Author Topic: Super URGENT Question re: 1st Place Ties at a Tournament for 5 People (Read 12480 times)

SirNobody · « **Reply #50 on:** June 25, 2012, 04:40:06 PM »

Hey,

Quote from: Prof Underwood on June 24, 2012, 03:29:54 AM

Can anyone think of an example where the winning % between the tied players would NOT work?

Six way tie. Player A only played Player E and won. Player B beat players C, D, and E. Player B lost to player F. Player F lost to players C and D. Player C beat player D.

So...

Player A (1-0) 100%
Player B (3-1) 75%
Player C (2-1) 66%
Player D (1-2) 33%
Player E (0-2) 0%
Player F (1-2) 33%

Player A has a higher winning percentage than Player B. So your system would place A ahead of B.
Player A and B both beat player E, so I'd think that removing the player E game from each player should be a wash, but if you remove the games they had with player E, Player B moves ahead of Player A, Player B is now 2-1 (66%) while Player A is 0-0 (Null).
I think Player C would also have a very strong argument that he should be placed ahead of player A. Player C has more wins against the group of players and Player C's wins both came against a player that won a game within the group, while Player A's only win was against a player that didn't win any games against the group.

Functionally your method works in this scenario in that it does determine 1st, 2nd, and 3rd, I don't feel like it determines them well. So I would say it doesn't actually "work" in the scenario.

Tschow,

Tim "Sir Nobody" Maly

Ken4Christ4ever · « **Reply #51 on:** June 25, 2012, 05:06:50 PM »

Since I brought it up already in this thread and am not sure about what should have been done, here is what happened at Midwest Regionals last month for type 1 2-player:

First and Second place were obvious from game points.
For Third place:
- Player A had 12 points, -1 LS differential, and won against Player C
- Player B had 12 points, 0 LS differential, and didn't play Player A or C
- Player C had 12 points, +2 LS differential, and lost against Player A

According to my understanding of the rules at the time that were explained by John (that head-to-head only counted if everyone had played head-to-head), I awarded Third place to Player C, who had the highest LS differential.

Based on the REG quote that has been provided, should I have ranked Player C lower since he lost against one of the tied players, and given Third place to Player B? Or should I have given Third place to Player A for being the only player to have beaten one of the other tied players?

If Player C should not be in Third place under the current system, what should I do to correct this situation?

Thank you for any guidance!
Ken

SirNobody · « **Reply #52 on:** June 25, 2012, 05:19:02 PM »

Hey,

Quote from: Prof Underwood on June 24, 2012, 11:12:37 PM

The Swiss system is set up so that players have games against people who having a similar amount of success in the tournament. So if a player doesn't play any of the other top 5 people in a tournament, then that player must have done more poorly all tournament long until the last game, and therefore was never close enough to the top to play any of those players.

This isn't quite true. The swiss style pairs you with a player that has had similar success SO FAR in the tournament. It doesn't know how you will do in the rounds that remain, so it can't factor those in. If you happen to play against several players that go on to lose the rest of their games it ends up looking like you didn't play anybody good. Alternatively if you are unlucky enough to get paired against a really good player early who goes on to win most of their games, it makes your competition look really tough. These scenarios aren't about how well you did in the tournament but rather about the random unknowable future results of your opponents games.

T2-2P from Nationals 2002. Bryon Hake went undefeated (5-0) and got 1st. But he didn't play against the 2nd or 3rd place winners, and only played 1 game against players that finished in the top 7.

T1-2P from Nationals 2007. Gabe Isbell lost 2 of his first 3 games then won his last 7 games. Kevin Shride and myself won our first 4 games each and stayed at the top tables the rest of the day. You would expect Gabe's competition to be significantly inferior to Kevin's or mine because he played from behind, but in fact all three of us played exactly 4 games against players that finished in the top 10. That's because Gabe's first and second round pairings happened to be against players that ended up in the top 10.

Tschow,

Tim "Sir Nobody" Maly

CJSports · « **Reply #53 on:** June 25, 2012, 05:22:02 PM »

Quote from: Ken4Christ4ever on June 25, 2012, 05:06:50 PM

Since I brought it up already in this thread and am not sure about what should have been done, here is what happened at Midwest Regionals last month for type 1 2-player:

First and Second place were obvious from game points.
For Third place:
- Player A had 12 points, -1 LS differential, and won against Player C
- Player B had 12 points, 0 LS differential, and didn't play Player A or C
- Player C had 12 points, +2 LS differential, and lost against Player A

According to my understanding of the rules at the time that were explained by John (that head-to-head only counted if everyone had played head-to-head), I awarded Third place to Player C, who had the highest LS differential.

Based on the REG quote that has been provided, should I have ranked Player C lower since he lost against one of the tied players, and given Third place to Player B? Or should I have given Third place to Player A for being the only player to have beaten one of the other tied players?

If Player C should not be in Third place under the current system, what should I do to correct this situation?

Thank you for any guidance!
Ken

I'm not positive on this but I think player B should've received third because he had a better differential than A and A had beaten C in head to head so B would come out on top. That's how I understand it.

Prof Underwood · « **Reply #54 on:** June 25, 2012, 08:03:32 PM »

Quote from: SirNobody on June 25, 2012, 05:19:02 PM

T2-2P from Nationals 2002. Bryon Hake went undefeated (5-0) and got 1st. But he didn't play against the 2nd or 3rd place winners, and only played 1 game against players that finished in the top 7.

Again, how can this possibly happen. In the championship, I can only assume that it was Bryon (4-0 at the time) against another player who was also 4-0 at the time. Even after losing to Bryon, that 4-1 player should have been in the top 7 at least since there CAN'T be more than 7 players with a 4-1 record in a 32 (or less) person tournament. And for that matter the game before that Bryon (3-0 at that time) should have played against another player who was 3-0. That player also would probably finish in the top 10 even if they lost both of their last 2 rounds.

Quote from: SirNobody on June 25, 2012, 04:40:06 PM

Six way tie. Player A only played Player E and won. Player B beat players C, D, and E. Player B lost to player F. Player F lost to players C and D. Player C beat player D.

Again, I don't see how this scenario can even happen. How can you have 6 players who all do well enough to finish at the top of a tournament, and yet Player A only played 1 game against ANY of the others to get there. I've played in a LOT of tournaments over the years, and I've never seen something like this happen. Can you send me an Excel sheet that shows round by round how you could possibly end up with this situation you are hypothesizing above?

Red Dragon Thorn · « **Reply #55 on:** June 25, 2012, 09:06:42 PM »

Yes, but have you played in 'a LOT' of big tournaments? This is where these things tend to happen - NC Regionals T12P 2008 - 6 way points tie for 3rd. I ended up 7th out of that grouping, despite beating the 2nd place player, because I hadn't played any of the other grouping, and had lost to the first place player.

EmJayBee83 · « **Reply #56 on:** June 26, 2012, 12:11:04 AM »

Quote from: Prof Underwood on June 25, 2012, 03:13:38 AM

Quote from: EmJayBee83 on June 25, 2012, 12:34:08 AM
On a side note, I once lost a tournament (took second) without losing a single game, solely because I received a first round bye with the resulting LS differential of zero.
Again, I don't see how this is possible unless you are leaving out the information that you also did NOT win all your games.

We played five rounds. I won the first three games I that I actually played accumulating a LS differential of +11 in the process, and my last game ended in a timeout tie with the person who ended up taking first. Having an additional game to pad his differential, the person who won had +12. The LS differential of 0 in the first round--which was given to me solely because of the luck of the draw--cost me the tournament.

(And no, I am not bitter about this. I remember it precisely because it was a fairly uncommon circumstance.)

My concern is that your proposed "strength of schedule" weights early round losses more heavily than later round losses. This is especially troubling because the rounds that you are weighting the heaviest are the same ones that have the most randomness in pairings.

Quote

Again, I don't see how this [my example--mjb] happens.

ProfU, this whole thing started with a question about a case where five players ended up going 4-1 in a tournament. You could simply replace the actual scores in games played in that tournament with the scores I used in my example, and the inexorable algorithm of Swiss pairings would have to work out as I said no matter how counter-intuitive it may seem. (At absolute worst you may have to move Mr. Nurge's loss to an earlier round.)

A much more common occurence is going to be similar to the question Ken4Christ4ever posted below. Three players tied with two of them having played each other and one having played neither. In this case it strikes me as more than a little unfair to start by eliminating from consideration the player who didn't play the others.

Prof Underwood · « **Reply #57 on:** June 26, 2012, 10:33:16 AM »

Quote from: Red Dragon Thorn on June 25, 2012, 09:06:42 PM

Yes, but have you played in 'a LOT' of big tournaments?

I guess that depends on how you define "a LOT", but by the end of this summer I'll have played in 4 Nats, close to 10 Regionals, and around 15 States.

Quote from: EmJayBee83 on June 26, 2012, 12:11:04 AM

my last game ended in a timeout tie with the person who ended up taking first.

So as I suspected, you did NOT win all your games. In this case you had 2 players who both went undefeated, and who tied each other in the championship. I think it's entirely fair to determine the winner of that by looking at strength of schedule, and the schedule of the guy who beat 4 people is tougher than the schedule of the guy who beat 3 people. It is unfortunate that you randomly got stuck with the bye, but that was NOT what cost you the tournament. You had your shot to win the tournament by winning the championship game. You didn't do that. So I still see that as a good tournament where you just came up a bit short. I'm glad that you enjoyed it and don't have a problem with the outcome.

Quote from: EmJayBee83 on June 26, 2012, 12:11:04 AM

My concern is that your proposed "strength of schedule" weights early round losses more heavily than later round losses.

I don't think so. If you lose and early round, and then play me at the end of the tournament and beat me, then we will have the same record (assuming we won the rest of our games). You will be ranked higher which at first looks like my late loss hurt more than your early one. But really both losses put us in a position where we did NOT have the victory assured, and the swiss tournament system paired was successful in getting us to play head-to-head to see who deserved the top spot between the two of us.

Quote from: EmJayBee83 on June 26, 2012, 12:11:04 AM

A much more common occurence is going to be ...Three players tied with two of them having played each other and one having played neither...it strikes me as more than a little unfair to start by eliminating from consideration the player who didn't play the others.

I don't think it unfair to say that the players who got their victory points against other top players should be ranked higher than the player who got their victory points against weaker players. That actually seems to be the most fair way to do it.

CactusRob · « **Reply #58 on:** June 26, 2012, 10:51:04 AM »

Quote from: Ken4Christ4ever on June 25, 2012, 05:06:50 PM

Since I brought it up already in this thread and am not sure about what should have been done, here is what happened at Midwest Regionals last month for type 1 2-player:

First and Second place were obvious from game points.
For Third place:
- Player A had 12 points, -1 LS differential, and won against Player C
- Player B had 12 points, 0 LS differential, and didn't play Player A or C
- Player C had 12 points, +2 LS differential, and lost against Player A

According to my understanding of the rules at the time that were explained by John (that head-to-head only counted if everyone had played head-to-head), I awarded Third place to Player C, who had the highest LS differential.

Based on the REG quote that has been provided, should I have ranked Player C lower since he lost against one of the tied players, and given Third place to Player B? Or should I have given Third place to Player A for being the only player to have beaten one of the other tied players?

If Player C should not be in Third place under the current system, what should I do to correct this situation?

Thank you for any guidance!
Ken

I feel a little bad for Ken because he is worried he did something wrong. No worries, you ruled in good faith and it's over. Moreover, a reasonable argument has already been made that you scored correctly. If we go back and try to change placings now, other tournaments would also need to be re-scored. As far as I am concerned those trains have left the station. I just want to nail down the best way to settle three way (or more) "ties" moving forward.

Ken4Christ4ever · « **Reply #59 on:** June 26, 2012, 10:58:22 AM »

Okay, thank you, Rob.

SirNobody · « **Reply #60 on:** June 26, 2012, 01:29:44 PM »

Hey,

Quote from: Prof Underwood on June 25, 2012, 08:03:32 PM

Quote from: SirNobody on June 25, 2012, 05:19:02 PM
T2-2P from Nationals 2002. Bryon Hake went undefeated (5-0) and got 1st. But he didn't play against the 2nd or 3rd place winners, and only played 1 game against players that finished in the top 7.
Again, how can this possibly happen.

In big swiss style tournaments (and this one wasn't actually that big) with timeouts things get very messy very fast. In this case Bryon played me in round 4. He was in 1st place, I was in 2nd. I had 2 full wins and a winning at time out, which was more than anyone else had (there were 18 players total in the event). I lost my last two games and finished behind anyone who went 3-2, which landed me 9th. Bryon's last round opponent finished 4th. The spreadsheet is on Bany's website if you'd like to look at it.

Quote

Quote from: SirNobody on June 25, 2012, 04:40:06 PM
Six way tie. Player A only played Player E and won. Player B beat players C, D, and E. Player B lost to player F. Player F lost to players C and D. Player C beat player D.
Again, I don't see how this scenario can even happen. How can you have 6 players who all do well enough to finish at the top of a tournament, and yet Player A only played 1 game against ANY of the others to get there.

The actual tournament results we're discussing involves a 5 way tie where one of the players didn't play anyone else they were tied with. It doesn't seem like much of a stretch to expand that to a six way tie where one player only played one of the other people involved. There was a 6 way tie for 5th at Nationals 2002 (outside of placing so it doesn't really matter but still pretty darn near the top) and that group of 6 included 1 player that didn't play anyone else in the group and 1 player that played 1 player in that group.

Also keep in mind that these ties may not be for first place. What if there's a massive tie for 2nd? Then you're evaluating how well the group did against each other while ignoring that one of them may have won against a player that finished better than all of them.

Quote from: Prof Underwood on June 26, 2012, 10:33:16 AM

Quote from: Red Dragon Thorn on June 25, 2012, 09:06:42 PM
Yes, but have you played in 'a LOT' of big tournaments?
I guess that depends on how you define "a LOT", but by the end of this summer I'll have played in 4 Nats, close to 10 Regionals, and around 15 States.

How many of those tournaments had single events that went 6+ rounds and included 30+ people?

Tschow,

Tim "Sir Nobody" Maly

Prof Underwood · « **Reply #61 on:** June 26, 2012, 05:24:56 PM »

Quote from: SirNobody on June 26, 2012, 01:29:44 PM

How many of those tournaments had single events that went 6+ rounds and included 30+ people?

I've probably been to a handful of tournaments with 30+ people, but the only tournaments that I've been to with 6+ rounds in a single event are my 3 Nats.

Here's an idea that I'm throwing out as a possible solution. What's everyone think of it?
1st tie-breaker is strength of schedule (with more games against tied players getting higher rankings)
2nd tie-breaker is head-to-head winning % against other tied players (assuming the same number of games against tied players).
3rd tie-breaker is LS differential

This would give the most popular ranking of the original scenario of this thread. It would give 3rd place to player A in Ken's scenario (who I think deserves it most for being the only player to beat one of the other players who had the same number of victory points). In SirNobody's example of:
Player A (1-0) 100%
Player B (3-1) 75%
Player C (2-1) 66%
Player D (1-2) 33%
Player E (0-2) 0%
Player F (1-2) 33%
...it would rank them B, C, and then D or F (whichever had higher LS diff).

So does this seem to be fair to most people?

YourMathTeacher · « **Reply #62 on:** June 26, 2012, 10:08:47 PM »

Is this all going to be on Tournament Tracker, or are hosts going to have to take a Calculus refresher course before their tournaments?

EmJayBee83 · « **Reply #63 on:** June 27, 2012, 12:06:49 AM »

Quote from: Prof Underwood on June 26, 2012, 10:33:16 AM

Quote from: EmJayBee83 on June 26, 2012, 12:11:04 AM
My concern is that your proposed "strength of schedule" weights early round losses more heavily than later round losses.
I don't think so.

ProfU, you seem to be confused by what I was saying. I was making a mathematical statement whose correctness is not really effected by an opinion to the contrary. Weighting early round losses more heavily than later round losses is a feature of your "strength of schedule" criterion.

If the PtB are really going to try and come up with a new tie-breaking system, I hope that they go back and test it against real tournament results and see if they pass the smell test. There are some situations that we know have occurred that at first blush strike us as seeming strange (q.v., Tim's 2002 T2-2P National results and ProfU's reaction to the same). Since our intuition fails us, any off-the-top-of-our-head changes may well make matters worse.

All in all, I think hosts are--at best--only going to get marginal improvements over just using LS Differential so there is not much reason to switch from the simpler system. This is, however, only based on my intuition about how things work.

Prof Underwood · « **Reply #64 on:** June 27, 2012, 09:39:41 AM »

Quote from: EmJayBee83 on June 27, 2012, 12:06:49 AM

If the PtB are really going to try and come up with a new tie-breaking system, I hope that they go back and test it against real tournament results and see if they pass the smell test.

That's why I included in my last post how my proposal would rank all 3 of the complicated situations that have been mentioned in this thread. I also am opening it up to everyone to try to find a scenario where that proposed method would NOT give results that seem fair.

As I'm thinking about it more I guess I could imagine at least 1 scenario where it might not work:
Player A goes 7-3 at Nats, where all 3 losses (and 1 win) are against other players who tie at 21 VPs.
Player B goes 3-5-2-0 at Nats (5 timeout wins, 2 timeout losses) to also tie with 21 VPs. Their 1 loss was early, and their 3 wins are against other players who tie at 21 VP.
The system I'm proposing would rank Player A higher than Player B because just looking at their games against tied players would have Player A with 4 games (1-3) and Player B with 3 games (3-0). But wouldn't most people believe that the undefeated player, who beat 3 top players should be ranked higher? Or would most people agree that someone who wins 7 games deserves to be ranked higher than someone who can only totally win 3 games?

Quote from: EmJayBee83 on June 27, 2012, 12:06:49 AM

Since our intuition fails us...This is, however, only based on my intuition

I saw what you did there

YourMathTeacher · « **Reply #65 on:** June 27, 2012, 11:07:17 AM »

This whole discussion is now moot. Since we have been comparing this process to the BCS system, it is worth noting that the BCS has agreed to have a playoff for the National Championship. Therefore, in the event of future ties in major tournaments with large populations, a winner-takes-all death match will determine the winner.

The Guardian · « **Reply #66 on:** January 19, 2013, 02:40:11 PM »

I tried to read most of this thread but may not have hit all of the posts. There's actually a pretty simple and fair way to do this.

If a group of people are tied, and they have all played the same number of games against each other, then you go to head to head record (head to head meaning against the rest of the tied group). If they have not played the same number of games against each other, you go to LS diff. You repeat this process each time a person is “placed.”

So for the original example:
5 way tie with 12 points.
Player A was 1-1.
Player B was 0-1.
Player C was 1-1.
Player D was 1-0.
Player E was 0-0.

Because each player did not play the same number of games, we go to LS diff. Player A and Player B tied with 8. At this point, you can call it a tie or go back to head to head and A has the better record thus winning (though in some instances it could still result in a tie).

For example sake, we'll say that A is now first and B comes in second. We now repeat the process but take out A and B.
3 way tie with 12 points.
Player C was 0-0.
Player D was 0-0.
Player E was 0-0.

Obviously at this point we go to differential and C takes third.

This is how ESPN breaks ties for fantasy footbal play-off rankings (using Points Scored instead of LS Diff obviously). In one of my leagues, there were 5 teams tied for the 4 final play-off spots. And no, I don't want to talk about who got left out...

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Author Topic: Super URGENT Question re: 1st Place Ties at a Tournament for 5 People (Read 12480 times)

SirNobody

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Ken4Christ4ever

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SirNobody

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CJSports

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Prof Underwood

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Red Dragon Thorn

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