Soccer is defined by rare events – goals. The reason for this is that the events that decide who wins and who loses in football happen only occasionally, while other events – such as passes happen all the time. These events can be observed, and fans can easily comment on matches based on the teams’ goals or points earned. On the other hand, players’ performance and contributions to the success of their team are difficult to measure precisely.
The nature of football has evolved with the years. Where once football was purely an attacking sport, it is now focused on developing a symmetry between scoring and not conceding. It has grown into a more balanced game of offense and defense. When tactical changes produced teams that were more defensive but still won (or won even more), their opponents adapted their playing styles in response.
Players have improved as the game has matured: They run faster, they shoot harder, they dribble quicker, and they pass more accurately. And as they have improved, so structures have been built to contain them. These structures—offside traps, pressing, triangular passing—are the reason that goals in football have become a rare event.
A single goal virtually guarantees at least a point, statistically speaking; two goals gets a team closer to a win than a draw; at more than two goals, teams gets very close to a win, though even three or four goals do not quite guarantee victory.
The pattern holds across all four leagues. There are slight variations – a single goal is slightly less valuable in the Bundesliga than in La Liga – but generally, goals are worth the same number of points in England and Germany, Italy and Spain.
We have to note one critical thing: goals are not created equal. Some are worth more than others, depending on whether they are the only goals scored or whether they already have company. The numbers tell us that scoring three goals doesn’t give you three times as many points as one single goal and four goals – an increase of 33.3 per cent in goals from having scored three – doesn’t give you 33.3 per cent more points than three goals do.
In other words, the exchange rate of each goal varies according to how many other goals have been scored in the game.
The graph below shows the marginal points per goal for the Major League Soccer over 2013,2014,2015 seasons. It shows how much each individual goal was worth. As expected, there is a diminishing return on marginal points per goal with each additional goal scored.
We can see that the most valuable goal is the first one, increasing the team’s predicted point value by one. This doesn’t change between countries: two goals in Italy are worth about the same number of points as are two goals in Spain.
All this makes us think how we can correctly evaluate player productivity on the pitch. If you are looking to build players-based models for soccer betting, this is one issue that needs to be addressed.
If a team’s first and second goal are vastly more valuable than the rest, then adding these late goals when averaging a striker’s goals and assessing his productivity – is simply wrong.
It is very difficult to precisely evaluate to what extent does player contribute in relation to team’s success. It is possible to have an idea about a players’ individual performance because player’s actions and events on the pitch are observable and recorded by data companies like Opta. However, assessment on player’s performance can be biased by the scoring illusion: the impact of offensive events tends to be overstated while defensive events like marking – equally important for the team, tend to be understated.
Firstly, an excellent individual performance against a strong team must be weighted more than an excellent performance against a weak team. Also, a player is likely to better play if he is surrounded by teammates who place him in good playing conditions. Therefore, the individual productivity of a player must be netted out of his teammates’ productivity. This is one way to counter the player productivity evaluation when they have lower marginal points produced by goals.
There are two observed approaches in evaluating a players’ productivity – “box-score” statistics and fixed-effect approach. The first approach is based on individual events (dribbles, passes, tackles etc.) while the second one relies on participation only.
The “box-score” approach has been implemented by David J. Berri and Martin B. Schmidt in basketball and we will look into that in another article. They identify the actions that make the success of a basketball team (points scored, rebounds etc.). Then, the calculate individual productivity by looking at how many of these actions the players make. Also, each in-play event is weighted accordingly to its importance for winning. This approach doesn’t take into consideration the opponent’s level and state and other factors such as the motivation of a player.
The “box-score” approach has been adapted to soccer by estimating the impact of different actions on the winning percentage of teams. The productivity of a player is then defined as the sum of his individual actions multiplied by their impact on the teams’ winning percentage.
Another example is the use of data envelopment analysis. The technique is often used to measure the relative productivity of players. In this approach, an efficiency frontier is obtained having in mind some inputs and outputs. The players who lie on the efficiency frontier are the most efficient – those who produce the most outputs relative to the inputs they use. This approach has been used on soccer where the playing time is used as input and the output consists of goals scored, assists, the percentage of successful passes and the percentage of successful tackles as outputs. We have to mention that the percentages of successful passes and tackles do not seem to be relevant indicators if they are not weighted according to the location where they occur on the field. Moreover, some very important events such as the ability to mark and lose one’s marker are not considered. Thus, this approach appears as an interesting technique to compare players’ productivity if the inputs and outputs to be considered are clearly identified.
We can mention two more examples of the “box-score” approach – the Wins Above Replacement in baseball and the Player Efficiency Rating in basketball. The second type of approach tries to assign values to the actions performed during a match. These approaches are based on the analysis of event stream data that describes the actions performed in a match, possibly in conjunction with optical tracking data.
There is another variation of the “box-score” approach called STARSS (Spatio-Temporal Action Rating System for Soccer), which leverages historical match data to assign a rating to the actions (e.g., a pass or a shot) performed by the players in a match. For a given match, the presented approach proceeds in three steps. First, the approach splits the match into phases, which are uninterrupted sequences of actions where one team is in possession of the ball. Second, it assigns a phase rating to each phase based on historical match data. The higher the assigned rating, the more likely that the phase will end in a goal. Third, the approach distributes the phase rating across the individual actions that constitute the phase. This approach can be related to the work on expected goals models, which aim to objectively quantify the quality of goal attempts. The STARSS work differs from the expected goals approach in two crucial aspects. First, the approach is not restricted to shots and rates players based on all actions contributing to the team’s offensive output. Second, the approach explicitly takes the spatio-temporal context of the actions into account.
The “box-score” approach is very appealing in sports where extensive individual statistics are available. Nowadays, companies such as Opta makes this approach easy to integrate and analyze.
The main idea behind the fixed-effect approach is that box-score statistics cannot take into consideration all the dimensions of a player’s contribution to his team’s success. Some key individual statistics might not be identified and might not appear in the box-score. For example, some defensive statistics like marking opponents are difficult to record. Also, personality traits like leadership, that are strongly related to productivity, cannot be measured.
In the fixed-effect approach, a player’s productivity is estimated according to his participation to different games. The better the results obtained by a team when a player is on the field, the higher the player’s productivity is. Thus, the fixed effect approach captures all the dimensions of a player’s productivity. It also has the advantage of being very low data-demanding as only the final scores and the line-ups for every game are needed in the calculation.
- Muller, T. Upmann and J. Prinz have tried a fixed-effect approach on network analysis. They model a team as a network and players as nodes. Edges between two players depend on their performance when they are together on the field. For example, if player A and player B get on average 2 points when they play together while player A gets on average 2.5 points (unconditionally on player B’s participation) and player B gets on average 1.5 points (unconditionally on player A’s participation), the edge from player A to player B will be 0.8 (2/2.5) and the edge from player B to player A will be 1.25 (2.5/2). The stronger the edges that arrive to a player, the more his teammates outperform when he is on the field. This approach seems appealing as it measures players’ contributions to results.
A simpler example of a fixed-effect approach is the plus-minus. This measure simply compares the goal difference when a player is on the field to the goal difference when he is not on the field. The plus-minus has been progressively improved in order to be adjusted for the level of teammates and the level of opponents. For example, a team’s success may be linked to a player’s performance during the season. The plus-minus system would show whether a player’s presence on the pitch is net positive or negative for his team, without considering his position. It shows the comparison of a player’s net influence on team performance with other teammates. This approach is a major forward movement in the field of soccer ignoring stats as goals, assists or tackles. The plus-minus also takes part in the controlling for the importance of goals (the first or second goals are much more important than the goal leading to 5-0) and the opponents’ strength (scoring against a heavy favorite is harder than against a weak opponent).
We have already mentioned about the importance of goals in the beginning of the article. For a player, scoring the first or second goal really ups his marginal points contributions. For example, in 2010/11 Berbatov’s marginal points (13.04 for 20 goals) contributions were just a notch above West Bromwich Albion’s Peter Odemwingie (12.57 for 15 goals), who scored five fewer goals than the Bulgarian. For West Brom and Odemwingie, less was actually more points-wise. The same could go for Louis Saha’s tally (11.31 for 13 goals) for Everton for Previous year, when his thirteen were almost as valuable in real terms as the eighteen Jermain Defoe (12.39 for 18 goals) scored for Tottenham. During those two seasons, Daren Bent was the real hero. Indeed, if Chelsea had analyzed goals using the marginal points contribution, rather than a simple count of who had scored the most, perhaps they would have realized that the way to turn around their desperate league form in January 2011 wasn’t by splashing 50 million GBP on Torres, but by paying half that for Bent – the most consistent marginal points producer each of these two seasons.
- Rosenbaum introduced Adjusted Plus-Minus in Basketball to estimate the average number of points a player scores per 100 possession after controlling for his opponents and teammates. To make these calculations, we need to first break the game into several “shifts” periods of play between substitutions, and measures both the point differential and total number of possessions in each shift. We then need to regress the point differential per 100 possessions from the shift onto indicators corresponding to the ten players on the court. This is a method that we will look more in detail in another article about basketball models and players’ evaluation.
Jean-Baptiste Vilain and R. Kolkovsky have attempted to measure the individual productivity based on fixed-effects and penalization methods. As mentioned above, the fixed-effect allows to consider individual productivity in all its dimensions and penalization allows to overcome the collinearity issue due to the fact that players often play with the same teammates. The table below reports the top 25 players according to their estimation. Their marginal contribution reflects their individual productivity in Big 5 clubs from 2007 to 2015.
This ranking seems quite consistent with the general perception of players’ productivity. Lionel Messi and Cristiano Ronaldo, who respectively won 4 and 3 Ballon d’Or over the period, top the ranking. Cesc Fabregas, Franck Lampard, Yaya Toure, Karim Benzema, Bastian Schweinsteiger, Xavi, Arturo Vidal and Franck Ribery complete the top 10. These eight players were all world class players over the period. Other players who were also considered as overachievers such as Andres Iniesta, Arjen Robben Wayne Rooney, Thomas Muller, Eden Hazard, Zlatan Ibrahimovic or Luis Suarez rank in the top 25. This estimation relies only on a fixed-effects model where players’ productivity is assessed according to their team’s performance when they are on the field.
For those of you who want to jump straight to ratings that are free and easy to check, the right place is Whoscored that uses Opta data. Their ratings are based on the in-house, comprehensive statistical algorithm that is available pre-match and during in-running. They include more than 200 player attributes and events in order to calculate player and team ratings. These ratings are rated based on their influence and winning percent in the game. Furthermore, the area of the pitch where the event took place is considered and added in the ratings’ calculations. Their ratings start from 6.0, with 10.0 being the highest score.
With the levelling off of total goals and the continued decrease in goal difference, the industry of football has delivered its customers exactly that – tight, low-scoring, nail-biting matches in which no team is guaranteed a thrashing. Slowly but surely, intentionally and through trial and error – and mostly by eliminating mistakes and weaknesses – teams have become more similar to one another over time. This doesn’t change one of the key objectives in sports analytics – quantify player and team performances as objectively as possible. Ideally, each player’s contributions to his could be summarized in a single number that allows managers and bettors to take better-informed decisions. There are two approaches to compute such a number. The first style of approach to this task focuses on aggregating a variety of statistics into a single number. Typically, these metrics consider statistics that can be derived from a “box-score” and this is the reason why this approach is called the “box-score”. The second one relies on participation only and it is called the fixed-effect.