Playoff Round Robins

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Mike Bentley
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Playoff Round Robins

Post by Mike Bentley »

I've played a couple of tournaments recently with the following format:

-Two prelim brackets.
-Top 3 teams from each prelim bracket make the top bracket.
-Top bracket plays a full round robin of 5 games.
-Winner determined solely based on the record in the 5 playoff games.

Both times, this format has felt unsatisfactory. I especially don't like the following scenario:

-Team A and Team B are both in Prelim Bracket Foo.
-Team A ends the prelims 5-0. Team B ends the prelims 2-3 with a loss to Team A, Team C (also a top bracket team) and Team D (who didn't make the top bracket). Team B still makes the top bracket.
-Team B wins out in the playoffs, going 5-0. Team A loses one playoff game to Team B and ends up with a 4-1 playoff record.
-Team B ends the tournament with an overall record of 7-3. Team A ends the tournament with an overall record of 9-1. Team B and Team A have played exactly the same opponents.
-Because this is an online tournament, there's no advantaged final. Team B is declared the winner.

You can see how this particular outcome is extremely unfair. Team A and Team B have played exactly the same opponents. Team A has beaten more of those opponents but is declared the loser.

Is there a better way to handle records in this case? I'm somewhat inclined to say a better policy is to at least carry over the prelim games against teams that made the top bracket. This results in an unbalanced playoff schedule, with teams playing extra games against the top teams from their original bracket. But this seems fairer to me than completely not counting those games. Maybe I'm ignoring the possibility that a prelim bracket imbalance would make things less fair for some teams in this situation.

At the bare minimum, any ties between teams from the original bracket ought to be resolved based on their prelim record.
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Zealots of Stockholm
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Re: Playoff Round Robins

Post by Zealots of Stockholm »

I think currently this is the fairest way to do things, though I can appreciate the concern. I also think this concern really only exists with a field size of exactly 12*, as 11 rounds is generally considered too much for online quizbowl, and only doing crossovers against the top 3 teams from the other bracket is only 8 games, which some may consider too few. I guess you could do a crossover between the top 4 in each bracket for 4 rounds for the top 8 teams and a round robin between the bottom 2 teams in each bracket, though that results in the bottom 4 teams playing one fewer round, and I personally would question whether the top team from a prelim bracket gets more out of playing the 4th best team from the other bracket than they would just playing the 2nd best team from their prelim bracket again.

A situation that can occur using the remedy you propose: Team A goes 5-0 in their prelim bracket, team B goes 4-1 in the same prelim bracket (losing only to team A), and team C goes 5-0 in the other prelim bracket. In playoffs, team A goes 5-0 again, team B goes 4-1 again (losing again to team A), and team C goes 3-2, losing to both team A and team B. Under current practice, team B finishes ahead of team C by playoff record, while under your proposal team B and team C both have 7 games count, during which they are each 5-2 and ranked by ppg in those 7 games. Especially if team A is massively ahead of every other team in the field, having a large margin of victory against every team, team B is pretty heavily penalized for having been in team A's prelim bracket. I like the current system, which rewards team B for their playoff victory and only counts the same schedule of games to compare teams, better.

*: with most other field sizes, I think a round robin schedule or a playoff schedule utilizing crossovers is better
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Cody
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Re: Playoff Round Robins

Post by Cody »

The alternative is a crossover, with 2 fewer games in this scenario. In that case, the purpose of the prelims is to seed teams for playoffs and hold playoff games in the first 5 rounds. This is fine, and so is 8 rounds for an online tournament.

In the event of a playoff round robin, prelim records are wiped (as stated). This means that the only purpose of the prelims, in terms of final rankings, is to seed teams for a playoff where games count. This reconceptualization eliminates any unfairness. The prelims are not designed to determine final ranking, and cannot do so.

See, for example, this post of mine with greater detail.
Cody wrote: Thu Feb 21, 2019 10:03 amThe community standard of bracketed round-robin preliminary & playoff rounds (or any other extensions, including super-playoffs) are a compromise that significantly improve on other formats (single/double/x-elimination, whatever NHBB’s monstrosity is) while being much easier to execute than the other fair compromise format we have accepted (power matching, which excels at large field sizes). A properly executed bracketed format meets many of the fundamental standards of fairness embodied by a whole-field round robin: a single loss will not eliminate a team from winning the tournament (hence also the “advantaged final”), teams play as much of the field as feasible, teams play as many other teams of similar strength as feasible, etc.

A key to the bracketed format is seeding / re-seeding. You cannot take all the teams from one bracket to a given tier in the playoffs, else we would not need to use a bracketed format. So, we snake seed teams for preliminary rounds based on a value judgement of their strength to spread them out and try to ensure that the appropriate teams make each tier of the playoffs. (Imperfections in seeding are the critical weakness of a bracketed format because they block teams from making the tier they may have “deserved” to make based on their strength. It’s a small but significant reason that power matching excels for large field sizes, circa 150+ teams. In the presence of perfect seeding, bracketed formats would be almost as perfect as a whole-field round robin.) At the conclusion of preliminary rounds, teams are reseeded based on win-loss and tiebreakers and put into playoff brackets where they play other teams of similar strength.

The critical take-away from the bracketed format scheme is that the preliminary rounds are designed specifically to seed teams for the playoffs in the fairest format we can devise, accepting that some imperfections will come into play (mitigated by proper design of the playoff format). The playoffs, against teams of similar strength, are how we determine the final standings. By this understanding, there is no tension in dropping games from the preliminary rounds in determining placement because they have served their purpose in slotting teams into playoff brackets.

Any attempt to carry-over records will yield a manifestly unfair situation where teams are ranked in games against opponents they didn't have in common. See, for example, this post of mine (and links there-in to previous threads) whose methods can be applied here. By double-counting certain games, you break the entire reason that the prelim-playoff structure exists and create a situation where teams gain extreme advantages (or are severely penalized) for prelim seeding *and* differences in team strength. For example, if team A is the clear best team in the field but teams B-F/E/D/C can duke it out then anyone placed in a prelim bracket with team A has been disadvantaged because they will almost assuredly carry over an extra loss compared to the other bracket. And this scenario only becomes more grim when you lack perfect prelim seeding.
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Re: Playoff Round Robins

Post by Cody »

Mike Bentley wrote: Wed Dec 02, 2020 8:58 pmBoth times, this format has felt unsatisfactory. I especially don't like the following scenario:

-Team A and Team B are both in Prelim Bracket Foo.
-Team A ends the prelims 5–0. Team B ends the prelims 2–3 with a loss to Team A, Team C (also a top bracket team) and Team D (who didn't make the top bracket). Team B still makes the top bracket.
-Team B wins out in the playoffs, going 5–0. Team A loses one playoff game to Team B and ends up with a 4–1 playoff record.
-Team B ends the tournament with an overall record of 7–3. Team A ends the tournament with an overall record of 9–1. Team B and Team A have played exactly the same opponents.
-Because this is an online tournament, there's no advantaged final. Team B is declared the winner.
Is this a real situation or a hypothetical? Because this is only possible (as far as I can tell) with the following records, and Team B winning a statistical tiebreaker. If Team B then goes 5–0 in the playoffs, congratulations to them – you have to win your playoff games 🤷‍♀️ (even then, it is only possible due to compromising on an advantaged final.)

Code: Select all

          W L
Team A    5 0
Team B    2 3
Team C    4 1
Team D    2 3
Team E    0 5
Team F    2 3
The problem with degenerate hypotheticals like this is that they don't happen and lead you astray from the 99.999% of scenarios you do need to handle.
Mike Bentley wrote: Wed Dec 02, 2020 8:58 pmAt the bare minimum, any ties between teams from the original bracket ought to be resolved based on their prelim record.
This is just head-to-head with extra steps to give it a gloss. If Team A finishes 5–0 in the prelims, and Team C finishes 4–1; then the reverse in the playoff. Breaking the tie on prelim record reduces to a head-to-head tiebreaker, which is not an acceptable tie-breaking method. This is the case for any two teams with common losses (e.g. Team D and Team E lose to Team F and Team D loses to Team E, as in the table below).

Code: Select all

          W L
Team A    5 0
Team B    4 1
Team C    3 2
Team D    0 5
Team E    1 4
Team F    2 3
Cody Voight, VCU ’14.
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