ECAC Byes and Home-Ice 2011-12

[burgie12]

I think this is something that I'm going to add to my run-downs.

Here are the probabilities of team's finishing in each of the twelve places if a team's likelihood of winning is based upon current KRACH.

There are multiple caveats with this.

1) KRACH is a retrodictive, not predictive, system.
2) I used a straight tie percentage of 13.0% (approximately the rate of ties in men's college hockey over the past few years).
3) A team's likelihood of winning is the normal win percentage (KRACH(1) / [KRACH(1) + KRACH(2)]) minus half of the tie percentage.
4) There were only 2500 trials run (which, really, is a pretty low number).
5) KRACH is not updated with the completion of a game (so if, for example, Brown were to win their first three games, one would assume that their KRACH would go up and they may even be favored in their game against Princeton).

Some of these caveats can be seen in the data. A percentage of 0.0 means that that finish occurred exactly once in 2500 trials. A percentage of "xxxx" means that that finish can happen, but did not occur.

One final note is that this is sorted by current standings, not projected standings (like lugnut's predictions are).

----------------------------------------------------------------------------------------------------
| Team         |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th |
----------------------------------------------------------------------------------------------------
| Union        | 56.8 | 29.1 | 13.6 |  0.3 |  0.1 |      |      |      |      |      |      |      |
| Cornell      | 34.3 | 43.8 | 20.3 |  1.6 |  0.0 | xxxx | xxxx |      |      |      |      |      |
| Colgate      |  8.8 | 26.1 | 49.7 | 14.1 |  1.1 |  0.2 | xxxx |      |      |      |      |      |
| Harvard      | xxxx |  0.9 | 15.0 | 62.0 | 14.0 |  5.5 |  2.2 |  0.4 | xxxx | xxxx | xxxx |      |
| Clarkson     | xxxx |  0.0 |  0.6 | 10.2 | 22.4 | 39.2 | 18.4 |  6.6 |  2.2 |  0.2 | xxxx |      |
| Quinnipiac   |      | xxxx |  0.6 |  9.5 | 50.1 | 23.4 | 11.1 |  4.1 |  1.0 |  0.2 | xxxx | xxxx |
| St. Lawrence |      | xxxx |  0.0 |  1.7 |  7.3 | 15.5 | 35.3 | 25.1 | 11.7 |  3.2 |  0.2 | xxxx |
| Yale         |      |      |      |  0.3 |  1.8 |  5.2 | 12.3 | 28.7 | 27.4 | 17.4 |  6.2 |  0.8 |
| Dartmouth    |      |      | xxxx |  0.2 |  3.2 | 10.2 | 18.4 | 22.7 | 26.4 | 13.2 |  4.5 |  1.2 |
| Princeton    |      |      |      | xxxx |  0.0 |  0.6 |  1.7 |  8.4 | 19.7 | 37.0 | 18.8 | 13.8 |
| Rensselaer   |      |      |      | xxxx | xxxx |  0.1 |  0.2 |  2.0 |  5.7 | 16.0 | 43.7 | 32.3 |
| Brown        |      |      |      |      | xxxx |  0.2 |  0.4 |  2.0 |  5.9 | 12.9 | 26.6 | 51.9 |
----------------------------------------------------------------------------------------------------

[burgie12]

Current Standings:
--- Bye Lock - 27
Union 26 - 34 [1-5]
Cornell 25 - 33 [1-7]
Colgate 23 - 31 [1-7]
--- Home Lock - 22+
Harvard 20 - 28 [1-11]
Clarkson 19 - 27 [1-11]
Quinnipiac 18 - 26 [2-12]
St. Lawrence 17 - 25 [2-12]
Yale 15 - 23 [4-12]
Dartmouth 15 - 23 [3-12]
Princeton 13 - 21 [4-12]
Rensselaer 13 - 21 [4-12]
--- Bye Eligible - 21
Brown 12 - 20 [5-12]
--- Home Eligible - 16+

Yale beat Dartmouth in Hanover a couple weeks ago and therefore hold the tiebreaker. They'll play each other on Friday to solidify who will hold onto this spot. For now, the Bulldogs hold onto 8th.

Princeton beat RPI in New Jersey in December and therefore wins the tiebreaker. These teams will also play each other next weekend.

Remaining League Schedules:

---------------------------------------------
|              |    |F2/17|S2/18|F2/24|S2/25|
---------------------------------------------
| Union        | UC |  PN |  QN | @CR | @CG |
| Cornell      | CR | @CK | @SL |  UN |  RP |
| Colgate      | CG | @SL | @CK |  RP |  UN |
| Harvard      | HA | @BN | @YA |  SL |  CK |
| Clarkson     | CK |  CR |  CG | @DA | @HA |
| Quinnipiac   | QN | @RP | @UN |  BN |  YA |
| St. Lawrence | SL |  CG |  CR | @HA | @DA |
| Yale         | YA |  DA |  HA | @PN | @QN |
| Dartmouth    | DA | @YA | @BN |  CK |  SL |
| Princeton    | PN | @UN | @RP |  YA |  BN |
| Rensselaer   | RP |  QN |  PN | @CG | @CR |
| Brown        | BN |  HA |  DA | @QN | @PN |
---------------------------------------------

Current KRACH Simulation: (2500 trials, 13.0% straight tie percentage)

------------------------------------------------------------------------------------------------------------
| Team         |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExPl |
------------------------------------------------------------------------------------------------------------
| Union        | 56.8 | 29.1 | 13.6 |  0.3 |  0.1 |      |      |      |      |      |      |      |  1.58 |
| Cornell      | 34.3 | 43.8 | 20.3 |  1.6 |  0.0 | xxxx | xxxx |      |      |      |      |      |  1.89 |
| Colgate      |  8.8 | 26.1 | 49.7 | 14.1 |  1.1 |  0.2 | xxxx |      |      |      |      |      |  2.73 |
| Harvard      | xxxx |  0.9 | 15.0 | 62.0 | 14.0 |  5.5 |  2.2 |  0.4 | xxxx | xxxx | xxxx |      |  4.16 |
| Clarkson     | xxxx |  0.0 |  0.6 | 10.2 | 22.4 | 39.2 | 18.4 |  6.6 |  2.2 |  0.2 | xxxx |      |  5.93 |
| Quinnipiac   |      | xxxx |  0.6 |  9.5 | 50.1 | 23.4 | 11.1 |  4.1 |  1.0 |  0.2 | xxxx | xxxx |  5.52 |
| St. Lawrence |      | xxxx |  0.0 |  1.7 |  7.3 | 15.5 | 35.3 | 25.1 | 11.7 |  3.2 |  0.2 | xxxx |  7.24 |
| Yale         |      |      |      |  0.3 |  1.8 |  5.2 | 12.3 | 28.7 | 27.4 | 17.4 |  6.2 |  0.8 |  8.56 |
| Dartmouth    |      |      | xxxx |  0.2 |  3.2 | 10.2 | 18.4 | 22.7 | 26.4 | 13.2 |  4.5 |  1.2 |  8.22 |
| Princeton    |      |      |      | xxxx |  0.0 |  0.6 |  1.7 |  8.4 | 19.7 | 37.0 | 18.8 | 13.8 | 10.03 |
| Rensselaer   |      |      |      | xxxx | xxxx |  0.1 |  0.2 |  2.0 |  5.7 | 16.0 | 43.7 | 32.3 | 10.98 |
| Brown        |      |      |      |      | xxxx |  0.2 |  0.4 |  2.0 |  5.9 | 12.9 | 26.6 | 51.9 | 11.18 |
------------------------------------------------------------------------------------------------------------

Miscellaneous Links:
Sioux Sports what-if calculator (no tiebreakers)
TBRW ECAC Playoff Possibilities Script
ECAC Tie-Breaking Guidelines
Playoff Status Standings with (terrible, inaccurate, and unexplained) predictions for final standings

So, I'm going to the Sabres game tonight and then spending the evening with family, so this is going to be more of a "pre-update." I'll probably have a short follow-up either very late tonight or mid-morning tomorrow. I will have a full rundown after Saturday's games chock full of all of the delicious goodness that you expect.

Also, I'm warning you now that I will be travelling and working the next two weeks, so it is very unlikely that I have an update going into the last game. Sorry, guys.

Individual Team Limits:
Clinching Scenarios
Union clinches a bye with any point earned tonight or any point lost by Quinnipiac.

Any point earned by Cornell tonight against Clarkson will also clinch them a bye.

Colgate can only clinch a bye tonight with a win, a Clarkson loss, and a Quinnipiac loss (I think). A Harvard loss (instead of a Clarkson loss) helps, but doesn't clinch a Top 4 spot for the Raiders. A Quinnpiac tie (instead of a loss) leaves Colgate on the cusp of clinching a weekend off, but still leaves some doubt.

Harvard clinches home-ice with a win and a non-tie in the Dartmouth / Yale game tonight.

Clarkson clinches home-ice with a win and losses by SLU and Dartmouth.

I don't think Quinnipiac can clinch home-ice tonight, but they can put themselves very, very close with a win, losses by Dartmouth and SLU, and non-wins by Princeton and Brown.

Out of the Running
Harvard is out of contention for the #1 seed with any point lost by them or gained by Union or Cornell.

Clarkson is out of contention for the #1 seed with any point lost by them or gained by Union.

Yale can't grab a bye if they lose and neither Harvard nor Clarkson lose OR if the Bulldogs tie and both Harvard and Clarkson win.

Dartmouth is in the same position as Yale. So, a Dartmouth / Yale tie tonight could push both of them out of the running.

Princeton is cannot finish in 4th or higher place if they lose a point OR Harvard or Clarkson gains a point OR a St. Lawrence win OR Quinnipiac wins and Dartmouth / Yale is not a tie.

Same with RPI, except that the Quinnipiac win scenario is already covered by RPI losing points.

[lugnut92]

New "Expected Standings":
1. Union (32)
2. Cornell (30)
3. Colgate (27)
4. Harvard (25)
-----
5. Quinnipiac (23)
6. Clarkson (23)
7. St. Lawrence (22)
8. Yale (20)
-----
9. Dartmouth (18)
10. Princeton (16)
11. Brown (15)
12. RPI (15)

So, the only difference between these standings and the real standings is the sequence of 11 and 12, which would break the other way based on RPI's season sweep. Also, RPI can do no better than 8th now. Sadface.

[burgie12]

Union 28 - 34 [1-3]
Cornell 26 - 32 [1-4]
--- Bye Lock - 26+
Colgate 23 - 29 [1-7]
--- Home Lock - 21+
Harvard 21 - 27 [2-9]
Quinnipiac 20 - 26 [3-9]
Clarkson 20 - 26 [2-9]
St. Lawrence 19 - 25 [3-9]
Yale 17 - 23 [4-11]
--- Bye Eligible - 22
Dartmouth 15 - 21 [5-12]
Princeton 13 - 19 [8-12]
Rensselaer 13 - 19 [7-12]
Brown 13 - 19 [8-12]
--- Home Eligible - 17

Quinnipiac took three points from Clarkson and holds 5th place on the series win.

Princeton is winning the H2H tiebreaker between themselves, RPI, and Brown (2-0-0 vs 2-1-0 (RPI) vs 0-3-0 (Brown)). RPI swept Brown and holds 11th place. The RPI / Princeton tiebreaker will be solidified tonight.

Remaining League Schedules:

---------------------------------------------
|              |    |S2/18|F2/24|S2/25|
---------------------------------------------
| Union        | UC |  QN | @CR | @CG |
| Cornell      | CR | @SL |  UN |  RP |
| Colgate      | CG | @CK |  RP |  UN |
| Harvard      | HA | @YA |  SL |  CK |
| Quinnipiac   | QN | @UN |  BN |  YA |
| Clarkson     | CK |  CG | @DA | @HA |
| St. Lawrence | SL |  CR | @HA | @DA |
| Yale         | YA |  HA | @PN | @QN |
| Dartmouth    | DA | @BN |  CK |  SL |
| Princeton    | PN | @RP |  YA |  BN |
| Rensselaer   | RP |  PN | @CG | @CR |
| Brown        | BN |  DA | @QN | @PN |
---------------------------------------------

Current KRACH Simulation: (5000 trials, 13.2% straight tie percentage)

Nope, I didn't have time to run this.  Fooled you, didn't I?

Miscellaneous Links:
Sioux Sports what-if calculator (no tiebreakers)
TBRW ECAC Playoff Possibilities Script
ECAC Tie-Breaking Guidelines
Playoff Status Standings with (terrible, inaccurate, and unexplained) predictions for final standings

Individual Team Limits:
Teams Losing Out (Floors)
Union's moved their floor up to 3rd. They could be passed by both teams from central New York, but that's it.

Cornell has also clinched a bye. They swept Quinnipiac and hold the tiebreaker over Harvard since they took three points on the season series. They would lose a tiebreaker to Clarkson, but since Harvard and Clarkson still have to play, it is impossible for the Knights to tie the Big Red and have the Crimson overtake them. So, with Cornell already behind Union and within passing distance of Colgate and either Harvard or Clarkson but not both, Schafer's men have earned themselves a weekend off.

Colgate can still only fall as far as 7th place. Yale can catch Colgate, but would fail to win any potential tiebreaker.

Harvard (since they lose so many gosh-darn tiebreakers) can fall as far as 9th place. Dartmouth can still tie their travel partner in points and would win a tiebreaker on ECAC wins.

Quinnipiac and Clarkson can be passed outright all the way down to Dartmouth. So, the Bobcats and Knights can still fall to 9th place.

St. Lawrence can be caught and passed (all at the same time) by every team down to Dartmouth. They can also be tied by either Brown and RPI or by just Princeton. However, the Saints hold the tiebreaker over each of the bottom three teams (ECAC wins over Brown and RPI, season series sweep over Princeton). So, the Saints' floor is also 9th place.

Yale can fall to 11th place. They can be passed by two of the three teams tied for 10th (and tied by the other). Since Yale holds the tiebreaker over each of Princeton, RPI, and Brown (all on ECAC wins), the Elis' floor is 11th.

Each of the bottom 4 teams can finish by themselves in 12th place.

Teams Winning Out (Ceilings)
Brown can still pull themselves into 8th place. They can get up to a tie with St. Lawrence, but would lose the tiebreaker on ECAC wins. The Bears do not have any "beneficial third teams" that they can have also tie with the Saints that would allow Brown to leapfrog SLU.

RPI can leapfrog SLU if Brown also ends up tied with 19 points. They would then win the H2H tiebreaker (3-1-0 vs 2-2-0 (SLU) vs 1-3-0 (Brown)). That means that RPI has the mathematical capability of 7th place.

Princeton, like Brown, can not leapfrog SLU (especially since they got swept by St. Lawrence). So, their ceiling is also 8th place.

Dartmouth can catch Harvard, but doing so would allow multiple other teams to catch and / or pass the Big Green. So, in letting the Crimson win out, Dartmouth can stay ahead of everyone currently in between them and Harvard in the standings and grab the #5 seed.

Yale can claim the #4 seed, just behind Colgate and just ahead of Clarkson (with Harvard and Quinnipiac both behind them) if they get lots of help.

St. Lawrence can climb past every team in front of them all the way up to 3rd place. (They can no longer catch Cornell because of their tie last night with Clarkson.)

Clarkson can still catch and tie Cornell and would win the tiebreaker on ECAC wins. They lost their chance to win the Cleary Cup (not that it was likely anyways), but they can still finish with the #2 seed.

Quinnipiac can catch Cornell, but would lose the resulting tiebreaker on H2H record and cannot bring in a "beneficial third team", so they can only grab the #3 seed.

Harvard can outright pass Cornell, handing them the #2 seed, and Union is out of reach for the Crimson.

Each of Colgate, Cornell, and Union can claim the Cleary Cup for themselves. So, they're all maxed out at the #1 seed.

Thresholds:
Bye Lock - The number of points required to secure a week off in March if 5th place finishes with as many points as possible. I can get Quinnipiac and Clarkson into a tie for 4th place with 26 points each. So, to guarantee yourself a weekend off, you need at least 26 points and the correct tiebreakers.

Bye Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 4. With Harvard in 4th place at 21 points with a game to play against Clarkson (who has 20 points), you need at least 22 points to finish with the #4 seed.

Home Lock - The number of points required to play at home in the first week of March if 9th place finishes with as many points as possible. It drops yet another full point to 21 points plus necessary tiebreakers. If someone with a better record against Dartmouth were sitting with 21 points right now, they would have home-ice in the bag.

Home Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 8. Yale (with 17 points) can lose out and still have another couple of games at home.

After tonight's games I will look into tiebreakers and "best case" / "interesting" scenarios.

[burgie12]

Union 30 - 34 [1-2]
Cornell 28 - 32 [1-2]
--- Bye Lock - 25
Colgate 23 - 27 [3-7]
Clarkson 22 - 26 [3-8]
--- Home Lock - 21+
Harvard 21 - 25 [3-9]
Quinnipiac 20 - 24 [3-9]
St. Lawrence 19 - 23 [3-9]
Yale 19 - 23 [4-9]
--- Bye Eligible - 23
Dartmouth 17 - 21 [5-11]
--- Home Eligible - 19+
Princeton 15 - 19 [9-12]
Rensselaer 13 - 17 [9-12]
Brown 13 - 17 [10-12]

St. Lawrence holds the tiebreaker for 7th place based on their season series win with a win in New Haven and a tie back in Canton.

RPI swept Brown and holds 11th place because of it.

Remaining League Schedules:

---------------------------------
|              |    |F2/24|S2/25|
---------------------------------
| Union        | UC | @CR | @CG |
| Cornell      | CR |  UN |  RP |
| Colgate      | CG |  RP |  UN |
| Clarkson     | CK | @DA | @HA |
| Harvard      | HA |  SL |  CK |
| Quinnipiac   | QN |  BN |  YA |
| St. Lawrence | SL | @HA | @DA |
| Yale         | YA | @PN | @QN |
| Dartmouth    | DA |  CK |  SL |
| Princeton    | PN |  YA |  BN |
| Rensselaer   | RP | @CG | @CR |
| Brown        | BN | @QN | @PN |
---------------------------------

Miscellaneous Links:
Sioux Sports what-if calculator (no tiebreakers)
TBRW ECAC Playoff Possibilities Script
ECAC Tie-Breaking Guidelines
Playoff Status Standings with (terrible, inaccurate, and unexplained) predictions for final standings

Individual Team Limits:
Teams Losing Out (Floors)
Union can only be caught by Cornell. The Dutchmen have clinched at least the #2 seed.

Cornell cannot be caught by any team behind them. They have also clinched at least the #2 seed.

Colgate can still fall all the way to 7th place. It is possible for Clarkson and Quinnipiac to both pass Colgate and have a three-way SLU / Harvard / Colgate tie. Since SLU would have to beat Harvard to make this tie possible, SLU would win the H2H tie (6 points vs 3 vs 3) and Harvard would win the resulting tie for 6th with the season series win (1-0-1 vs 0-1-1).

Both Quinnipiac and Yale hold tiebreakers over Clarkson (season series win for the Bobcats and ECAC wins for the Bulldogs), so Clarkson can be passed / tied all the way down to 8th place.

Harvard can fall into a 3-way tie for 7th place with SLU and Dartmouth and would finish with the #9 seed and would be travelling to Canton for their first playoff series this season. (Dartmouth wins the three-way tie 6 points vs 4 vs 2 and SLU wins the H2H matchup with Harvard on their season sweep.)

Quinnipiac can be passed outright by everyone below them through Dartmouth. Therefore, the Bobcats can also fall to the #9 seed.

St. Lawrence and Yale both hold the tiebreaker over Princeton (SLU by their season sweep and Yale by ECAC wins) and I can't find a way to add a third team in the mix to let the Tigers leapfrog either team. So, SLU and Yale both have floors of 9th place.

Dartmouth can no longer fall into the basement. They swept Brown and will not be able to lose a tiebreaker to the Bears. They would lose a tiebreaker to RPI on Points vs Top 4 (RPI would have to beat Cornell and Colgate, giving them 3 points against Cornell (a guaranteed Top 4 team) and cancelling out Dartmouth's advantage from their win over Colgate. Dartmouth would not be able to put in two other teams that would allow them to come back from their three-point disadvantage in this criteria.) and can therefore finish in the #11 seed.

Princeton, RPI, and Brown can all finish in 12th place.

Teams Winning Out (Ceilings)
Brown cannot win a tiebreaker against Dartmouth and can only climb to 10th place because of it.

RPI can beat Dartmouth in a tiebreaker and can therefore reach the #9 seed. However, they are still assured of playing no more home games this season.

Princeton will not win a tiebreaker against Yale or SLU by themselves and I cannot find a third team to pair either of them with to allow the Tigers to leapfrog either team. So, Princeton's home slate will end after this upcoming weekend because they cannot finish any higher than 9th.

A Dartmouth / SLU / Harvard / Quinnipiac tie for 5th place would break in that exact order (8 points (DC) vs 8 (SLU) vs 5 (HU) vs 3 (QU) with Dartmouth winning the H2H against SLU and Harvard beating Quinnipiac for 7th), so Dartmouth still has the slimmest of hopes of finishing in 5th.

Yale cannot win a tiebreaker against Colgate for 3rd place. The Raiders would win based on their season sweep of the Big Red (giving them the win on Points vs Top 4). Also, I can't find a "beneficial third team" to push Yale over the top. However, Yale can put themselves into a tie with either Clarkson or Harvard and pass every other team standing between them. The Elis would own the tiebreaker over either the Knights or Crimson on ECAC wins, meaning that a two-way tie for 4th with either team lands Yale in the #4 seed. A Harvard / Colgate / Yale tie would break in that exact order, so if Yale does end up tied at 23 points with Harvard, it would be best if Colgate didn't also wind up with 23.

St. Lawrence, however, would like to tie with Harvard. That season sweep over Harvard looms large and also functions as the extra points needed to put the Saints into the #3 seed. (Three-way tie between SLU, Harvard, and Colgate breaks in that order on H2H points (6 vs 3 vs 3) and then Harvard won the season series against Colgate and claims 4th.)

Everyone from Quinnipiac through Colgate (so, currently seeds 3-6) can all finish in third place by themselves.

Either Cornell or Union (or both?) will win the Cleary Cup and either of them could claim the #1 seed.

Thresholds:
Bye Lock - The number of points required to secure a week off in March if 5th place finishes with as many points as possible. If Clarkson and Harvard both win on Friday and Colgate picks up at least a couple points this weekend, then either Tech or Harvard will be in with 25 points while the other will be sitting on the outside looking in with 24.

Bye Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 4. With Clarkson in 4th place at 22 points with a game to play against Harvard (who has 21 points), you need at least 23 points to finish with the #4 seed.

Home Lock - The number of points required to play at home in the first week of March if 9th place finishes with as many points as possible. It holds steady after last night's games at 21 points plus necessary tiebreakers. If someone with a better record against Dartmouth were sitting with 21 points right now, they would have home-ice in the bag (yes, I'm looking at you, Harvard).

Home Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 8. Yale (with 19 points) can lose out and still have another couple of games at home. Since Princeton has failed to earn a tiebreaker win against SLU, Yale, or Dartmouth, the requisite "you have to have the correct tiebreakers" quote goes in here.

[Yale13]

How would Yale lose a tie-break against Harvard for 4th place? They split the season series, and if they end up tied at 23 pts Harvard would have no more than 7 ECAC wins while the Bulldogs would have 11.

[burgie12]

I should have done the tiebreakers before I did this post. It would've helped. Tiebreakers will be up later / tomorrow / later in the week.

Best-case scenarios:
Union (1st place)
1) Defeat or tie Cornell
2) Lose to Cornell but earn more points on Saturday against Colgate than Cornell does against RPI

Cornell (1st place)
1) Defeat Union and earn at least as many points on Saturday against RPI as Union does against Colgate.
Note: Cornell can still earn a share of the Cleary Cup with a tie against Union. However, they would no longer be able to claim the #1 seed.

Colgate (3rd place)
1) Earn at least 3 points
2) Earn 2 points AND neither Clarkson nor Harvard earns 4 points
3) Earn 1 point AND Clarkson also finishes with 24 points AND both Harvard and Quinnipiac finish with 23 points or fewer (just for you, Ralph)
4) Earn 1 point AND both Clarkson and Harvard finish with 23 points or fewer
5) Earn 0 points AND Clarkson ties Harvard AND both Clarkson and Harvard lose on Friday (to Dartmouth and SLU, respectively) AND Quinnipiac earns 2 or fewer points AND St. Lawrence does not defeat Dartmouth

Clarkson (3rd place)
1) Earn 4 points AND Colgate earns 2 or fewer points
2) Earn 3 points AND Colgate earns 1 or fewer points
3) Defeat Harvard AND lose to Dartmouth AND Colgate earns 0 points AND Quinnipiac does not earn 4 points
4) Tie Harvard AND tie Dartmouth AND Colgate earns 0 points AND Harvard does not defeat SLU AND Quinnipiac does not earn 4 points
5) Lose to Harvard AND defeat Dartmouth AND Colgate earns 0 points AND Harvard loses to SLU AND Quinnipiac does not earn 4 points
6) Tie Harvard AND lose to Dartmouth AND Colgate earns 0 points AND SLU defeats Harvard and Dartmouth AND Quinnipiac does not earn 4 points

Harvard (3rd place)
1) Earn 4 points AND Colgate earns 2 or fewer points
2) Defeat Clarkson AND tie SLU AND Colgate earns 1 or fewer points
3) Tie Clarkson AND defeat SLU AND Colgate earns 1 or fewer points AND Clarkson does not defeat Dartmouth
4) Defeat Clarkson and lose to SLU AND Colgate earns 0 points AND Clarkson ties Dartmouth AND SLU defeats Dartmouth AND Quinnipiac earns 2 or fewer points
5) Defeat Clarkson and lose to SLU AND Colgate earns 0 points AND Clarkson loses to Dartmouth AND SLU does not defeat Dartmouth AND Quinnipiac does not earn 4 points

Quinnipiac (3rd place)
1) Earn 4 points AND Colgate earns 1 point AND Clarkson earns 2 points AND Harvard earns 2 or fewer points
2) Earn 4 points AND Colgate earns 0 points AND Clarkson earns 2 or fewer points AND Harvard earns 2 or fewer points
3) Earn 3 points AND Colgate earns 0 points AND Clarkson ties Harvard AND Clarkson and Harvard lose on Friday AND SLU does not defeat Dartmouth

St. Lawrence (3rd place)
1) Earn 4 points AND Colgate earns 0 points AND Harvard defeats Clarkson AND Clarkson ties Dartmouth AND Quinnipiac earns 3 points
2) Earn 4 points AND Colgate earns 0 points AND Harvard defeats Clarkson AND Clarkson loses to Dartmouth AND Quinnipiac does not earn 4 points

Yale (4th place)
1) Earn 4 points AND Colgate earns 1 or more points AND Harvard does not defeat Clarkson AND Clarkson and Harvard lose on Friday (to Dartmouth and SLU, respectively) AND SLU does not defeat Dartmouth
2) Earn 4 points AND Colgate earns 0 points AND Clarkson ties Harvard AND Clarkson and Harvard lose on Friday AND SLU does not defeat Dartmouth

Dartmouth (5th place)
1) Earn 4 points AND Harvard earns 0 points AND Quinnipiac ties Yale AND Quinnipiac and Yale lose on Friday (to Brown and Princeton, respectively)

Princeton (9th place)
1) Earn 4 points AND Dartmouth earns 1 or fewer points
2) Earn 3 points AND Dartmouth earns 0 points

Rensselaer (9th place)
1) Earn 4 points AND Dartmouth earns 0 points AND Princeton earns 1 or fewer points

Brown (10th place)
1) Earn 4 points AND RPI does not earn 4 points
2) Defeat Princeton AND tie Quinnipiac AND Princeton does not defeat Yale AND RPI earns 2 or fewer points

[burgie12]

The race for a bye:
Colgate (Bye)
1) Earn at least 2 points
2) Earn 1 point AND Clarkson defeats Harvard
3) Earn 1 point AND Clarkson ties Harvard AND Harvard does not defeat SLU on Friday
4) Earn 1 point AND Clarkson ties Harvard AND Harvard defeats SLU on Friday AND Clarkson ties Dartmouth AND Quinnipiac does not earn 4 points
5) Earn 1 point AND Clarkson ties Harvard AND Harvard defeats SLU on Friday AND Clarkson loses to Dartmouth
6) Earn 1 point AND Harvard defeats Clarkson AND SLU defeats Harvard on Friday
7) Earn 1 point AND Harvard defeats Clarkson AND SLU does not defeat Harvard AND Clarkson does not defeat Dartmouth
8) Earn 1 point AND Harvard defeats Clarkson AND SLU does not defeat Harvard AND Quinnipiac does not earn 4 points

Clarkson (Bye)
1) Earn at least 3 points
2) Defeat Harvard AND lose to Dartmouth AND Colgate earns 0 points
3) Defeat Harvard AND lose to Dartmouth AND Quinnipiac does not earn 4 points
4) Tie Harvard AND tie Dartmouth AND Colgate earns 0 points AND Harvard does not defeat SLU
5) Tie Harvard AND tie Dartmouth AND Colgate earns 0 points AND Quinnipiac does not earn 4 points
6) Tie Harvard AND tie Dartmouth AND Harvard does not defeat SLU AND Quinnipiac does not earn 4 points
7) Lose to Harvard AND defeat Dartmouth AND Colgate earns 0 points AND Harvard loses to SLU
8) Lose to Harvard AND defeat Dartmouth AND Colgate earns 0 points AND Quinnipiac does not earn 4 points
9) Lose to Harvard AND defeat Dartmouth AND Harvard loses to SLU AND Quinnipiac does not earn 4 points
10) Tie Harvard AND lose to Dartmouth AND Colgate earns 0 points AND SLU defeats Harvard and Dartmouth
11) Tie Harvard AND lose to Dartmouth AND SLU defeats Harvard and Dartmouth AND Quinnipiac does not earn 4 points
12) Lose to Harvard AND tie Dartmouth AND Colgate earns 0 points AND SLU defeats Harvard and Dartmouth AND Quinnipiac earns 2 or fewer points

Harvard (Bye)
1) Earn 4 points
2) Defeat Clarkson AND tie SLU
3) Tie Clarkson AND defeat SLU AND Colgate earns 1 or fewer points
4) Tie Clarkson AND defeat SLU AND Clarkson does not defeat Dartmouth
5) Defeat Clarkson AND lose to SLU AND Colgate earns at least 1 point AND neither Clarkson nor SLU defeats Dartmouth AND Quinnipiac does not earn 4 points
6) Defeat Clarkson AND lose to SLU AND Colgate earns 0 points AND Clarkson defeats Dartmouth AND SLU does not defeat Dartmouth AND Quinnipiac does not earn 4 points
7) Defeat Clarkson AND lose to SLU AND Colgate earns 0 points AND Clarkson ties Dartmouth
8) Defeat Clarkson AND lose to SLU AND Colgate earns 0 points AND Clarkson loses to Dartmouth AND Quinnipiac does not earn 4 points
9) Defeat Clarkson AND lose to SLU AND Colgate earns 0 points AND Clarkson and SLU lose to Dartmouth

Quinnipiac (Bye)
1) Earn 4 points AND Colgate earns 2 or more points AND Clarkson and Harvard earn 2 or fewer points each
2) Earn 4 points AND Colgate earns 1 point AND Clarkson earns 2 points
3) Earn 4 points AND Colgate earns 1 point AND Clarkson earns 1 or fewer points AND Harvard earns 2 or fewer points
4) Earn 4 points AND Colgate earns 0 points AND Clarkson earns 3 or more points AND Harvard earns 2 or fewer points
5) Earn 4 points AND Colgate earns 0 points AND Clarkson earns 2 or fewer points
6) Earn 3 points AND Colgate earns 1 or more points AND Clarkson ties Harvard AND Clarkson and Harvard lose on Friday AND SLU does not defeat Dartmouth
7) Earn 3 points AND Colgate earns 0 points AND Clarkson ties Harvard AND Clarkson loses to Dartmouth AND St. Lawrence does not earn 4 points

St. Lawrence (Bye)
1) Earn 4 points AND Colgate earns 1 or more points AND Harvard defeats Clarkson AND Clarkson ties Dartmouth AND Quinnipiac earns 3 points
2) Earn 4 points AND Colgate earns 1 or more points AND Harvard defeats Clarkson AND Clarkson loses to Dartmouth AND Quinnipiac does not earn 4 points
3) Earn 4 points AND Colgate earns 0 points AND Harvard defeats Clarkson AND Clarkson defeats Dartmouth AND Quinnipiac does not earn 4 points
4) Earn 4 points AND Colgate earns 0 points AND Harvard defeats Clarkson AND Clarkson loses to Dartmouth
5) Earn 4 points AND Colgate earns 0 points AND Harvard does not defeat Clarkson AND Quinnipiac earns 3 points

The race for home-ice:
Harvard (Home-ice)
1) Earn 1 or more points
2) Dartmouth does not earn 4 points
3) Yale earns 1 or fewer points
4) Quinnipiac earns 1 or fewer points

Quinnipiac (Home-ice)
1) Earn 2 or more points
2) Earn 1 point AND Dartmouth does not earn 4 points
3) Earn 1 point AND Dartmouth earns 4 points AND SLU does not defeat Harvard
4) Tie Yale AND lose to Brown AND Yale loses to Princeton
5) Tie Yale AND lose to Brown AND Yale ties Princeton AND Clarkson does not defeat Harvard
6) Earn 0 points AND Dartmouth earns 4 points AND SLU loses to Harvard
7) Earn 0 points AND Dartmouth defeats Clarkson AND Dartmouth ties SLU AND SLU does not lose to Harvard
8) Earn 0 points AND Dartmouth ties Clarkson AND Dartmouth defeats SLU AND SLU does not tie Harvard
9) Earn 0 points AND Dartmouth earns 2 or fewer points

St. Lawrence (Home-ice)
1) Earn 3 or more points
2) Defeat Dartmouth
3) Tie Dartmouth AND lose to Harvard AND Dartmouth does not defeat Clarkson
4) Tie Dartmouth AND lose to Harvard AND Yale earns 0 points
5) Earn 0 points AND Dartmouth does not lose to Clarkson AND Yale earns 0 points

Yale (Home-ice)
1) Earn 2 or more points
2) Earn 1 point AND Dartmouth does not earn 4 points
3) Earn 1 point AND SLU does not defeat Harvard
4) Earn 0 points AND Dartmouth earns 2 or fewer points

Dartmouth (Home-ice)
It's a mess and my brain is fried. Earn 4 points and you're in. Beat SLU and come into that game two or less points behind them and I can't find a way to keep you out. Otherwise, good luck.

[burgie12]

How would Yale lose a tie-break against Harvard for 4th place? They split the season series, and if they end up tied at 23 pts Harvard would have no more than 7 ECAC wins while the Bulldogs would have 11.

Good call. I originally had it as a three-way tie between Colgate, Yale, and (Clarkson / Harvard). Harvard wins that three-way tiebreaker and would push Yale down to 5th. Yale would finish second in a three-way tie that involved Clarkson (Clarkson loses the three-way on wins and then Colgate wins the head-to-head matchup against Yale on Points vs Top 4) and therefore grab the #4 seed. That was the original intent of my post and then I changed around the words and presented false info. Thank you for catching that.

[sshablak]

Are you serious lol ?
How do you sleep at night ? Or don't you ?

[lugnut92]

Your final "Expected Standings":
1. Union (32)
2. Cornell (31)
3. Colgate (25)
4. Clarkson (24)
-----
5. Harvard (23)
6. Quinnipiac (23)
7. St. Lawrence (21)
8. Yale (21)
-----
9. Dartmouth (19)
10. Princeton (17)
11. Brown (14)
12. RPI (14)

Again, not much difference between the current standings and the projected standings. I say final because there won't be much use in posting them again between games next weekend. I'm sure everyone can figure out who will be favored in a given match-up and figure it out from there.

[burgie12]

Current KRACH Simulation: (57,460 trials, straight 13.2% tie percentage)

------------------------------------------------------------------------------------------------------------
| Team         |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExpPl |
------------------------------------------------------------------------------------------------------------
| Union        | 68.9 | 31.1 |      |      |      |      |      |      |      |      |      |      |  1.31 |
| Cornell      | 31.1 | 68.9 |      |      |      |      |      |      |      |      |      |      |  1.69 |
| Colgate      |      |      | 63.0 | 29.2 |  5.8 |  1.9 |  0.2 |      |      |      |      |      |  3.47 |
| Clarkson     |      |      | 16.4 | 32.3 | 23.2 | 22.2 |  5.3 |  0.6 |      |      |      |      |  4.69 |
| Harvard      |      |      | 18.5 | 21.6 | 20.0 | 20.6 | 11.1 |  7.3 |  0.9 |      |      |      |  5.10 |
| Quinnipiac   |      |      |  1.9 | 13.1 | 29.2 | 26.3 | 16.4 | 12.3 |  0.9 |      |      |      |  5.82 |
| St. Lawrence |      |      |  0.3 |  3.2 | 12.0 | 15.3 | 32.9 | 15.2 | 21.2 |      |      |      |  7.08 |
| Yale         |      |      |      |  0.5 |  9.7 | 13.0 | 27.6 | 43.6 |  5.6 |      |      |      |  7.21 |
| Dartmouth    |      |      |      |      |  0.0 |  0.8 |  6.6 | 21.2 | 60.1 | 11.2 |  0.2 |      |  8.75 |
| Princeton    |      |      |      |      |      |      |      |      | 11.2 | 69.7 | 18.1 |  1.0 | 10.09 |
| Rensselaer   |      |      |      |      |      |      |      |      |  0.1 |  1.0 | 50.1 | 48.8 | 11.48 |
| Brown        |      |      |      |      |      |      |      |      |      | 18.1 | 31.7 | 50.2 | 11.32 |
------------------------------------------------------------------------------------------------------------
ExpPl = Expected Place     Dartmouth finished in 5th place in 10 of 57,460 trials

[lugnut92]

Current KRACH Simulation: (57,460 trials, straight 13.2% tie percentage)

Using this simulation, would it be possible to put together a table of the likelihoods of each potential pairing for first-round matchups? Obviously one way to do it would be the simple (Team A, 5th)*(Team B, 12th)+(Team A, 6th)*(Team B 11th)..., but that could be inaccurate if the scenarios that put A in 5th all required B to take 10th (or something like that). I just ask because I think it would be interesting (and nice to know where I'll be spending that weekend).

[burgie12]

Using this simulation, would it be possible to put together a table of the likelihoods of each potential pairing for first-round matchups?

The simulation is set up to save the place and number of points earned for each team. So, yes, it can. But, I foolishly deleted the info for each of those individual 57,460 trials and just have the overall places.

I will run this again overnight and take the info from those 65,533 runs (65,535 row limit and a 2-row header) and post the expected playoff match-ups.

[lugnut92]

That sounds awesome. Thanks!

[burgie12]

Legend:

T1 = 1st Team (team leading coming in)
T2 = 2nd Team (team trailing coming in)
T3... etc.

Pt = # of points earned by each team when they tie
   XX = # of points / how the tie is earned does not matter
        (tiebreaker is already clinched)
Win = Winning Team
Crit = Criteria
   H2H = Head-to-head points
   Wins = # ECAC Wins
   PvT4 = Points vs Top 4
   PvT8 = Points vs Top 8
   H2HGD = Head-to-head goal differential
   GDvT4 = Goal Differential vs Top 4 teams
   GDvT8 = Goal Differential vs Top 8 teams
T1P = Points earned by Team 1 in *Criteria*
T2P = Points earned by Team 2 in *Criteria*
Other = Other pertinent information to the tie (how the tie is earned)
   "XX-YY" = XX Ties YY
   "XX>YY" = XX Defeats YY
   "XX=T4" = XX will be a Top 4 team
   "XX=T8" = XX will be a Top 8 team
   "XXN" = XX earns exactly N points
   "XXN+" = XX earns N or more points
   "XXN-" = XX earns N or fewer points
   If a tie is already clinched, 
      then the final # of points in *Criteria* may not
      be exactly as listed.  It can also be anything listed in "Other"

Team Abbreviations:

BN = Brown
CK = Clarkson
CG = Colgate
CR = Cornell
DA = Dartmouth
HA = Harvard
PN = Princeton
QN = Quinnipiac
RP = Rensselaer
SL = St. Lawrence
UN = Union
YA = Yale

2-way Tiebreakers:

-----------------------------------------------------------
| T1 | T2 | Pt || Win || Crit |T1P|T2P| Other             |
-----------------------------------------------------------
| UN | CR | 32 ||  CR ||  H2H | 1 | 3 |                   |
| UN | CR | 31 ||  UN || Wins |13 |12 | UN-CR CG>UN CR>RP |
| UN | CR | 31 ||  CR ||  H2H | 1 | 3 | CR>UN CG-UN CR-RP |
| UN | CR | 30 ||  CR ||  H2H | 1 | 3 |                   |
-----------------------------------------------------------
| CG | CK | XX ||  CG || Wins |12 |11 | 12v10 11v10 11v9  |
| CG | HA | XX ||  HA ||  H2H | 1 | 3 |                   |
| CG | QN | XX ||  CG || Wins |11 |10 | 11v9              |
| CG | SL | XX ||  CG || PvT4 | 6 | 0 | 8v4               |
| CG | YA | XX ||  CG || PvT4 | 7 | 6 | 6v4               |
-----------------------------------------------------------
| T1 | T2 | Pt || Win || Crit |T1P|T2P| Other             |
-----------------------------------------------------------
| CK | HA | XX ||  HA ||  H2H | 0 | 4 | 1v3               |
| CK | QN | XX ||  QN ||  H2H | 1 | 3 |                   |
| CK | SL | XX ||  CK ||  H2H | 4 | 0 |                   |
| CK | YA | XX ||  YA || Wins | 9 |10 | 9v11              |
-----------------------------------------------------------
| HA | QN | XX ||  HA ||  H2H | 3 | 1 |                   |
| HA | SL | XX ||  SL ||  H2H | 1 | 3 | 0v4               |
| HA | DA | XX ||  DA || Wins | 6 | 9 |                   |
-----------------------------------------------------------
| T1 | T2 | Pt || Win || Crit |T1P|T2P| Other             |
-----------------------------------------------------------
| QN | SL | XX ||  SL ||  H2H | 0 | 4 |                   |
| QN | YA | 22 ||  QN ||  H2H | 3 | 1 | QN-YA QN-BN YA>PN |
| QN | YA | 22 ||  YA || Wins | 9 |10 | YA>QN QN>BN YA-PN |
| QN | YA | 21 ||  QN ||  H2H | 3 | 1 | QN-YA BN>QN YA-PN |
| QN | YA | 21 ||  YA || Wins | 9 |10 | YA>QN QN-BN PN>YA |
| QN | DA | 21 ||  DA || Wins | 8 | 9 |                   |
| QN | DA | 20 ||  QN || PvT4 | 6 | 3 | BN>QN YA>QN DA-CK |
|    |    |    ||     ||      |   |   | DA>SL CG=T4 CK=T4 |
| QN | DA | 20 ||  QN || PvT4 | 6 | 4 | BN>QN YA>QN DA>CK |
|    |    |    ||     ||      |   |   | DA-SL CG=T4 CK=T4 |
| QN | DA | 20 ||  QN || PvT4 | 5 | 2 | BN>QN YA>QN DA>CK |
|    |    |    ||     ||      |   |   | DA-SL SL>HA HA>CK |
|    |    |    ||     ||      |   |   | YA>PN CG1+        |
| QN | DA | 20 ||  QN || PvT8 |11 | 7 | BN>QN YA>QN DA-CK |
|    |    |    ||     ||      |   |   | DA>SL HA>SL CG=T4 |
|    |    |    ||     ||      |   |   | HA=T4             |
| QN | DA | 20 ||  QN || GDT4 |-7 |-15| BN>QN YA>QN DA>CK |
|    |    |    ||     ||      |   |   | DA-SL CG=T4 HA=T4 |
-----------------------------------------------------------
| T1 | T2 | Pt || Win || Crit |T1P|T2P| Other             |
-----------------------------------------------------------
| SL | YA | XX ||  SL ||  H2H | 3 | 1 |                   |
| SL | DA | XX ||  DA ||  H2H | 1 | 3 | 0v4               |
| SL | PN | XX ||  SL ||  H2H | 4 | 0 |                   |
-----------------------------------------------------------
| YA | DA | XX ||  YA ||  H2H | 4 | 0 |                   |
| YA | PN | XX ||  YA || Wins | 9 | 8 |                   |
-----------------------------------------------------------
| DA | PN | XX ||  DA ||  H2H | 3 | 1 |                   |
| DA | RP | XX ||  RP || PvT4 | 2 | 5 | 4v7 4v5 2v3       |
| DA | BN | XX ||  DA ||  H2H | 4 | 0 |                   |
-----------------------------------------------------------
| T1 | T2 | Pt || Win || Crit |T1P|T2P| Other             |
-----------------------------------------------------------
| PN | RP | XX ||  PN ||  H2H | 4 | 0 |                   |
| PN | BN | 17 ||  BN || PvT4 | 6 | 7 | 6v8 4v9 4v8       |
| PN | BN | 16 ||  PN ||  H2H | 3 | 1 | YA>PN BN>QN BN-PN |
| PN | BN | 16 ||  BN || PvT4 | 6 | 7 | YA-PN BN-QN BN>PN |
|    |    |    ||     ||      |   |   | 6v8 4v9 4v8       |
| PN | BN | 15 ||  BN || PvT4 | 6 | 7 | 6v8 4v9 4v8       |
-----------------------------------------------------------
| RP | BN | XX ||  RP ||  H2H | 4 | 0 |                   |
-----------------------------------------------------------

[burgie12]

The teams that don't win any multi-way tiebreaker will have the tiebreaker restarted with just the remaining teams. For example, in the Colgate / Clarkson / Harvard tie, Harvard wins the three-way tie. Clarkson earned the second-most points between the three teams, but loses the head-to-head tiebreaker against Colgate and would therefore finish third in that tie, not second.
3-way Tiebreakers:

--------------------------------------------------------------------
| T1 | T2 | T3 | Pt || Win || Crit |T1P|T2P|T3P| Other             |
--------------------------------------------------------------------
| CG | CK | HA | XX ||  HA ||  H2H | 3 | 4 | 5 | 3v2v7             |
| CG | CK | QN | XX ||  QN ||  H2H | 4 | 3 | 5 |                   |
| CG | CK | SL | XX ||  CK ||  H2H | 4 | 6 | 2 |                   |
| CG | CK | YA | XX ||CG/YA|| Wins |11 | 9 |11 |                   |
| CG | HA | QN | XX ||  HA ||  H2H | 3 | 6 | 3 |                   |
| CG | HA | SL | XX ||  SL ||  H2H | 3 | 3 | 6 |                   |
| CG | HA | YA | XX ||  HA ||  H2H | 3 | 5 | 4 |                   |
| CG | QN | SL | XX ||  SL ||  H2H | 4 | 2 | 6 |                   |
| CG | SL | YA | XX ||  SL ||  H2H | 4 | 3 | 5 |                   |
--------------------------------------------------------------------
| T1 | T2 | T3 | Pt || Win || Crit |T1P|T2P|T3P| Other             |
--------------------------------------------------------------------
| CK | HA | QN | XX ||  HA ||  H2H | 2 | 4 | 6 | 1v4v7             |
| CK | HA | SL | XX ||  SL || Wins | 9 | 7 |11 |                   |
| CK | HA | YA | XX ||  HA ||  H2H | 3 | 5 | 4 | 2v6v4             |
| CK | QN | SL | XX ||  CK ||  H2H | 5 | 3 | 4 |                   |
| CK | QN | YA | XX ||  QN ||  H2H | 3 | 5 | 4 | 3v6v3             |
--------------------------------------------------------------------
| T1 | T2 | T3 | Pt || Win || Crit |T1P|T2P|T3P| Other             |
--------------------------------------------------------------------
| HA | QN | SL | XX ||  SL ||  H2H | 4 | 1 | 7 | 3v1v8             |
| HA | QN | YA | XX ||  HA ||  H2H | 5 | 4 | 3 | 5v3v4             |
| HA | SL | YA | XX ||  SL ||  H2H | 3 | 6 | 3 | 2v7v3             |
| HA | SL | DA | XX ||  DA ||  H2H | 2 | 4 | 6 |                   |
--------------------------------------------------------------------
| T1 | T2 | T3 | Pt || Win || Crit |T1P|T2P|T3P| Other             |
--------------------------------------------------------------------
| QN | SL | YA | XX ||  SL ||  H2H | 4 | 7 | 1 | 3v7v2 2v7v3       |
| QN | SL | DA | 21 ||  DA ||  H2H | 2 | 4 | 6 |                   |
| QN | SL | DA | 20 ||SL/DA||  H2H | 2 | 5 | 5 | SL-DA DA>CK HA>SL |
|    |    |    |    ||     ||      |   |   |   | BN>QN YA>QN       |
| QN | SL | DA | 20 ||  DA ||  H2H | 2 | 4 | 6 | DA>SL DA-CK SL-HA |
|    |    |    |    ||     ||      |   |   |   | BN>QN YA>QN       |
| QN | YA | DA | 21 ||QN/YA||  H2H | 5 | 2 | 5 | QN-YA BN>QN DA>SL |
|    |    |    |    ||     ||      |   |   |   | DA>CK YA-PN       |
| QN | YA | DA | 21 ||  YA ||  H2H | 4 | 2 | 6 | YA>QN QN-BN DA>SL |
| QN | YA | DA | 21 ||  YA ||  H2H | 4 | 2 | 6 | DA>CK PN>YA       |
--------------------------------------------------------------------
| T1 | T2 | T3 | Pt || Win || Crit |T1P|T2P|T3P| Other             |
--------------------------------------------------------------------
| SL | YA | DA | XX ||  YA ||  H2H | 4 | 5 | 3 | 3v5v4             |
| SL | YA | PN | XX ||  SL ||  H2H | 7 | 3 | 2 |                   |
--------------------------------------------------------------------
| YA | DA | PN | XX ||  YA ||  H2H | 6 | 3 | 3 |                   |
--------------------------------------------------------------------
| DA | PN | RP | XX ||DA/PN||  H2H | 5 | 5 | 2 |                   |
| DA | PN | BN | XX ||  DA ||  H2H | 7 | 3 | 2 |                   |
| DA | RP | BN | XX ||DA/RP||  H2H | 6 | 6 | 0 |                   |
--------------------------------------------------------------------
| PN | RP | BN | XX ||  PN ||  H2H | 6 | 4 | 2 | 7v4v1             |
--------------------------------------------------------------------

4-way Tiebreakers: (H2H is the Criteria in all wins)

-----------------------------------------------------------------
| T1 | T2 | T3 | T4 || Win ||T1P|T2P|T3P|T4P| Other             |
-----------------------------------------------------------------
| CG | CK | HA | QN ||  HA || 5 | 4 | 9 | 6 | 5v3v10v6          |
| CG | CK | HA | SL ||  HA || 5 | 6 | 7 | 6 |                   |
| CG | CK | HA | YA ||  HA || 5 | 5 | 8 | 6 | 5v4v9v6           |
| CG | CK | QN | SL ||  CK || 6 | 7 | 5 | 6 |                   |
| CG | CK | SL | YA ||  CK || 6 | 8 | 5 | 5 |                   |
| CG | HA | QN | SL ||  SL || 5 | 6 | 3 |10 |                   |
-----------------------------------------------------------------
| CK | HA | QN | SL ||  SL || 5 | 7 | 4 | 8 |                   |
| CK | QN | SL | YA ||CK/SL|| 7 | 6 | 7 | 4 | QN-YA QN-BN YA>PN |
|    |    |    |    ||     ||   |   |   |   | leads to QN/YA tie|
|    |    |    |    ||     ||   |   |   |   | at 22 points won  |
|    |    |    |    ||     ||   |   |   |   | by QN on H2H (3-1)|
| CK | QN | SL | YA ||CK/SL|| 7 | 5 | 7 | 5 | QN-YA QN-BN YA>PN |
|    |    |    |    ||     ||   |   |   |   | leads to QN/YA tie|
|    |    |    |    ||     ||   |   |   |   | at 22 points won  |
|    |    |    |    ||     ||   |   |   |   | by YA on Wins     |
|    |    |    |    ||     ||   |   |   |   | (9-10)            |
-----------------------------------------------------------------
| T1 | T2 | T3 | T4 || Win ||T1P|T2P|T3P|T4P| Other             |
-----------------------------------------------------------------
| HA | QN | SL | YA ||  SL || 6 | 3 |10 | 5 | 6v4v10v4 5v3v11v5 |
|    |    |    |    ||     ||   |   |   |   | 5v4v11v4          |
| HA | QN | SL | DA ||SL/DA|| 5 | 3 | 8 | 8 |                   |
| HA | QN | YA | DA ||  YA || 7 | 5 | 8 | 4 | SL>HA CK>HA QN-BN |
|    |    |    |    ||     ||   |   |   |   | YA>QN PN>YA DA>CK |
|    |    |    |    ||     ||   |   |   |   | DA>SL             |
|    |    |    |    ||     ||   |   |   |   | creates a 5-way   |
|    |    |    |    ||     ||   |   |   |   | tie won by SL     |
| HA | QN | YA | DA ||HA/YA|| 7 | 6 | 7 | 4 | SL>HA CK>HA BN>QN |
|    |    |    |    ||     ||   |   |   |   | YA-QN YA-PN DA>CK |
|    |    |    |    ||     ||   |   |   |   | DA>SL             |
|    |    |    |    ||     ||   |   |   |   | creates a 5-way   |
|    |    |    |    ||     ||   |   |   |   | tie won by SL     |
| HA | SL | YA | DA ||SL/YA|| 4 | 7 | 6 | 7 |                   |
-----------------------------------------------------------------
| T1 | T2 | T3 | T4 || Win ||T1P|T2P|T3P|T4P| Other             |
-----------------------------------------------------------------
| QN | SL | YA | DA ||  SL || 5 | 7 | 6 | 6 |                   |
-----------------------------------------------------------------
| SL | YA | DA | PN ||S/Y/D|| 7 | 7 | 7 | 3 |                   |
-----------------------------------------------------------------
| DA | PN | RP | BN ||  DA || 9 | 7 | 6 | 2 |                   |
-----------------------------------------------------------------

5-way Tiebreakers: (H2H is the Criteria in all wins)

-------------------------------------------------------------------
| T1 | T2 | T3 | T4 | T5 || Win ||T1P|T2P|T3P|T4P|T5P| Other      |
-------------------------------------------------------------------
| CG | CK | HA | QN | SL ||HA/SL|| 7 | 7 |10 | 6 |10 |            |
| HA | QN | SL | YA | DA ||  SL || 7 | 5 |11 | 9 | 8 | 7v6v11v8v8 |
-------------------------------------------------------------------

[burgie12]

Potential First-Round Match-ups: (15,491 Trials, straight 13.2% tie chance)

----------------------------------------------------------------------
|    |  HA  |  QN  |  SL  |  YA  |  DA  |  PN  |  RP  |  BN  || HOST |
----------------------------------------------------------------------
| CG |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.3 |  2.5 |  4.5 ||  7.3 |
| CK |  0.0 |  0.0 |  0.0 |  0.0 |  0.6 |  7.7 | 24.3 | 18.9 || 51.5 |
| HA | XXXX |  0.2 |  0.0 |  0.6 |  8.5 | 11.3 | 22.3 | 16.3 || 59.1 |
| QN |  0.0 | XXXX |  0.7 |  0.0 | 12.1 | 17.2 | 23.9 | 30.3 || 84.2 |
| SL |  0.3 |  0.6 | XXXX |  4.1 | 15.2 | 25.2 | 15.3 | 14.7 || 75.5 |
| YA |  0.0 |  0.0 |  0.8 | XXXX | 35.1 | 32.5 | 11.5 | 14.0 || 93.9 |
| DA |  0.7 |  0.1 | 19.4 |  0.9 | XXXX |  5.8 |  0.3 |  1.3 || 28.5 |
----------------------------------------------------------------------
|ROAD|  1.0 |  0.9 | 20.9 |  5.6 | 71.5 |100.0 |100.0 |100.0 ||15491 |
----------------------------------------------------------------------

Every match-up that has a probability of 0.0 did not occur in any of the 15,491 trials. I have no idea if any of them are possible and just didn't happen or actually cannot occur.

The difference between 100% and the sum of "ROAD" and "HOST" is the probability that the team gets a bye.

lugnut, start checking out the hotels in the beautiful metropolis of Potsdam.

[FlagDUDE08]

lugnut, start checking out the hotels in the beautiful metropolis of Potsdam.

Here, I'll make it easy: Stay at the casino just outside Massena. You have a 40% chance of being there, with about the same chances of winning something.

[Ralph Baer]

Potential First-Round Match-ups: (15,491 Trials, straight 13.2% tie chance)

----------------------------------------------------------------------
|    |  HA  |  QN  |  SL  |  YA  |  DA  |  PN  |  RP  |  BN  || HOST |
----------------------------------------------------------------------
| CG |  0.0 |  0.0 |  0.0 |  0.0 |  0.0 |  0.3 |  2.5 |  4.5 ||  7.3 |
| CK |  0.0 |  0.0 |  0.0 |  0.0 |  0.6 |  7.7 | 24.3 | 18.9 || 51.5 |
| HA | XXXX |  0.2 |  0.0 |  0.6 |  8.5 | 11.3 | 22.3 | 16.3 || 59.1 |
| QN |  0.0 | XXXX |  0.7 |  0.0 | 12.1 | 17.2 | 23.9 | 30.3 || 84.2 |
| SL |  0.3 |  0.6 | XXXX |  4.1 | 15.2 | 25.2 | 15.3 | 14.7 || 75.5 |
| YA |  0.0 |  0.0 |  0.8 | XXXX | 35.1 | 32.5 | 11.5 | 14.0 || 93.9 |
| DA |  0.7 |  0.1 | 19.4 |  0.9 | XXXX |  5.8 |  0.3 |  1.3 || 28.5 |
----------------------------------------------------------------------
|ROAD|  1.0 |  0.9 | 20.9 |  5.6 | 71.5 |100.0 |100.0 |100.0 ||15491 |
----------------------------------------------------------------------

Every match-up that has a probability of 0.0 did not occur in any of the 15,491 trials. I have no idea if any of them are possible and just didn't happen or actually cannot occur.

The difference between 100% and the sum of "ROAD" and "HOST" is the probability that the team gets a bye.

lugnut, start checking out the hotels in the beautiful metropolis of Potsdam.

Any special reason for running 15,491 trials?