2.1 Association Football

In a game of Association Football, or football for short, each team aims to score goals (1 point) against the opposition (by getting the ball into a 24ft × 8ft goal) and the team with the most goals after the game duration wins. Football is the biggest sport in the world, making up 43% of the sports industry. There are hundreds of professional leagues across the world (e.g., the EPL and Spanish La Liga are two of the world’s most popular leagues). In a classic football league, each team plays every other team twice, once at home and once away. This means that the typical season consists of (2N) – 2 games, where N is the number of teams in the league (e.g., in the EPL there are 20 teams meaning each team plays 38 games). There are also a number of cup competitions that run alongside the main leagues (e.g., The Champions League and The FA Cup).

A number of factors can affect a game of football such as weather, the quality of pitch, and injuries. There are also a number of tactical decisions (e.g., team formation and style of play) that can increase a team’s chances of winning a game. The 11 players are set up in a formation with 1 goalkeeper and 10 outfield players. An example formation for the outfield players is 4-4-2 which commonly denotes 4 defenders, 4 midfielders, and 2 strikers. The team formation is a key decision in football tactics to which effects team performance. Teams can also make in-game player substitutions (up to 3 in a game) which can help change the team’s current in-game performance. Injuries happen across the football season, and this can have significant impact on the teams - in the 2016–2017 EPL season there were a total of 735 injuries, which are often preventable muscular injuriesFootnote ¹¹.

Increasingly, player recruitment plays a big part in modern day football. Players are bought and sold between teams across the world. Youth players are developed through clubs academies until they are ready to play in the first team. They can also be loaned out to other clubs to gain more experience. What makes football different in comparison to the other sports in this paper is the rarity of goals. This is highlighted in Table 1 where Anderson and Sally (Reference Anderson and Sally2014) show that over the 2010/2011 season there is a goal scored on average every 69 minutes. Due to this, a draw/tie is much more common in football than in other sports.

2.2 American Football

In a game of American Football,Footnote ¹⁴ teams aim to score touchdowns while attacking (worth six points), which is followed by a kick (one point if scored). Teams can also score field goals (three points) or a safety (two points). A game-day squad is made up of 45 players split into the offence, defence, and specialFootnote ¹⁵ teams. The coach makes a decision on how these players are positioned when on the field of play and usually also makes decisions on what plays to run during the game (where a play is a tactic used to move the ball down the field). Many factors affect teams’ performances in American Football such as weather and even the air pressure of the ballFootnote ¹⁶.

American Football makes up an estimated 13% of the global sports market. However, it is mainly played in North America where the main professional league is the NFL. There are 32 teams that make up the NFL, each team plays 16 games in the regular season. The teams that do well in the regular season make it into the playoffs where teams play up to four more games to determine the winner of the league. In the NFL, players are traded rather than bought or sold as in football and, instead of having youth teams to develop younger players, players are drafted from the college leagues. Much of the team and player performances in American Football are easier to quantify than other sports in this paper. This is due to the nature of the game as the yards that teams gain (which lead to points being scored) or prevent are measured and attributed to each player that contributes.

2.3 Rugby Union

In Rugby Union, each team aims to score triesFootnote ¹⁷ against the opposition, these are worth five points and are followed by a conversion—a kick at between the posts, worth two points. Teams can also score points through penalties and drop-goalsFootnote ¹⁸, both worth three points. The team with the most points after 80 minutes wins. Teams are split into forwards and backs where the forwards are the eight players that make up the scrumFootnote ¹⁹. Unlike football, there is a standard way to set up players on a rugby field so there is not a formation decision for the coach to makeFootnote ²⁰. There are still many other tactical decisions for the coach to make such as player selection, line-out formation, and style of play. Usually, club rugby is played in a league format similar to football where each team plays against every other teams both home and away [e.g., in the Aviva Premiership (England) there are 12 teams, each play 22 games in a season]. Rugby Union has been the fastest growing sport since it became professional in 1995. It is popular in countries such as Britain, Australia, New Zealand, and South Africa. Due to Rugby being a high impact sport, it presents many injury-related challenges. In particular, how can the medical teams be assisted and how can players be further monitored.

2.4 Basketball

In basketball, teams aim to score a point by getting the ball in the basket. When scored within a given zone, it is worth two points, outside of this zone it is worth three points. A free throw is worth one point. The winning team is the team who accumulate the most points. The main league is the National Basketball Association (NBA) in the USA, and it makes up about 6% of the global sports market. In the NBA, there are 30 teams, all teams play 82 games in the regular season and the top teams make the post-season playoffs (a knockout style competition to decide the overall NBA winner).

Basketball is the only team sport that we consider in this paper, which is played indoors at the professional level. Thus, weather-related factors do not have an affect on the game. Basketball is very high scoring in comparison to the others (as highlighted in Table 1). It is also much more fluid and faster flowing in comparison to the other American sports which similarly to football makes quantifying an individual’s impact on a game outcome more challenging. In the NBA, there are on average 296 passes per team per game, this compares to 453 per team per game in the EPL, although in football there are more players on the pitch over a bigger playing area. If we look at this per player, each basketball player makes 59 passes per game, whereas each football player completes on average 41 passes per game.

2.5 Cricket

Cricket is played in a number of forms (e.g., Test and Twenty20), in this paper we focus on One Day International games (ODIs) due to existing literature also being focused on ODI games. In an ODI, there is 1 innings per team made up of 50 overs each (1 over = 6 balls), which can end earlier if all batsmen are out. In each innings, the batting team aims to score runs and bowling team aims to take wickets and prevent runs being scored. The winning team is the team with the most runs scored in their innings. Cricket is hugely popular in countries such as India, England, and Australia. The Indian market in particular makes up the majority of the market and is reportedly worth $5.3 billion.

Hitting runs and taking wickets are the main metrics used to measure player performances. Cricket, like Baseball, relies on a number of individual performances by players which make up the team performance, whereas other sports rely more on the team performance as a whole. Due to both cricket and baseball being bat-and-ball games rather than invasion games like the rest of the sports in this paper means that they present different challenges and factors for us to consider. At the core of this is that, even though they are team games, the performance of players is mainly based on a 1v1 scenario (batsman vs. bowler). This means that when we evaluate or predict performance we can focus on how an individual batsman performs against an individual bowler or vice versa.

2.6 Baseball

Baseball is a game made up of nine innings, where an inning is made up of both teams batting (while the other team fields) until they receive three outs. The batting team aims to score runs (a batsman gets round all bases), the fielding team aims to strike batsman out (three swing and misses) and stop runs being scored. If the score remains tied at the end of the regulated number of innings, then an extra inning is played. The team with the most runs at the end of nine innings is the winning team. Baseball makes up 12% of the global sports market. The performances of the Baseball teams/players are often measured by key statistics based on their abilities to hit runs or get outsFootnote ²¹.

Baseball is mainly an American sport and the main league is Major League Baseball (MLB). In the MLB, there are 30 teams where every team plays 162 games in the regular season with the best teams making the playoffs. The playoff is a knockout-style competition formed of 12 teams, where each round is a ‘best out of 7 games’, to decide the ‘World Series’ winner. Teams play games much more frequently in a Baseball season than in other sports’ which may mean players have to be rotated more and monitored closely for injury.

3.1 Bookmakers accuracy

As we will show, some of the match outcomes problems, presented by the sports in this paper, are more predictable than others. Bookmakers use sophisticated pricing models that assign ‘odds’ to an outcome (which reflect the likelihood) to maximize their chances of making a profit, this is discussed in Graham and Stott (Reference Graham and Stott2008). By comparing who the bookmakers made favourite (shortest odds) and the actual match outcome, we calculate a percentage accuracyFootnote ²² and use this to evaluate how predictable each sports outcome is. This provides an estimation of the predictability of each sport. Bookmakers price markets based on their own predictions of the match as well as using the bets that are placed as an indicator of the likely match outcome.

To demonstrate the variability across team sports, we focus on the prediction of match outcomes (see Figure 1). As can be seen, football has the lowest accuracy showing it is the least predictable. This is to be expected due to the frequency of goals being far less than frequency of points scored in the other sports (as discussed in Section 2). A draw/tie is also much more common in football meaning there are three possible outcomes to consider instead of just two. Basketball is shown to have the highest accuracy by the bookmakers. This may be due to the high number of points scored in a game or a smaller playing area with less players.

Figure 1. Bookmakers accuracy across 2017/2018 season

3.2 Statistical approaches

A number of studies have focused on finding ways that the game of football could be modelled and to find inefficiencies in the UK football betting market. Dixon and Coles (Reference Dixon and Coles1997) set out to exploit the inefficiencies and bias in UK football betting markets. Building upon the seminal work by Maher (Reference Maher1982), they developed an initial model to assign probabilities to each of the different game outcomes (home win, away win, and draw/tie). Using this, they are also able to form a new betting strategy. The model is based on the different abilities of both teams, calculated from prior matches. These abilities are broken into attack and defence and normalized based on the abilities of the opponents. Their model also takes into account a home advantage as discussed in Clarke and Norman (Reference Clarke and Norman1995). They are able to gain positive returns in a betting strategy. They use a technique based on a Poisson regression model, modifying Maher’s basic bivariate Poisson model to give Equation (3).

(3) \begin{align} Pr(X_{i,j}=x, Y_{i,j}=y)=\tau_{\lambda, \mu}(x,y)\frac{\lambda^x exp(-\lambda)}{x!}\frac{\mu^y exp(-\mu)}{y!}\end{align}

where λ = α_i βj γ and μ = α_j β_i. In these equations, x and y represent the goals scored by the home and away team, respectively ( $[x,y] \in \mathbb{N}$ ), α is the attacking parameter, β is the defensive parameter, γ represents the home advantage ( $[\beta,\gamma,\alpha] \in \mathbb{R}$ ), and τ is a corrective factor used by Dixon and Coles to introduce an association between home and away goals that is missing in the independent Maher model. Finally, i represents the ID of the home team and j the ID of the away team. When the model described in Dixon and Coles (Reference Dixon and Coles1997) is run and tested across the past six seasons (2013–2019), it was found to have a prediction accuracy of 56.65%.

Dixon and Robinson (Reference Dixon and Robinson1998) studied the effect of the scoring rate which is changing depending on the current score of a game of football. They found that the scoring rate generally increases for both teams throughout the match, most likely due to tiredness of players that leads to mistakes in defending. They also found the scoring rates of home and away teams depend on the current score. Each scoreline is modelled as a different game state, and an example of the different possible game state changes throughout a game is shown in Figure 2.

Figure 2. Change in game state for a 3-3 scoreline (Dixon & Robinson Reference Dixon and Robinson1998)

When the scores are level, the scoring rates are similar to those at 0-0. If the home team is leading, the home and away rates generally decrease and increase, respectively. If the away team is leading, the rates of both home and away teams tend to increase. Their findings can be used to find match outcome probabilities and to attempt to improve on Dixon and Coles (Reference Dixon and Coles1997). This is done by finding the probability of each state (shown in Figure 2) and integrating over all the possible times and for each possible route to arrive at the final game state (x, y).

Crowder et al. (Reference Crowder, Dixon, Ledford and Robinson2002) again build upon the work of Dixon and Coles (Reference Dixon and Coles1997) by changing the original models’ calculations of attack and defence efficiencies. The new framework assumes that the efficiencies evolve through time (rather than remaining constant) according to some unobserved bivariate stochastic process. The original stochastic process model is replaced with an approximation that yielded a more tractable computation without comprising the predictive power. Dixon and Pope (Reference Dixon and Pope2004) evaluate the value and significance of the statistical forecasts from their earlier work in relation to betting market prices. They performed a detailed re-examination of match outcome odds and correct score odds across a number of years between 1993 and 1996. They suggest that the football betting market (at the time) remained inefficientFootnote ²³ and the earlier models discussed in Dixon and Coles (Reference Dixon and Coles1997) could still be used effectively to earn positive returns when used with a strict trading rule to select the games to place a bet on.

More recently, Angelini and Angelis (Reference Angelini and De Angelis2017) were able to better the forecasting accuracy of Dixon and Coles. This paper uses a Poisson autoregression with exogenous covariates (PARX) model which is discussed in Agosto et al. (Reference Agosto, Cavaliere, Kristensen and Rahbek2016). By using this model, with the same betting strategy that is used in Dixon and Coles (Reference Dixon and Coles1997), they are able to generate betting return on investment of 33.62% on average when tested across three seasons (2013–2016 EPL). McHale and Scarf (Reference McHale and Scarf2011) focus on international matches instead of English League games. The authors present a new model for the number of goals scored by each team in a match and can be used for match outcome predictions. The model used in this paper is based on copula functions (Nelsen Reference Nelsen2006) which generate bivariate-dependent discrete distributions which are used to forecast the match scorelines. As this paper is based on international football matches, it may not be as successful if used for domestic leagues due to significant differences between international and league football. In comparison to the domestic leagues, there is a gulf in quality between teams that could play against each other internationally. Furthermore, international teams do not play as often. Therefore, datasets detailing the performance of international teams may not be as reflective of the current ability/form of the team and players. In a different study, Karlis and Ntzoufras (Reference Karlis and Ntzoufras2008) use the Skellam distribution (Skellam Reference Skellam1948) to predict the winning margin of games during the EPL 2006/2007 season. The Skellam distribution models the difference between two independent Poisson-distributed variables. Using these distributions, probabilities are assigned to the possible goal differences and therefore the match outcomes.

Turning to American football, there are a number of applications of statistical techniques to predict match outcomes and scoreline predictions. A birth-process model (Harville Reference Harville1980) uses a linear approach to create a baseline for NFL predictions in American Football, building on work that he had originally tested on college and high school American Football (Harville Reference Harville1976). More recently, Boulier and Stekler (Reference Boulier and Stekler2003) compare their model with human prediction and the bookmakers in the NFL between 1994 and 2000. They evaluate the use of ‘Power Scores’ (published in the New York Times) as a predictor by creating forecasts generated from probit regressors. A probit model is a type of regression where the dependent variable can take only two values, for example, home win or away win (Cappellari & Jenkins Reference Cappellari and Jenkins2003). This model was able to improve the accuracy of the predictions made by human experts. However, it was not able to improve the bookmakers’ accuracy. In turn, Leung (2014) uses the teams’ current ability based on other rating systems such as ‘Elo Ratings,’Footnote ²⁴ which were initially designed to rank chess players (Coulom Reference Coulom2007). Leung makes predictions on the outcomes of college American Football matches using historic results and a sum of other metricsFootnote ²⁵, the highest total sum is the predicted winner. The paper states that the model achieves a high accuracy, but it does not detail how this was tested. Finally, Baker and McHale (Reference Baker and McHale2013) look to predict the exact scores in a game of American Football. The authors use similar methods which were used for football in Dixon and Coles (Reference Dixon and Coles1997). The model takes each team’s attacking and defensive abilities and finds the probabilities of the final state of the game scoreline using a Chapman–Kolmogorov forward equation (Gardiner Reference Gardiner2009). This achieves an accuracy of 66.9% outperforming Boulier and Stekler (Reference Boulier and Stekler2003) who achieved 61%.

In basketball, Zak et al. (Reference Zak, Huang and Siegfried1979) calculate the production efficiency of points scoring for each team and using the ‘Richmond’ technique (Richmond Reference Richmond1974) they are able to estimate the potential scoring output of teams. Therefore, this could be used to make match outcome predictions. They also evaluate the basketball home-field advantage. Finally, ‘Yoopick’ (Goel et al. Reference Goel, Pennock, Reeves and Yu2008) outlines a different approach to create a sports prediction market. The market they create directly allows estimation of the entire point spread probability distribution within a single unified market. Punters bet on the outcome of the points difference of a game landing in a given interval with the interval prices determined by Hanson’s logarithmic market scoring rule market maker (Hanson Reference Hanson2007). This paper has yet to be tested against the accuracy of the more traditional betting markets.

In the next section, we will explore the ML methods that have been applied to the match outcome prediction problem for the sports this paper focuses on.

3.3 ML approaches

Most of the ML works involve Bayesian approaches and we focus on such approaches primarily. We also generally cover other approaches that have most recently come to the fore.

3.3.2 Other ML methods

A number of other ML methods have been applied to the sports match outcome prediction problem. In what follows, we elaborate on these methods and summarize their key properties in terms of outcome prediction.

Jayalath (Reference Jayalath2018) considers ODI Cricket prediction and focuses on quantifying the significance of important features using ‘classification and regression tree’ and logistic regression approaches. The study identifies that the key feature to improve a team’s chances of winning is home advantage. Building on this, Jayantha et al. (Reference Jayantha, Anthony, Abhilashab, Shaikb and Srinivasaa2018) create a model for predicting ODI games using ML techniques and also outline a team recommendation system, which is discussed in Section 4.3. The prediction model in the paper uses a support vector machine (SVM) model with linear, poly, and radial basis function (RBF) kernels. They use features such as batting and bowling averages to create power rankings for each player. The model takes the line-ups of the two teams and the player statistics in these line-ups. The SVM models are trained with historic win or lose percentages. When tested with the linear, poly, and RBF kernels, they achieve an accuracy of 70.83%, 68.75%, and 75%, respectively.

As discussed in Section 3.3.1, Joseph et al. (Reference Joseph, Fenton and Neil2006) apply other ML techniques beyond Bayesian approaches for football. A decision tree and a K-nearest neighbour model were developed. The MC4 decision tree achieved an overall average test percentage result of 41.72%. The K-nearest neighbour method uses a likeness approach, where the model finds similar instances to the test case and then a voting mechanism is used to predict the outcome. This performed better than the MC4 decision tree by achieving a test accuracy of 50.58%, the Bayesian approach in the same paper achieved an accuracy of 59.21%. Baboota and Kaur (Reference Baboota and Kaur2018) again looks at applying ML techniques to football match outcomes and compares the results to bookmakers. They use feature engineering and exploratory data analysis to find the feature set with the most important factors for predicting match outcome. They use a number of features with different weightings such as form, shots on target, goals, and more. They model the ternary classification problem to a binary classification one, and a prediction is made for whether a team will win the match or not. The methods that are tested by the authors are Gaussian naive Bayes, SVM (with RBF and linear kernels), random forest, and gradient boosting. They use training data from 2005 to 2014 in the EPL and they find that the best performing algorithm was the gradient boosting method (56.7%), followed by the random forest (56.4%), SVM models (RBF 54.5%, linear 54.2%), and then finally the poorest performing was the Gaussian naive Bayes method (52.6%). Similarly, Hucaljuk and Rakipovié (2011) test a number of features and classifiers. The features they use are the form of the team, previous meetings of the teams, current league position, number of injuries, and average number of goals scored and conceded in a game. Six different learning classifiers are tested using these features: Naive Bayes, Bayesian Networks, LogitBoost, K-nearest neighbours, random forest, and artificial neural networks. Datasets from the UEFA Champions LeagueFootnote ²⁷ (a cup competition as mentioned in Section 2.1) are used in this paper, focusing on only 96 games. They achieve an accuracy of up to 68% when using neural networks. This is considerably higher than results in the EPL. This may be because in the Champions League, the best teams in Europe’s top leagues compete against weaker teams from smaller football nations in the earlier stages of the competition meaning the match outcomes are more predictable. There are also fewer games played in the Champions League, so there are less data available for testing the models as shown by the test-set in this paper only using 96 games.

McCabe (Reference McCabe2002) uses neural networks to predict games of Rugby LeagueFootnote ²⁸ in Australia. This work is extended in McCabe and Trevathan (Reference McCabe and Trevathan2008) where again a model is created with a neural network system using a multi-layer perception with a number of different features such as prior performance data, game location, and team rankings. This model is able to perform well in Rugby League competitions with the average accuracy reaching up to 67.5%. This work was also applied to football results in the EPL. The results from this were compared to top human expert ‘tipsters’ who also make weekly predictions on the same games in the form of a competition called TopTipperFootnote ²⁹ and they were able to reach the top percentile with the model against the other human experts.

Shi et al. (Reference Shi, Moorthy and Zimmermann2013) consider the problem of predicting college basketball games in the US NCAAB league. Five different ML models are developed: decision trees, rule learners, artificial neural networks (multi-layer perception), naive Bayes, and a random forest, using data from 2009 to 2013. The methods all achieve between 68.4% and 74.5% accuracy. Their evaluation shows that a high level of accuracy is achieved when using neural networks, and this can be used to beat humans predictors. Finally, part of the work performed in Landers and Duperrouzel (Reference Landers and Duperrouzel2018) focuses on making predictions on NFL match outcomes and point spreads which they apply to ‘Pick’em’ styleFootnote ³⁰ online competitions. Their model uses 28 features such as bookmakers favourite, average points (home and away), game location, and more team performance-related statistics. These features are used with an average perceptron and a boosted decision tree classifier algorithm to create their model. They tested the model over three NFL seasons and find the decision tree provided the best results achieving an average accuracy of 58%. This work is compared to Boulier and Stekler (Reference Boulier and Stekler2003) (discussed in Section 3.2) which achieves 61% and to the bookmakers who achieve 65.8% accuracy.

In Table 2, we summarize the ML approaches that have been used for match outcome predictions. These algorithms mainly use key team performance metrics as their features such as points/goals scored and conceded, league position, and form. However, there are some key factors that are not yet accounted for by the approaches that we have discussed. These are largely the external factors that can impact the results of sports outcomes (e.g., weather, player moods, changes in coaching, player transfers, or impact of injuries).

Table 2 ML approach summary.

In this section, we have evaluated the different approaches that have been used to make sports outcome predictions. Across all the different forms of predictions that we have discussed, all appear to reach a ‘glass ceiling’ which we discuss further in Section 7. The papers we evaluated also show that football is the hardest game to predict due to the low-scoring nature of the game. There are many decisions that impact the outcome of sports matches. In the following section, we explore some of the decision-making processes that exist in team sports.

4.1 Player transfers

The recruitment of new players is a different process in every sport and usually involves decisions from managers/coaches alongside the directors higher up in the sports organizations. In football, players are bought and sold between clubs (as discussed in Section 2) whereas, in many American sports, players are draftedFootnote ³¹ and traded. In most cases, clubs gather information on players (scouting), therefore the amount teams pay for a player relates to how well they think that the player will perform in the future and how much they will impact the team. There are a number of elements that add uncertainty to the process, namely concerning whether a player will continue performing well, if the player will fit into their new team, if the player will settle in to a new environment/surroundings, and if the player will stay fit. These uncertainties are discussed when drafting a college player into the NFL in Hendricks et al. (Reference Hendricks, DeBrock and Koenker2003). Here, it is suggested that statistical discrimination and option value influence choices in this market meaning that some players could be over-valued. Modelling the uncertainties that exist in future performances of players and predicting how well they will impact a team would provide huge benefits to sports teams. This will allow the decision makers to evaluate the risk of player before paying large sums of money. These types of predictions can also help assign a monetary value to a player, so that a fair price is paid. There are a number of factors that affect the price of a player, some of these are explored in Dobson and Gerrard (Reference Dobson and Gerrard1999). In Figure 4, we show the generic recruitment process that sports teams follow when investing in new players.

Figure 4. The player recruitment process

All of the stages within the player recruitment process present different challenges that can be improved through the use of AI methods. These are discussed below and correspond to the numbered processes in Figure 4.

1. 1. The first stage is identifying which areas in the team need to be improved. We can go about this firstly by looking at the statistics of the team performance to identify what in particular needs improvement (e.g., more goals in football or more wickets in cricket). We can also highlight which individual players are not pulling their weight in the team and look to improve these.

2. 2. The next process is gathering intelligence on a large set of players, this can be done in a number of ways. Teams have access to league statistics where they can find information regarding player info. These statistics are becoming more detailed and could be used alongside AI to efficiently evaluate current ability and potential. This is an important inexpensive stage of the process as it can save money further down the line by avoiding sending scouts to watch players who are not right for a team. This can also help to identify players who are overlooked by other clubs and help find the best value players.

3. 3. Once we have basic statistics on players, scouts are deployed who will gather more subjective information which may not be shown in the statistics. However, most teams have a limited number of scouts (N) and a limited scouting budget. Therefore, we must optimize this process so that the scouts time is not wasted and as many players are watched as possible.

4. 4. The information that the scouts collect is collated alongside the statistics collected in process 2. Once all this information has been gathered, a team can use the statistics, scouts data, and scouts opinions to rank the players they have watched. Using this teams can identify the players they would like to sign to improve their team and estimate the costs involved for transfer fees and/or wages.

5. 5. Usually in a transfer or trade window, teams will want to buy and sell multiple players to improve the squad. This presents a budget optimization challenge as we want to purchase as many highly rated players from the information gathering process who can positively impact the team. Therefore, the objective of this optimization is to maximize the quality of the players who are purchased while staying within the constraints of the transfer/wage budgets. There are also other constraints set by the leagues such as squad sizes and wage caps. Finally, if a team is to sell their current players, they can increase their transfer/wage budgets and create room for more new players. This is something that would need to be treated with caution though, as it could ruin the cohesion of the players within the team if we were to sell/buy too many players.

The processes we have discussed aim to improve the probability that a team will be successful in the transfer market and presents interesting computational challenges that are yet to be addressed by AI. The scouting process relates to AI literature which focuses on learning from imperfect classifiers. An example of this is shown in Simpson et al. (Reference Simpson, Roberts, Psorakis and Smith2013) where human decisions, with prior knowledge about the ability of that human’s decision making, are combined with Bayesian approaches to make decisions. This can be applied to scouting as we can use the teams scouts opinions on players, with the knowledge of their prior scouting performance, alongside AI methods to rate players. The challenge of deploying the scouts relates to optimization literature such as Dang et al. (Reference Dang, Dash, Rogers and Jennings2006), Ramchurn et al. (Reference Ramchurn, Polukarov, Farinelli, Jennings and Truong2010) as we aim to maximize the number of high quality players the scouts assess while meeting the time and budget constraints. The transfer budget optimization problem discussed in process 5 also relates to this literature as we are aiming to maximize the quality of players who are bought within the transfer and wage budgets where we can also sell current players to increase budgets.

Boon and Sierksma (Reference Boon and Sierksma2003) discuss the scouting of new team members to fill open positions and enhance the quality of teams. They calculate the potential value that new players into a team would have, focusing specifically on football. Their model uses linear programming to form an optimal team based on the quality of the players and their positional weightings that they calculate. Once an optimal team is formed they can use this for scouting purposes. Using a database of scouted players, players can be substituted into the team to calculate the effects that this would have and what value would be bought into the team. This model could be improved by taking into account the multiple positions that players can play in and the different roles players can take in different positions (e.g., a central midfielder could be a defensive player and sit deeper or could be more attacking to push further forward). Boon and Sierksma mainly focus on how scouted players will impact a team rather than looking to identify players who could be scouted and finding players who may have been overlooked by other teams. The challenges presented by player transfers could also be modelled as a case-based reasoning problem, where new players could be devised by evaluating similar players/transfers and similar situations that have happened in the past, by adapting the problem and solution to the new situation (Kolodner Reference Kolodner2014).

In the next section, we explore how teams train youth players in their academies which is another route that teams can take to improve their squad and bring in new players.

4.2 Training and developing players

Young players can be trained by professional teams from ages as young as sixFootnote ³². Thus, teams can play a huge part in how they develop players and how they bring these players into the first team squad once they are old/good enough. The process of bringing players through youth systems can be fine-tuned and optimized at many stages. This can involve making sure that their training is tuned to improve their skills efficiently and ensuring that they are given the right amount of experience at the right times either in the first teams or by being sent out on loan to smaller clubs. The challenge of personalizing the training regime of youth players therefore involves a number of prediction and optimization problems that could be addressed by AI techniques. This is particularly so when such training regimes need to cope with significant degrees of uncertainties in player performance (e.g., injuries, variability in mood, or weather conditions). A number of studies have explored the effects of injuries to youth players. Price et al. (Reference Price, Hawkins, Hulse and Hodson2004) highlight the nature and severity of injuries that occur at academy level, and le Gall et al. (Reference le Gall, Carling, Williams and Reilly2010) evaluate the fitness characteristics of young players in youth academies, highlighting which of these characteristics improve players chances of proceeding to higher levels.

De Silva et al. (Reference De Silva, Caine, Skinner, Dogan, Kondoz, Peter, Axtell, Birnie and Smith2018) have also used the player tracking data that are available as a tool for training youth players and for physical performance management in football. They tested their work in a professional Premier League football academy. This research uses standard statistical analysis to compare the activity demands in key playing positions, such as central midfielders and centre forwards. This study helps to provide insights from an elite performance environment regarding the relationship between player activity levels during training and matches and how they vary by playing position. This is an example of where ML-based analytics could be used by a top club to extend their knowledge and make changes to some of their training practices.

Finally, Fister et al. (Reference Fister, Ljubic, Suganthan, Perc and Fister2015) outline the challenges for computational intelligence in sport. The authors discuss the problems and current work that exist in sports (not just team sports) domain and in particular training for athletes. They open up a number of research questions in the area of training for sports and showed a necessity for developing an artificial personal trainer to optimize sessions. They also outline the process of sport training, showing the key components and a programming model. The paper mainly focuses on training which is not specific to any sport or skill such as for strength and power. However, it is still a useful tool for us to identify the stages in the team sport training process that can be optimized using AI.

Next, we turn our focus on the team selection problem where managers/coaches select the players to play in games.

4.3 Match preparation

Team selection is a key tactical decision in team sports which has to factor in a number of uncertainties. In essence, the challenge involves picking a set of players to play in a game, which will maximize the chances of winning. The selection must be from the registered squad of players as sports regulating bodies allow each team to select and register a squad of players governed primarily by financial criteria (e.g., in the EPL teams are allowed to register a squad of 25). Transfer windows give teams opportunities to make adjustments to their registered squad within the governing body’s rules.

There are many different combinations of possible team selections which is different for each sport. For example, in football, there is a squad of 25 players and need to select a team of 11; therefore, there are 4457400 different possible team line-ups. This is calculated using nCr where n is the number of players and r is the size of the team. It is worth noting that this would change depending on the formation of the team that is selected (number of defenders, midfielders, and forwards) as some players are unable to play in certain positions, in football there are a total of 165 possible formations that players could be formed in.

There are number of factors that coaches must consider when selecting a team. Examples of these include, but are not limited to: player injuries, players abilities to deliver the tactics/role, the opposition team, the current fitness of the players, and motivation of the coach to succeed in the game. The team selection process also involves thinking about developing younger players. This is a balancing act between selecting a team that will win against thinking about using youth players. In most cases, these players are bought into games as substitutes or are selected to be used in less important games such as pre-season friendlies or cup games. It is also important to note that we must consider how players will work together as a team with the other players who are selected.

In American football, cricket, and baseball, it is generally easier (compared to football and basketball) to identify which players have been performing well and therefore the challenge of finding a team that maximizes the chances of winning is slightly easier. That said, there is a lack of academic work which has focused on solving this problem. In football and basketball, it can typically be a challenge to attribute each player’s contribution to a team. In these sports, there are a number of other factors that make a good performance other than just scoring or creating goals.

Deep learning has also been applied to model the behaviours of players in both basketball and football (Le et al. Reference Le, Carr, Yue and Lucey2017a; Seidl et al. Reference Seidl, Cherukumudi, Hartnett, Carr and Lucey2018). Here, deep imitation learning has been used to ‘ghost’ teams so that a team can compare the movements of its players to the league average or the top teams in the league. A simulation is run to see how an AI team would move in certain situations with the AI team created by ‘ghosting’ the characteristics of average and top teams. This helps to identify where teams can make changes to their players’ movements and change events to improve the probability of scoring a basket/goal or reduce the probability of conceding. Le et al. (Reference Le, Yue, Carr and Lucey2017b) are also an example of multi-agent approaches to imitate and learn the movements of players in a game of football. The authors show that having a coordination model for the roles of players gives substantially improved imitation in comparison to conventional baselines.

Other factors that may need to be considered in this area involve predicting what an opposition will do: their line-up, their formation, their set pieces, what style they will play, what areas of the pitch they target, where a player will aim a penalty, and many more. An example of work that forms teams based on an opposition is shown in Jayantha et al. (Reference Jayantha, Anthony, Abhilashab, Shaikb and Srinivasaa2018) where the authors create a team recommendation system for cricket teams which is based on selecting players who increase the probability of the team winning.

The team selection problem in sport relates to team formation literature in the multi-agents domain such as Chalkiadakis and Boutilier (Reference Chalkiadakis and Boutilier2012) which proposes new methods for coalition team formation. Coalition formation is the analysis of one or more groups of agents, called coalitions, that together jointly determine their actions. They integrate decision making during repeated coalition formation under type uncertainty using Bayesian reinforcement learning techniques. Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) form optimal teams for fantasy sports games under the constraints that the fantasy sports problem presents (discussed further in Section 5.2). They do this by predicting the performance of football players (in terms of how may fantasy points they will score) and then form a team which maximizes the number of expected points. This could be extended to aid team selection for sports teams and improve teams chances of winning. Vilar et al. (Reference Vilar, Araújo, Davids and Bar-Yam2013) discuss the complex social systems that are presented by team sports. The authors focus on the pattern-forming dynamics that emerge from collective offensive and defensive behaviours. They evaluate the differences in strategies and formations of two teams in a single game of football to understand the successful and unsuccessful relationships in the teams. This type of study provides significant results to demonstrate how complex systems analysis can help to better understand performance in football, by assessing team behaviour as a collective rather than individually. Forming optimal team line-ups in football is also discussed in Boon and Sierksma (Reference Boon and Sierksma2003) which we discussed in Section 4.1 where the form teams based on the players ability and how able they are to play in each position.

There have also been game theoretic approaches to optimizing teams of agents in other domains. These approaches have shown success in real-world applications. An example of this is shown for Stackelberg Security Games (SSGs), the success of SSG is discussed in Sinha et al. (Reference Sinha, Fang, An, Kiekintveld and Tambe2018). In an SSG, a defender must defend a set of targets using a number of resources, whereas the attacker is able to learn the defender’s strategy and attack after planning. Fang et al. (Reference Fang, Stone and Tambe2015) use game theory and the application of an SSG to optimize protection of endangered animals and fish stocks.

An important factor to be considered in the team selection process is to ensure that the players selected in the team are right for the team tactics. The approaches to tactical decision making, made by the manager/coach, are discussed in the next section.

4.4 In-game tactics

The in-game tactics used by teams to enhance their chances of winning games vary a lot from sport to sport. When creating tactics there are many factors that must be considered such as the opposition team and their weaknesses as well as the ability of the players available. Getting tactics right can give teams a huge advantage and can allow weaker teams to win games that they are not expected to. In football, tactics covers the formation that the team will use, the ‘style’ that they play in, set piece selection, and many more. In American Football, tactics cover the plays that are selected by the coaches and coordinators.

There have been a number of studies that aim to better understand the tactics in sports. One aim of these papers is to assess the impact of the individual actions performed by players during games. Decroos et al. (Reference Decroos, Bransen, Van Haaren and Davis2019) aim to do this by creating a framework to value any type of player action based on its impact on the outcome of a game and use a CatBoost (Prokhorenkova et al. Reference Prokhorenkova, Gusev, Vorobev, Dorogush and Gulin2018) approach to achieve this. Fernández and Bornn (Reference Fernández and Bornn2019) provide a model to assess the expected ball possession that each team should have in a game of football. The expected possession value (EPV) assigns a point value to every tactical option available to a player at each moment of a possession, allowing analysts to evaluate each decision that a player makes. In this paper, ML is used to estimate the parameters which are used in the model, such as pass and turnover probabilities which are estimated using logistic regression. A similar model is also applied to basketball (Cervone et al. Reference Cervone, D’Amour, Bornn and Goldsberry2014) where points are predicted and player decisions are valued. Similarly, Yue et al. (Reference Yue, Lucey, Carr, Bialkowski and Matthews2014) focus on play prediction in basketball developing models for anticipating near-future events given the current game state. These models are validated using 2012/2013 NBA data and show that their model can make accurate in-game predictions. Building on this, Zheng et al. (Reference Zheng, Yue and Hobbs2016) study the problem of modelling spatiotemporal trajectories of the players using expert demonstrations. In particular, they look to see how a basketball player makes decisions with long-term goals in mind, such as moving around opposition players or scoring points. They propose a model that uses both long-term and short-term goals and instantiate this as a hierarchical neural network trained using a large dataset of tracking data from professional basketball games. They show that this model generates more realistic trajectories compared to non-hierarchical baselines as judged by human expert sports analysts. This work could be improved by modelling the defensive team as well as the offensive team to give a more accurate simulation of the plays. Finally for basketball, Wang and Zemel (Reference Wang and Zemel2016) focus on offensive play call classification. This helps teams understand the opposition’s strategies to influence the final match outcome. They apply variants of neural networks to SportVUFootnote ³³ tracking data and find they are able to label play sequences quickly with high precision. Using a recurrent neural network (RNN), they are able to achieve a precision of 90% and recall rate of 59% (when making predictions if the probability of the classifier is above 70%). There is a difficulty to annotate datasets in sports, especially when using spatiotemporal data due to a level of subjectivity. Active learning Cohn et al. (Reference Cohn, Ghahramani and Jordan1996) could be used for this, where the data labelling cost can be significantly reduced.

Other papers that focus on tactics in team sports include Bojinov & Bornn (Reference Bojinov and Bornn2016) which evaluates how in football a ‘pressing’ tactic affects performance and disrupts the opposition’s defences. By doing so, they are able to define and learn a spatial map of each team’s defensive weaknesses and strengths which is useful for coaches when preparing to face an opposition. In a similar fashion, Hobbs et al. (Reference Hobbs, Power, Sha, Ruiz and Lucey2018) aim to quantify the value of transitionsFootnote ³⁴ in a game of football. They aim to explore how teams create goal-scoring opportunities based on their transitions and find that if a team counter-attacks immediately rather than looking to maintain possession, the chances of scoring rise by 4.4% and chances of having a shot rise by 24.4%Footnote ³⁵.

Power et al. (Reference Power, Hobbs, Ruiz, Wei and Lucey2018) focus on set pieces in football (e.g., corners, free-kicks, and penalties). They discuss a number of ‘myths’ regarding set pieces and then prove/disprove these myths. For example, they show that a team is more likely to score from set piece than in normal possession (1.8% chance of scoring from set-pieces vs. 1.1% in open play). They also find that the type of delivery and the defensive set-up of the oppositions can significantly affect the chances of scoring. Finally, Lucey et al. (Reference Lucey, Bialkowski, Carr, Foote and Matthews2012) model team behaviours in football using entropy maps, created from teams ball movements, which give a measure of predictability of team behaviours across the field. This provides a useful tool for coaches and decision makers to be able to analyze opposition teams.

We have highlighted the studies that focus on the tactics within team sports. These approaches aim to decompose and break-down how teams play which give more interesting insights for coaches. This can be useful for teams when setting up their own tactics to maximize their chances of winning against another team. In the next section, we explore work that focuses on individual players’ performances.

4.5 In-Game player performance

Measuring player performance is an important factor in the decision-making processes in team sport. This helps to provide the feedback to identify when changes need to be made to team line-ups, tactics, and when transfers need to be made. A number of papers focus on ways to measure performance objectively with data. Whitaker et al. (Reference Whitaker, Silva and Edwards2017) use a Bayesian approach to determine the abilities of players using a number of different event types. They implement a Poisson model for event types and can then infer player abilities from this. These inferences allow EPL players to be ranked and differences between players to be visualized. Power et al. (Reference Power, Ruiz, Wei and Lucey2016) focus on measuring the risk and reward of passes in a game of football. This gives new methods to evaluate player passing performance and identify key players in a team who execute the key passes consistently. Similarly, McHale and Relton (Reference McHale and Relton2018) also aim to identify key players in a team by using network analysis and pass difficulty in a game of football. They aim to provide analysis to managers and coaches for them to identify their best team line-up, and in the analysis of opposition teams.

Power et al. (Reference Power, Cherukumudi, Ganguly, Wei, Sha, Hobbs, Ruiz and Lucey2019) focus on the performance of football goalkeepers. They simulate each goalkeepers performance when facing a number of example shots and compare which goalkeeper would concede the least number of goals. They do this by using a ‘spatial descriptor’ for each goalkeeper which is made up from features such as clean sheet percentage, win percentage, and save percentage for different thirds of the goal. This type of player performance modelling was also explored within baseball to evaluate how a batter will perform against certain pitchers (Alcorn Reference Alcorn2018). In these papers, players’ performances are simulated in different scenarios to give a basis for a fair comparison of players. This type of analysis could be built on in all sports to identify the impacts that the individuals have within the complex team systems. Coaches could use this to identify how changes in their style of play, with their current set of players, would affect the performance of the team. Theses simulations could also be used for player recruitment as potential new players could be simulated to show how they would perform in a new team.

Turning to basketball, Felsen and Lucey (Reference Felsen and Lucey2017) evaluate NBA players’ body pose and shooting styles to find any correlations between the player body shape and shooting success. They find statistically significant differences in distributions of attributes describing the style of movement of different phases of the shot. In American Football, Burke (Reference Burke2019) uses deep learning to quantify quarterback (QB) decision-making again allowing us to identify the NFL QB’s who have the best decision-making skills, this is a vital part of the QB position in a game of American Football. Their model correctly identifies the targeted receiver in 60% of cross-validated cases. They find when passers target the predicted receiver, passes are completed 74% of the time, compared to 55% when the QB targets any other receiver. Their approach gives a new way for teams to quantitatively assess QB decision-making performance. Finally, Correia et al. (Reference Correia, Araujo, Craig and Passos2011) assess players’ decisions when making passes in Rugby Union based on the positions of oppositions and team mates.

In Table 3, we summarize the AI approaches that have been used for sports strategies and decision making.

Table 3 Strategy and decision-making AI approach summary.

The majority of the work that we have discussed in this section focuses on finding new insights into tactical analysis in sport. These studies help identify the strengths of different tactical process and find new ways of evaluating player and team performances. There are good examples of work in football and basketball however not as many in American football or rugby where tactical decisions are also key to winning games. There still remains a number of areas where AI could impact tactical decision making. This work would mainly be focused around how individual agents (the players) perform in different teams, with different tactics and how much impact they have on the game outcomes. This type of analysis could benefit all of the processes that we showed in Figure 3 as AI could improve player transfers, match preparation and help to gain better feedback from the outcomes of games.

In the next section, we turn our focus on fantasy sports games and the computational challenges that these present.

5.1 Player performance prediction

Predicting the player performance is key to selecting which players are worth having in a fantasy team. If a player (and the team he plays for) performs well, more points will be accumulated for the fantasy team. There are a number of factors that need to be considered when predicting how well an individual is likely to perform and this varies significantly based on the sport being played and the position that the player plays in. For example, in football when a striker’s performance is predicted, the aim is to predict the number of goals that he/she may score whereas for a defender we focus on predicting if his/her team will keep a clean sheet (concede no goals). Also, it must be considered how likely a player is to play in a given game, as players may not play due to injuries and tactical decisions. If a player does not play, they receive no fantasy points. These examples show a small number of many uncertainties that need to be considered when making predictions on future performances. The predictions of games (discussed in Section 3) can also be used to help predict the number of points that a player will score, as if a player is playing in a team which is likely to win then that player would have a better chance of scoring more fantasy points.

When predicting player points, a feature set for each player (in a given game week) is taken as an input, this is referred to as X where n is the number of features (shown in Equation (4)). Example features for an American Football player would be yards gained per game, number of touchdowns scored, and games played. In football, example features would be goals scored, number of assists, number of clean sheets, and minutes played. The feature set could also be made up of previous fantasy points scored from a number of prior weeks. Once a feature set is formed, a target vector Y represents the points scored by the player in the given game week, corresponding to the feature data in X. Equation (4) shows X and Y for n features and i players where p _ix _n is the n feature for the i player and p _iy _w is the ith player’s points in game-week w. Next, a ML algorithm can be trained using X and Y to produce a function φ that can output the prediction of Y using the features in X. A row of X, X _j can be used with this to make a prediction on the corresponding row in Y. This gives φ(X _j) = Y _j. Different ML methods can be tested across the different sports.

(4) $$X = \left( {\matrix{ {{p_1}{x_1}} & {\quad {p_1}{x_2}} & {\quad {p_1}{x_3}} & {\quad {\rm{ }} \cdots } & {\quad {p_1}{x_n}} \cr {{p_2}{x_1}} & {\quad {p_2}{x_2}} & {\quad {p_2}{x_3}} & {\quad {\rm{ }} \cdots } & {\quad {p_2}{x_n}} \cr \vdots & {\quad \vdots } & {\quad \vdots } & {} & {\quad \vdots } \cr {{p_i}{x_1}} & {\quad {p_i}{x_2}} & {\quad {p_i}{x_3}} & {\quad {\rm{ }} \cdots } & {\quad {p_i}{x_n}} \cr } } \right)Y = \left( {\matrix{ {{p_1}{y_w}} \cr {{p_2}{y_w}} \cr \vdots \cr {{p_i}{y_w}} \cr } } \right)$$

When making player performance predictions in a daily fantasy contest, we can be much more precise as the predictions only need to focus on how that player will perform in the specific game. Whereas, in more traditional leagues, future performances must be considered as well as just the next game. Thus, a player who will perform well in multiple future games will be selected and not just one who will perform well in a single game (which may be against a poor opposition). This is considered by the model shown in Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) where predictions for a players’ performance are made for a number of future game-weeks.

Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) predict a player’s performance and the number of points that a player will score based on the prediction of a given game using the Dixon & Robinson (Reference Dixon and Robinson1998) framework. The authors choose to use this approach as the Dixon and Robinson model treats football as a dynamic situation-dependent-process as well as its proven success in the football betting domain. Dixon and Robinson’s score predictions work by taking each club’s attacking and defending efficiencies from past results and then using these to derive the probabilities of the side scoring a goal in a given match (discussed in more detail in Section 3.2). Using the match outcome prediction, Matthews attributes the probability of a player scoring points based on the four most significant point-scoring categories in the FPL.

1. 1. Player appearance in a game (worth two points per player playing over 60 minutes and one point for any player playing under 60 minutes). For this, a three-state categorical distribution is used, the states are starting, substitute, or unused. Three probabilities are computed for each category and the highest probability is assigned to the player to obtain the predicted points.

2. 2. Clean sheetFootnote ³⁸ (worth four points to a defender/goalkeeper and one point to a midfielder). For clean sheets, the probability of a team not conceding can be calculated using the scoreline distributions from the Dixon and Robinson model and points can be predicted based on these probabilities.

3. 3. Goals scored (worth six points for a defender/goalkeeper, five points for a midfielders, and four points for a striker). This is calculated using a Bernoulli distribution (Gelman et al. Reference Gelman, Carlin, Stern, Dunson, Vehtari and Rubin2004) or a Binomial distribution over a single trial, describing a players probability of scoring the goal given he was playing at that time.

4. 4. Goals created (worth three points per player). Another Bernoulli distribution is used for this, again describing the players probability of creating the goal given he was playing at the time.

Turning to American Football, the NFL study (Landers and Duperrouzel, Reference Landers and Duperrouzel2018) for player point prediction starts by engineering features from FanDuel that their model uses. In their paper, they test two different feature sets (FD ₁ and FD ₂). They also test two different methods and compare using the different feature sets. The methods they test are a least squares with averaged perceptron (Lehtokangas et al. Reference Lehtokangas, Saarinen, Kaski and Huuhtanen1995) and a boosted decision tree (Schapire Reference Schapire2003). These methods are evaluated using the coefficient of determination (R ²) to measure the accuracies (R ²). The boosted decision tree achieves average accuracy of 0.417 using FD ₁ and 0.250 using FD ₂ while the least squares approach achieves 0.401 on FD ₁ and 0.146 on FD ₂. Other related work has shown similar results to those in Sugar and Swenson (Reference Sugar and Swenson2015). It is noted that different methods could be tested for different positions in American Football. This is because the roles of different positions differ more than in other sports (e.g., QB vs. running back).

The current studies for player predictions show applications of ML techniques providing good benchmarks in both football and American Football. Further techniques could be tested in these sports to improve the current benchmarks. These could also be tested with new feature sets such as time-series data which would analyze the form of the players over a given number of game-weeks. Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) focus on the FPL fantasy game, it may be useful to test this work on a DFS site to see if it also performs well in these fantasy games. Landers and Duperrouzel (Reference Landers and Duperrouzel2018) only focus on DFS so it would also be interesting to see how their predictions would work in a more traditional multiple-week league. There also remain gaps in the literature for predicting performances of players in other sports where fantasy games are popular such as Basketball and Baseball.

The player score predictions become more valuable when combined with a good team optimizer, allowing the maximum points to be accumulated each week. The methods for team formation that currently exist in the literature are outlined in the next section.

5.2 Team formation optimization

Selecting the best team of players within the given constraints of the fantasy site is vitally important, and as shown in Figure 5 this process is repeated sequentially across a season with constraints for changes that can be made to the team. This process involves choosing players with different abilities, prices, and risks that need to be considered. As discussed in the previous section, we may also need to consider the future performances of these players over a number of given game-weeks. In formation problems, there are a number of actors, with their own abilities and characteristics that have form a team to perform a task to achieve a common objective in a real-world domain. Within the fantasy sports team formation problem, there are a number of players (the actors) with their own abilities (predicted points) and we are looking to maximize the number of these points (the common objective). Therefore, it is key to get the best players possible into a high performing fantasy team. The fantasy problem relates to other works in the AI community. In particular, Dang et al. (Reference Dang, Dash, Rogers and Jennings2006) focus on choosing the best sensors to survey an area, Ramchurn et al. (Reference Ramchurn, Polukarov, Farinelli, Jennings and Truong2010) focus on dispatching optimal teams of emergency responders, and Chalkiadakis and Boutilier (Reference Chalkiadakis and Boutilier2012) look at the appropriate set of agents to work within a coalition formation problem.

In fantasy sports, the main aim is to select a number of players, all of whom are assigned a value, in different positions within a given budget. For example, in the FPL, there are around 500 players available to select from, all with a position and a given value and 15 need to be selected (2 goalkeepers, 5 defenders, 5 midfielders, 3 forwards). The total value of the selected team mostly not exceeds £100 m. Eleven of those fifteen players are put up as your ‘starting 11’ (in a selected formation) and they will be the ones who will earn your fantasy points. The remaining players are ‘subs’ and will automatically come into the starting 11 if one of the current players does not play. This means that the players are selectable in over 6.5 × 10⁹ ways. One team is selected at the start of the season and then one transfer is permitted per game-week. In DFS competitions, a fresh team is created each week, therefore the optimization is simpler. Figure 6 shows example of team formation set-ups from FPL and DraftKings.

Figure 6. Example fantasy team set-ups. (a) FPL team selection. (b) DraftKings team selection

Formally, a generic fantasy sport team optimization problem can be defined as the following set of equations (excluding other different constraints that the different leagues have in place).

(5) \begin{equation}\left( \begin{array}{ccccc}p_1 \rightarrow pos_1 & \quad p_2 \rightarrow pos_2 & \quad p_3 \rightarrow pos_3 \\[3pt] p_4 \rightarrow pos_4 & \quad p_5 \rightarrow pos_5 & \quad p_6 \rightarrow pos_6 \\[3pt] p_7 \rightarrow pos_7 & \quad \dots & \quad p_n \rightarrow pos_i \\\end{array} \right)\end{equation}

where a player p is added to each of the i positions in the fantasy team (only if the players position matches the slot in the fantasy team, for example, a QB cannot be selected as the running back in the fantasy team).

(6) \begin{gather} argmax\left(\sum_{n=1}^{N} {points}_{n}\right) \nonumber\\ \text{s.t. } \sum_{n=1}^{N}{selected_n} = teamSize \\ \sum_{n=1}^{N} {value}_{n} \leq budget\nonumber\end{gather}

where n represents the ID of a player, which is used to identify if that player is selected (selected _n = {0,1}) and what the player value is $ (value_n = \{\mathbb{Z}\}) $ . Our objective is to maximize the total number of points ( $ (points_n=\{\mathbb{R}\}) $ ) while staying within the given team size and ensuring that the combined salaries/values of the players are below the given budget constraint.

Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) approach the FPL team optimization as a sequential team formation problem which is formalized as a Markov decision process (MDP). The model in this paper considers the limited transfers that could be made meaning that the future performances of players are considered when making changes. A reinforcement learning approach is used, working under uncertainty regarding the underlying MDP dynamics. In an MDP, the agent (in this case the fantasy competitor) and the environment (fantasy game) interact continually, the agent selecting actions (by selecting a team each game-week) and the environment responding to these actions (in the form of points) and presenting new situations to the agent. Using an MDP means that the model is able to assess the possible rewards that come from the possible actions that are made (in FPL this would be the action of making a transfer). The problem can then be treated as an optimization problem. Matthews et al., set up the problem as a multi-dimensional knapsack packing (MKP) (Korte & Vygen Reference Korte and Vygen2012) and solve the optimization using IBM ILOG’s CPLEX 12.3. A number of different set-ups of the MKP were tested. These include Q-Learning and Bayesian Q-Learning with different parameters. By doing this, Matthews was able to obtain a model that ranked in the 1.1st percentile and gives a benchmark for how AI and ML models are able to perform in the FPL.

When forming fantasy teams for the NFL in DFS competitions, Landers and Duperrouzel (Reference Landers and Duperrouzel2018) compare four different approaches for team optimization, these are:

1. 1. Selecting a completely random team to loosely model the behaviour of a human with no knowledge of the sport.

2. 2. Selecting a random team from a filtered dataset with just the higher performing players. This is to loosely mimic the behaviour of a player with general knowledge about the sport.

3. 3. A filtered optimized approach picks a team from the filtered set and uses a brute force algorithm to select the best team based on maximizing the predicted points that fits the constraints.

4. 4. Filtered actual best selects the best possible team from the filtered dataset to give a view of what the best performing team would be (this approach does not consider the budget constraint on total player values).

Using the player points prediction models discussed in the last section, 100 teams are selected using each of the above methods for each prediction method. The authors are able to evaluate the performances using the following metrics: The average points return of the 100 teams, the maximum points return, and the percentage of teams that produce a profitFootnote ³⁹. This is compared against the work in Sugar and Swenson (Reference Sugar and Swenson2015) which achieves a success rateFootnote ⁴⁰ of 71.4%, whereas Landers and Duperrouzel (Reference Landers and Duperrouzel2018) achieve a success rate of 82% for weeks 3–9 in the 2016 season. However, this would need more testing due to the small sample size (seven game-weeks) meaning the results are not statistically significant.

Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012) were able to achieve good results by solving their optimization problem as an MKP. As a brute force method for team optimization is used on a filtered dataset in (Landers and Duperrouzel, Reference Landers and Duperrouzel2018) there may be more efficient ways for this to be done, such as a similar approach using CPLEX in Matthews et al. (Reference Matthews, Ramchurn and Chalkiadakis2012). Using this type of approach would ensure an optimal team is selected and improves the run-time efficiency in comparison to a brute force approach. Another area to explore would be to model the uncertainties in the players’ performances rather than predicting their points. This would allow teams with different levels of risk and reward to be selected which may be useful in a DFS competition as multiple teams can be entered. This could be achieved by using a stochastic optimization approach (Ermoliev & Wets Reference Ermoliev and Wets1988). There also remain gaps in the fantasy sports process where AI could be used to forecast the player prices, assess opponents fantasy teams, and create AI betting strategies to maximize the chances of generating profits in DFS fantasy games. DFS strategies are discussed in Haugh and Singal (Reference Haugh and Singal2018) where a portfolio of teams is used to maximize the chances of generating profits.

In Table 4, we summarize the approaches that have been used for the points prediction and optimization in the discussed papers. In the next section, we will discuss the impact that injuries have to sports teams and how AI can be used effectively in this domain.

Table 4 Fantasy sports approach summary.

6.1 Sports medicine research

There have been a number of studies in the Sports Medicine community focused on the causes of injuries in sports and studying a number of large datasets. Firstly, Hägglund et al. (Reference Hägglund, Waldén and Ekstrand2006) evaluate how previous injury is a risk factor for future injuries at the top level of football. The study compares two seasons (2001–2002) worth of injury data from 12 elite Swedish male football teams. They use a multivariate model to determine the relation between a previous injury and the risk it causes. They found players who were injured in the 2001 season had a greater risk of injury in the following season compared with non-injured players. Particularly, players with a previous hamstring, groin, and knee joint injuries were 2–3 times more likely to suffer the same injury in the following season. This work was extended in Hägglund et al. (Reference Hägglund, Waldén and Ekstrand2009, Reference Hägglund, Waldén and Ekstrand2013), looking at 14 football teams across Europe between 2001 and 2012. This study focused on the injury characteristics and variation of injuries during a match, season, and consecutive seasons over the time period discussed. It found that the rate of some injury types decreased over the last 11 years. However, training and match injury rates and the rates of muscle and severe injuries remain high. It was also found that the risk of injury increased with time in each half of matches. Clearly, such works point to patterns in datasets that could be used in ML algorithms to determine the risk of injury and to optimize the recovery process.

Fuller (Reference Fuller2018) models the effect of the player workloads on the injuries in the EPL. The study shows how a team’s injury-burden varies from day-to-day during a season, based on a team’s match and training schedules. It also compares successful and unsuccessful Premier League teams and how their training loads effect their number of injuries. They find that a successful team undertakes fewer training sessions each week so there are fewer opportunities in which to influence training activities and to reduce injuries. A similar study (Bowen et al. Reference Bowen, Gross, Gimpel and Li2016) investigates the relationship between physical workload and injury risk in elite youth football players. They also found higher workloads were associated with a greater injury risk. This highlights that workloads can be used as a metric in an AI model for injury prediction. Workloads have been seen as a significant factor in injury prediction, and Hullin et al. (Reference Hullin, Gabbett, Lawson, Caputi and Sampson2016) evaluate the acute:chronic workload ratio (ACWR) in Rugby League players and find that a greater ACWR increases injury risk. The ACWR is calculated by dividing the acute workload (fatigue) by the chronic workload (fitness). This is defined as:

(7) \begin{equation} ACWR_t = L_{t-7}/L_{t-28}\end{equation}

where L is the players loadFootnote ⁴¹, t is the current day. Therefore, it is a ratio of the last 7 days load to the last 28 days load. This, along with other related variables, could be key in using ML to predict injury.

There are examples of injury studies in other sports such as basketball and American Football. In basketball, Podlog et al. (Reference Podlog, Buhler, Pollack, Hopkins and Burgess2015) survey the injuries in the NBA over a 25-year period and identify the relationship of injuries to team performance. In American Football, Ward et al. (Reference Ward, Tankovich, Ramsden, Drust and Bornn2018) find that regardless of the position, training days with high amounts of volume and intensity share an association with increased risk of injury while training days of a high amount of low intensity training share a relationship with a decreased risk of injury. Finally, Zelič et al. (Reference Zelič, Kononenko, Lavrač and Vuga1997) use decision trees and Bayesian classification to diagnose sports injuries more effectively, and this shows a novel use of ML techniques to sports injuries and provides a useful tool for teams’ doctors and physiotherapists. However, it does not aim to predict and help prevent injuries.

In the next section, we discuss the applications using the data from the wearable sensors that we discussed at the start of this section.

6.2 Wearable sensor research

Due to the amount of data that are collected from the wearable sensors, some sports teams have begun to look at ways that this can be used to benefit sports men and women. Firstly, a study Kelly et al. (Reference Kelly, Coughlan, Green and Caulfield2012) researched how wearable sensors can be used to automatically detect collisions in Rugby. As we discussed in Section 2.3, Rugby is very high impact sport and tackling is the most common cause of injury in Rugby, and therefore having a way of automatically modelling tackles can improve the work of the medical staff. The work was compared against collisions which were manually labelled using data from elite club and international level players. The paper tested a number of different algorithms for this problem such as SVMs, neural networks, and convolutional neural networks (CNN). The results show the model is able to identify collisions to a high level of accuracy, achieving a recall and precision rating of 0.933 and 0.958, respectively, using CNNs. The model can give coaching and medical staff tackle-specific measurements, in real time, which can be used in injury prevention and rehabilitation strategies. Following on from this, Cust et al. (Reference Cust, Sweeting, Ball and Robertson2018) reviewed the ways that ML and AI can be used to classify certain movements in sport.

In the next section, we will discuss the findings from this paper and highlight the computational challenges and open areas that exist for AI in the team sports domain.