How skill beats luck in the World Cup of Development

This blog periodically points out the role of randomness in development, much to the frustration of many readers. This post is how to set things up so that skill triumphs over luck. Today’s official metaphor is, of course, for us sports-obsessed nuts, the World Cup. Early rounds have seen remarkable upsets: Switzerland beats Spain, Japan beats Cameroon, Serbia beats Germany. Yet no super long shot team has ever won the World Cup. In fact, 14 of the 18 previous World Cups were won by only 4 teams: Brazil, Germany, Italy, and Argentina.

The World Cup uses a tournament to make skill beat luck. There’s a preliminary round won by 16 out of 32 teams, and then there’s four rounds of elimination to determine the champion. To simplify for illustration, let’s just discuss a five-round single elimination tournament for 32 teams.

The tournament magnifies the importance of skill versus luck. Based on the above upsets, a weak team still manages to win a single game sometimes, let’s say for illustration 15 percent of the time. So roughly for every 7 games, there will be one huge upset, which explains why the Cup with lots of games has seen a few surprising upsets.  To win a single elimination 5-round tournament, however, this weak team would have to reel off 5 straight upset wins. The probability of this is .15 x .15 x .15 x .15 x .15 = 0.000076, i.e. 13,000 to 1 odds against this weak team winning the tournament.

In contrast, a strong team who wins a single game 85 percent of the time has a .85 x .85 x .85 x .85 x .85 = .44 probability of winning the tournament. Of course, there’s still a slightly worse than even chance that this particular strong team does NOT win, but the probability that SOME strong team will win is very, very high. (We have to make all the probabilities for all 32 teams consistent by making sure they add up to one, but I ignore this since I am only discussing a few teams.)

OK, now it's time for the clumsy transition from the World Cup metaphor to development. As this blog likes to frequently point out, economic growth has a lot of random variation. Over a short period of time (metaphorically equivalent to one game), a country with bad policies and bad institutions still might have a good growth rate. But over a long period of time (equivalent to playing many successive games), the consistent winners are very likely to be countries with good policies and good institutions. So in deciding whether a particular set of policies and institutions are good or bad, you need to look at long periods (tournaments) and not at short ones (single games). How long  the long periods have to be will depend on how important luck is in the short term; the evidence we have on economic growth is that short term luck is very important, and the periods have to be pretty darn long for proper analysis. (Hint: the periods were NOT long enough in this Rodrik analysis as to why the Washington Consensus sucks.)

POSTSCRIPT for those who hate LUCK: we are all intensely uncomfortable with the idea that luck matters at all in something we really care about -- like the World Cup. Not even this luck-reducing therapy is likely to be enough.  The example above still implies which of the strong teams wins is random. But what do the words “random” or “luck” really mean? They could capture temporary and non-replicable fluctuations in human skill as well as pure luck. There are two competing narratives: (1) a strong player on a strong team just happens to be in the right place at the right time to receive the right pass to score a Cup-winning goal. (2) a heroic player consciously exerts extraordinary skill at the most crucial moment to score the Cup-winning goal. Scientifically we can’t really distinguish (1) from (2). Psychologically, we intensely prefer (2). Fine, go with that, just remember it’s not replicable. Same goes for heroic entrepreneurs and political reformers.

POSTSCRIPT 2 for those who hate LUCK: luck matters even as much as it does for the World Cup because there has already been a lot of screening to select the best teams in the world. Saying luck matters does not imply the Balding Middle-Aged Econ Prof All-Stars would have a chance in hell against Brazil. Likewise, in development, luck matters for growth in the sample of societies as much as it does because most of them are already doing their best to achieve growth. If some whack job does a demolition job on their own economy, like Mugabe or Chavez, it’s pretty clear that bad policy will overwhelm good luck pretty quickly.