Potential problems with the Buchholz score
/ TF2 Discussion
“Median Buchholz score: wins x 1 + draws x 0.5” – ozfortress staff
Is this really correct? Can the current system do tiebreakers fairly?
If one is careful enough after looking at the ladder at the end of the regular season, he/she may spot an interesting trend that “Buchholz” and “Wins” are the same for all teams across all three divisions. What is going on here? If Buchholz is calculated incorrectly, it can cause problems for open and intermediate divisions as ties are separated using the Buchholz score. (premier is not a Swiss system, each team will play against every other team, hence no point displaying Buchholz on the ladder)
So, I’m going to try to understand how this works and do some maths. Currently, ozfortress league uses the “Median Buchholz” to determine tiebreakers after tied wins.
“The Buchholz System is the sum of the scores of each of the opponents of a player.”
“The Median Buchholz is the Buchholz reduced by the highest and the lowest scores of the opponents.”
These two definitions are sourced from Fédération Internationale des or the World Chess Federation, as Buchholz is originally used to determine tiebreakers in chess tournaments. For ozfortress league, in my opinion, Buchholz should be interpreted as the sum of a team’s opponent’s wins. For example, team A has versed three teams (team B, C and D) in a season, so A’s Buchholz should equal to the sum of wins for B, C and D. And the Median Buchholz is just removing the highest and lowest number in the Buchholz calculation.
From the definitions, we can see why Buchholz is widely used for the swiss system. It is an indicator for the strength of the teams one has versed (not won). If tied at the same score, a stronger team by the Buchholz definitions is the team who has versed harder teams than the weaker team.
I’ll calculate some of the Median Buchholz for the tied teams in ozfortress season 23 after round seven using my method.
Case 1: chiken vs i play 6's because i hate pyro
Teams are tied at 4th place after points and tied wins in open. The ozfortress’ Buchholz has put chiken above.
chiken has more Buchholz from my calculations. The ladder seems consistent here as ozfortress has placed chiken higher than i play 6's because i hate pyro using their Buchholz score algorithms.
Case 2: ad hominem attack vs twitch.tv/sskaz
Teams are tied at 2nd place after points and tied wins in intermediate. The ozfortress’ Buchholz has put ad hominem attack above.
twitch.tv/sskaz has more Buchholz from my calculations. There is a discrepancy here comparing ozfortress’ calculations with mine.
Buchholz recalculation for intermediate division:
The above two cases should’ve provided some clarity into my method. I’m now going to present the recalculated Median Buchholz scores for every team in intermediate division without showing detailed steps.
It is worth to note there are some (probably insignificant) details missing, for example, the treatment of forfeit wins, bye rounds and disbanded teams. In my calculations, I used ozfortress’ definition of wins and ignored bye rounds. So far, forfeited wins do not count as wins in the ozfortress league ruleset and disbanded teams automatically forfeit all their games (including played games before the disband).
To conclude, it is clear we get different numbers and when it matters, case 2 showed at least that I am wrong or ozfortress is. Regardless, it is worth to question how Buchholz work, rather than blindly letting the system do it for us, as it can decide playoff qualifications or seeding. We have been using Buchholz for at least two years since the introduction of warzone in mid-2016, I’m not confident to say the majority of the community know how it operates. Personally, I think we shouldn’t use something that we don’t understand fully, or we should at least try to validate or fix it.
Feel free to point me wrong, I’m not sure myself either. By the way, do you know the details behind how the Swiss system picks the matches for a round?
tL;dr: I googled Buchholz and my methods gave different numbers compared to the ozf numbers.
The point of this post is to share my interpretation of Buchholz. I’m not claiming which method is correct, I think we should take a closer look at it.
This will be looked at after the end of the season