Re: ECAC Byes and Home-Ice - A Mathematical Journey 2012-13
Hey burgie12, I do hope you get well soon. In the meantime, just to keep everyone abreast of the chart, I'll give this a quick update. I'm not going to do all of the fancy math that burgie12 does, but I can at least handle this part.
Current Standings (by Points %):
Quinnipiac 32-
40 [1]
--- Bye Lock -
27+
--- Home Lock -
24
Rensselaer 21-
29 [2-10]
St. Lawrence 20-
28 [2-11]
Union 20-
28 [2-11]
Yale 19-
27 [2-11]
Dartmouth 19-
27 [2-11]
Clarkson 17-
25 [2-12]
Princeton 17-
25 [2-12]
Brown 15-
23 [2-12]
Cornell 13-
21 [3-12]
Colgate 13-
21 [4-12]
--- Bye Eligible -
20+
Harvard 10-
18 [7-12]
--- Home Eligible -
17
St. Lawrence beat Union on 9 February, so they currently have the advantage in the tiebreaker. The two teams will meet again on the final weekend to firm up this tiebreaker.
Yale and Dartmouth split their series, but because Yale has more ECAC wins, they get the nod there.
Clarkson swept the series with Princeton, so they get the nod.
Cornell won the series over Colgate by a point total of 3-1, so Cornell gets the nod.
Miscellaneous Links:
TBRW's ECAC Page (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:
----------------------------------------------
| | ||F2/22|S2/23|F3/01|S3/02|
----------------------------------------------
| Quinnipiac | QN || YA | BN | @HA | @DA |
| Yale | YA || @QN | @PN | CG | CR |
| Union | UC || @CG | @CR | SL | CK |
| Dartmouth | DA || @CK | @SL | PN | QN |
| St. Lawrence | SL || HA | DA | @UC | @RP |
| Princeton | PN || BN | YA | @DA | @HA |
| Rensselaer | RP || @CR | @CG | CK | SL |
| Colgate | CG || UC | RP | @YA | @BN |
| Clarkson | CK || DA | HA | @RP | @UC |
| Brown | BN || @PN | @QN | CR | CG |
| Cornell | CR || RP | UC | @BN | @YA |
| Harvard | HA || @SL | @CK | QN | PN |
----------------------------------------------
Individual Team Limits:
Teams Losing Out (Floors)
Quinnipiac cannot be caught; they have clinched the regular season championship.
Rensselaer cannot be caught by Harvard, so they cannot reach 12th. With games remaining, they can't get down to 11th. To try for 10th, the one way I found is with a 5-way tie between Princeton, Union, RPI, Cornell, and Brown for 6th.
St. Lawrence canot be caught by Harvard, so they can't go into 12th. They can go into 11th, with a five-way tie for 7th alongside Colgate, Cornell, Clarkson, and Yale.
Union cannot be caught by Harvard, so they can't go into 12th. They can go into 11th, with a three-way tie for 9th alongside Colgate and Cornell.
Yale and
Dartmouth cannot be caught by Harvard, so they can't finish in 12th. Both may finish in sole possession of 11th.
Any of the remaining six teams can finish in 12th place by themselves.
Teams Winning Out (Ceilings)
Quinnipiac cannot be caught; they have clinched the regular season championship.
If
Harvard wins out, they'll reach 18 points. The easiest way I have found for Harvard to attain 7th is if Brown beats Princeton, and then Brown is swept by Cornell and Colgate, while any games by Clarkson thru Colgate involving top 6 teams results in losses.
Colgate cannot reach second. Even if they win out and RPI loses out, RPI still has a game against SLU, and that would pull SLU ahead of these teams. In order to get into a possible 3rd for Colgate, there has to be a 5-way tie with Clarkson, Union, SLU, and Dartmouth. However, Clarkson beats them on points between all teams affected, so 3rd is out. In fact, with that 5-way tie, Colgate would end up 6th or 7th (not going to bother figuring it out). Now to try to get them into 4th, let's have Colgate, RPI, and QPac win out, and because of the tiebreaks, SLU win out. With this, I was able to get Colgate to 4th, but also involving a five-way tie 5th between Union, Dartmouth, Clarkson, Princeton, and Yale.
Cornell cannot reach second either, by virtue of the same reasons as Colgate. For 3rd, we get the same 5-way tie as before, only replace Colgate with Cornell. With this one, Cornell and Clarkson end up breaking from the pack in the first tie-break, they'd have the same ECAC wins, but Cornell would win the points vs. top 4 tiebreak, 4-2, so Cornell indeed can finish 3rd.
The remaining teams can all finish by themselves in 2nd place.
Thresholds:
Bye Lock - Because Union, RPI, and SLU still need to play each other, 4th place cannot reach the potential of 28. I was able to get them to 27, though, and given that's the potential of 5th, 27 + tiebreak (Yale) becomes the lock.
Bye Eligible - 20 is the bare minimum based upon the 4th place team's total; I was able to get a 4th place 5-way tie at 20.
Home Lock - With Colgate, Cornell, Harvard, and Quinnipiac losing out, the lowest potential that is available for the remaining teams is 23 points (Brown), so we are going to make 24 points the home lock.
Home Eligible - The base is, of course, 17, because that is where 8th place currently is. I'm able to get 17 with Clarkson alone, and Princeton with a tiebreak, so we'll label it as 17 alone at this time.
However, considering the URL is a straight IP address and the user isn't using DNS renaming, I suspect the address changed, possibly from a server upgrade.