How Likely Were Ties in OWL Stage 1?

Given the number of ties in Stage 1 rankings, some people have complained that this format was always likely to have annoying tie-break situations. I ran some simulations to answer that very question! Also this was done very quickly so who knows if its right — feel free to fact check me and tell me why I’m dumb!

Hey everyone, it’s been a long time since I put out a Beezy-Work on anything, been working on a bunch of stuff behind the scenes and haven’t found the time. But today I saw some discussion on Twitter about the tie-breaking in OWL stage 1 rankings, and how many teams were tied in different places. I became curious as to how likely it was to end up with so many ties given this format. So I ran some simulations and found fairly interesting results.

Let’s start with what I did. I created a very simple model that took 20 teams each playing 7 games and constructed a possible viable score line at the end of that 7 games. Constraints being that a winning map differential was +4, +3, +2+, +1 and the losing differential was the opposite. Also any win was mirrored by a loss — so team X winning meant team Y losing etc. Then, I ranked teams based on #wins and map differential. I repeated this 900 times. I used random selection to determine outcomes, and didn’t try to incorporate any type of elo system or ‘likelihood of x team winning’.

784 out of the 900 (87%) Simulations had at least one positional tie (at least 2 teams with the same wins and map differential). In fact, 750 (83%)of those simulations included at least one tie that would have had impacts on playoff seeding (tie of teams Rank 8 or better). So, based on format alone, there was over an 80% chance that some sort of additional tie-breaker method would have been required to form proper seeding for OWL Stage 1 Finals.

But let’s answer the question at hand — how likely was it that our current situation, where 4 teams were involved in tiebreakers, would have occurred based on this format. The answer is, kind of unlikely. There were 312 simulations (34.6%) where at least 4 teams in the playoff seeding region were tied (not necessarily all for same place, could have been 2 and 2). So there you have it. It was very likely that at least 1 tiebreaker situation occurred, but relatively unlikely that 2 tiebreaker situations occurred.

Fun Fact — The most absurd scenario of all simulations I ran was a 5-way tie for second place with 5 teams each with 4 wins and a map differential of +3.

Edit — As pointed out by @gewaldro15 this analysis did not incorporate likelihood of no head-to-head tiebreaker.