Tiebreaker - Revision history

Kevin Wang: /* Tiebreaker statistics */

2025-12-14T23:20:48Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-11-12T23:10:28Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-11-12T23:07:41Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-11-12T23:07:09Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-11-12T23:06:05Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-07-14T14:32:12Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker statistics */

2025-07-14T14:30:46Z

Tiebreaker statistics

Kevin Wang: /* Tiebreaker games */

2025-07-14T14:30:19Z

Tiebreaker games

Kevin Wang: /* Tiebreaker games */

2025-07-14T14:29:30Z

Tiebreaker games

Kevin Wang: /* Tiebreaker questions */

2025-07-14T13:38:22Z

Tiebreaker questions

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 ==Tiebreaker statistics==
-Tiebreaker games (or half-games) are the default way to resolve ties and should be used if at all possible. If it is not possible to play them out, a statistical measure may be used instead.
+Tiebreaker games (or half-games) are considered the default way to resolve ties and should be used if at all possible. If it is not possible to play them out, a statistical measure may be used instead.
 The most common reasons why a tie will not be played out are "there isn't enough time" and "there are not enough questions". All tournaments are subject to this first scenario but the second is a constraint only imposed on the [[tournament director]]s of regular-season [[mirror]]s, as they cannot control the writing team. In contrast, tournaments with tailor-made sets like nationals have the opportunity to write extra packets to allow more tiebreakers in their schedule. The number of questions required remains a bottleneck, though: it is impractical to write an arbitrary number of extra questions that may not be seen and even though tiebreakers can be reused across disjoint [[bracket]]s the number required grows with schedule complexity and consequently with field size. As such it is common to both have more tiebreaker packets and employ question-saving measures like using half-packets.

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 If each team's game against this common opponent was the one double-counted instead, then B would win the tiebreaker instead. Imagine another scheme where random games are double-counted until one team wins. Though straightforwardly terrible its symmetry actually gives both teams equal odds to win, which makes it clear that it is only the choice to select the head-to-head game that produces an effect in this tiebreaker.
-The following are several instances in which unorthodox tiebreaking statistics were - it is not recommended that these be replicated:
+The following are several instances in which unorthodox tiebreaking statistics were used - it is not recommended that these be replicated:
 * The 2011 [[NGCSU]] mirror of [[MUT]] broke ties using "quality" (also called "difficulty rating"), which ultimately reversed first with second and 3rd with 4th place.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=213230#p213230 Re: MUT Mirror 4/2 @ NGCSU] by [[AlphaQuizBowler]] » Sat Apr 02, 2011 5:03 pm</ref> The metric purportedly originated from the FIRST robotics competition and was calculated as one plus the difference in score divided by total score with preference given to values closer to unity.
 :* Thus a score of 350-220 would yield "quality" of 1.28 and 0.72 while one of 100-95 would yield 1.03 and 0.97, with the latter winning the tiebreaker.

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 PPG is a better choice because it incorporates tossup performance while also including PPB; however, it is very susceptible to the [[strength of schedule]] and thus should only be used when there are common opponents. PPB is more robust to this but only captures one facet of a team's strength. This is the same fundamental dilemma that the [[A-value]] and [[D-value]] metrics for developed to handle, but these are impractical to use while running a tournament and are thus only used for their original purpose of determining nationals qualification.
-There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B but they otherwise have a tied record. Using a H2H tiebreaker makes this one match matter more than all their other matches; besides the inherent unfairness in this unequal weighting, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
+There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B but they otherwise have a tied record against common opponents. Using a H2H tiebreaker makes this one match matter more than all their other matches; besides the inherent unfairness in this unequal weighting, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
 If each team's game against this common opponent was the one double-counted instead, then B would win the tiebreaker instead. Imagine another scheme where random games are double-counted until one team wins. Though straightforwardly terrible its symmetry actually gives both teams equal odds to win, which makes it clear that it is only the choice to select the head-to-head game that produces an effect in this tiebreaker.

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 PPG is a better choice because it incorporates tossup performance while also including PPB; however, it is very susceptible to the [[strength of schedule]] and thus should only be used when there are common opponents. PPB is more robust to this but only captures one facet of a team's strength. This is the same fundamental dilemma that the [[A-value]] and [[D-value]] metrics for developed to handle, but these are impractical to use while running a tournament and are thus only used for their original purpose of determining nationals qualification.
-There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B but they otherwise have a tied record. Besides the inherent unfairness in having any one match be worth more, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
+There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B but they otherwise have a tied record. Using a H2H tiebreaker makes this one match matter more than all their other matches; besides the inherent unfairness in this unequal weighting, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
 If each team's game against this common opponent was the one double-counted instead, then B would win the tiebreaker instead. Imagine another scheme where random games are double-counted until one team wins. Though straightforwardly terrible its symmetry actually gives both teams equal odds to win, which makes it clear that it is only the choice to select the head-to-head game that produces an effect in this tiebreaker.

@@ Line 62: / Line 62: @@
 PPG is a better choice because it incorporates tossup performance while also including PPB; however, it is very susceptible to the [[strength of schedule]] and thus should only be used when there are common opponents. PPB is more robust to this but only captures one facet of a team's strength. This is the same fundamental dilemma that the [[A-value]] and [[D-value]] metrics for developed to handle, but these are impractical to use while running a tournament and are thus only used for their original purpose of determining nationals qualification.
-There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B. Besides the inherent unfairness in having any one match be worth more, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
+There are almost {{u|no scenarios where [[head-to-head]] record should be used}} because it double-counts the results of the match that these two teams played. [https://en.wikipedia.org/wiki/Without_loss_of_generality Without loss of generality], let's imagine that team A beat team B but they otherwise have a tied record. Besides the inherent unfairness in having any one match be worth more, it is especially unfair to team B for that to be the head-to-head game. The argument for team A winning the tiebreaker is that they won that one match; however, in this scenario it is also necessarily true that A lost at least one game to a team that B beat.<ref>Statement (a): Both team A and B have an equal number of losses ''N''. It is known that one of the losses of team B is to team A. This means that A's losses are strict subset of B's losses as A cannot lose to themselves. Since A and B have an equal number of losses A has at least one loss to a team that B beat (not in B's losses).</ref>
 If each team's game against this common opponent was the one double-counted instead, then B would win the tiebreaker instead. Imagine another scheme where random games are double-counted until one team wins. Though straightforwardly terrible its symmetry actually gives both teams equal odds to win, which makes it clear that it is only the choice to select the head-to-head game that produces an effect in this tiebreaker.

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 The following are several instances in which unorthodox tiebreaking statistics were - it is not recommended that these be replicated:
 * The 2011 [[NGCSU]] mirror of [[MUT]] broke ties using "quality" (also called "difficulty rating"), which ultimately reversed first with second and 3rd with 4th place.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=213230#p213230 Re: MUT Mirror 4/2 @ NGCSU] by [[AlphaQuizBowler]] » Sat Apr 02, 2011 5:03 pm</ref> The metric purportedly originated from the FIRST robotics competition and was calculated as one plus the difference in score divided by total score with preference given to values closer to unity.
-:* Thus a score of 350-220 would yield "quality" of 1.28 and 0.72 while one of 100-95 would yield 1.03 and 0.97.
+:* Thus a score of 350-220 would yield "quality" of 1.28 and 0.72 while one of 100-95 would yield 1.03 and 0.97, with the latter winning the tiebreaker.
 :* The effect of this statistic was to award games to teams that won games by fewer points on average, which reversed the order expected using PPG or PPB. Despite being created to "promote a more cooperative spirit and improve sportsmanship," it also created a perverse incentive in which teams could directly benefit by ''not'' scoring points or even intentionally getting them wrong.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=213279#p213279 Re: MUT Mirror 4/2 @ NGCSU] by [[NGTech]] » Sat Apr 02, 2011 9:44 pm</ref>
 * The [[2019 ICT]] accidentally made use of an alphabetical tiebreaker to seed teams going into playoffs after the schedule was not updated properly after a field expansion sponsored by LetterOne.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=356839#p356839 Re: The ICT format is awful and unfair (or: why I now play for the "Ann Arbor Campus, University of Michigan")] by [[Important Bird Area]] » Wed Apr 10, 2019 9:26 pm</ref>

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 * The [[2019 ICT]] accidentally made use of an alphabetical tiebreaker to seed teams going into playoffs after the schedule was not updated properly after a field expansion sponsored by LetterOne.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=356839#p356839 Re: The ICT format is awful and unfair (or: why I now play for the "Ann Arbor Campus, University of Michigan")] by [[Important Bird Area]] » Wed Apr 10, 2019 9:26 pm</ref>
 :* The post's title expressed its author's affiliation as "Ann Arbor Campus, [[University of Michigan|Michigan]]" to take advantage of this rule. This fake name would still not have beaten [[Amherst]], which wielded its lexicographical supremacy at the tournament to receive a higher seed than [[Maryland]].
-* The [[2025 Prison Bowl]] Open mirror broke ties using the difference between the highest scorer and the team's average, with preference given to teams with a smaller gap.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=407379#p407379 Re: Prison Bowl Open @ Online (7/12/2025)] by [[Stinkweed Imp]] » Thu Jul 10, 2025 9:09 pm</ref> Team "Cheng Type" missed top bracket after losing this tiebreaker to two teams with lower PPG and fewer powers - had either PPG or PPB been used they would have been ahead of at least one team.
+* The [[2025 Prison Bowl]] Open online mirror broke ties using the difference between the highest scorer and the team's average, with preference given to teams with a smaller gap.<ref>[https://hsquizbowl.org/forums/viewtopic.php?p=407379#p407379 Re: Prison Bowl Open @ Online (7/12/2025)] by [[Stinkweed Imp]] » Thu Jul 10, 2025 9:09 pm</ref> Team "Cheng Type" missed top bracket after losing this tiebreaker to two teams with lower PPG and fewer powers - had either PPG or PPB been used they would have been ahead of at least one team.
 ==Tiebreaker questions==

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 It may also be necessary to do tiebreakers when rebracketing between stages of play like prelims, playoffs, or superplayoffs. For example splitting an 8x8 [[round robin]] into equally sized upper/lower playoff brackets requires selecting four teams from each bracket, meaning a tiebreaker is necessary if there is a tie for fourth. This is quite common: if all teams have an equal chance of winning there's a ~90% chance that there's a tie for fourth, with the majority of those being [[circle of death|circles of death]] in which three or more teams are tied. The slightly more realistic scenario where team i has an i/(i+j) chance to beat team j has a slightly lower chance of a tie for fourth of ~75%.<ref>Value calculated empirically with the following Python code:<div class="mw-collapsible mw-collapsed">
   import random
   from collections import Counter

@@ Line 24: / Line 24: @@
              winner = random.choice([i, j])
              # The following line is used to weight the strength of teams by their index
-             # winner = random.choice([i] * i + [j] * j)
+             # winner = i if random.random(i + j) < i else j
              wins[winner] += 1
      sorted_wins = sorted(wins, reverse=True)

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 It is possible for any game to end in a tie, either at the end of regulation gameplay or after [[protest]]s are resolved. These are always broken by entering [[overtime]] and reading additional questions, meaning that these are also the only kinds of tiebreakers with an explicit procedure outlined in the rules.
-ACF rule C6 states that a sudden-death tossup is played if the game ends in a tie, with additional ones being read if there is no change in score. Addendum CX also allows for the options of using an "NAQT-style" tiebreaker or letting the match end as a tie.
+ACF rule C6 states that a sudden-death tossup is played if the game ends in a tie, with additional ones being read if there is no change in score. Addendum CX also allows for the options of using an "NAQT-style" tiebreaker or letting the match end as a tie, though these are rarely used.
 NAQT rule F7 outlines a three-tossup overtime period that is played in its entirety, with the affordance for more sudden-death tossups if the score remains tied.