ECAC Byes and Home-Ice 2011-12

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

Just pretend this was all written after midnight

If things stay nice and quiet here at work, I might have an updated tiebreakers / best-case scenarios post.

Cornell 30 - 32 [1-2]
Union 30 - 32 [1-2]
--- Bye Lock - 25
Harvard 23 - 25 [3-6]
Colgate 23 - 25 [3-6]
Quinnipiac 22 - 24 [3-7]
Clarkson 22 - 24 [3-7]
--- Bye Eligible - 23+
Yale 21 - 23 [5-8]
--- Home Lock - 21+
Dartmouth 19 - 21 [8-9]
St. Lawrence 19 - 23 [7-9]
--- Home Eligible - 19+
Princeton 15 - 19 [10-12]
Rensselaer 15 - 17 [10-11]
Brown 13 - 17 [11-12]

Cornell won last night and holds 1st place because of it.

Harvard won in Cambridge back in November and holds 3rd as a result.

Quinnipiac won the 7-6 shootout a couple weeks back and holds the tiebreaker for 5th place.

Dartmouth won the match-up in Canton in November and has a firm grip on 8th. The two teams will play tonight for the season finale. If they end tied, then the Big Green will win the tiebreaker.

Princeton swept RPI and currently holds 11th place.

Remaining League Schedules:

---------------------------
|              |    |S2/25|
---------------------------
| Cornell      | CR |  RP |
| Union        | UC | @CG |
| Harvard      | HA |  CK |
| Colgate      | CG |  UN |
| Quinnipiac   | QN |  YA |
| Clarkson     | CK | @HA |
| Yale         | YA | @QN |
| Dartmouth    | DA |  SL |
| St. Lawrence | SL | @DA |
| Princeton    | PN |  BN |
| Rensselaer   | RP | @CR |
| Brown        | BN | @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:
Cornell and Union will duke it out to the last day. Cornell now firmly holds the tiebreaker. The Dutchmen will need to earn more points than the Big Red to take the #1 seed.

Harvard can only fall to 6th place. They can be passed by Colgate and Clarkson and either Quinnipiac or Yale, but not both. So, the Crimson have clinched a home-ice spot (seems strange to be saying that on the next-to-last night of the regular season about the team in 3rd place). A win guarantees them 3rd place. There are a number of other scenarios that will still land the Crimson in 3rd.

Colgate is in the same position as Harvard (but they no longer control their own destiny for 3rd, they would need help from Clarkson). They can fall to 7th, but cannot fall further because Quinnipiac and Yale play each other tonight in the battle of the valley (or whatever they call it down there).

Quinnipiac and Clarkson can be passed outright all the way down to 7th place. They can also climb up to 3rd with some help. Neither team holds the tiebreaker over Colgate and Quinnipiac does not hold a tiebreaker over Harvard (Clarkson cannot finish the season tied in points with Harvard). A three-way Qpac / Colgate / Clarkson tie would break in that order.

Yale holds the tiebreaker over Dartmouth, but not over SLU. So, if the Bulldogs lose to Quinnipiac and the Saints beat Dartmouth, Yale can find themselves in 8th place. On the flip side, Yale cannot finish with the #4 seed. The Crimson did not hold up their end of the bargain and did not lose tonight against SLU. The Elis can only climb up to 5th, at best.

Dartmouth and St. Lawrence can not be caught by Princeton, so they each have a floor of 9th place. A Dartmouth victory or tie will give them 8th place and means that the teams don't even need to go back home, there will be a rematch in the same place next weekend. A St. Lawrence victory gives them home-ice, but does not necessarily mean that it will be a rematch in Canton. The Big Green might have to go to New Haven and face Yale, instead.

Princeton can fall to 12th place if RPI gains at least a point in Ithaca and Brown wins the match-up between the Tigers and Bears tonight. Princeton cannot catch anybody ahead of them, and so are guaranteed to finish no higher than 10th.

RPI swept Brown and therefore can't finish in the basement. The Engineers also will not win a tiebreaker against Princeton, so they'll have to earn more points against Cornell than the Tigers do against Brown to finish in 10th.

Brown cannot win a tiebreaker against RPI, so can only climb as high as 11th.

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. 25 points (a win by either Colgate or Harvard) is enough to assure themselves a spot in the Top 4. A win by Quinnipiac or Clarkson is not enough. They will need help from the opponents of the teams around them to grab a bye.

Bye Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 4. Colgate can still lose and find themselves with a guaranteed pair of games the weekend of March 9th. However, they would need a Harvard win (over Clarkson) and a Quinnipiac tie (against Yale). (For the record, Harvard can also finish with the #4 seed with a loss tonight, as long as Colgate loses and Quinnipiac does not win.) Since Yale cannot finish in the Top 4 and they can get to 23 points, the plus symbol has to be added in.

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. You no longer need those fancy "tiebreakers" to have another pair of home games, as long as you have 21 points.

Home Eligible - The number of points that a team can achieve and still have the possibility of finishing in the Top 8. This moves down to 20 points plus tiebreakers since the Dartmouth-SLU game could end in a tie and one of them would have to grab home-ice.

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

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 | XX ||  CR ||  H2H | 1 | 3 |                   |
-----------------------------------------------------------
| HA | CG | XX ||  HA ||  H2H | 3 | 1 |                   |
| HA | QN | XX ||  HA ||  H2H | 3 | 1 |                   |
| HA | YA | XX ||  YA || Wins | 7 |11 |                   |
-----------------------------------------------------------
| CG | QN | XX ||  CG || Wins |11 |10 | 11v9              |
| CG | CK | XX ||  CG || Wins |11 |10 | 11v9              |
| CG | YA | XX ||  CG || PvT4 | 7 | 6 | 5v4               |
-----------------------------------------------------------
| QN | CK | XX ||  QN ||  H2H | 3 | 1 |                   |
-----------------------------------------------------------
| CK | YA | XX ||  YA || Wins | 9 |10 | 9v11              |
-----------------------------------------------------------
| YA | DA | XX ||  YA ||  H2H | 4 | 0 |                   |
| YA | SL | XX ||  SL ||  H2H | 1 | 3 |                   |
-----------------------------------------------------------
| DA | SL | XX ||  DA ||  H2H | 3 | 1 |                   |
-----------------------------------------------------------
| PN | RP | XX ||  PN ||  H2H | 4 | 0 |                   |
| PN | BN | XX ||  BN || PvT4 | 6 | 7 | 6v8 4v7 4v8       |
-----------------------------------------------------------
| RP | BN | XX ||  RP ||  H2H | 4 | 0 |                   |
-----------------------------------------------------------

The teams that don't win any multi-way tiebreaker will have the tiebreaker restarted with just the remaining teams. For example, in the Harvard / Colgate / Yale tie, Harvard wins the three-way tie. Yale 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|
------------------------------------------------
| HA | CG | QN | XX ||  HA ||  H2H | 6 | 3 | 3 |
| HA | CG | YA | XX ||  HA ||  H2H | 5 | 3 | 4 |
------------------------------------------------
| CG | QN | CK | XX ||  QN ||  H2H | 4 | 5 | 3 |
| CG | CK | YA | XX ||CG/YA|| Wins |11 | 9 |11 |
------------------------------------------------
| PN | RP | BN | XX ||  PN ||  H2H | 6 | 4 | 2 |
------------------------------------------------

[lugnut92]

Re: ECAC Byes and Home-Ice 2011-12

Any way you can do the projected pairings again? I imagine running the 729 possibilities wouldn't take too long...

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

I finally listened to myself and did the tiebreaker post first.

Best-case scenarios:
Cornell (1st place)
1) Earn at least as many points against RPI as Union does against Colgate.

Union (1st place)
1) Earn more points against Colgate than Cornell does against RPI

Harvard (3rd place)
1) Win
2) Tie AND Colgate does NOT win

Colgate (3rd place)
1) Win AND Harvard does NOT win
2) Tie AND Harvard loses AND Quinnipiac does NOT win

Quinnipiac (3rd place)
1) Win AND Harvard loses AND Colgate does NOT win

Clarkson (3rd place)
1) Win AND Colgate loses AND Quinnipiac does NOT win
Note: That means that Clarkson cannot tie for 3rd place and still finish with the #3 seed. They must win it outright.

Yale (5th place)
1) Win AND Harvard does NOT lose
2) Win AND Colgate does NOT lose
Note: Yale takes the #5 seed with a win as long as it is not a 3-way tie for 4th between Harvard, Colgate, and Yale (Harvard takes the final bye spot after Clarkson took the #3 seed and Colgate wins the head-to-head to finish in 5th). Any other scenario where Yale gets to 23 points puts them in the #5 spot.

Dartmouth (8th place)
1) Win
2) Tie

St. Lawrence (7th place)
1) Win AND Yale loses

Princeton (10th place)
1) Earn at least as many points against Brown as RPI does against Cornell

Rensselaer (10th place)
1) Earn more points against Cornell as Princeton does against Brown

Brown (11th place)
1) Win AND RPI earns at least a point against Cornell

The race for the bye:
Harvard (Bye)
1) Earn at least a tie against Clarkson
2) Lose to Clarkson AND Colgate loses to Union AND Quinnipiac does NOT win against Yale

Colgate (Bye)
1) Earn at least a tie against Union
2) Lose to Union AND Clarkson ties Harvard AND Quinnipiac loses to Yale
3) Lose to Union AND Clarkson loses to Harvard AND Quinnipiac does NOT beat Yale

Quinnipiac (Bye)
1) Win AND Harvard wins or ties AND Colgate loses
2) Win AND Harvard loses

Clarkson (Bye)
1) Win AND Colgate wins or ties AND Quinnipiac does NOT win
2) Win AND Colgate loses

Other Interesting Scenarios:
St. Lawrence (Home-ice)
1) Win

Princeton (11th place)
1) Tie AND RPI wins against Cornell

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

I'm going to keep it as a Monte Carlo for now. During the off-season I'm going to take a serious look at changing how to predict ties with KRACH (or another ranking system) and making this in a different programming language (so that I can do this without Excel and so I can significantly speed this up).

Also, these stats are going to be slightly off because I originally had the KRACH ratings assuming that North Dakota and Alaska would both hold on to win. But, UAA won the first game of their series with UA_. That changes the KRACHs slightly, but not to an extreme degree. Hopefully, that didn't change the percentages too much.

Current KRACH Simulation: (2,500 trials, straight 13.27% tie percentage)

------------------------------------------------------------------------------------------------------------
| Team         |  1st |  2nd |  3rd |  4th |  5th |  6th |  7th |  8th |  9th | 10th | 11th | 12th | ExpPl |
------------------------------------------------------------------------------------------------------------
| Cornell      | 83.8 | 16.2 |      |      |      |      |      |      |      |      |      |      |  1.16 |
| Union        | 16.2 | 83.8 |      |      |      |      |      |      |      |      |      |      |  1.84 |
| Harvard      |      |      | 62.7 | 14.1 | 11.9 | 11.3 |      |      |      |      |      |      |  3.72 |
| Colgate      |      |      | 15.4 | 43.1 | 31.9 |  9.6 |      |      |      |      |      |      |  4.36 |
| Quinnipiac   |      |      | 11.9 | 26.3 | 22.6 | 22.2 | 17.0 |      |      |      |      |      |  5.06 |
| Clarkson     |      |      | 10.0 | 16.5 |  6.8 | 42.0 | 24.8 |      |      |      |      |      |  5.55 |
| Yale         |      |      |      |      | 26.8 | 15.0 | 33.3 | 24.9 |      |      |      |      |  6.56 |
| Dartmouth    |      |      |      |      |      |      |      | 52.3 | 47.7 |      |      |      |  8.48 |
| St. Lawrence |      |      |      |      |      |      | 24.9 | 22.8 | 52.3 |      |      |      |  8.27 |
| Princeton    |      |      |      |      |      |      |      |      |      | 88.9 |  1.7 |  9.4 | 10.20 |
| Rensselaer   |      |      |      |      |      |      |      |      |      | 11.1 | 88.9 |      | 10.89 |
| Brown        |      |      |      |      |      |      |      |      |      |      |  9.4 | 90.6 | 11.91 |
------------------------------------------------------------------------------------------------------------
ExpPl = Expected Place

SLU is not favored in their game against Dartmouth, but have a better "Expected Place" than Dartmouth because half the time SLU beats Dartmouth, Yale loses to Quinnipiac, too.

There were 37 instances where Union tied Colgate but still got the #1 seed. 1098 of the 2500 trials had both Union and Cornell winning.

Colgate is the team favored to finish in both 4th and 5th place, meaning that Quinnipiac is not favored to finish anywhere.


Potential First-Round Match-ups: (2,500 trials, straight 13.27% tie percentage)

-------------------------------------------------
|    |  DA  |  SL  |  PN  |  RP  |  BN  || HOST |
-------------------------------------------------
| HA |      |      |  1.3 | 10.0 | 11.9 || 23.2 |
| CG |      |      |  3.2 |  8.6 | 29.7 || 41.4 |
| QN |      |      | 17.8 | 21.0 | 23.0 || 61.8 |
| CK |      |      | 23.5 | 39.9 | 10.2 || 73.6 |
| YA | 24.9 |      | 32.4 | 17.4 | 25.2 ||100.0 |
| DA | XXXX | 52.3 |      |      |      || 52.3 |
| SL | 22.8 | XXXX | 21.9 |  3.0 |      || 47.7 |
-------------------------------------------------
|ROAD| 47.7 | 52.3 |100.0 |100.0 |100.0 || 2500 |
-------------------------------------------------

I am certain that the (HA/CG/QN/CK) vs (DA/SL), YA vs SL, DA vs (PN/RP/BN), SL vs BN match-ups are not possible. All of the other potential match-ups occurred at least 33 times.

Again, the hosting team is on the left and the road team is on top. The difference between 100% and the sum of ROAD and HOST is the probability that the team wins a bye.

[lugnut92]

Re: ECAC Byes and Home-Ice 2011-12

Thanks. I would give you rep, but the system won't let me. I really don't want to go to Clarkson next weekend...

[aweise]

Re: ECAC Byes and Home-Ice 2011-12

Before I forget....thanks for doing this, burgle. Your incessant number-crunching makes me envious.

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

I suppose there should be a end-of-season summation post.

Congratulations go to Union on their back-to-back Cleary Cups.

Union 32 [1]
Cornell 30 [2]
Harvard 25 [3]
Colgate 23 [4]
--- Bye ---
Quinnipiac 23 [5]
Yale 22 [6]
Clarkson 22 [7]
St. Lawrence 21 [8]
--- Home-Ice ---
Dartmouth 19 [9]
Rensselaer 17 [10]
Princeton 16 [11]
Brown 14 [12]

Colgate and Quinnipiac split the season series which allows Colgate to win the tiebreaker on ECAC wins (11 vs 9).

Yale and Clarkson also split the season series and Yale wins the tiebreaker on ECAC wins as well (10 vs 9).



Union gets some help from their travel partner and gets to be the #1 seed for the ECAC Playoffs for the second consecutive season.

Harvard earns their way into the #3 seed with last night's win over Clarkson.

Colgate backs their way in with losses in each of their last four games, but earned enough points early in the season to finish in the Top 4.

Your ECAC Playoff Match-ups:

-----------------------------------------------------------------------------
| H |   Home Team  | Last6 | A | Away Team  | Last6 | @H (Date) | @A (Date) |
-----------------------------------------------------------------------------
| 5 | Quinnipiac   | 3-2-1 |12 | Brown      | 0-4-2 | 4-1 02/24 | 2-2 01/07 |
| 6 | Yale         | 3-2-1 |11 | Princeton  | 1-4-1 | 6-2 01/07 | 5-2 02/24 |
| 7 | Clarkson     | 2-3-1 |10 | Rensselaer | 3-2-1 | 4-1 11/04 | 3-2 01/28 |
| 8 | St. Lawrence | 5-1-0 | 9 | Dartmouth  | 2-4-0 | 1-3 11/18 | 3-1 02/25 |
-----------------------------------------------------------------------------

SLU was the only team to lose a game against their first-round opponent.
Quinnipiac also lost a point by tying the Bears in January.

There will be a post up later this week giving the probability that each team wins each series and whether it's a sweep or a 3-game series. Of course, it's going to be severly flawed because it won't be able to take home-ice and momentum into the equation, but it'll be the best that I can generate.

In the meantime, celebrate (or commiserate) and look forward to some excellent hockey next weekend.

[LTsatch]

Re: ECAC Byes and Home-Ice 2011-12

Nice job to both Burgie and Lugnut, great fun.

[Veritas]

Re: ECAC Byes and Home-Ice 2011-12

Gentlemen:

An amazing thread!

I must add that it does bring back memories (nightmares) of grad school in the mid-80's when I spent an entire semester crunching the NATO order of battle against the Warsaw Pact forces using derivatives of the Lanchester Equations. Started using a HP scientific calculator. Then bought a IBM PC-AT and VisiCalc with a classmate teaching me how to create a template of Lanchester in VisiCalc. Nearly went mad.

Thanks for doing all of that work!!!

[rdf8585]

Re: ECAC Byes and Home-Ice 2011-12

Count me as another one who appreciates burgie12's work. I checked this thread often throughout the past several weeks.

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

Warning: Here be maths!

Although, honestly, if it took you this long to figure out that there would be math in this thread, you have bigger problems.

(Link to spreadsheet) Currently, there are about a million and a half sorting criteria on the "Quarterfinal Totals" sheet, so that will throw some kind of error / warning / something if you open the spreadsheet in Excel 03. Also, this is kinda just thrown together and ugly, so there are all kinds of random formulas off to the side and tons and tons of summing to make sure that everything is coming in where I expect it to. And, the macro is super, super ugly. I would recommend not looking at it unless you want to shake your head shamefully at me for coding very, very poorly.

The odds can be calculated on the teams' current KRACH ratings or the teams' current ECAC Bradley-Terry Ratings (which are more useful when the season hasn't been finished yet. Honestly, they're no better than the current standings right now.)

If there's someone that can help me with some maths with which I'm having an issue, that'd be cool. Here's what I mean: In order for #2 Cornell to host #12 Brown in Atlantic City, Brown has to beat Quinnipiac (18.29% chance) and then also beat Union (7.33% chance) and Cornell has to advance past their quarterfinal opponent, whomever it may be. Now, obviously, Cornell can't play Clarkson, because then Harvard would have to play Yale, which means that Colgate would have to play Quinnipiac, who obviously didn't make it to the quarters. So, despite the fact that Cornell has a 78.63% chance of advancing to the semis, we can take out the scenarios where they advance over Clarkson. That reduces it to 52.43% chance. (0.1829) * (0.0733) * (0.5243) = 0.70% Now, we can assume that there will be something else that I haven't taken into account which will lower this slightly, right? I mean, clearly, I didn't take everything into effect. But, when I sum up the probability of each of the individual cases, I get an answer of 0.019%. That's a little too much error for my liking.

In fact, this happens with every potential scenario. And, yes, I understand why this is happening. I just didn't expect it to be off by a factor of 4. And, the factor changes depending on the odds of the different first round match-ups. Again, I understand why the factor will change depending on the first round match-up odds. I'd just like a better way of dealing with the inaccuracies of the "model" that I tried to use.

Anyways, the sum of the semifinal scenarios is only 49%, while we expect a number of 200% (because there are two semis). So, all of the semifinal scenarios that you see reported are the percentage of the odds (if that makes sense).

Required example: Remember that 0.019% you saw in the potential 2v12 semifinal pairing? It shows up as 0.078% in the chart because every single scenario is multiplied by 4.09 to make the sum of all of the scenarios equal to 200%.

[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

With all of that out of the way, here's the reason why you showed up in the thread:

This is straight maths, no Monte Carlo simulation.

Team i's probability of winning a game against Team j is Rating(i) / [Rating(i) + Rating(j)]. There is no possibility of a tie. Ratings are not recalculated after a day of games, so "momentum" is completely ignored.

Since KRACH is not being recalculated with the conclusion of each game, the chance of winning Game 1 of your series will be the same as the chance of winning Game 2 or 3. That helps make calculations a tiny bit easier.

All values presented are percentages.

Current Ratings:

-------------------------------------
|  # |     Team     | KRACH |  ECAC |
-------------------------------------
|  1 | Union        | 192.8 | 254.1 |
|  2 | Cornell      | 146.4 | 207.3 |
|  3 | Harvard      | 109.5 | 130.3 |
|  4 | Colgate      |  99.0 | 109.2 |
|  5 | Quinnipiac   | 102.0 | 109.2 |
|  6 | Yale         |  71.5 | 100.0 |
|  7 | Clarkson     |  67.4 | 100.0 |
|  8 | St. Lawrence |  73.2 |  91.6 |
|  9 | Dartmouth    |  56.5 |  76.8 |
| 10 | Rensselaer   |  42.0 |  64.2 |
| 11 | Princeton    |  50.9 |  58.5 |
| 12 | Brown        |  38.3 |  48.4 |
-------------------------------------

First Round Outcome Probabilities: (KRACH)

------------------------------------------------------------------------------------------------------
|       Home       |       Away      |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |
------------------------------------------------------------------------------------------------------
| # |     Team     |  # |     Team   |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |
------------------------------------------------------------------------------------------------------
| 5 | Quinnipiac   | 12 | Brown      | 72.70 \ 27.30 | 52.85 \  7.45 | 28.86 \ 10.84 | 81.71 \ 18.29 |
| 6 | Yale         | 11 | Princeton  | 58.42 \ 41.58 | 34.12 \ 17.29 | 28.38 \ 20.20 | 62.50 \ 37.50 |
| 7 | Clarkson     | 10 | Rensselaer | 61.61 \ 38.39 | 37.96 \ 14.74 | 29.14 \ 18.16 | 67.10 \ 32.90 |
| 8 | St. Lawrence |  9 | Dartmouth  | 56.44 \ 43.56 | 31.85 \ 18.98 | 27.75 \ 21.42 | 59.60 \ 40.40 |
------------------------------------------------------------------------------------------------------

First Round Outcome Probabilities: (ECAC B-T Ratings)

------------------------------------------------------------------------------------------------------
|       Home       |       Away      |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |
------------------------------------------------------------------------------------------------------
| # |     Team     |  # |     Team   |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |
------------------------------------------------------------------------------------------------------
| 5 | Quinnipiac   | 12 | Brown      | 69.31 \ 30.69 | 48.03 \  9.42 | 29.49 \ 13.06 | 77.52 \ 22.48 |
| 6 | Yale         | 11 | Princeton  | 63.09 \ 36.91 | 39.81 \ 13.62 | 29.38 \ 17.19 | 69.19 \ 30.81 |
| 7 | Clarkson     | 10 | Rensselaer | 60.90 \ 39.10 | 37.09 \ 15.29 | 29.00 \ 18.62 | 66.09 \ 33.91 |
| 8 | St. Lawrence |  9 | Dartmouth  | 54.39 \ 45.61 | 39.59 \ 20.80 | 26.99 \ 22.63 | 56.57 \ 43.43 |
------------------------------------------------------------------------------------------------------

Resulting Quarterfinal Match-ups: (KRACH)

----------------------------------------------------------------------------------
| Quarter |   5   |   6   |   7   |   8   |   9   |  10   |  11   |  12   | HOST |
----------------------------------------------------------------------------------
|    1    |       |       |       | 20.43 | 13.84 | 16.80 | 30.64 | 18.29 | 100.0|
|    2    |       |       | 34.27 | 26.84 | 18.19 | 13.84 |  6.86 |       | 100.0|
|    3    |       | 51.07 | 28.23 | 10.99 |  7.45 |  2.26 |       |       | 100.0|
|    4    | 81.71 | 11.43 |  4.60 |  1.34 |  0.91 |       |       |       | 100.0|
----------------------------------------------------------------------------------
|   ROAD  | 81.71 | 62.50 | 67.10 | 59.60 | 40.40 | 32.90 | 37.50 | 18.29 |      |
----------------------------------------------------------------------------------

Resulting Quarterfinal Match-ups: (ECAC B-T Ratings)

----------------------------------------------------------------------------------
| Quarter |   5   |   6   |   7   |   8   |   9   |  10   |  11   |  12   | HOST |
----------------------------------------------------------------------------------
|    1    |       |       |       | 20.06 | 15.39 | 18.19 | 23.89 | 22.48 | 100.0|
|    2    |       |       | 35.45 | 25.04 | 19.22 | 13.37 |  6.93 |       | 100.0|
|    3    |       | 53.64 | 26.07 | 10.16 |  7.79 |  2.35 |       |       | 100.0|
|    4    | 77.52 | 15.55 |  4.58 |  1.33 |  1.02 |       |       |       | 100.0|
----------------------------------------------------------------------------------
|   ROAD  | 77.52 | 69.19 | 66.09 | 56.57 | 43.43 | 33.91 | 30.81 | 22.48 |      |
----------------------------------------------------------------------------------

"Likelihood" refers to the probability that the First Round series finish in a manner that will result in the shown Quarterfinal match-up
"Overall" is just "Advances" times "Likelihood"
Quarterfinal Outcome Probabilities: (KRACH)

--------------------------------------------------------------------------------------------------------------------------------
|     Home    |        Away       |  Game Winner  |  Series Sweep | 3-game Series |    Advances   |            |    Overall    |
--------------------------------------------------------------------------------------------------| Likelihood |----------------
| # |   Team  |  # |     Team     |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |            |  Home \  Away |
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| 1 | Union   | 12 | Brown        | 83.43 \ 16.57 | 69.60 \  2.75 | 23.07 \  4.58 | 92.67 \  7.33 |    18.29   | 16.95 \  1.34 |
| 1 | Union   | 11 | Princeton    | 79.11 \ 20.89 | 62.59 \  4.36 | 26.15 \  6.90 | 88.74 \ 11.26 |    30.64   | 27.19 \  3.45 |
| 1 | Union   | 10 | Rensselaer   | 82.11 \ 17.89 | 67.42 \  3.20 | 24.12 \  5.25 | 91.55 \  8.45 |    16.80   | 15.38 \  1.42 |
| 1 | Union   |  9 | Dartmouth    | 77.34 \ 22.66 | 59.81 \  5.14 | 27.11 \  7.94 | 86.92 \ 13.08 |    13.84   | 12.03 \  1.81 |
| 1 | Union   |  8 | St. Lawrence | 72.48 \ 27.52 | 52.54 \  7.57 | 28.91 \ 10.98 | 81.45 \ 18.55 |    20.43   | 16.64 \  3.79 |
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| 2 | Cornell | 11 | Princeton    | 74.20 \ 25.80 | 55.06 \  6.66 | 28.41 \  9.88 | 83.47 \ 16.53 |     6.86   |  5.72 \  1.13 |
| 2 | Cornell | 10 | Rensselaer   | 77.71 \ 22.29 | 60.38 \  4.97 | 26.92 \  7.72 | 87.31 \ 12.69 |    13.84   | 12.08 \  1.76 |
| 2 | Cornell |  9 | Dartmouth    | 72.15 \ 27.85 | 52.06 \  7.75 | 28.99 \ 11.19 | 81.06 \ 18.94 |    18.19   | 14.75 \  3.45 |
| 2 | Cornell |  8 | St. Lawrence | 66.67 \ 33.33 | 44.44 \ 11.11 | 29.63 \ 14.81 | 74.07 \ 25.93 |    26.84   | 19.88 \  6.96 |
| 2 | Cornell |  7 | Clarkson     | 68.48 \ 31.52 | 46.89 \  9.94 | 29.56 \ 13.61 | 76.45 \ 23.55 |    34.27   | 26.20 \  8.07 |
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| 3 | Harvard | 10 | Rensselaer   | 72.28 \ 27.72 | 52.24 \  7.69 | 28.96 \ 11.11 | 81.20 \ 18.80 |     2.26   |  1.83 \  0.42 |
| 3 | Harvard |  9 | Dartmouth    | 65.96 \ 34.04 | 43.51 \ 11.58 | 29.62 \ 15.28 | 73.13 \ 26.87 |     7.45   |  5.45 \  2.00 |
| 3 | Harvard |  8 | St. Lawrence | 59.93 \ 40.07 | 35.92 \ 16.05 | 28.78 \ 19.24 | 64.71 \ 35.29 |    10.99   |  7.11 \  3.88 |
| 3 | Harvard |  7 | Clarkson     | 61.90 \ 38.10 | 38.32 \ 14.52 | 29.20 \ 17.97 | 67.51 \ 32.49 |    28.23   | 19.06 \  9.17 |
| 3 | Harvard |  6 | Yale         | 60.50 \ 39.50 | 36.60 \ 15.60 | 28.92 \ 18.88 | 65.51 \ 34.49 |    51.07   | 33.46 \ 17.61 |
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| 4 | Colgate |  9 | Dartmouth    | 63.67 \ 36.33 | 40.53 \ 13.20 | 29.45 \ 16.81 | 69.99 \ 30.01 |     0.91   |  0.64 \  0.27 |
| 4 | Colgate |  8 | St. Lawrence | 57.49 \ 42.51 | 33.05 \ 18.07 | 28.10 \ 20.78 | 61.15 \ 38.85 |     1.34   |  0.82 \  0.52 |
| 4 | Colgate |  7 | Clarkson     | 59.50 \ 40.50 | 35.40 \ 16.41 | 28.67 \ 19.52 | 64.07 \ 35.93 |     4.60   |  2.95 \  1.65 |
| 4 | Colgate |  6 | Yale         | 58.06 \ 41.94 | 33.71 \ 17.59 | 28.28 \ 20.42 | 61.99 \ 38.01 |    11.43   |  7.09 \  4.34 |
| 4 | Colgate |  5 | Quinnipiac   | 49.25 \ 50.75 | 24.26 \ 25.75 | 24.62 \ 25.37 | 48.88 \ 51.12 |    81.71   | 39.94 \ 41.77 |
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[burgie12]

Re: ECAC Byes and Home-Ice 2011-12

Quarterfinal Outcome Probabilities: (ECAC B-T Ratings)

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|     Home    |        Away       |    Any Game   |  Series Sweep | 3-game Series |    Advances   |            |    Overall    |
--------------------------------------------------------------------------------------------------| Likelihood |----------------
| # |   Team  |	 # |     Team     |  Home \  Away |  Home \  Away |  Home \  Away |  Home \  Away |            |  Home \  Away |
--------------------------------------------------------------------------------------------------------------------------------
| 1 | Union   | 12 | Brown        | 84.01 \ 15.99 | 70.58 \  2.56 | 22.57 \  4.30 | 93.15 \  6.85 |    22.48   | 20.94 \  1.54 |
| 1 | Union   | 11 | Princeton    | 81.29 \ 18.71 | 66.07 \  3.50 | 24.73 \  5.69 | 90.80 \  9.20 |    23.89   | 21.69 \  2.20 |
| 1 | Union   | 10 | Rensselaer   | 79.83 \ 20.17 | 63.73 \  4.07 | 25.71 \  6.50 | 89.44 \ 10.56 |    18.19   | 16.27 \  1.92 |
| 1 | Union   |  9 | Dartmouth    | 76.79 \ 23.21 | 58.97 \  5.39 | 27.37 \  8.27 | 86.34 \ 13.66 |    15.39   | 13.29 \  2.10 |
| 1 | Union   |  8 | St. Lawrence | 73.50 \ 26.50 | 54.03 \  7.02 | 28.63 \ 10.32 | 82.66 \ 17.34 |    20.06   | 16.58 \  3.48 |
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| 2 | Cornell | 11 | Princeton    | 77.99 \ 22.01 | 60.83 \  4.84 | 26.77 \  7.56 | 87.60 \ 12.40 |     6.93   |  6.07 \  0.86 |
| 2 | Cornell | 10 | Rensselaer   | 76.35 \ 23.65 | 58.30 \  5.59 | 27.57 \  8.54 | 85.87 \ 14.13 |    13.37   | 11.48 \  1.89 |
| 2 | Cornell |  9 | Dartmouth    | 72.97 \ 27.03 | 53.24 \  7.31 | 28.79 \ 10.66 | 82.03 \ 17.97 |    19.22   | 15.76 \  3.45 |
| 2 | Cornell |  8 | St. Lawrence | 69.35 \ 30.65 | 48.10 \  9.39 | 29.48 \ 13.03 | 77.58 \ 22.42 |    25.04   | 19.42 \  5.61 |
| 2 | Cornell |  7 | Clarkson     | 67.46 \ 32.54 | 45.51 \ 10.59 | 29.62 \ 14.29 | 75.12 \ 24.88 |    35.45   | 26.63 \  8.82 |
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| 3 | Harvard | 10 | Rensselaer   | 66.99 \ 33.01 | 44.88 \ 10.90 | 29.63 \ 14.60 | 74.51 \ 25.49 |     2.35   |  1.75 \  0.60 |
| 3 | Harvard |  9 | Dartmouth    | 62.92 \ 37.08 | 39.58 \ 13.75 | 29.36 \ 17.30 | 68.94 \ 31.06 |     7.79   |  5.37 \  2.42 |
| 3 | Harvard |  8 | St. Lawrence | 58.72 \ 41.28 | 34.48 \ 17.04 | 28.47 \ 20.01 | 62.95 \ 37.05 |    10.16   |  6.39 \  3.76 |
| 3 | Harvard |  7 | Clarkson     | 56.58 \ 43.42 | 32.01 \ 18.85 | 27.80 \ 21.33 | 59.81 \ 40.19 |    26.07   | 15.59 \ 10.48 |
| 3 | Harvard |  6 | Yale         | 56.58 \ 43.42 | 32.01 \ 18.85 | 27.80 \ 21.33 | 59.81 \ 40.19 |    53.64   | 32.08 \ 21.56 |
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| 4 | Colgate |  9 | Dartmouth    | 58.71 \ 41.29 | 34.47 \ 17.05 | 28.46 \ 20.02 | 62.93 \ 37.07 |     1.02   |  0.64 \  0.38 |
| 4 | Colgate |  8 | St. Lawrence | 54.38 \ 45.62 | 29.57 \ 20.81 | 26.98 \ 22.63 | 56.56 \ 43.44 |     1.33   |  0.75 \  0.58 |
| 4 | Colgate |  7 | Clarkson     | 52.20 \ 47.80 | 27.25 \ 22.85 | 26.05 \ 23.85 | 53.30 \ 46.70 |     4.58   |  2.44 \  2.14 |
| 4 | Colgate |  6 | Yale         | 52.20 \ 47.80 | 27.25 \ 22.85 | 26.05 \ 23.85 | 53.30 \ 46.70 |    15.55   |  8.29 \  7.26 |
| 4 | Colgate |  5 | Quinnipiac   | 50.00 \ 50.00 | 25.00 \ 25.00 | 25.00 \ 25.00 | 50.00 \ 50.00 |    77.52   | 38.76 \ 38.76 |
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Resulting Semifinal Match-ups: (KRACH)

----------------------------------------------------------------------------------------------------
| Semis |   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |  11  |  12  | HOST |
----------------------------------------------------------------------------------------------------
|   1   |      |      |      |11.049|11.122| 7.810| 7.103| 4.243| 2.111| 0.321| 0.007|      |43.765|
|   2   |      |      |22.425| 5.624| 5.675| 0.117| 0.004| 1.697| 0.811| 0.841| 1.386| 0.078|38.657|
|   3   |      |      |      | 4.796| 4.865| 0.086| 0.002| 0.342| 0.164| 0.165| 0.254| 0.014|10.690|
|   4   |      |      |      |      |      | 1.692| 0.910| 0.285| 0.141| 0.056| 0.060| 0.004| 3.149|
|   5   |      |      |      |      |      | 1.769| 0.890| 0.286| 0.141| 0.058| 0.062|      | 3.207|
|   6   |      |      |      |      |      |      | 0.303| 0.065| 0.032| 0.001|      | 0.003| 0.402|
|   7   |      |      |      |      |      |      |      | 0.078| 0.039|      | 0.000| 0.000| 0.117|
|   8   |      |      |      |      |      |      |      |      |      | 0.008| 0.000| 0.000| 0.008|
|   9   |      |      |      |      |      |      |      |      |      | 0.004| 0.000| 0.000| 0.004|
|  10   |      |      |      |      |      |      |      |      |      |      |	0.000|      | 0.000|
----------------------------------------------------------------------------------------------------
| ROAD  |      |      |22.425|21.470|21.661|11.474| 9.211| 6.997| 3.439| 1.454| 1.770| 0.099|      |
----------------------------------------------------------------------------------------------------
|ADVANCE|43.765|38.657|33.114|24.619|24.868|11.876| 9.329| 7.005| 3.443| 1.454| 1.770| 0.099|      |
----------------------------------------------------------------------------------------------------

Resulting Semifinal Match-ups: (ECAC B-T Ratings)

----------------------------------------------------------------------------------------------------
| Semis |   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |  11  |  12  | HOST |
----------------------------------------------------------------------------------------------------
|   1   |      |      |      |10.290| 9.764|10.253| 7.888| 3.271| 2.023| 0.293| 0.007|      |43.788|
|   2   |      |      |20.515| 6.825| 6.489| 0.287| 0.007| 1.653| 0.999| 1.206| 0.821| 0.119|38.921|
|   3   |      |      |      | 4.349| 4.186| 0.140| 0.003| 0.327| 0.198| 0.186| 0.120| 0.017| 9.525|
|   4   |      |      |      |      |      | 2.248| 0.831| 0.254| 0.157| 0.072| 0.039| 0.006| 3.607|
|   5   |      |      |      |      |      | 2.248| 0.740| 0.241| 0.148| 0.071| 0.039|      | 3.487|
|   6   |      |      |      |      |      |      | 0.433| 0.088| 0.054| 0.001|      | 0.005| 0.581|
|   7   |      |      |      |      |      |      |      | 0.050| 0.031|      | 0.000| 0.000| 0.081|
|   8   |      |      |      |      |      |      |      |      |      | 0.006| 0.000| 0.000| 0.006|
|   9   |      |      |      |      |      |      |      |      |      | 0.004| 0.000| 0.000| 0.004|
|  10   |      |      |      |      |      |      |      |      |      |      |	0.000|      | 0.000|
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| ROAD  |      |      |20.515|21.464|20.439|15.176| 9.901| 5.884| 3.611| 1.838| 1.025| 0.147|      |
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|ADVANCE|43.788|38.921|30.039|25.071|23.925|15.758| 9.982| 5.890| 3.615| 1.838| 1.025| 0.147|      |
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[sshablak]

Re: ECAC Byes and Home-Ice 2011-12

Four upset possibilities ! One upset already !