Discussion of using power matching at NSC

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Discussion of using power matching at NSC

Post by Deviant Insider » Thu Jun 04, 2009 8:47 am

Is it worth my time to describe the different ways that power matching could be done with this tournament and why it would be better?
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Re: PACE NSC: format changes, 2010 information

Post by Matt Weiner » Thu Jun 04, 2009 4:07 pm

Shcool wrote:Is it worth my time to describe the different ways that power matching could be done with this tournament and why it would be better?
Speaking only for myself: In the event that such things exist, of course it is, but keep in mind that PACE NSC wants to have actual playoffs, and thus needs to be able to predict how many teams will qualify. I'm not trying to go out of my way to bash NAQT here, but since you brought it up, I think taking 60 teams to the playoffs and deciding their national championship on something as archaic as double-elimination, when even local high school tournaments these days use playoff brackets, is awful. If your proposed solution ends up with "well, sometimes you will have 19 teams in the PACE playoffs and you'll just have to figure out what to do with them because power matching in the prelims is more important than playoffs that make sense at this national tournament" then it's not going to be "better" at all.

We were shown a way to do a basic swiss pair among stacks of 32 that lets us predict 24 teams into the playoffs, but it involves just 5 games worth of prelims before teams are eliminated from contention. I do not think most programs would be interested in rolling the dice that way at nationals.
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Re: PACE NSC: format changes, 2010 information

Post by Deviant Insider » Thu Jun 04, 2009 5:20 pm

You can use power matching to get the same results you are currently getting from divisions. I'll explain two ways of doing it.

Both of them are based on the fact that, starting with 64 teams, you can play 6 rounds and end up with 1 6-0 team, 6 5-1 teams, 15 4-2 teams, 20 3-3 teams, 15 2-4 teams, 6 1-5 teams, and 1 0-6 team. In this thread, Dwight and I explained how to set up 5 rounds for 32 teams. You can use the exact same method to get 6 rounds for 64 teams. I can map it out match by match if you want. Within those 6 rounds, there are no chances of repeat matches, and all teams are guaranteed to play teams with their own record (ignoring a potential play-in round, though repeats can be made effectively nonexistent even with a play-in round). There is a chance of an A Team playing its own B Team, but it could be set up so that would only happen if they had the same record after five matches, and it would be unlikely even then unless they were both 5-0 or 0-5.

One way of setting it up is to start with that power pairing as the first six rounds. You would then declare the 6-0 team and 5-1 teams have made the top divisions, put the three highest scoring 4-2 teams in the top divisions, and pair up the rest of the 4-2 teams for a match to qualify for the top divisions. All of the 3-3 teams would be paired up to play a match to see which ones made the second divisions and which ones made the third divisions. The twelve top 2-4 teams would be paired up to play for a chance to be in the third divisions. During the seventh round, the 10 top teams and 10 bottom teams could play matches that could be used to split the top teams from appearing in the same top division or the same bottom division. After round 7, you are ready for playoffs using the same system you already had planned.

Another way to set it up would be to have a play-in match. It would be easier, though not necessary, to have the play-in match not count towards your record but count towards your seed. It could be set up so that a play-in winner would be guaranteed a match against a play-in loser, so there would be some incentive to win the first match. You would then play six rounds of power pairing, and what I described as the 7th round above would be done during the 8th round. Because it is done to break ties, it would correspond to the way your current schedule handles the 8th round. This time, after round 8 you are ready for playoffs.

One disadvantage to this system is that there would be more occurrences of teams facing opponents in the playoffs that they already faced in the prelims. Because it uses fewer rounds than NAQT, you wouldn't run into as many repeats, but you would have a few. The advantage is that the elite teams would spend less time beating up on teams that are not a challenge for them. Additionally, the good teams could get away with losing two matches and still make the top divisions. (They could do that under the old system, but only if they got lucky. With this system, two losses guarantees you a spot in the top divisions.)

If a decent programmer worked on it, you could avoid repeat matches during the round 7/round 8 matches that determine which teams get the final spots in the top divisions. It's not the type of thing you want to figure out by hand at the last second, because it is actually quite messy, but somebody good with Excel could probably handle it with a good macro.
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Re: PACE NSC: format changes, 2010 information

Post by jonpin » Thu Jun 04, 2009 6:03 pm

Honestly, from my perspective, that long list of ideas just isn't worth a very marginal and debatable improvement in fairness and experience. For a large tournament like NAQT, using groups would require at least three stages (something like 24 groups of 8; 6 groups of 8; two groups of 6; final four) and be heavily dependent on pre-tournament seeding. Power matching gives everyone several rounds of a random schedule, followed by several rounds of a competitive schedule. However, since strength-of-schedule varies significantly, it does a poor job of selecting the very top teams for playoffs, so a generous cut is needed. At that point, no playoff format other than double-elimination could handle the large but variable number of playoff teams.

PACE doesn't have that problem. PACE is small enough that two group stages are sufficient to narrow the field down to the final set of teams. Thus a group stage can be used to narrow the field down. Group stages result in several rounds of a balanced schedule followed by several rounds of a competitive schedule. Since groups result in identical SOS within one, there is perfect comparison and never any reason to move more than 2/6 or 3/8 into the playoffs (2/8 is perfectly fine as well). Further, once that fraction of the field is taken to make the playoffs, the remaining teams are few enough that groups are again the optimal format.

Let's look at it this way. NAQT used 10 games of power-matching over 15 rounds. The net result was cutting the field from 192 to 71 (37%). PACE used 7 rounds of group-play to cut the field from 64 to 16 (25%). Furthermore, I don't think any teams that missed the PACE playoffs have a legitimate complaint that they deserved to make it but were screwed by a group of death (which is among the strongest arguments against group-play). The top team in the second level was Chattahoochee, who lost two straight games to Southside to be eliminated; Southside finished 8th in their playoff bracket. The only preliminary group to place two teams in the final top 8 was Stanley; the third-place team in that group went 2-5 in their second-level bracket.

For a huge tournament, power-matching is indeed the only practical preliminary format. For a tournament that is merely large, group-stage preliminaries are fairer. Group-stage playoffs are indisputably fairer than double-elim playoffs.

Also note that your cut to the top 16 requires giving teams automatic spots based on paper tiebreakers. PACE doesn't do that. It's my understanding that they do not allow a team to automatically move on from a tie (correct me if I'm wrong but a 3-way tie for 2 spots results in a 1-v-2 half-game followed by a 3-v-loser half-game, correct?).
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Re: PACE NSC: format changes, 2010 information

Post by dtaylor4 » Thu Jun 04, 2009 9:38 pm

jonpin wrote:Also note that your cut to the top 16 requires giving teams automatic spots based on paper tiebreakers. PACE doesn't do that. It's my understanding that they do not allow a team to automatically move on from a tie (correct me if I'm wrong but a 3-way tie for 2 spots results in a 1-v-2 half-game followed by a 3-v-loser half-game, correct?).
It depends. This year, if the teams were tied for an even-numbered seed, then it was 2v3, winner plays 1 with the winner of the second game taking the top seed.. If the three were tied for an odd placing, it would be 1v2 for the top placing, loser plays 3 for the next two. In either case, teams were seeded based on PPG.

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Re: PACE NSC: format changes, 2010 information

Post by jonpin » Thu Jun 04, 2009 9:48 pm

dtaylor4 wrote:
jonpin wrote:Also note that your cut to the top 16 requires giving teams automatic spots based on paper tiebreakers. PACE doesn't do that. It's my understanding that they do not allow a team to automatically move on from a tie (correct me if I'm wrong but a 3-way tie for 2 spots results in a 1-v-2 half-game followed by a 3-v-loser half-game, correct?).
It depends. This year, if the teams were tied for an even-numbered seed, then it was 2v3, winner plays 1 with the winner of the second game taking the top seed.. If the three were tied for an odd placing, it would be 1v2 for the top placing, loser plays 3 for the next two. In either case, teams were seeded based on PPG.
Right. The former case (tied for 2nd-4th) is 3 teams for 1 spot (3rd and 4th being on the same tier); the latter (1st-3rd) is 3 teams for 2 spots (1st and 2nd being the same tier). What is NOT done in the latter case is giving #1 the top spot and having 2 play 3 for the second spot, which would be analogous to Coach Reinstein's suggestion to give the top three 4-2 teams an automatic Super Sixteen position, while the other twelve have to play for it.
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Re: PACE NSC: format changes, 2010 information

Post by Deviant Insider » Thu Jun 04, 2009 10:06 pm

If that's the biggest objection, then my proposals can be adjusted so that half-games are used. You have 15 teams and nine spots, so the top six can play half games with the winners getting three of the spots, and the three losers can then go in a pool with the nine other teams, who would play half-games to determine who gets the other six spots. You could do something similar with 2-4 teams so that you fill six spots with 15 teams.
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Re: PACE NSC: format changes, 2010 information

Post by Sir Thopas » Thu Jun 04, 2009 10:24 pm

Shcool wrote:If that's the biggest objection, then my proposals can be adjusted so that half-games are used. You have 15 teams and nine spots, so the top six can play half games with the winners getting three of the spots, and the three losers can then go in a pool with the nine other teams, who would play half-games to determine who gets the other six spots. You could do something similar with 2-4 teams so that you fill six spots with 15 teams.
My biggest objection, at least, is that it seems pointless to do all this. One thing round robins are good for is creating ridiculously balanced schedules. Power-matching schedules, at least as far as I have experienced them, are always going to be uneven. It is certainly a goal to (1) have teams play very balanced schedules, and (2) have things run as smoothly as possible. Round robins satisfy both of these goals much better; the advantaged of power matching is made redundant by the multiple and comprehensive playoff matches against similarly skilled opponents. At worst, power matching creates discrepancies among schedules and severely entangles which games should count in the playoff brackets; at best, it is rather useless.
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Re: Discussion of using power matching at NSC

Post by Matt Weiner » Thu Jun 04, 2009 10:39 pm

I agree with Guy. One reason that HSNCT has no choice but to take 71 teams to the playoffs is that power matching is actually a very rough way to sort a field; you have to let in all the 6-4 teams because with rematches, the order of games being so crucial, and the need to have a few matches between teams of equal skill (which are a demand everyone has for the purpose of power matching, but actually screw it up since you're handing someone a loss that doesn't generate any meaning for the ranking), you run a real risk of excluding a top-spot contender if you cut it off anywhere else. A carefully seeded tournament where you play a representative sample of the field in the prelims followed by seven teams at your own level in the playoffs is actually superior in a lot of ways.

Power matching may impress as a logistical feat due to the mathematical elegance that its planning requires (I, for one, am always impressed that--despite the combination of 192 teams, a system no one on the outside fully understands, and the fact that one misplaced piece of paper can blow the whole thing up--the HSNCT works so smoothly each year) but as an ideal way to achieve fairness in a quizbowl tournament when you have a small enough number of teams to explore other options, it falls short.
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Re: Discussion of using power matching at NSC

Post by Sen. Estes Kefauver (D-TN) » Thu Jun 04, 2009 10:41 pm

Exactly. There does not seem to be an actual benefit to using power matching given the size of the NSC compared to the current situation. I think that having teams play approximately half of their games in a pool that gives a nice sampling of all teams so that we can see where they fall in reference to the rest of the field generally, and then spend the other half of their games playing teams that were at about their skill level combines the best of both worlds. It allows you to both get a good idea of how your team plays against teams of all skill levels (and it also guarantees non-contending teams a chance to play a couple of really good teams, which can be a big draw if you want to improve, and is something NAQT's system does not guarantee for all teams) and then it allows you the chance to play a bunch of teams that are at your skill level and get a much more accurate ranking of where you fall in the field. I see nothing negative about these traits, and I see nothing that is "fixed" by replacing this with a swiss-pairing system. If you can present a reason why power matching is indeed fairer, I would love to see it, but given the presentation so far, it seems to be more like "power matching is automatically superior" with no actual arguments to confirm that.
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Re: PACE NSC: format changes, 2010 information

Post by jonpin » Thu Jun 04, 2009 10:46 pm

Shcool wrote:If that's the biggest objection...
But it wasn't. It was the least and last. The biggest was that it's an unnecessary fix to a problem that doesn't exist. With group play, everyone gets 7 games against a balanced schedule, is compared within a set of teams where there is no difference in schedule, and cleanly advances a relatively small fraction of teams. With power-matching, everyone plays 6 games (plus some weird non-counting "play-in" game?) and maybe a half-game or two, is compared within the set of all teams with significant difference in strength of schedule (if I have time tomorrow, I will attempt to document some HSNCT situations of Team X with a higher PPT against a harder schedule than Team Y, but Team Y has a better record), and generally is more effort and work.
One more thing to note is that it also prevents the head TD from saying "This is a difficult protest to resolve, we're going to have someone spend 10 minutes looking stuff up and get back to the teams after their next round." Admittedly, I don't know if that ever happens.

...Yeah, what Guy, Matt and Charlie said.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Fri Jun 05, 2009 8:17 am

The big problem with divisions, especially when you have good academic questions, is that a lot of matches are played that are a waste of time. They are good in the sense of hearing good questions, but they are not good in the sense that both teams know in advance who is going to win, and then one team proceeds to pummel the other one.

When I saw our division for PACE, I emailed our team telling them that it was going to come down to two matches. That's exactly what happened. Those two matches didn't start until 3:00, so we spent the first six hours at a national tournament playing matches that, from a competitive aspect, were not exciting. That's an overstatement, since duPont Manual is a good young team, and TJ C played respectably against us, especially considering that they are a C Team, but it's about what happened. Our first seven matches at PACE were against duPont Manual, Southside B, Wilmington Charter C, Rocky Mount, TJ C, Georgetown A, and Chaska. (I don't mean to call out anybody, and it is a testament to these programs that they qualify multiple teams and have those teams do repectably.) Our first seven matches at NAQT were against North White, Torrey Pines, Ames, EO Smith, Mission San Jose, Half Hollow Hills West, and East Brunswick. The NAQT matches were more exciting because they were closer. Our one exciting match of the first seven at PACE was against Chaska.

Look at how State College A spent their first seven matches at PACE: Hunter B, Cosby, Lewis County, Gonzaga, Bellaire B, Walton, and Northmont. That's not a list of bad teams--two of them are better than New Trier--but none of them could come within 400 points of SC. Compare that to NAQT, where SC started with Muscatine, Bellarmine, Cave Spring, Bergen, Dorman, TJ, and Half Hollow Hills West. If I was State College, I would rather play the second list than the first list, especially if the tournament was set up so that I was going to make the playoffs anyways.

The 7th round of PACE featured Georgetown A vs Wilmington Charter C, Wilmington Charter A vs Saint Viator, and Hunter A vs Blake. Again, I don't mean to diminish the losing sides in those matches, who are well above average teams, but they were being sent to the slaughter after already having been eliminated from the top divisions. They could have been playing competitive matches during that round if power matching was used.

The posters above make good points. Namely, power matching is less necessary at PACE than other tournaments because the staff does its research well and it comes at the end of the year, so you end up with pretty even divisions. Also, because it is over two days, the top teams play each other eventually anyways. However, if you want more high quality matches, then you should use power matching.
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Re: Discussion of using power matching at NSC

Post by at your pleasure » Fri Jun 05, 2009 8:39 am

but they are not good in the sense that both teams know in advance who is going to win, and then one team proceeds to pummel the other one.
But what Dees has said, and I will say, is that that can also be counted as an advantage since a middling or even a very good non-playoff or non-championship contender-may still want a chance to play at least one of the top few teams. You submit that there is no excitement in non-close games; but I submit that it can be exciting as well to see one of the best teams in the country play well. Rembember, all the rebracketed games on Sunday should be against teams in your own class, and hence more exciting.
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Re: PACE NSC: format changes, 2010 information

Post by Deviant Insider » Fri Jun 05, 2009 10:30 am

jonpin wrote:
Shcool wrote:If that's the biggest objection...
But it wasn't. It was the least and last. The biggest was that it's an unnecessary fix to a problem that doesn't exist. With group play, everyone gets 7 games against a balanced schedule, is compared within a set of teams where there is no difference in schedule, and cleanly advances a relatively small fraction of teams. With power-matching, everyone plays 6 games (plus some weird non-counting "play-in" game?) and maybe a half-game or two, is compared within the set of all teams with significant difference in strength of schedule (if I have time tomorrow, I will attempt to document some HSNCT situations of Team X with a higher PPT against a harder schedule than Team Y, but Team Y has a better record), and generally is more effort and work.
One more thing to note is that it also prevents the head TD from saying "This is a difficult protest to resolve, we're going to have someone spend 10 minutes looking stuff up and get back to the teams after their next round." Admittedly, I don't know if that ever happens.

...Yeah, what Guy, Matt and Charlie said.
Keep in mind that NAQT did its power matching incorrectly. Teams that won their last match should, as much as possible, play teams that lost their last match, which is not what happened. This problem extended from rounds three on, which meant that their schedule resembled some of the proposed schedules that Dwight and I explained how to fix in our posts in the thread I linked above. Because NAQT did their pairing incorrectly, it is not a surprise at all that the weakest 7-3 teams were clearly worse than the strongest 6-4 teams.

Also, the matches I describe above as half matches could be played as full matches, and they could all be completed in the same number of rounds as PACE's current schedule to play divisions and break ties. The play-ins are part of a second, and unnecessary, proposal.
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Re: PACE NSC: format changes, 2010 information

Post by Down and out in Quintana Roo » Fri Jun 05, 2009 11:59 am

Shcool wrote:Keep in mind that NAQT did its power matching incorrectly. Teams that won their last match should, as much as possible, play teams that lost their last match, which is not what happened. This problem extended from rounds three on, which meant that their schedule resembled some of the proposed schedules that Dwight and I explained how to fix in our posts in the thread I linked above. Because NAQT did their pairing incorrectly, it is not a surprise at all that the weakest 7-3 teams were clearly worse than the strongest 6-4 teams.
This is true. I'm still proud of our 5-5 record, but after we tanked and lost five games in a row after winning the first one, we knew we were going to face subpar teams, one or two of which absolutely should not have been there. And then, in our last two games, we were 3-5 but faced a 2-6 team, and 4-5 but faced a 3-6 team.

Personally, while bracketing does seem to have an inherent flaw of predetermining which teams are already going to win, that's precisely the reason why it works, as nothing else (if done fairly) can accurately and wholly prove which of the best teams should be in the playoffs. At PACE, we knew it would be a stretch to win more than two games in the prelims, and we didn't, but we were okay with it.
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Re: PACE NSC: format changes, 2010 information

Post by AlphaQuizBowler » Fri Jun 05, 2009 12:07 pm

Caesar Rodney HS wrote: Personally, while bracketing does seem to have an inherent flaw of predetermining which teams are already going to win...
Could you explain this?
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Re: Discussion of using power matching at NSC

Post by Golran » Fri Jun 05, 2009 12:50 pm

I think what it means is that a team can go through their schedule before their first match and take a good guess at which games they will win, and likely determine their record before even playing.
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Re: PACE NSC: format changes, 2010 information

Post by Deviant Insider » Fri Jun 05, 2009 12:58 pm

AlphaQuizBowler wrote:
Caesar Rodney HS wrote: Personally, while bracketing does seem to have an inherent flaw of predetermining which teams are already going to win...
Could you explain this?
Look at the PACE NSC Lulu Division: Dorman A, TJ A, Carbondale, Dunbar B, Wilmington Charter B, Seton Hall, Winfield, and GDS B. If you were placed in that division and wanted to make the top playoff divisions, then you looked at the schedule and knew you had to beat either Dorman or TJ. Carbondale had a small chance of doing this, and the other schools, realistically, did not.

If they had used power matching, then the only way of getting eliminated would be to lose three times, and your third loss would have to come against a team that had already lost twice. This format would have given all of these teams a better chance of making the top bracket, and it is possible that three of them would have made it.

Looking at the overall results, this does not appear to be an injustice. Carbondale and Dunbar B took some lumps at the second playoff level, so it is difficult to build a case that they was robbed. However, the playoff teams are more predetermined in divisional play, since it decreases the number of combinations of teams that can end up in the top bracket. With power matching, there would be the possibility of Dorman, TJ, and Carbondale all making the top playoff level no matter how they were originally seeded. With divisions, it was set up so that only two of the three could make it no matter how well those teams played as a group for the first seven rounds.
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Re: Discussion of using power matching at NSC

Post by cvdwightw » Fri Jun 05, 2009 1:17 pm

If teams are seeded well, then power matching is an inferior alternative. Power matching is great for determining where teams are in the case where you don't have a lot of information about a lot of the teams. So, for instance, I doubt NAQT really wants to seed 192 teams for HSNCT, especially because a lot of them are wild card bids and/or based on tournament performances in small, isolated areas.

PACE, on the other hand, does have a really good idea of where their teams are. Generally, teams that should make the playoffs, make the playoffs, unless there's a slightly-lower-seeded team that happens to play better that day. Similarly, with the exception of the annual BRACKET OF DEATH, NAQT ICT does a pretty good job of separating teams based on ability levels through the bracket-rebracket format.

With power matching, you are guaranteed to play games against teams with relatively similar records the whole day. In no way does this guarantee that you're going to play a team that's of the same ability - no offense to Edison (CA), but they were nowhere in the same league as TJ A this year, and yet 5-3 Edison (losses to: MLK, Brookwood, Charter B) ended up playing 5-3 TJ A (losses to: Charter A, State College A, Chaska) in Round 14 of HSNCT.

With bracketed play, you are guaranteed to play only a couple of early games against teams of similar ability (maybe more if you're a middle seed), but then you are guaranteed at least 7 games against teams that are more-or-less right where you are, all at the end of the tournament. You're trading off the expectancy of playing 70% of your games against similar teams for the certainty of playing at least ~60% of your games against similar teams. For lots of teams, that certainty - and the certainty of playing really, really good teams - is as good or better than the "I hope the next team in our room is of a similar ability."
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Re: Discussion of using power matching at NSC

Post by AlphaQuizBowler » Fri Jun 05, 2009 1:31 pm

dinoian wrote:I think what it means is that a team can go through their schedule before their first match and take a good guess at which games they will win, and likely determine their record before even playing.
I guess I disagree with that mindset, then. There are such things as upsets that don't result from poor questions. Sometimes a worse team beats a better team by playing better, having less negs, or just getting a good round. Quizbowl is a competition, which means that the best team doesn't always win if they don't play their best.
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Re: Discussion of using power matching at NSC

Post by DumbJaques » Fri Jun 05, 2009 2:33 pm

It seemed to me that HSNCT this year featured a bunch of instances in which a team slid into a top 20 finish (or just on the first day, a very high placement) by playing 1-2 good opponents all tournament. This seems like a way worse shortcoming than, say, having some games that are meaningless. If a perfect power matching system could be developed that worked with the bracketed playoff format, well, that would probably be ideal, but I don't really think that's happening any time soon.
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Re: Discussion of using power matching at NSC

Post by First Chairman » Fri Jun 05, 2009 2:50 pm

I did want to point out that aside from the practical issues of having divisions instead of power matching through the tournament, back in the day when we started PACE, the other national competitions that existed had very nebulous procedures in determining schedules. ASCN had power-matched schedules until a team won 3 games (automatic into playoffs) or lost three games (automatic out) before going to a single-elimination playoff; the matches were probably not power-matched so much as they were just "random draw of a team with a similar record." Panasonic had its weird algorithms. Just Asking! had a completely random draw which was open, and Chip had... his process.

What we knew was that it was punitive for a great team which had an outstanding record to be placed in such scenarios. Random draw means one must accept as a potential outcome a matchup of #1 vs #2 in the nation in the first round, something I don't think I wanted at all. Having carefully drafted divisions based on geography and performance (as we knew it) was our way to reward teams for a great year's work and use an actual year's worth of performances to determine preliminary round play. Yes, you have some deadwood in each bracket, but each of the top teams would not have to worry about being eliminated too early unless they really laid eggs throughout the Saturday rounds. Then their performance would dictate how Sunday's playoff-round-robin rounds would go. I think that was a reasonable theoretical rationale for how we set up the two-day tournament that did not kick out a great team for having the schedule of death (which is often publicized by Chip at that time).

I also admit, blow-outs are part of the game, but a good team knows that questions from tournament to tournament can differ in writing style, moderating, and difficulty. As much as a team may be able to predict how well they do in their prelim division, data drives how matchups will occur on Sunday, which is where the run for the championship really begins.

I don't mind with having a smaller field and playing in divisional format because I think logistically it's easier to handle. It's also nicer for the roving reporters to plan their liveblogs.
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Re: PACE NSC: format changes, 2010 information

Post by Mechanical Beasts » Fri Jun 05, 2009 3:00 pm

Shcool wrote:Look at the PACE NSC Lulu Division: Dorman A, TJ A, Carbondale, Dunbar B, Wilmington Charter B, Seton Hall, Winfield, and GDS B. If you were placed in that division and wanted to make the top playoff divisions, then you looked at the schedule and knew you had to beat either Dorman or TJ. Carbondale had a small chance of doing this, and the other schools, realistically, did not.

If they had used power matching, then the only way of getting eliminated would be to lose three times, and your third loss would have to come against a team that had already lost twice. This format would have given all of these teams a better chance of making the top bracket, and it is possible that three of them would have made it.

Looking at the overall results, this does not appear to be an injustice. Carbondale and Dunbar B took some lumps at the second playoff level, so it is difficult to build a case that they was robbed. However, the playoff teams are more predetermined in divisional play, since it decreases the number of combinations of teams that can end up in the top bracket. With power matching, there would be the possibility of Dorman, TJ, and Carbondale all making the top playoff level no matter how they were originally seeded. With divisions, it was set up so that only two of the three could make it no matter how well those teams played as a group for the first seven rounds.
So it's entirely true that power-matched games don't suffer from the existence of brackets, because there are none. That's pretty obvious. So yes, that way any combination of teams may make the playoffs (sixty-four choose sixteen), instead of eight times (eight choose two). But if you bracket well, this is minimally a problem: you are limited to situations where Carbondale is the fifteenth-best team by some metric but was in a bracket with the first and ninth and missed the playoffs, while the sixteenth-best team upset the ninth and lost to the seventh... or something.

But unless I totally miss my guess, in power-matching you're determining matchups merely by the outcome of one (and then two, and then three, but a fluke result at the one-stage carries over because the two-stage's game was determined by that outcome) game. In bracketing you determine matchups by looking at a season's worth of data. Doesn't the latter have more potential for screwups?
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Re: Discussion of using power matching at NSC

Post by Down and out in Quintana Roo » Fri Jun 05, 2009 3:10 pm

dinoian wrote:I think what it means is that a team can go through their schedule before their first match and take a good guess at which games they will win, and likely determine their record before even playing.
It's a moot point now (see what happens when i have to go back to teaching for the rest of the afternoon? darn), but yes, that is what i meant.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Fri Jun 05, 2009 3:16 pm

If power matching is done well, it uses both a season's worth of data and results from previous matches. That's why there is a lower potential for screwups and is more likely to select the best teams. (Edit: The season's worth of data is used to seed teams, and all rounds are set up using that seeding. Teams flip seeds whenever there is an upset.)

NAQT did not do that, because they only use data from matches on NAQT questions to seed teams and do not set up the pairings in an optimal manner. There is no need for PACE (or even NAQT) to repeat those mistakes. In the other thread, Dwight mapped out how it can be done correctly for 32 teams in five rounds, and his methods can easily be extended for 64 teams in six rounds.

I am not advocating random placement into the first round, random pairings of second round winners, or anything random at all. PACE has done a good job in the past using results to seed teams, and they will need to continue doing this if they want to do divisions or power matching well.
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Re: Discussion of using power matching at NSC

Post by Kouign Amann » Fri Jun 05, 2009 3:21 pm

AlphaQuizBowler wrote:
dinoian wrote:I think what it means is that a team can go through their schedule before their first match and take a good guess at which games they will win, and likely determine their record before even playing.
I guess I disagree with that mindset, then. There are such things as upsets that don't result from poor questions. Sometimes a worse team beats a better team by playing better, having less negs, or just getting a good round. Quizbowl is a competition, which means that the best team doesn't always win if they don't play their best.
In particular, a worse team can beat a better one if they manage to get a round that happens to play to their strengths. A good example of this was at the MATT, when noted middle-of-the-road/getting better St. Anselm's was up 80ish at the half over nationally competitive GDS. GDS is obviously a much better team (evidenced by them getting tossups 11-20 to blow us out of the water in the second half), but we hung with them by virtue of hearing questions that happened to be right up our alley. It is not inconceivable that such a lucky streak might extend a whole game. Thus, it is possible that a seemingly "for sure" game in a schedule, with one team clearly better than the other, though perhaps not by such a big gap as the example, could be an upset. One cannot simply say, "OK, we're going to win games against blah, blah, blah, and blah, and then lose to blah and blah." You have to actually play the games. That's why we hold national championships instead of just voting for the best team.
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Re: Discussion of using power matching at NSC

Post by cvdwightw » Fri Jun 05, 2009 4:30 pm

Reinstein: I love power-matching. I think it's the best way to even out schedules in the case that you have absolutely no idea which teams are good or not. But the fact remains that this system has been tried before, except that there were four Swiss-pair rounds after the initial six instead of play-in games.

In 2003 the NAQT HSNCT used this exact format, with power matching done very similarly to the way it's been outlined (for instance, in round 3, the LW and WL teams from different brackets played each other, but then it would be impossible to tell, when adding the next bracket for Round 4, how many LWW or WLW teams you had; you know you'll have 2 WWL teams and 2 LLW teams, but it could be that in one bracket the other 2-1 team is WLW and in the other the other 2-1 team is LWW). I've gone through each of the 64 teams (with playoff finish at the end) and looked at how Reinstein's proposition would have revamped the 2003 HSNCT:

Maggie Walker A: 6-0 (WWWWWW) - 5th
TJ A: 5-1 (WWWWWL) - 1st
Walton: 5-1 (WWWWLW) - 4th
Dunbar: 5-1 (LWWWWW) - T-6th
State College A: 5-1 (WWWLWW) - t-6th
Russelville: 5-1 (LWWWWW) t-19th
Booker T. Washington: 5-1 (WWLWWW) t-19th
DCC: 4-2 (WWLWLW) t-13th
Capistrano Valley A: 4-2 (LWWWLW) t-8th
Dorman A: 4-2 (WWWWLL) - 2nd
Central Macon: 4-2 (WWWLWL) - t-8th
Eleanor Roosevelt: 4-2 (WLWWLW) - t-8th
St. John's: 4-2 (WWLWWL) - 3rd
TJ B: 4-2 (WWWLLW) - t-19th
Solon: 4-2 (WWLWWL) - t-13th
St. Andrew's A: 4-2 (WLLWWW) - t-13th
Plano East: 4-2 (WWLLWW) - t-13th
Cookeville: 4-2 (WLWLWW)
State College B: 4-2 (WLWLWW)
Blake: 4-2 (WLLWWW)
Bentley: 4-2 (WLWWWL)
St. Benedict at Auburndale: 4-2 (WLWLWW)
Fort Mill: 3-3 (WLWWLL) - t-19th
Wilmington Charter: 3-3 (LLWWLW) t-8th
Cutter Morning Star: 3-3 (WWLLWL) - t-13th
Caddo Magnet: 3-3 (WWWLLL) t-13th
Chattahoochee: 3-3 (WLWLWL) - t-19th
Dorman B: 3-3 (WLWWLL) t-8th
James Island: 3-3 (WLWLWL)
Westmont Hilltop: 3-3 (LWWLWL)
Maggie Walker B: 3-3 (WWLWLL)
Johnson Central A: 3-3 (LWLWLW)
Ithaca B: 3-3 (LWLWLW)
Catonsville: 3-3 (LWWLLW)
Westiminster: 3-3 (LLWWLW)
Weddington: 3-3 (LLLWWW)
Ithaca A: 3-3 (WLLLWW)
Columbia: 3-3 (LWWLWL)
Conserve A: 3-3 (WLLWWL)
Maggie Walker C: 3-3 (LWLLWW)
St. Andrew's B: 3-3 (LLWLWW)
Kent City: 3-3 (LWWLLW)
Petoskey: 2-4 (LWLWLL) - t-19th
Bob Jones: 2-4 (WLLWLL)
James Madison: 2-4 (LLLWWL)
Conserve B: 2-4 (LLWLWL)
Isidore Newman: 2-4 (WWLLLL)
Fisher Catholic: 2-4 (LWLLWL)
Caesar Rodney: 2-4 (LWLWLL)
Garfield Heights: 2-4 (LWLLLW)
Kelso: 2-4 (LWLLWL)
Sanford: 2-4 (LLWWLL)
Mauldin: 2-4 (LLWLLW)
Capistrano Valley B: 2-4 (WLLLLW)
Regis: 2-4 (LLLLWW)
Cape Coral: 2-4 (LLLWLW)
Johnson Central B: 2-4 (LLWWLL)
Defiance A: 1-5 (LWLLLL)
Estherville-Lincoln Central: 1-5 (WLLLLL)
Defiance B: 1-5 (LLLWLL)
Claremore: 1-5 (LLWLLL)
Lamoni: 1-5 (LLLLWL)
2 teams forfeited all five games by not showing up

The Reinstein system excludes 7 of the 24 teams that ultimately made the playoffs (not that bad, since the Reinstein system takes 16 instead of 24), including two of the T-8th teams (bad), plus possibly making 2nd-place Dorman A and/or 3rd-place St. John's win a tiebreaker game just to get in (really bad). Furthermore, there is absolutely no control over who played good teams - and in fact, appears to somewhat penalize teams for playing good teams (because they can't rack up the huge points against bad teams) if PPG is used as the tiebreaker. Could we really say, after Round 6, that Capistrano Valley A (played 2 ultimately playoff teams) and St. Benedict at Auburndale (played 2 ultimately playoff teams) were somehow better than Central Macon (played 5 ultimately playoff teams), Wilmington Charter (played 4 ultimately playoff teams), or Fort Mill (losses to Walton, Dunbar, and DCC)?

I think what this shows, is that we can't say which teams should be playoff teams based solely on 6 rounds. There are some teams that got a bit of bad luck in their first six games, that recovered nicely, and some teams that got gift schedules in the first six games and then faltered against tougher competition.

On the other hand, when we make brackets, we can say that exactly two of these teams will make it out of the bracket. And because the teams are playing the exact same teams (other than each other), we know that no team is going to make the playoffs based on a gift schedule or get screwed out based on a wacky schedule. If the brackets are well-formed, then the teams that should be in the playoffs will mostly make the playoffs.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Fri Jun 05, 2009 4:59 pm

Where are these results posted? I am interested in seeing how the pairing was done both for the first six games and after that.
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Re: Discussion of using power matching at NSC

Post by Tower Monarch » Fri Jun 05, 2009 5:00 pm

Shcool wrote:Where are these results posted? I am interested in seeing how the pairing was done both for the first six games and after that.
http://naqt.com/hsnct/2003/results/stats.html
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Re: Discussion of using power matching at NSC

Post by cvdwightw » Fri Jun 05, 2009 5:41 pm

The first six games were paired using equal-records, and though I'm not sure that they were done 100% correctly, they were pretty close (e.g. as a LWWW team I played a WWWL team).

The last four rounds were done using a Swiss pair algorithm that NAQT screwed up for Round 7, leading to the St. Andrew's coach making a scene and nearly demanding that the Round 7 games be replayed because of the screwup. From what I remember, the top team played the top team it had not yet played, then the rest of the one loss teams were grouped, with any leftover playing the top 2-loss team, then the rest of the two loss teams were grouped, with any leftover playing the top 3-loss team; etc. This got hairy once 7-0 Maggie Walker ran out of one-loss teams it hadn't already beaten.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Fri Jun 05, 2009 7:29 pm

It's difficult to draw too many conclusions from 2003 because of differences in the game. There were more upsets then, because the good teams were not as good and the question quality was not as good. Additionally, it was very difficult to seed teams at a national tournament because you couldn't look up a bunch of SQBS results online from tournaments using good questions. It's hard to say that a team that finished well in the playoffs deserved to finish well in the playoffs, though it may be the best info we have to go by.

Let me try to make an apples to apples comparison, for what it is worth. I can't tell exactly how teams were seeded for the 2003 NAQT, but I can figure out how teams would have been placed into divisions for the PACE system. If you use the PACE system and don't adjust for geography, the 1, 16, 17, 32, 33, 48, 49, and 64 teams should all end up in the same division. If you use my system and don't adjust, then those same teams should play all of their matches against each other for the first three rounds. Similarly, the 2, 15, 18, 31, 34, 47, 50, and 63 seeds should all be placed together, for the first seven rounds of the PACE system and the first three rounds of my system.

Here is how the divisions break down as they were seeded by NAQT in 2003:
Division 1: MW A, Mauldin, St Benedict, Fisher, Plano East, Lamoni, Chattahoochee, Kelso
After six matches of my system, MW A would have been in, and St. Benedict and Plano East would have been on the bubble.
This division had one team (MW A) that was in the top 16 and one team that might have been (Plano East), so my system covered it well, and the PACE system probably would have.

Division 2: State College, Weddington, Blake, Russellville, Booker T, Wilmington Charter, St. Andrew's, Dunbar
After six matches of my system, State College, Booker T, Dunbar, and Russellville would have been in, and Blake and St. Andrew's would have been on the bubble.
This division had three teams (SC, Dunbar, and WC) in the top 16 and one team (Andrew) that might have been. In addition, Russellville and BTW were part of a six way tie for 19th. I think my system beats what the PACE system would have gotten here, since letting only two of these teams in the top 16 would have been very bad. It's hard to believe that WC would have made the playoffs in the PACE system, since they lost to BTW and Dunbar, and their only win against this group of teams was against Weddington, who is probably the weakest of the bunch.

Division 3: Walton, Defiance B, Fort Mill, Ithaca B, Cutter Morning Star, Johnson Central A, Dorman B, Sanford
After six matches of my system, Walton would have been in, and the rest of the teams would have been gone.
This division had two teams (Walton and Dorman B) in the top 16 and one team (Cutter Morning Star) that could have been. Dorman B lost head-to-head in its preliminary match against CMS, so the PACE system likely would have put in Walton and CMS.

Division 4: TJ B, Garfield Heights, Capistrano B, NW Penn Collegiate, Isidore Newman, Kent City, Eleanor Roosevelt, Conserve B
After six matches of my system, TJ B and Eleanor Roosevelt would have been on the bubble, and the rest of the teams would have been gone.
Eleanor Roosevelt was the only top 16 team in this division. The PACE system probably would have put in TJ B and/or Isidore Newman despite the fact that those teams are not so great.

Division 5: TJ A, Caesar Rodney, Conserve A, Cape Coral, DCC, Johnson B, State College B, Capistrano A
After six matches of my system, TJ A would have been in, and DCC, State College B, and Capistrano A would have been on the bubble.
This division had two teams (TJ and Capistrano) in the top 16 and one team (DCC) that might have been. It's possible that the PACE system would have gotten this right, though given Capistrano's loss to SC B, it's hard to tell.

Division 6: Caddo, Columbia, James Island, Claremore, MW B, Defiance A, Estherville, Montgomery Blair
After six matches of my system, none of these teams would have still been alive.
Caddo is the only team that MIGHT have been in the top 16. The PACE system would have pushed Caddo and probably MW B into the top 16 despite the fact that they weren't that good.

Division 7: Dorman A, St. Andrew's B, Bob Jones, MW C, Solon, James Madison, Bentley, Westmont Hilltop
After six matches of my system, none of these teams would have been in, and Dorman, Bentley, and Solon would have been on the bubble.
This division had one team (Dorman) in the top 16 and one team (Solon) that might have been. The PACE system might have worked, but it would have put Solon in the top division without testing them as much as they deserved.

Division 8: Central Macon, Petoskey, Ithaca, Westminster, St. John's, Catonsville, Cookesville, Regis
After six matches of my system, none of these teams would have been in, and Central Macon, Cookeville, and St. John's would have been on the bubble.
This division had two teams (St. John's and Central Macon) in the top 16, and it's probable that the PACE system would have handled it well.
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Re: Discussion of using power matching at NSC

Post by Mechanical Beasts » Fri Jun 05, 2009 8:08 pm

So the way I read this, if you set up questionable brackets, the PACE system, which relies entirely on those brackets, is not as good as powermatching. (I suppose that your assumption is that these brackets are questionable because most of your criticisms are "look at these six playoff teams that my system finds in this one bracket" or whatever; the PACE system does not take them all!") But isn't what Dwight said (I love powermatching when you are short information) essentially just that?

Maybe I'm being dense, but I think you ought to be illustrating how, assuming reasonably good bracketing (i.e. there's a bracket with the 1, 9, 10, etc., and that's pretty close to the 1, 9, 10, etc. team of the field), powermatched results are actually superior: like, I could imagine it's better to decide between the 9 and 10 teams based on giving them games against 7 and 8 and 11 and 12, as well as each other. But does powermatching consistently enough give you that advantage without introducing separate disadvantages? I don't think we have enough evidence yes or no yet.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Fri Jun 05, 2009 10:55 pm

Let me take it from the point of view of bubble teams. Let me follow the #16 and #17 teams through both scenarios.

If you are 16 or 17 in the PACE scenario, you will play the 1, 32, 33, 48, 49, and 64 seeds and each other in some order, probably playing each other last. You are only allowed one loss, unless you get lucky because a team you lose to goes and loses to a team that you beat, and you are likely to lose to the top seeded team, so it probably comes down to the head-to-head match. Unless the 32 or 33 seed is better than advertised, one of 16 and 17 is going on and one is not. If the seeding is a little bit off so that those two teams actually should have been in the top 15, then only one of them is going anyways. If the seeding is a little bit off so that neither of those two teams actually should have been in the top 20, then probably one of them is going anyways. For their first six matches, these teams probably go an uneventful 5-1, and then they play each other in what should be a good match.

In the power matching scenario, 16 and 17 play their first matches against 49 and 48, respectively. If they both win, then they play each other. The team that wins that match plays 1 next but can afford to lose that match and one more. The team that loses that match probably plays 32 or 33 next and, while they can afford to lose, goes into a deep hole if they do so. Their fourth opponents, if things go as expected, are the 24 and 25 seeds. You're now getting to the point where matches are unpredictable and, if the seedings were off a little bit, the team that is seeded in the mid teens but belongs in the mid twenties is going to take some hits. If the 16 and 17 seeds win as expected, then they are each 3-1, which means they still have breathing room. If they lose, then one or both of them are 2-2, which means that they are still alive but barely.

If they are 3-1, then whichever one of them lost the head-to-head match in the second round will play the loser of a match that should have featured 4 vs 5. The team that won the second round match will most likely play the 12 seed if it gets to 3-1. If they are 2-2, then they should play a team that was initially seeded in the 40s and is also 2-2.

It is difficult to predict what would happen to them in the sixth match. If they are 4-1, then they will play a team effectively seeded somewhere from 3-12, with the winner going right to the top bracket and the loser having to play tiebreakers. If they are 3-2, then they will play a team effectively seeded somewhere from 13-32, with the winner earning the right to play tiebreakers. If they are 2-3, then they are already eliminated from contention for the top brackets, which they deserved by dropping two matches to teams seeded lower than themselves. The tiebreakers would involve playing teams seeded 8-22, with the top six scoring teams having two chances to win one game and the bottom nine having one chance to win one game.

As you can see, with power matching, each bubble team plays several other bubble teams rather than one other bubble team, which is how you legitimately figure out which bubble teams are better than the others.
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Re: Discussion of using power matching at NSC

Post by First Chairman » Sat Jun 06, 2009 8:50 am

Of course, it should also be noted that qualification process into playoffs for PACE involves actually playing minimatches between teams with a tie in record. We do not take head-to-head into account, but we will seed matchups based on PPG to that point and arrange matches in a manner that reflects the number of seats in the championship bracket under contention. Thus if there are bubble teams with the same record, they will play each other off on stretch round-style questions (I think this year we had increased the minimatches from 5/5 to 10/10, but Matt can correct me).
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Re: Discussion of using power matching at NSC

Post by Important Bird Area » Sat Jun 06, 2009 3:07 pm

Shcool wrote:NAQT did not do that, because they only use data from matches on NAQT questions to seed teams and do not set up the pairings in an optimal manner. There is no need for PACE (or even NAQT) to repeat those mistakes.
This is not true. The initial seeding of teams for Saturday play at HSNCT takes into account the team's entire record; this year we consulted both Byko's rankings (through February) and the previous week's PACE standings to make sure that we didn't generate anything anomalous.
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Re: Discussion of using power matching at NSC

Post by Deviant Insider » Sat Jun 06, 2009 4:35 pm

I stand corrected, Jeff, and I am glad that I was wrong. Note that that was one of two criticisms I made of the NAQT system.
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Re: Discussion of using power matching at NSC

Post by Important Bird Area » Sat Jun 06, 2009 4:38 pm

Shcool wrote:Note that that was one of two criticisms I made of the NAQT system.
Noted, and the other is presently the subject of internal discussion re: possible changes for the 2010 HSNCT. (No decision as of yet... but we have 11 months to work with.)
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Re: Discussion of using power matching at NSC

Post by First Chairman » Sat Jun 06, 2009 5:00 pm

bt_green_warbler wrote:
Shcool wrote:NAQT did not do that, because they only use data from matches on NAQT questions to seed teams and do not set up the pairings in an optimal manner. There is no need for PACE (or even NAQT) to repeat those mistakes.
This is not true. The initial seeding of teams for Saturday play at HSNCT takes into account the team's entire record; this year we consulted both Byko's rankings (through February) and the previous week's PACE standings to make sure that we didn't generate anything anomalous.
Cool... which of course we have done whenever the tournaments flip weekends (look at NAQT standings, context, and performances just in case). :cool:
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Re: Discussion of using power matching at NSC

Post by Charbroil » Tue Jun 09, 2009 6:36 pm

bt_green_warbler wrote:
Shcool wrote:NAQT did not do that, because they only use data from matches on NAQT questions to seed teams and do not set up the pairings in an optimal manner. There is no need for PACE (or even NAQT) to repeat those mistakes.
This is not true. The initial seeding of teams for Saturday play at HSNCT takes into account the team's entire record; this year we consulted both Byko's rankings (through February) and the previous week's PACE standings to make sure that we didn't generate anything anomalous.
...I was actually told while registering my team and getting my Saturday card that all of the Saturday assignments were pseudo-random, and that our card assignment (IIRC, something like 177) was totally as a result of luck.

If not, I have to admit that I'm kind of confused as to how we got such a low card--certainly, most of our wins were on MSHSAA format games, but regardless of how deserved our finish tied for 27th was, we certainly shouldn't have been only 15 teams from the bottom...
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Re: Discussion of using power matching at NSC

Post by Sen. Estes Kefauver (D-TN) » Tue Jun 09, 2009 7:02 pm

I'm pretty sure card numbers have nothing to do with where you are seeded in the tournament field.
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Re: Discussion of using power matching at NSC

Post by cvdwightw » Tue Jun 09, 2009 7:09 pm

I don't think the card numbers were "seeds" in the traditional sense. Rather, they were handed out such that things like State College vs. Georgetown Day didn't happen in Round 3, creating a cascade of unfairness as teams pinballed their way into other teams that had already been affected by early matchups of two really good teams (upsets could still cause this cascade, but that wouldn't be NAQT's fault - that would just be a less-good team having a better match). For instance, I'm pretty sure that each initial group of 4 had the 2 winners and 2 non-winners of each game play each other, so cards 1 and 189 had the same record through 2 games.
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Re: Discussion of using power matching at NSC

Post by BuzzerZen » Tue Jun 09, 2009 10:28 pm

Yeah, I'm pretty sure, based on inspection of cards over the last few years, that the current system has teams seeded into 16-team groups during their first four rounds. If you have card 1+16n after 4 rounds, you have won four games and are the top team in your initial group. After that, things get complex.
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Re: Discussion of using power matching at NSC

Post by Important Bird Area » Tue Jun 09, 2009 10:37 pm

Our policy is pretty much what Dwight just said; the actual number doesn't mean anything, but we do sort the teams for the first few rounds in order to avoid two really strong teams running into each other right away and generating a cascade of odd-looking results.
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