Some relevant research literature and methodology

In US sports, where leagues are constructed with profit as a relevant objective, it should not come as a surprise that league size (or number of teams in the league) is a question that has been addressed. Indeed, this is the case.

Already in the classic paper by Quirk and El-Hodiri, the question is treated. Other US authors has followed up , while Szymanski, applying Tullock’s model of a rent-seeking contest, tries to sum up in his excellent contribution.
The classic arguments in this brand of literature may perhaps be summed up as follows: Adding a new team to a league adds more matches and hence more (potential) revenue.

On the other hand, adding a performance-wise bad team may lead to decreased uncertainty of outcome (predictability) and hence less demand. This constitutes a trade-off that could be optimized and hence equilibrium outcomes, as more than one team is involved.
This is of course, although very elegant, an extremely simplified view, which has limited impact and relevance for the potential link to national team performance – which is the topic here.
Apart from this work (discussed above), to the best of my knowledge, limited (or none) empirical work on potential causality between uncertainty of outcome in national leagues and national team quality exists.
Uncertainty of outcome (UoO), introduced by Rottenberg [16], is a complex phenomenon. The excellent review [2] gives a good survey on the topic and potential traps. More recent contributions [1, 4, 8, 14] indicate the popularity of the concept in sports economic and management research.

The main (simplified) reason for such an inherent complexity may perhaps be the concept of time. Most measures of UuO are static, measuring ’distances’ between teams on a league table based on points or ranks. However, such a measure can of course not capture the ’win-dispersion’ dimension – i.e. the same team winning each season. So, even if ’distance’ between teams on a table is ’small’, uncertainty of outcome may be considered low if the same teams have occupied (say) the three first places the last seasons.
Here, however, the most used (although perhaps not the most popular) approach is adapted, mostly due to the fact that the pretention of solid analysis is not the main point here. Hence, a ’static’ measure for UoO is applied; namely the one introduced in.
This measure is straightforwardly logically constructed by introducing a league table with (theoretically) minimal competition. In such a league, the best team beats all other teams, the second best all other teams but the best and so on. Based on such a league, a total variation can be constructed by ’square-summing’ differences between the actual league points, and the theoretical league of minimal competition.

This square sum, could then be normed by dividing with the maximal total variation, also a square sum, where two theoretical leagues are compared; the previous one of minimal competition, and the other extreme alternative, a league of maximal com- petition, where all teams are equally good or all matches end in a draw. The resulting number, ρL, would then provide a measure for UoO measured as a percent (%).
Another argument for choosing this measure, apart from its logic straight-forwardness, is its inherent constructive computational characteristics – see for instance .
Just like uncertainty of outcome, measuring, or observing, football team quality is not necessarily straightforward. Luckily, a measure  exists, namely the FIFA [3] rank. The neat thing about this measure is not it’s potential lack of sharpness, but the simple fact that decisions of vital interest for football teams are made based on it.

Qualifications for important tournaments, seeding etc. are made based on this ranking system. Hence, even tough it may not be a very good quality measure, it is still almost always in all national teams best interest to climb as high as possible on the rank. As a consequence, it is a simple and reasonable team quality measure.