Footballer earnings, superstar and tournament effects

In ECON110, we talk about the reasons that not all workers in the same labour market receive the same wage. In the 1980s, Sherwin Rosen identified 'superstar effects', where if a worker can satisfy the demand from many consumers, they get paid a higher wage. Essentially, the worker is rewarded for generating high revenues for their employer, as you would expect. This explains much of the rise in salaries over time for top sportspeople - as television (and more recently internet) viewership has grown, the value generated by a top sportsperson (in terms of the number of viewers they attract) has grown, and their salaries have grown as a result.

Rosen, along with Ed Lazear, also described 'tournament effects'. With tournament effects, people are paid a 'prize' for their relative performance (that is, for winning the 'tournament'). The prize may take the form of a bonus, a raise, or a promotion. The point is that each worker only needs to be a little bit better than the second best worker in order to 'win' the tournament.

As an example of tournament effects, consider a team of 20 players, who are all roughly equally talented but can be ranked from 1st to 20th in terms of their ability to attract consumers to buy products that they have endorsed. Let's assume that each player can endorse no more than two products (due to time constraints). Now say that there are 20 firms willing to pay the players to endorse their products, and we can rank the companies by their willingness-to-pay. The firm with the highest willingness-to-pay is willing to pay $20 million, and the second $19 million, the third $18 million, and so on down to the last firm which is willing to pay just $1 million. What happens?

The top player receives endorsements of $39 million (from the two firms willing to pay the most), the second player receives $35 million (from the third and fourth firms), the third player receives $31 million (from the fifth and sixth firms), and so on. The table below shows player earnings for all 20 players (ranked from 1st to 20th). Notice that the top earning players earn a lot, but half of the players earn nothing. This arises even though the players are all roughly equally talented, and leads to a highly skewed earnings distribution.

Obviously the example above is totally made up and very simplistic, but it's not so far from what we observe in the real world. Consider the earnings of top footballers. Even if we consider only the top ten players (by earnings, according to Forbes' 2016 list), this is what we see:

It would be difficult to argue that Ronaldo or Messi generate more than twice as much value as the others on this list, so the difference must be generated by something other than just superstar effects; that is, tournament effects. That is, when we look at players at a similar level of play, the difference in earnings is mostly tournament effects. In contrast, the difference in average salaries in England between Premier League footballers (£1.7 million) and League Two footballers (£40,350) is likely to be a mix of superstar effects (Premier League footballers generate more value for their employers than League Two footballers) and tournament effects (there's a limited number of places for Premier League footballers, so slightly worse players end up in lower divisions paying less).

One last point: It's been argued (I saw this argument first in Tim Harford's book The Logic of Life) that the size of the 'prize' for a tournament will be larger the more luck is involved. That is, if the difference between the tournament 'winner' and the others is mostly luck, the size of the bonus for working hard to win the tournament must be high in order to sufficiently incentivise the worker to work hard. So, if you buy that the difference in the graph above is mostly a tournament effect, does that mean that the earnings difference between Ronaldo and Messi at the top, and Neymar in third, is mostly down to luck?