Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13
Current Standings (by Points ):
Quinnipiac 34-40 [1]
--- Bye Lock - 25+
--- Home Lock - 23+
St. Lawrence 22-28 [2-9]
Rensselaer 21-27 [2-9]
Union 20-26 [2-11]
Yale 19-25 [1-11]
Dartmouth 19-25 [2-11]
Clarkson 19-25 [2-11]
Brown 17-23 [2-11]
Princeton 17-23 [2-11]
Cornell 15-21 [4-12]
Colgate 15-21 [4-12]
--- Bye Eligible - 21+
--- Home Eligible - 17+
Harvard 10-16 [10-12]
Yale wins the three-way tiebreaker based on ECAC wins. Each of the Bulldogs, Big Green, and Knights have split their respective season series. Yale's 9-9-1 record gives them 5th over Dartmouth's and Clarkson's 8-8-3 records.
Dartmouth and Clarkson have to go down to Record vs Top 8 to determine 6th place. They split the season series, have identical records, and identical 2-3-1 records against teams in the Top 4. Dartmouth has a 6-5-1 record against Top 8 teams while Clarkson has a 3-7-2 record.
Brown completed their sweep of Princeton last night and hold 8th place because of it.
Miscellaneous Links:
TBRW's ECAC Page (still... currently down)
Sioux Sports' What-If Calculator (which doesn't use tiebreakers)
ECAC Tiebreakers page (which you will come to know and love)
Remaining League Schedules:
Individual Team Limits:
Teams Losing Out (Floors)
Quinnipiac has clinched 1st place.
St. Lawrence cannot be caught by Cornell, Colgate, or Harvard. Anyone else can catch and pass the Saints, even simultaneously.
There aren't enough points left to push everybody past Rensselaer, so we have to leave at least one of Cornell and Colgate behind the Engineers. If we leave the Big Red back, we can make a four-way tie for 7th with Brown, Colgate, and Princeton where RPI would eventually finish in third, leaving them in 9th.
Union can be passed by everyone down to a three-way tie between Cornell, Colgate, and themselves. The Big Red already beat Colgate and would have swept the Dutchmen, so they'd finish 9th. The tiebreaker for 10th would go down to Record vs Top X. If the teams are adjusted properly (for example, not RPI or Princeton), then the Dutchmen will lose the tiebreaker and finish in 11th.
Each of Yale, Dartmouth, Clarkson, Brown, and Princeton (the remaining teams with more points than Harvard's maximum) can be passed by everybody else to finish by themselves in 11th.
Cornell, Colgate, and Harvard can each finish by themselves in 12th.
Teams Winning Out (Ceilings)
Harvard can catch the Central New York pair and nobody else, so their ceiling is pretty easy to figure out. If you need it spelled out for you, it's 10th.
Due to the North Country and Capital District pairs having to face off next weekend, two teams (in addition to Quinnipiac) need to finish ahead of Cornell or Colgate, meaning that they each have a ceiling of 4th place. There would have to be a three-way tie, but it's pretty easy to find teams where the Raiders and Big Red can win (for example: Union, Yale).
Princeton's ceiling of 23 points could leave them in a three-way tie for 2nd with two of the North Country / Capital District teams, with just the Bobcats ahead of them. If the games fall correctly, then Princeton, SLU and RPI each end up with a 1-1-2 head-to-head record and Princeton's 10-9-3 record would beat the hypothetical 9-8-5 records of the Engineers and Saints.
Brown is in the same situation (obviously, since they have the same number of points). If we leave Princeton at 23 to allow Brown's sweep to boost their head-to-head score and make the two North Country / Capital District teams at 23 points Clarkson and St. Lawrence (instead of RPI and SLU), then Brown and Clarkson win the four-way tie having won 8 points in the six head-to-head games. Brown won the season series against Clarkson (they won in Potsdam and tied in Providence), so the Bears can also win the tiebreaker to finish in 2nd.
Each of the teams in between 2nd and 7th (inclusive) can finish by themselves in 2nd.
Thresholds:
Bye Lock - If Yale wins out, it doesn't hurt the potential of any of the Top 4 teams. With SLU having to face both RPI and Union, we'll let each team win their game tonight and then let Clarkson lose both of their games next weekend. That leaves SLU and Union at 24 points each and RPI at 25. There is some set of game results between these three teams so that one team remains tied with Yale while the other two finish at 26 points. So, it's 25 plus tiebreakers to guarantee yourselves a tie resulting in a weekend off.
Bye Eligible - If we let SLU and RPI win out, then Union (20 points) and Clarkson (19 points) still need to face each other, meaning that 21 points (plus tiebreakers) would be the minimum for 4th place. Hey, look at that, that's the same thing that was decided in the Cornell / Colgate winning out scenarios.
Home Lock - With Colgate, Cornell, and Harvard, losing out, we can let everyone coalesce around 23 points. Yes, each of Brown, Princeton, Dartmouth, and Yale can simultaneously finish at 23 points. And, then, it's really pretty easy to let the North Country / Capital District teams finish with at least 23. So, it's 23 plus tiebreakers to earn another pair of home-ice games after the season is over.
Home Eligible - If Brown and Princeton lose out, then Cornell and Colgate each earn a win over the Bears and sit at 17 points. If they also lose out, then it's a 4-way tie for 8th place (Princeton wins the first tiebreaker at 4-2-0, Brown loses the three-way tiebreaker, and Cornell wins the head-to-head tiebreaker against Colgate so it would break PN/CR/CG/BN) with the Crimson stuck in 12th. So, it takes 17 points plus the proper tiebreakers to be eligible for two more home games.
Current Standings (by Points ):
Quinnipiac 34-40 [1]
--- Bye Lock - 25+
--- Home Lock - 23+
St. Lawrence 22-28 [2-9]
Rensselaer 21-27 [2-9]
Union 20-26 [2-11]
Yale 19-25 [1-11]
Dartmouth 19-25 [2-11]
Clarkson 19-25 [2-11]
Brown 17-23 [2-11]
Princeton 17-23 [2-11]
Cornell 15-21 [4-12]
Colgate 15-21 [4-12]
--- Bye Eligible - 21+
--- Home Eligible - 17+
Harvard 10-16 [10-12]
Yale wins the three-way tiebreaker based on ECAC wins. Each of the Bulldogs, Big Green, and Knights have split their respective season series. Yale's 9-9-1 record gives them 5th over Dartmouth's and Clarkson's 8-8-3 records.
Dartmouth and Clarkson have to go down to Record vs Top 8 to determine 6th place. They split the season series, have identical records, and identical 2-3-1 records against teams in the Top 4. Dartmouth has a 6-5-1 record against Top 8 teams while Clarkson has a 3-7-2 record.
Brown completed their sweep of Princeton last night and hold 8th place because of it.
Miscellaneous Links:
TBRW's ECAC Page (still... currently down)
Sioux Sports' What-If Calculator (which doesn't use tiebreakers)
ECAC Tiebreakers page (which you will come to know and love)
Remaining League Schedules:
Code:
---------------------------------------- | | ||S2/23|F3/01|S3/02| ---------------------------------------- | Quinnipiac | QN || BN | @HA | @DA | | St. Lawrence | SL || DA | @UC | @RP | | Rensselaer | RP || @CG | CK | SL | | Union | UC || @CR | SL | CK | | Yale | YA || @PN | CG | CR | | Dartmouth | DA || @SL | PN | QN | | Clarkson | CK || HA | @RP | @UC | | Brown | BN || @QN | CR | CG | | Princeton | PN || YA | @DA | @HA | | Cornell | CR || UC | @BN | @YA | | Colgate | CG || RP | @YA | @BN | | Harvard | HA || @CK | QN | PN | ----------------------------------------
Teams Losing Out (Floors)
Quinnipiac has clinched 1st place.
St. Lawrence cannot be caught by Cornell, Colgate, or Harvard. Anyone else can catch and pass the Saints, even simultaneously.
There aren't enough points left to push everybody past Rensselaer, so we have to leave at least one of Cornell and Colgate behind the Engineers. If we leave the Big Red back, we can make a four-way tie for 7th with Brown, Colgate, and Princeton where RPI would eventually finish in third, leaving them in 9th.
Union can be passed by everyone down to a three-way tie between Cornell, Colgate, and themselves. The Big Red already beat Colgate and would have swept the Dutchmen, so they'd finish 9th. The tiebreaker for 10th would go down to Record vs Top X. If the teams are adjusted properly (for example, not RPI or Princeton), then the Dutchmen will lose the tiebreaker and finish in 11th.
Each of Yale, Dartmouth, Clarkson, Brown, and Princeton (the remaining teams with more points than Harvard's maximum) can be passed by everybody else to finish by themselves in 11th.
Cornell, Colgate, and Harvard can each finish by themselves in 12th.
Teams Winning Out (Ceilings)
Harvard can catch the Central New York pair and nobody else, so their ceiling is pretty easy to figure out. If you need it spelled out for you, it's 10th.
Due to the North Country and Capital District pairs having to face off next weekend, two teams (in addition to Quinnipiac) need to finish ahead of Cornell or Colgate, meaning that they each have a ceiling of 4th place. There would have to be a three-way tie, but it's pretty easy to find teams where the Raiders and Big Red can win (for example: Union, Yale).
Princeton's ceiling of 23 points could leave them in a three-way tie for 2nd with two of the North Country / Capital District teams, with just the Bobcats ahead of them. If the games fall correctly, then Princeton, SLU and RPI each end up with a 1-1-2 head-to-head record and Princeton's 10-9-3 record would beat the hypothetical 9-8-5 records of the Engineers and Saints.
Brown is in the same situation (obviously, since they have the same number of points). If we leave Princeton at 23 to allow Brown's sweep to boost their head-to-head score and make the two North Country / Capital District teams at 23 points Clarkson and St. Lawrence (instead of RPI and SLU), then Brown and Clarkson win the four-way tie having won 8 points in the six head-to-head games. Brown won the season series against Clarkson (they won in Potsdam and tied in Providence), so the Bears can also win the tiebreaker to finish in 2nd.
Each of the teams in between 2nd and 7th (inclusive) can finish by themselves in 2nd.
Thresholds:
Bye Lock - If Yale wins out, it doesn't hurt the potential of any of the Top 4 teams. With SLU having to face both RPI and Union, we'll let each team win their game tonight and then let Clarkson lose both of their games next weekend. That leaves SLU and Union at 24 points each and RPI at 25. There is some set of game results between these three teams so that one team remains tied with Yale while the other two finish at 26 points. So, it's 25 plus tiebreakers to guarantee yourselves a tie resulting in a weekend off.
Bye Eligible - If we let SLU and RPI win out, then Union (20 points) and Clarkson (19 points) still need to face each other, meaning that 21 points (plus tiebreakers) would be the minimum for 4th place. Hey, look at that, that's the same thing that was decided in the Cornell / Colgate winning out scenarios.
Home Lock - With Colgate, Cornell, and Harvard, losing out, we can let everyone coalesce around 23 points. Yes, each of Brown, Princeton, Dartmouth, and Yale can simultaneously finish at 23 points. And, then, it's really pretty easy to let the North Country / Capital District teams finish with at least 23. So, it's 23 plus tiebreakers to earn another pair of home-ice games after the season is over.
Home Eligible - If Brown and Princeton lose out, then Cornell and Colgate each earn a win over the Bears and sit at 17 points. If they also lose out, then it's a 4-way tie for 8th place (Princeton wins the first tiebreaker at 4-2-0, Brown loses the three-way tiebreaker, and Cornell wins the head-to-head tiebreaker against Colgate so it would break PN/CR/CG/BN) with the Crimson stuck in 12th. So, it takes 17 points plus the proper tiebreakers to be eligible for two more home games.
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