ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

[aweise]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

The main reason that so many teams can play catch-up is that Yale, Union, and RPI have all finished their series against each other. Add in the fact that the ECAC uses a travel partner schedule instead of the series style employed by the WCHA / CCHA / Atlantic means that no one has 2 games against any single team remaining, cutting down on the number of splits that have to be put in place to bump up everyone's point totals.

We always seem to have this discussion every year. The ECAC is so competitive that any team can beat any other. Plus, there's always a race for first, a first-round bye, and home ice in round 1.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Here's a quick post following the Friday games. Clarkson can still finish anywhere from 1st to 12th, and they are the only team with a possible range still that large. Also interesting (from my perspective, anyways) is that a Brown-SLU tie knocks both teams out of contention for the bye spot.

--- Bye Lock - 30
UC 27 - 37 [1-7]
Yale 26 - 36 [1-7]
--- Home Lock - 24
DC 22 - 32 [1-9]
RPI 21 - 31 [1-10]
Cornell 20 - 30 [1-10]
PU 20 - 30 [1-10]
QU 16 - 24 [3-11]
CCT 15 - 27 [1-12]
Brown 11 - 23 [4-12]
SLU 11 - 23 [4-12]
--- Bye Eligible - 23+
Harvard 7 - 17 [7-12]
Colgate 6 - 16 [8-12]
--- Home Eligible - 15

Remaining League Schedules:
UC - Colgate, @CCT, @SLU, QU, PU
Yale - @CCT, @QU, @PU, Colgate, Cornell
DC - PU, @Colgate, @Cornell, SLU, CCT
RPI - Cornell, @SLU, @CCT, PU, QU
Cornell - @RPI, Harvard, DC, @Brown, @Yale
PU - @DC, Brown, Yale, @RPI, @UC
QU - Yale, Brown, @UC, @RPI
CCT - Yale, @SLU, UC, RPI, @Harvard, @DC
Brown - @SLU, @PU, @QU, Harvard, Cornell, Colgate
SLU - Brown, CCT, RPI, UC, @DC, @Harvard
Harvard - @Cornell, @Colgate, @Brown, CCT, SLU
Colgate - @UC, DC, Harvard, @Yale, @Brown

A lot of my number crunching comes from the Sioux Sports what-if calculator. I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. This season's slack.net ECAC Playoff Possibilities Script is up again and should make future looks into tiebreakers that much easier.

Cornell holds 5th place over Princeton based on points vs. Top 4 teams (3 v 0). Brown beat St. Lawrence in Providence and therefore holds the tiebreaker for 9th place (subject to the upcoming game in Canton, obviously).

Let's start with some certainties...

Union's possible finishes narrows down to 1st-7th place. Basically, I got it by making a 4-way tie for 1st with Yale, Dartmouth, Princeton, and Cornell. Then, there was a 3-way tie for 5th place between Clarkson, RPI, and Union. Head-to-head points in the 5th place tiebreaker goes to Clarkson (6 v 4 v 2). And, the individual tiebreaker for 6th place broke the Engineers way, based on the third tiebreaker (points vs Top 4, 10 v 9). Basically, it's really, really improbable for Union to finish in 7th place, but there is still a minute possibility.

I think Dartmouth's basement moves up to 9th place. Quinnipiac, St. Lawrence, and Brown can all catch the Big Green individually, but Brown still has to face the other two teams. So, there could theoretically be a 4-way tie for 7th place, but Dartmouth would win the tiebreaker and would take the #7 seed. So, the lowest Dartmouth can go is if Brown loses those points to the Saints and Bobcats, placing Gaudet's players in 9th place.

Clarkson can still take the #1 seed, but they would end up sharing the Cleary Cup with the Dutchmen. The season series would be split and both the Knights and Dutchmen would have 13 wins. So, the tiebreaker would come down to Points vs. Top 4 teams. At that point, Dartmouth and RPI would be good teams to have in that comparison for the Knights. Union would like to see Cornell in the Top 4, instead.

Clarkson can also still finish in 12th place. They would either tie with Harvard or Colgate for 11th place. A tie with the Crimson goes into a points vs Top 4 teams comparison. The Crimson would like to see Cornell crack the Top 4 in that case. The Knights would want to see Princeton in the Top 4 for them to not finish in 12th. A Colgate-Clarkson tie would go to the Raiders based on the season series win for Colgate.

Brown's ceiling drops to 4th place. They can get in a 4-way tie for 3rd place, but any such tie would be guaranteed to have either Dartmouth or Rensselaer (or both). Brown would be able to finish in second place in any of those 4-way ties, but could not take 1st because they were swept by both Big Green and the Engineers already. So, their new effective ceiling is 4th place.

SLU suffers from a similar fate where they have not / cannot won any season series against any of the top-tier teams within the conference. So, the best I can see them doing is taking the last bye spot by getting up to 23 points, tying with Dartmouth, with Yale, Union, and Cornell ahead of them in the standings. St. Lawrence would finish in 4th place based on wins (11 v 10).

Next, let's look at the "thresholds" that are being employed...

The "Bye Lock" threshold drops all the way from 31+ points to 30. With Cornell, Rensselaer, and Princeton all losing points tonight, the threshold dropped significantly. Union inches that much closer to locking up 4th place or higher.

On the other hand, the "Bye Eligible" threshold shoots up from 21+ points to 23+ with Dartmouth and Princeton both picking up points tonight and the fact that DC, RPI, Cornell, and PU all have two games against each other remaining in their schedule.

The "Home Lock" threshold slips from 25 points to 24. St. Lawrence can get to 9th place with 23 points and still not even be tied with 8th place Quinnipiac.

The "Home Eligible" threshold has to go up to at least 15 points. Clarkson can lose out and still hold 2 points more than St. Lawrence, Harvard, and Brown (who would be in a 3-way tie for 9th). I didn't develop the naming convention, so I'm not sure whether it should be 15+ or 15, but I'm going to say 15, because Clarkson doesn't need to hold any tiebreakers to take 8th place with only 15 points.

Hopefully, I didn't miss anything. I'm sure you guys will let me know if you do see something wrong, though.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

And, the update at the end of the weekend's games. I will probably have another post on Tuesday, but it will likely just contain the numbers... no explanations should be necessary with only one game played.

--- Bye Lock - 29+
UC 29 - 37 [1-5]
Yale 28 - 36 [1-5]
DC 24 - 32 [1-8]
--- Home Lock - 23
Cornell 22 - 30 [1-9]
RPI 21 - 29 [1-10]
PU 20 - 28 [3-10]
QU 16 - 24 [4-11]
CCT 15 - 25 [3-12]
Brown 13 - 23 [4-12]
--- Bye Eligible - 22+
SLU 11 - 21 [6-12]
Harvard 7 - 17 [7-12]
--- Home Eligible - 15
Colgate 6 - 14 [9-12]

Remaining League Schedules:
UC - Colgate, @CCT, @SLU, QU, PU
Yale - @CCT, @QU, @PU, Colgate, Cornell
DC - PU, @Colgate, @Cornell, SLU, CCT
Cornell - @RPI, Harvard, DC, @Brown, @Yale
RPI - Cornell, @SLU, @CCT, PU, QU
PU - @DC, Brown, Yale, @RPI, @UC
QU - Yale, Brown, @UC, @RPI
CCT - Yale, @SLU, UC, RPI, @Harvard, @DC
Brown - @SLU, @PU, @QU, Harvard, Cornell, Colgate
SLU - Brown, CCT, RPI, UC, @DC, @Harvard
Harvard - @Cornell, @Colgate, @Brown, CCT, SLU
Colgate - @UC, DC, Harvard, @Yale, @Brown

A lot of my number crunching comes from the Sioux Sports what-if calculator. I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. This season's slack.net ECAC Playoff Possibilities Script is up again and should make future looks into tiebreakers that much easier.

Let's start with some certainties...

Union almost clinches a bye. If it's a two-way tie between the two Capital District teams, then the Dutchmen would hold onto 4th place based on points vs Top 4 teams (7 v 6 based on their sweep of Cornell and their single point against Dartmouth as opposed to RPI sweeping Dartmouth and getting swept by Cornell). A 3-way tie between Dartmouth, RPI, and Union sees RPI taking 3rd place on head-to-head points (6 v 3 v 3) and Dartmouth would win the 4th-place tiebreaker because they took 3 points during the season series.

Yale cannot be caught by both Rensselaer and Princeton, so their range narrows further to 1st-5th place.

Dartmouth can only fall all the way to 8th place if they get caught in a 3-way tie for 6th place with both RPI and Quinnipiac. The Big Green would fall to 8th place based on head-to-head points (5 v 5 v 2). Quinnipiac would then take 6th since they would win the season series 3 points to 1. But, Dartmouth has still clinched a home playoff series.

Cornell can slip to 9th place (and out of a home series) by finishing the season tied with Brown (instead of Quinnipiac) in the standings. The Bears would sweep the season series and take 8th place.

RPI can fall to 10th if it's a 3-way tie between St. Lawrence, Quinnipiac, and RPI. St. Lawrence takes 8th place by virtue of head-to-head record (5 v 4 v 3). Quinnipiac would win the season series against the Engineers and send Tute down to 10th place.

The Engineers' drive for 1st place is still alive, which they can get if they tie with Union and get the proper help. It all depends upon which teams make up the other two in the Top 4. If Dartmouth is one of those teams, then Rensselaer finishes in first place by a count of 8 to 5.

Princeton does not have the tiebreakers to beat out Yale for 2nd place. Any team that the Tigers beat on the season would not be able to get enough points to make it a 3-way tie. So, Princeton's ceiling is 3rd place.

Quinnipiac can get enough points for 3rd place, but would be in a 3-way tie with Dartmouth and Cornell. Cornell would win the head-to-head comparison (7 v 3 v 2) to take third place. The Big Green would then win the head-to-head matchup by wins (11 v 10). So, the way to get the Qpac Cats up to 4th place is to allow Dartmouth to take points and keep the Big Red down.

Clarkson can still finish in 3rd place if Cornell beats Dartmouth and the other games break the Knights' way.

Brown, despite not playing today, still has aspirations of finishing in 4th place.

St. Lawrence's ceiling falls to 6th place because Rensselaer and Princeton still have to play each other during the last week of play, meaning that the Saints cannot finish ahead of both of them.

Harvard did not play today and the range of possible finishes for the Crimson does not change.

Colgate's loss today knocks them out of contention for a home playoff spot and ensures that they'll be on the road in the first weekend of March.

Next, let's look at the "thresholds" that are being employed...

The "Bye Lock" threshold drops down to 29+ points. Any of the current top 4 teams would be able to finish with 29 points, tied with Rensselaer with the other Top 4 teams all ahead of the Engineers.

The "Bye Eligible" threshold sits at 22+ points. (I'm not sure how I missed it yesterday, but Cornell and RPI can tie for 4th place with 22 points each. The Big Red would take the free weekend in March by virtue of their series sweep.)

The "Home Lock" threshold slips down to 23 points. With Quinnipiac and Brown still having to play each other, only one team can finish with 23 points, and therefore take 8th place.

The "Home Eligible" stays put at 15 points. Theoretically, Clarkson can lose out and still play at home in March.

Hopefully, I didn't miss anything. I'm sure you guys will let me know if you do see something wrong, though.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

--- Bye Lock - 29+
UC 29 - 37 [1-5]
Yale 28 - 36 [1-5]
DC 24 - 32 [1-8]
--- Home Lock - 23
Cornell 22 - 30 [1-9]
RPI 21 - 29 [1-9]
PU 20 - 28 [3-9]
CCT 17 - 25 [3-10]
QU 16 - 24 [4-11]
Brown 13 - 23 [4-12]
--- Bye Eligible - 22+
SLU 11 - 19 [7-12]
Harvard 7 - 17 [7-12]
--- Home Eligible - 16
Colgate 6 - 14 [9-12]

Remaining League Schedules:
UC - @CCT, @SLU, QU, PU
Yale - @QU, @PU, Colgate, Cornell
DC - @Colgate, @Cornell, SLU, CCT
Cornell - Harvard, DC, @Brown, @Yale
RPI - @SLU, @CCT, PU, QU
PU - Brown, Yale, @RPI, @UC
CCT - UC, RPI, @Harvard, @DC
QU - Yale, Brown, @UC, @RPI
Brown - @PU, @QU, Harvard, Cornell, Colgate
SLU - RPI, UC, @DC, @Harvard
Harvard - @Cornell, @Colgate, @Brown, CCT, SLU
Colgate - DC, Harvard, @Yale, @Brown

Clarkson can be caught by Harvard and the Crimson can win the tiebreaker if Cornell is a Top 4 team. But, SLU would not be able to pass the Knights if they lose their season finale to that Boston team. And, a 3-way tie between CCT, SLU, and HU for 9th place immediately puts the Saints in 11th based on head-to-head points (6 v 6 v 2). So, Clarkson's basement is 10th place.

SLU's ceiling drops to 7th because the Saints can no longer catch the Tigers.

Harvard's aspiration of finishing in 7th are evaporating quickly. Again, they would need Cornell to be a Top 4 team to win the tiebreaker with Clarkson.

The Home Eligible threshold moves up to 16 points. The Qpac Cats can still finish with home ice without gaining another point.

The list of four teams that are going to be on the road early in March is getting dangerously close to becoming defined even before the last weekend is played.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

UC 31 - 37 [1-2]
Yale 30 - 36 [1-2]
--- Bye Lock - 28+
DC 24 - 30 [3-6]
Cornell 22 - 28 [3-7]
PU 22 - 28 [3-7]
RPI 21 - 27 [3-8]
--- Home Lock - 21+
CCT 17 - 23 [4-10]
--- Bye Eligible - 22+
QU 16 - 22 [6-11]
Brown 13 - 21 [6-12]
SLU 13 - 19 [7-12]
Harvard 9 - 17 [7-12]
--- Home Eligible - 16
Colgate 8 - 14 [9-12]

Remaining League Schedules:
UC - @SLU, QU, PU
Yale - @PU, Colgate, Cornell
DC - @Cornell, SLU, CCT
Cornell - DC, @Brown, @Yale
PU - Yale, @RPI, @UC
RPI - @CCT, PU, QU
CCT - RPI, @Harvard, @DC
QU - Brown, @UC, @RPI
Brown - @QU, Harvard, Cornell, Colgate
SLU - UC, @DC, @Harvard
Harvard - @Colgate, @Brown, CCT, SLU
Colgate - Harvard, @Yale, @Brown

A lot of my number crunching comes from the Sioux Sports what-if calculator. I'm using the ECAC Hockey's tie-breaking guidelines to split ties that I come across. This season's slack.net ECAC Playoff Possibilities Script is up again and should make future looks into tiebreakers that much easier.

I'm not 100% sure on my number crunching tonight because I'm on the road and haven't put as much effort into it as normal. However, I am absolutely certain that Union and Yale have both clinched a bye and are the only two teams fighting for the Cleary Cup.

Also, Quinnipiac and Brown still have to face each other (tonight, even, to make matters that much simpler). So, one of them can catch Rensselaer, but not both. And, if Brown is the team to catch the Engineers, they'd lose pretty much every possible tiebreaker since they got swept by the men of Troy. That is why RPI has locked up home-ice in March.

I'm not sure about Quinnipiac's ceiling, but based on preliminary looks into tiebreakers and very quick number crunching, my initial guess is that the Qpac Cats' ceiling is 6th place.

Also, it appears that Clarkson is the only school that can finish in any of the three tiers.

I'll have a more comprehensive look on Sunday and Tuesday / Wednesday and, finally on Friday, heading into the last night of games.

[AspyDad]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Burgie 12 if you need any help with the math on this thread, I'm here for you.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

UC 33 - 37 [1-2]
Yale 32 - 36 [1-2]
--- Bye Lock - 27+
Cornell 24 - 28 [3-6]
DC 24 - 28 [3-6]
RPI 23 - 27 [3-6]
PU 22 - 26 [3-6]
--- Bye Eligible - 24+
--- Home Lock - 20+
CCT 17 - 21 [7-9]
QU 17 - 21 [7-10]
Brown 14 - 20 [7-12]
SLU 13 - 17 [8-12]
--- Home Eligible - 17+
Colgate 10 - 14 [9-12]
Harvard 9 - 15 [9-12]

Remaining League Schedules:
UC - QU, PU
Yale - Colgate, Cornell
Cornell - @Brown, @Yale
DC - SLU, CCT
RPI - PU, QU
PU - @RPI, @UC
CCT - @Harvard, @DC
QU - @UC, @RPI
Brown - Harvard, Cornell, Colgate
SLU - @DC, @Harvard
Colgate - @Yale, @Brown
Harvard - @Brown, CCT, SLU

slack.net ECAC Playoff Possibilities Script is awesome. That is all.

Cornell holds 3rd place over Dartmouth based on their season series win (3-1). Clarkson holds 7th place over Quinnipiac based on their number of ECAC wins (8 v 6).

With 3rd through 6th place being separated by only 2 points, all of those 4 teams can finish in any of the spots.

Tiebreakers for 3rd-6th place (winning team(s) listed first):
Cornell / Dartmouth - season series (3 v 1)

Cornell / Rensselaer - season series (4 v 0)

Cornell / Princeton (variable) - goes down to Record vs Top 4 teams... Cornell wins if it's a tie for 4th or 5th (if Dartmouth and / or Rensselaer gets involved). If Cornell beats Yale and loses to Brown while Princeton sweeps and the teams tie for 3rd, then it comes down to Record vs Top 8 teams, which looks like the Big Red wins no matter which teams end up on which side of the 8/9 line. If Cornell beats Brown and loses to Yale while Princeton sweeps and the teams tie for 3rd, then the Tigers win the Record vs Top 4 teams.

Rensselaer / Dartmouth - season series (4 v 0)

Rensselaer / Princeton - no matter what happens on Friday (as long as the tiebreaker actually gets applied)... A Friday tie gives Rensselaer the win on season series (3 v 1). A Princeton win on Friday and loss on Saturday with Rensselaer tying Quinnipiac gives Rensselaer the win on Record vs Top 4 teams. A Princeton win on Friday and tie on Saturday with Rensselaer beating Quinnipiac gives Rensselaer the win on ECAC wins (12 v 11). A Friday win for Rensselaer means that the tiebreaker cannot possibly be applied.

Dartmouth / Princeton - season series (4 v 0)


Cornell / Dartmouth / Princeton - head-to-head record (5 v 5 v 2) knocks out Princeton and Cornell wins the head-to-head tiebreaker

Cornell / Rensselaer / Dartmouth - head-to-head record (7 v 4 v 1) and Rensselaer wins the head-to-head tiebreaker (see above)

Cornell / Rensselaer / Princeton - head-to-head record (6 where Princeton and Rensselaer each have 2 and can only pick up 2) while Rensselaer wins the head-to-head tiebreaker

Rensselaer / Dartmouth / Princeton - head-to-head record (RPI already has 6 with the possibility to pick up points this weekend while Dartmouth is stuck at 4 and Princeton come into the weekend with 0). Dartmouth wins the head-to-head tiebreaker.


Cornell / Rensselaer / Dartmouth / Princeton - head-to-head record (The Big Red already has 9 points. The Engineers have 6 but can only get up to 8. The Big Green is stuck at 5 points. The Tigers come in with 2 but can only move up to 4.). Once Cornell takes 3rd, it moves down to the 3-way tie detailed directly above.


Tiebreakers for 7th-12th place (winning team(s) listed first):
Clarkson / Quinnipiac - ECAC wins, even if the Knights tie their last two games and Quinnipiac picks up their two points with a win and loss

Clarkson / Brown - season series (4 v 0)

Clarkson / St. Lawrence - season series (4 v 0)

St. Lawrence / Quinnipiac - season series (3 v 1)

St. Lawrence / Colgate - season series (4 v 0)

Brown / Quinnipiac - ECAC wins

Brown / St. Lawrence - season series (4 v 0)

Harvard / St. Lawrence - season series (either 4 v 0 or 3 v 1)

Harvard / Brown (variable) - very, very variable... Harvard sweeping their remaining 3 games with Brown only picking up 1 point gives Harvard the tiebreaker on ECAC wins (7 v 6). Harvard taking 5 points while Brown gets swept goes down to Record vs Top 4 teams. If RPI can grab a bye, then the Crimson pulls out a tie in points vs Top 4 teams (4 v 4). I thought that Harvard won the Record vs Top 8 competition (which they do in most scenarios), but I was able to find a way to get a tie. That means that it would go all the way down to head-to-head goal differential (which Harvard wins if they beat the Bears by at least 2 goals on Tuesday). If Harvard beats Brown by 1 goal on Tuesday, then it goes to Goal Differential against Top 4 teams. Since the Top 4 teams where this would even come into play would be Union, Yale, RPI, and Dartmouth and Harvard and Brown have already finished their series against these teams, Harvard already has Top 4 goal differential (-14 v -17) locked up. If the Engineers do not finish in the Top 4, then the Bears win on Record vs Top 4 teams (either 4 v 2 or 4 v 3).

Harvard / Colgate (variable) - very, very variable... they split the season series, but ECAC wins could break in either direction. Record vs Top 4 teams can also break in either direction depending on the teams involved. The Crimson would like to see Princeton get a bye while the Raiders are hoping to beat the Bulldogs and / or keep the Dartmouth Big Green in the Top 4. As far as I can tell, Record vs Top 8 would go to Colgate.

Colgate / Brown (variable) - once again breaks down to Record vs Top 4 teams... If Princeton and Cornell pick up the two remaining bye spots, then the Bears win 4 v 3. Any other combination of bye teams gives the tiebreaker to the Raiders.


Clarkson / St. Lawrence / Quinnipiac - head-to-head record (6 v 3 v 3) and SLU wins the head-to-head tiebreaker

Clarkson / Brown / Quinnipiac - head-to-head record (6 v 4 (Qpac) v 2 (Brown)) and Brown wins the head-to-head tiebreaker

Clarkson / Brown / St. Lawrence - head-to-head record (8 v 4 v 0) and Brown wins the head-to-head tiebreaker

Brown / St. Lawrence / Quinnipiac - head-to-head record (6 v 4 v 2) and SLU wins the head-to-head tiebreaker

Brown / St. Lawrence / Colgate - head-to-head record (6 v 4 v 2) and SLU wins with head-to-head tiebreaker

Harvard / St. Lawrence / Colgate - head-to-head record (either 6 v 4 v 2 with the Crimson beating the Saints and St. Lawrence winning the head-to-head tiebreaker against Colgate or 5 v 5 v 2 dropping the Raiders to 12th place and Harvard winning the season series 3 v 1)

Harvard / Brown / St. Lawrence - head-to-head record (6 v 6 v 0) drops St. Lawrence from the tiebreaker and Harvard would win the head-to-head tiebreaker based on wins (7 v 6) as detailed above


Clarkson / Brown / St. Lawrence / Quinnipiac - head-to-head record (10 v 6 v 5 v 3) goes to Clarkson and then it goes to the 4th 3-way tiebreaker detailed above

Brown / Harvard / St. Lawrence / Colgate - head-to-head record is either 8 v 7 v 5 v 4 with the Bears winning or 8 v 8 v 4 v 4 with Harvard and Brown tying for 9th and St. Lawrence and Colgate tying for 11th (SLU wins the head-to-head tiebreaker). The Harvard / Brown tie depends on whether or not Rensselaer makes it into a bye position.

No possible 5-way ties.

Quinnipiac can't win any tiebreakers that would be applicable (for example, they'd win a tiebreaker against Colgate, but who cares since they can't actually tie). Clarkson has set them up in a very, very good position with their series wins against the teams near them. The mess from 9th to 12th place is going to come down to the last couple games... as usual. Shocking, right?

[aweise]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Someone get burgie some oxygen...

[goblue78]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Wow. Excellent (and exhausting) work.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

On Friday night (after that night's games), I will have a post giving a detailed list of the possible scenarios that will give each team their best possible finish. But, "Sully" will likely have a quicker set of possible finishes up on the ECAC blog. Tom Reale or Gary Russinko of Without a Peer will also likely have a similar post, or at least a couple of tweets regarding possible finishes. Brendan Roche (aka alslammerz) also does an excellent job of keeping up with the ECAC as a whole and will probably have a post up on the WHRB blog, at least with how the Crimson can improve their standing. Basically, what I'm saying, is that if you're looking for timeliness, you probably shouldn't come here. I would only bookmark this thread if you're looking for a half-azzed, poorly done attempt to find all of the different possible scenarios.

UC 33 - 37 [1-2]
Yale 32 - 36 [1-2]
--- Bye Lock - 27+
Cornell 24 - 28 [3-6]
DC 24 - 28 [3-6]
RPI 23 - 27 [3-6]
PU 22 - 26 [3-6]
--- Bye Eligible - 24+
--- Home Lock - 18+
CCT 17 - 21 [7-9]
QU 17 - 21 [7-10]
Brown 14 - 18 [7-12]
SLU 13 - 17 [8-12]
--- Home Eligible - 17+
Harvard 11 - 15 [9-12]
Colgate 10 - 14 [9-12]

Remaining League Schedules:
UC - QU, PU
Yale - Colgate, Cornell
Cornell - @Brown, @Yale
DC - SLU, CCT
RPI - PU, QU
PU - @RPI, @UC
CCT - @Harvard, @DC
QU - @UC, @RPI
Brown - Cornell, Colgate
SLU - @DC, @Harvard
Harvard - CCT, SLU
Colgate - @Yale, @Brown

slack.net's ECAC Playoff Possibilities Script is awesome. That is all.

Cornell holds 3rd place over Dartmouth based on their season series win (3-1). Clarkson holds 7th place over Quinnipiac based on their number of ECAC wins (8 v 6).

FINALLY! All of the teams have played the same number of (league) games.

With 3rd through 6th place being separated by only 2 points, all of those 4 teams can finish in any of the spots.

None of these tiebreakers have changed since my post this morning (so, if you want details, look above):

Tiebreakers for 3rd-6th place (winning team(s) listed first):
Cornell / Dartmouth
Cornell / Rensselaer
Cornell / Princeton (variable)
Rensselaer / Dartmouth
Rensselaer / Princeton
Dartmouth / Princeton

Cornell / Dartmouth / Princeton
Cornell / Rensselaer / Dartmouth
Cornell / Rensselaer / Princeton
Rensselaer / Dartmouth / Princeton

Cornell / Rensselaer / Dartmouth / Princeton

There are a couple different tiers in the race for 7th / 9th place. But, the tiebreakers abound! For tiebreakers that don't involve Brown or Harvard, I eliminated the associated text. I delved deeper into most of the Brown / Harvard-related tiebreakers and reworded them while also finding new scenarios that I did not see yesterday.

Tiebreakers for 7th-12th place (winning team(s) listed first):
Clarkson / Quinnipiac
Clarkson / Brown
Clarkson / St. Lawrence
St. Lawrence / Quinnipiac
St. Lawrence / Colgate
Brown / Quinnipiac - ECAC wins
Brown / St. Lawrence - season series (4 v 0)
Harvard / St. Lawrence - season series (either 4 v 0 or 3 v 1)

Harvard / Brown (variable) - very, very variable... A Harvard sweep this upcoming weekend with Brown only picking up 1 point gives Harvard the tiebreaker on ECAC wins (7 v 6).
If Harvard only takes 3 points while Brown gets swept, the tiebreaker goes down to Record vs Top 4 teams.
Brown wins Record vs Top 4 teams (4 v 2 (Cornell, Dartmouth) or 4 v 3 (Cornell, Princeton) or 2 v 1 (Dartmouth, Princeton) *not possible*) if RPI does not finish in the Top 4.
If RPI can grab a bye, then the Crimson pulls out a tie in points vs Top 4 teams (4 v 4 (Cornell) or 2 v 2 (Dartmouth)).
If Harvard beats Clarkson and ties St. Lawrence, then Harvard wins Record vs Top 8 (7 v 6).
If Harvard ties Clarkson and beats St. Lawrence, then the Crimson and Bears tie Record vs Top 8 (6 v 6).
Head-to-Head Goal Differential is a wash at 0.
Top 4 Goal Differential is already locked in in favor of the Crimson (-5 v -12 (Cornell) or -14 v -17 (Dartmouth)).

Harvard / Colgate (variable) - very, very variable... still too close to call. They split the season series and that's about the only thing that's certain here. Harvard wants to see Princeton move into a Top 4 position. Colgate wants to see Dartmouth stay in a bye position.

Colgate / Brown (variable) - once again breaks down to Record vs Top 4 teams... If Princeton and Cornell pick up the two remaining bye spots, then the Bears win 4 v 3. Any other combination of bye teams gives the tiebreaker to the Raiders (5 v 4 (Cornell, Dartmouth or Cornell, Rensselaer) or 6 v 2 (Dartmouth, Rensselaer)).


Clarkson / St. Lawrence / Quinnipiac

Clarkson / Brown / Quinnipiac - Nothing changes here. Brown can still end up in a 3-way tie with these two teams.

Clarkson / Brown / St. Lawrence - Still possible. And, head-to-head record is still 8 v 4 v 0.

Brown / St. Lawrence / Quinnipiac - No changes. Brown wins the head-to-head record (6 v 4 v 2) and SLU wins the head-to-head tiebreaker

Brown / St. Lawrence / Colgate - No change here, either. Brown takes home the 3-way tiebreaker based on head-to-head record (6 v 4 v 2) and SLU wins with head-to-head tiebreaker.

Harvard / St. Lawrence / Colgate - The head-to-head record gives Harvard the win (6 v 4 v 2 if Harvard beats SLU) or drops Colgate down to 12th place (5 v 5 v 2 if Harvard and SLU tie). The Saints win the SLU / Colgate head-to-head tiebreaker and the Crimson win the Harvard / St. Lawrence tiebreaker (3 v 1).

Brown / Harvard / St. Lawrence (variable) - If they tie at 15 points, then Harvard beat St. Lawrence on Saturday and the head-to-head record goes to 6 v 6 v 0, dropping St. Lawrence to the lowest position. The Harvard / Brown head-to-head tiebreaker would fall in the "Harvard sweeps" category, meaning that the Crimson takes the top spot based on wins (7 v 6).
If they tie at 14 points because Harvard and St. Lawrence tie, then the head-to-head tiebreaker goes to the Bears (6 v 5 v 1).
If they tie at 14 points by Harvard beating St. Lawrence and tying Clarkson with St. Lawrence tying Dartmouth, then the head-to-head record is 6 v 6 v 0 (once again dropping St. Lawrence). The Harvard / Brown tiebreaker depends on which teams make it into the Bye position. If RPI gets into the Top 4, then the Harvard / Brown tiebreaker goes down to Top 4 Goal Differential, which breaks in favor of the Crimson. If Rensselaer does not get into the Top 4, then the Bears win the head-to-head tiebreaker.


Clarkson / Brown / St. Lawrence / Quinnipiac

Brown / Harvard / St. Lawrence / Colgate - If Harvard and St. Lawrence tie, then Brown wins 9th place by head-to-head points (8 (Brown) v 7 (Harvard) v 5 (St. Lawrence) v 4 (Colgate)). The Harvard / St. Lawrence / Colgate tie drops the Raiders to 12th place by head-to-head points (5 v 5 v 2). Harvard takes 10th place based on winning the season series 3-1.
If Harvard beats St. Lawrence to come up with this 4-way tie, then the head-to-head record becomes a pair of ties (8 (Brown) v 8 (Harvard) v 4 (St. Lawrence) v 4 (Colgate)). The Harvard / Brown tie would come down to which teams finish with a bye. The St. Lawrence / Colgate tie goes to the Saints on the basis of their season sweep.

[StayPuftMMcu]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Because of Clarkson's tiebreaker wins and Brown's loss last night, the "home lock" is now 18 points for Clarkson and 19 points for Quinnipiac. Odd situation, that.

[burgie12]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Because of Clarkson's tiebreaker wins and Brown's loss last night, the "home lock" is now 18 points for Clarkson and 19 points for Quinnipiac. Odd situation, that.

You're right. I forgot to look at the home / bye levels because I was so focused on the tiebreakers.

[LynahFan]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

I threw together a little Monte Carlo simulation of the last 12 games for a thread over on eLynah. Here are the probabilities I came up with, where the results of the remaining games are based on the current KRACH ratings (including all games, not just ECAC games) of the teams. My method does allow for ties (though this could use some improvement) AND my code is not up to date with the latest tiebreaking procedure (it's from 2003 or so), but with those caveats, here's approximately the situation (after 1 million trial runs):

	1	2	3	4	5	6	7	8	9	10	11	12
Union	81.0%	19.0%										
Yale	19.0%	81.0%										
Cornell			83.1%	14.7%	2.2%							
Dartmouth		9.8%	36.2%	42.7%	11.3%						
Rensselaer		2.5%	29.5%	25.3%	42.7%						
Princeton		4.6%	19.6%	29.8%	46.0%						
Quinnipiac						68.0%	30.6%	1.3%	0.1%		
Clarkson						32.0%	68.0%				
St. Lawrence							0.8%	54.9%	44.2%		
Brown								0.6%	43.8%	45.9%	9.7%	
Colgate										9.7%	73.2%	17.0%
Harvard											17.0%	83.0%

[goblue78]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Nice job, but with only 4096 possibilities, wouldn't it be easy enough to use the Krach results exactly? (OK, to be fair, with ties, there are 531,441 possibilities, but still...) By the way, how do you adjust Krach for tie predictions?

[LynahFan]

Re: ECAC Home Stretch - A mathematical approach to Byes and Home-ice (2010-2011)

Yes, but:

a) I didn't have time to write the code to cycle through all the possibilities methodically - much easier just to assign random results to the remaining games and let 'er rip

and

b) I wanted to keep it general so that I might be able to use it in future seasons earlier in the season, when the # of permutations would be prohibitive

For ties, here's what I did so far (I emphasize that I am NOT happy with this):

I looked across all games played this year, and about 13% have been ties. Say that KRACH tells me that the probability of A beating B is 70%. I choose a random number between 0 and 1 for the result. Normally, you if the number is less than .7, you would call that a W for team A, and if it's above .7, it's an L. I added a "gray" zone centered on 0.7 that is .13 wide, and if the random number ends up in that range, it's a tie. So, for this example, a random number between .635 and .765 would be called a tie. If the raw probability is within 6.5% of 0 or 100, I slide the "tie zone" so that it ends halfway between the probability and the end of the scale. For example, if the probability of a win is 95%, then the "tie zone" would go from 84.5% to 97.5% (still 13% wide). Therefore, each game has a 13% chance of being a tie, so the total number of ties will be 13% (for a large sample).

Of course, the obvious problem is that every game should NOT have the same probability of having a tie. A pair of teams with a large discrepancy in KRACH ratings should clearly have less probability of tying than two teams with nearly identical ratings. So I need to figure out how to scale the "tie" zone based on the discrepancy in the pair under consideration, while making sure that the total number of ties comes out approximately correct, and I just didn't have time to think about that any farther yet. So, the results I have given are probably a little bit biased in favor of the lower teams - it gives them a higher probability of tying the really good teams than they probably really should get credit for.