A data scientist by profession, a generalist by interest, and a sports fan by instinct. Hopefully this blog reflects all three.

16 Apr 2022

Some brief thoughts on round robins

Inspired by a question I was discussing with Owen Riley, I took a look at how preliminary round-robin brackets have shaken out at ACF Nationals. The precipitating question was: how often does a lower-ranked team that pulls an upset of a top-ranked team manage to make the top bracket based on that upset (i.e. there are no other upsets in the bracket)?

How often do brackets break cleanly?

The tournament director’s dream, a round-robin bracket that entirely breaks cleanly is a thing of beauty – two smooth unbroken sequences of wins and losses descending and ascending. However, for this analysis we’re more interested in brackets that break partially cleanly (i.e., the top team goes undefeated and the second-place team only loses to the top team).

Scenario %
Top team goes undefeated 78.57%
Top 2 teams break cleanly 59.52%
Top 3 teams break cleanly 33.33%
Entire bracket breaks cleanly 21.43%

How often are there upsets?

I’m defining upsets here as a team finishing ahead of another team with a better points per bonus (PPB).

Scenario %
Upset in top 1 19.05%
Upset in top 2 28.57%
Upset in top 3 33.33%

How often does a bracket break cleanly, given that there is an upset?

Scenario %
Clean break, given upset in top 1 62.50%
Clean break, given upset in top 2 41.67%
Clean break, given upset in top 3 35.71%

So a team that upsets the bracket leader in PPB is relatively much more likely to hang on than one that upsets the #2 or #3 team. This makes intuitive sense if you assume that the distribution of top teams follows a roughly pyramidal shape (i.e. there are more teams that are Tier 3 contenders than Tier 2 contenders than Tier 1, and so on), and so the skill level of the middle-of-the-bracket teams are likelier to be more condensed.

It’s also interesting that there’s not too much of difference between the top 2 and top 3; this isn’t nearly comprehensive enough to solely base tournament format changes on, but it lends support to arguments for limiting the number of teams that are taken to top bracket after prelims.

I promised a brief post and I don’t have much more to say for now, so I’ll leave it with a little heatmap showing bracket outcomes.