Now that the objective has been formulated in a limited way, so that the “calculability of football” can only be devoted more or less exactly to determining the level of probabilities for certain (the relevant) match outcomes, one can nevertheless very confidently go on to work on how one can get close to such a “truth” – one likes to philosophise about the term “probability” at this point; an apparent truth? – can be achieved. The examination of the determined values for their good approximation will be carried out later elsewhere. Here, however, it is mentioned in advance so that the determination of the values loses its apparent (!) arbitrariness. This is mentioned (repeatedly) in particular because a probability determined for all game outcomes can only ever mean – regardless of its size: “It comes or it doesn’t come.” Supplemented by, “I knew that before.” No, the values are pretty well determined and this can be verified.
So, if you think about football and the relevant parameters responsible for a match outcome, it becomes clear quite quickly that it’s the goals that do it. You can’t really care about possession, the corner kick ratio or the number of shots on goal/goal chances. The round has to go into the square. The fact that here, of all places, the reporter’s wisdom, which elsewhere is declared so much a useless, rather erroneous banality, is used for the sake of argument may seem curious, but mathematically it cannot be otherwise.
An important preliminary consideration is this: the whole system presented works best in league play. Although a “solution” has also been found for the European Cup and other international comparisons, including international matches and the major European Championship and World Cup tournaments from the qualifying stage onwards, it is sufficient here first to look at the original use and introduction of the system. The most important reason why it works so well there in particular is clear in itself: the teams play against each other again and again every year (with minor changes) and already in a single season you have two comparisons per pairing as well as a complete everyone-versus-everyone constellation (this only in relation to European Cup or international matches, where this is far and away not the case).
It is worth mentioning at this point that there is at least one other approach to approaching the probabilities well. This is the approach that is used comparably in chess, for example. The only difference is that in chess the result is actually only represented by victory – draw – defeat, whereas in football there is a 5:1 or a 1:0 victory. If one were to completely neglect the amount, one would certainly also be making a mistake. In this respect, the approach used here is already a logical one, since it includes the amount of the results.
So in football it is the goals that count. There is a piece of wisdom – in relation to which there is relatively little trust — that everything always balances out in the end. Well, the doubts are more philosophical, otherwise it expresses, roughly speaking, the reliability of statistical figures, as well as one looks at longer periods of time, which at the same time is really a mathematical law. The only question remains: what is a long period of time? Well, intuitively speaking, the more results you have, the better.
In league play, which is a closed system, every goal that one team scores is conceded by another. In this respect, one can quite well define the so-called average team as the one that scores exactly half the average goals per game and concedes the other half. If, in the long run, 2.9 goals per game are scored in the 1st division, then they must be considered to score 1.45 per game and concede 1.45 per game.
Anyway, it is best to explain the whole concept using the 1st German Bundesliga. It is interesting to note that the biggest constant in this division is the record champion Bayern Munich. It is logical that no team from the relegation zone is suitable for this, because they have to leave the division from time to time. But it could also be a perennial chaser, another team that consistently plays at the top.
Well, the aim of the procedure is to first determine the goal expectations. How many goals will this team score per game (approximately), how many will it concede? This is already an expression and measure of playing strength. The more goals you score per game, the fewer you concede, the better you are. It is the offensive and defensive strength of the team(s) that is expressed in this way. However, these are only average expectations.
In addition, it must always be taken into account that there are individual parameters and generally valid ones. The team’s playing strength, measured in goal expectations for and goal expectations against, are individual. The goal average is generally valid for the league. The procedure explained here will first determine goal expectations for a very specific pairing. How one then determines the probabilities from this is explained elsewhere.
So, the constant Bayern Munich has really scored quite close to 2.0 goals per match and conceded 1.0 goals in the long-term average (according to the Eternal Table, before the 2010/2011 season, they actually scored a goal ratio of 3254:1781 in 1534 matches, which corresponds to averages of 2.12 : 1.16, but there used to be more goals). So it is safe to assume that this is repeated, confirmed, a good benchmark. Now, obviously, against teams from the bottom half of the table, they would exceed that expectation on a match-by-match basis, but against teams from the top half, they might not achieve it, mind you, as goal expectations. Statistically, of course, outlier results are common enough.
If one first omits the parameter of home advantage, which must be included and taken into account in addition to match strength, then one could calculate the goal expectations for the first and second leg, so to speak. The home advantage, which is included later, runs in analogy to the still quite simple formula for calculating the expectation for a pairing based only on the goal expectations, only it would already become unwieldy, confusing quite quickly.
So, let’s assume that Bayern has goal expectations of 2:1 per game. Then the result of the formula should be that against the average team exactly their goal expectation is calculated. To check the formula, so to speak. Any (other) opposing team would of course have to score more favourably or unfavourably, depending on whether it is above or below average.
So now more concretely: In order to determine how many goals Bayern Munich expects to score against another team, and this, so to speak, on a neutral pitch, you have to put the goals they expect to concede into the appropriate ratio with the Bayern value. Simply put, you could say that Bayern 2 (their own goal expectation) divided by 1.45 (the average number of goals a team scores in the league) = 1.38 goals times the average of all teams.
So 1.38 is their value based on each game. If the opponent is now, for example, below average, so let’s say they concede 1.6 goals per game, then this value has an unfavourable effect on them, in terms of expected goals conceded, at the same time it has a favourable effect on expected goals for Bayern. Their factor for goals conceded results in a 1.6 (their expected goals conceded) / 1.45 (the average expected goals conceded) = 1.1, so they concede 1.1 times as many goals per game as the average team.
The two factors calculated – Bayern’s 1.38 and the opponent’s 1.1 work in the same direction. They increase the goals scored by Bayern and the goals conceded by the opponent. Who else but Bayern should inflict the (conceded) damage on them in the match? Accordingly, you multiply the two values. That is only logical. For this match, Bayern would score even more goals than “normally” (i.e. on average). How much more? Well, another 1.1 times more. So we have a factor for this match of 1.1 * 1.38 = 1.52. This indicates how many times more goals than average Bayern expects to score in this match. This formulation implies that the determined value of 1.52 – which is “only” a factor – is multiplied by the average number of goals scored by a team, i.e. 1.45 again.
The result is a goal expectation for Bayern of 1.52 * 1.45 = 2.20 goals. This is immediately clear from a visual point of view: the others score 1.1 times as many as the average, Bavaria scores 2 on average, i.e. 2 * 1.1 = 2.2. That is correct, sounds logical, makes sense, it fits. To check, one can still use the average team, which logically results in a factor of 1.0 at this point, which has no effect at all on the expectation of goals scored for exactly.