Thursday, March 5, 2009

Probabilities of Advancing From a Qualifying Pool

In yesterday's post, I went through a few simulations showing the 4-team round robin vs. the double elimination tournament used to advance 2 teams. This relates to both the World Baseball Classic as well as other sports such as the Olympic competition and the World Cup. In a couple of these I used examples of 4 teams with "true" winning percentages of .700, .600, .400, and .300. Yesterday's post analyzed the percentage of times that the tournament correctly advanced the best two teams (the .700 and the .600 team) and the result was 52% of the time with the round robin, 60% of the time with the double elimination and proper seeding, and 45% of the time with double elimination and poor seeding.

Today I want to add a few more numbers. Here I present the percentage of times that each of the teams advanced to the next round. In an ideal world, the best two teams would always advance to the next round. The following chart shows how close we get:

As we can see, even under the most favorable circumstances, the best teams do not always advance. Keep in mind also that the differences between the team's true skill levels are not small. This pool is roughly equivalent to being made up of the following: the 1927 Yankees, the 2004 Red Sox, the 1998 expansion Tampa Bay Devil Rays, and worst ever St. Louis Browns team of 1911. One would think that the Red Sox and Yankees would advance every time, but no - we see Ruth and Company advancing only 82% of the time under the round robin, and only 87% of the time with a properly seeded double elimination tournament.

The table only underscores my point in a previous post that anything can happen in these short tournaments! Six games is simply not enough to definitively advance the best two teams, and even under the best of circumstances, there is a not insignificant probability that the top team is ousted. Probability dictates that there will be upsets - so don't be surprised when a top flight team is sent home early in the upcoming WBC.

However, we once again see that if the teams can be seeded correctly, then the double-elimination tournament far surpasses the round robin in the ability to advance the best teams.