Finals Series after League Table

In many sports, the initial part of the season consists of a round-robin tournament (in which each team plays all other teams one or more times), but the season winner is determined by a later 'finals series' in which the top teams from the league compete.

For example, in the Super 12 rugby competition in the southern hemisphere, each of the 12 teams plays all other teams once. The top four teams from this part of the competition play in semifinals and a final to determine the eventual winner of the competition. (The top team in the league plays the fourth team and the second team plays the third in the semifinals.)

It might seem that adding a finals series should increase the probability of the best team winning the competition since the best team would still have a chance of winning even if it was unlucky enough to lose a few matches in the initial part of the season and did not top the league. But is this true?

Is the top team's chances of winning now higher?

We investigate with a simulation.

In the diagram below, each of 10 teams plays all other teams at home and away in the first part of the season. Teams get 3 points for a win and 1 point for a draw (which happens with probability 0.2). The top four teams compete in a finals series in which the top team plays the fourth team in the first semifinal and the second and third teams play in the other semifinal. The winners compete in the final.

In the simulation, all teams have the same probability of winning except for Team A whose probability of winning a match can be adjusted with the slider. Increase Team A's probability of winning to 0.55 — more than double its probability of losing.

Click Run League to perform a simulation. The dot plots on the right show the ranks of Team A after the initial part of the competition and also after the finals series.

Click Accumulate and run the simulation about 100 times. Observe that Team A has less chance of winning the finals series (getting rank 1) than of being top of the league in the initial part of the season. (A bit more information about this kind of test is provided later.)

Although the precise results depend on the number of teams and the format of the finals series, it seems that finals series are added more as a marketting ploy than as a serious attempt to find the best team!

When a single summary statistic is recorded from each run of a simulation (e.g. the range of points in simulated league tables), we obtain a single batch of numerical or categorical values. Confidence intervals and hypothesis tests for a single mean or proportion are therefore appropriate analysis tools.

If two or more summary statistics are recorded from each simulation run, the simulation results are pairs of values. Relevant statistical methods therefore include correlation, regression and contingency table analysis.