Well, it happened again. For seven straight World Cups, the Mexican national soccer team was good enough to advance from group play, but not good enough to win the first game in the knock-out round (Round of 16). Thus, the curse of the “fifth game” (quinto partido) lives – once again, Mexico played four games (three in group play, one in the Round of 16), but couldn’t get to the fifth.
What are the odds of this happening? We can take a stab at calculating this, using the ELO football ratings. One nice thing about ELO ratings is that they are historical; you can look up a team’s rating at any point in time. Another nice thing is that, given the ratings of two teams, ELO will tell you the probably of victory of a head-to-head clash between them. Of course, you have to trust that the ELO system knows what it is doing. But it is based on actual results, so it seems to be a reasonable way to approach this analysis.
Let’s look at the seven “Round of 16” matchups that Mexico has lost. Listed are the ELO rating for each team (at the time the game was played), and the expected win probability for the head-to-head match-up. For example, just before the 1994 knockout match, Bulgaria’s ELO rating was 1830, and Mexico’s was 1850. According to ELO, this means that Mexico had a 55.7% chance of winning the game versus Bulgaria. In fact, the game ended in a tie, and Mexico lost the penalty kick shoot out.
| Year | Teams | ELO rating | Win% |
| 1994 | Bulgaria | 1830 | 44.3% |
| 1994 | Mexico | 1850 | 55.7% |
| 1998 | Germany | 2075 | 74.9% |
| 1998 | Mexico | 1885 | 25.1% |
| 2002 | USA | 1788 | 35.6% |
| 2002 | Mexico | 1891 | 64.4% |
| 2006 | Argentina | 1981 | 69.7% |
| 2006 | Mexico | 1836 | 30.3% |
| 2010 | Argentina | 1986 | 63.2% |
| 2010 | Mexico | 1892 | 36.8% |
| 2014 | Netherlands | 2103 | 76.6% |
| 2014 | Mexico | 1897 | 23.4% |
| 2018 | Brazil | 2142 | 84.8% |
| 2018 | Mexico | 1843 | 15.2% |
You can see that Mexico was the underdog in most of these games (I’ve highlighted their win probabilities). Only the 2002 game was a big upset; other than that (and maybe Bulgaria) the games went according to form. But still, maybe they should have won a game somewhere along the line?
Well, yes. Multiplying the Win% of all opponents, the odds of Mexico losing all seven of these games is 3.4%. Another way to look at it: given this set of probabilities, the median number of expected wins is 2; the average (mean) is about 2.5.
No matter how you slice it, probability says it’s unlikely that they would have lost all seven games. In five of the seven years, they were significant underdogs, so it’s not surprising that they lost any one of those games. But somewhere along the line they should have gotten a win. It’s frustrating for Mexico fans, because in several of those games they played well and came close to winning. And now that the streak is up to seven, the pressure of quinto partido will only build.
Ayy, que lastima!