook. Please note; there are videos in the seminar, so sound may be slightly distorted.
Ninth segment of the Ocean Odyssey describes Ocean Pressure and how that limits the depth to which people can dive. Produced specifically for students and is suitable for elementary and older students.
UW Library Professor Joe James wrote a book discussing the future of libraries, called Libraries 2020. One of the contributors is the former director of the King County Library System (KCLS), Bill Ptacek.