Football is a sport with very simple rules. There are two teams, each has a goal, and the one that puts a ball more often into the goal of the other without using the hands wins the game. Even though football is very easy to grasp for humans, it is incredible hard to describe in numbers. The 22 players are more or less allowed to move freely across the field and face few restrictions on the actions that they may perform. From a math perspective, this leads to many degrees of freedom. A football game is a game of very high dimensionality. In plain language, an incredible amount of different things can happen.
If we want to describe a football game in numbers, we can't get around measuring things and trying to put these numbers into perspective. For this reason, analysts, both professional and bloggers, started recording various actions that took place in football games. Many of this numbers focus on the ball, such as shots, shots on target, shot locations, assists and passes. Some focus on players such as maximum speed or total number of kilometers of a player. Each of this numbers provide valuable insight on a part of the game. Yet each of them shed light only on a tiny fraction of the game as such. Given the dimensionality of a football game, in fact even all of them combined do not cover all aspects of a match.
Because of these missing factors, it is hard to tell for many numbers if a high or a low value is indicative for a good play. In many cases the correct answer will be 'it depends'. If a player took three shots in a game, is that good or bad? They could be from poor locations. Or they could be with a very high block chance because a defender's position. Even if all three would have been on target or even goals, that could be bad. Maybe he had seven more opportunities to shot, but he passed instead and lost the ball.
Because of the dimensionality of the game, it is unlikely that we will see in the coming years (if ever) a complete model of the game that allows us to judge the actions of each player, with and without ball. An alternative approach to describing football is to look for factors that partly explain the results of matches without trying to understand exactly why these factors correlate with the outcome. I call this a 'top-down' approach. A common analysis done along this strand is using the teams as factor. E.g. the
Euro Club Index and
ClubElo do just that. They assume that each club has a given (albeit time-varying) score value that summarizes the club's performance in matches. This obviously is a simplification, because all the dimensionality of a football game is reduced to just two numbers: the score values of the two teams. However, this simplification is very useful, because it allows the algorithms to explain, at least partly, the games' outcomes.
Lately, some analysts walked further along that road (
Daniel Altman,
Dave Laidig and
yours truly). They relaxed the assumption that all teams have a given score value and instead assumed that each player has an individual score. In principle, this allows to explain more details of game, but still poses a simplification. The dimensionality of the game is still reduced from almost infinity to 22 numbers per game. Yet this is more powerful than just two numbers. These model could, in theory, judge the impact of different lineups on the result. Barcelona is not always having the same performance. There may be a difference if Messi plays as opposed to when he is not playing.
Daniel Altman deserves particular credit for laying out a
number of traits a soccer metric should have in order to be useful. I will wrap that up here, however, I recommend reading his article, too
A soccer metric should be
accessible in the sense that non-expert should be able to understand and interpret the number. If players act in order to maximize the metric, this should be in the interest of the team. In Daniel's words, it should be
incentive compatible. The metric for individual players should be
aggregable to a team value that correlates with the match outcome. This aggregation should be
fungable in the sense that the aggregation function is a sum. The metric should be
non-context dependent, i.e. it should not increase dimensionality through the back door again. An
isomorphic score will make sure that equally good players have the same score. The metric should be based on as little information as needed (
parsimonious). Furthermore, the metric should be
individually and systematically robust. And finally, it should be
well-named such that the name transports the meaning.
These traits are normative and we may go without some of them, too. However, I strongly feel that this is a very good set of traits to follow in order to maximize the usefulness of the metric. One point that I find particularly important is the individual robustness. I would define it narrower than Daniel, by demanding that for any score value X at time t, the
expected score value at time t+1 is also X. In other words, the metric should be an
unbiased predictor of the future. The score should neither follow a trend, e.g. increasing with the number of minutes played, nor should it regress to the mean.
If and to which extend Goalimpact fulfils the traits will be another post.
Recommended reading:
