ECAC Predictions

[Section A]

So I was wondering who, out of the top 6 teams, has the most difficult remaining schedule. So for each of the top 6, I added up the current standings of all the opponents. For example, for us, we play Yale (#6), Princeton (#11), RPI (#3), Union (#10), Clarkson (#8), and St. Lawrence (#9), to give a total "score" of 47. Obviously, the lower the score, the more difficult the remaining schedule. So from the most difficult schedule to the least, and with the "score" in parentheses, I came up with...

1. RPI (31)
2. Yale  (36)
3. Dartmouth (42)
T4. Brown (47), Colgate (47), Cornell (47)

To break that three-way tie for fourth (and obviously, there would be a tie between travel partners Colgate and Cornell), I used "record against remaining opponents from earlier in the season" as the first tiebreaker and "wins" as the second, to give...

1. RPI
2. Yale
3. Dartmouth
4. Cornell (3-1-2 against remaining opponents)
5. Colgate (4-2-0 against remaining opponents)
6. Brown (5-1-0 against remaining opponents)


Alright so I don't know if that accomplished anything :-), but it gives you an idea of how RPI and Yale have much tougher schedules than we do, perhaps strengthening the comment mentioned by someone else that fourth place is ours to lose.

[Keith K \'93]

Likewise, using a sum of Bradley Terry rating or opponents points to characterize remaining schedule:

             BT    Pts
RPI        1074.7  110
Dartmouth   803.9   96
Yale        751.3   96
Cornell     498.2   87
Colgate     498.2   87
Brown       480.4   82

...shows that Yale and RPI have tougher slates ahead although these measured put Dartmouth's schedule a little above Yale's.  Naturally Cornell and Colgate have the same SoS remaining.

[Section A]

Forgive me for not understanding the Bradley Terry stuff too well, but why is Dartmouth's schedule considered more difficult, using those measures, than Yale's, despite Dartmouth facing teams lower in the standings?



Post Edited (02-12-04 20:14)

[Keith K \'93]

Position in the standings is a coarse measure that will miss any large gaps in "strength" between teams located close in the standings. Example: say there's a big dropoff between 6th and 7th place in the standings (top 6 are all very good and bottom six are very bad).  The standings won't see much difference between the 6th and 7th place teams.  Points or BT rating will see the differnce between the two teams.

Just glancing at the schedule, the obvious difference is that Yale plays Vermont while Dartmouth plays Brown.

[jtwcornell91]

Keith K '93 wrote:
Likewise, using a sum of Bradley Terry rating or opponents points to characterize remaining schedule:

Adding the BT ratings is not really the right thing to do with them, since they're on a multiplicative scale.  Also, for opponents ranked a lot higher or lower, it doesn't really matter how much stronger or weaker they are.  Imagine two teams with ratings of around 100.  Team A has opponents with ratings of 50 and 6000, while Team B has opponents with ratings of 500 and 5000.  Team A's opponents have a total rating of 6050 to Team B's 5500, so by that measure they're facing stronger opposition.  But it's likely Team A will do better than Team B in the two games, since neither team has much chance to beat their stronger opponent, and Team A is a 2:1 favorite against their weaker opponent, while Team B is a 5:1 underdog.

What you want is something like the expected winning percentage of some canonical team vs each team's remaining schedule.  Or the weighted average we use to define SOS on the KRACH pages.  (But there the weighting depends on the team's own rating, so it's hard to compare schedules for opponents with different ratings.  Again, you'd want to use some typical rating, like the geometric mean of the teams being compared.)

[jeh25]

Keith K '93 wrote:

Position in the standings is a coarse measure that will miss any large gaps in "strength" between teams located close in the standings. Example: say there's a big dropoff between 6th and 7th place in the standings (top 6 are all very good and bottom six are very bad).  The standings won't see much difference between the 6th and 7th place teams.  Points or BT rating will see the differnce between the two teams.

In psychophysics, we'd summarize this by noting that standings only provide ordinal level data whereas the BT ratings provide at least interval (and possibly ratio) level data. The classic example used to explain this to a bunch of psych students is a marathon; if I know 3 runners finished 1st, 2nd and 3rd, then I only know the order in which they finished. That is, I know *who* is better but not *how much* better. Conversely, if I know they took 2:15, 2:26 and 2:27 respectively to finish, I can conclude that #1 was much better while 2 and 3 are closely matched.

For the math types in the room, the 4 levels of measurement (nominal, ordinal, interval and ratio) proposed by SS Stevens have different allowable mathematical operations.  Although I've never seen it, I've heard  that much of the 70s was spent arguing that you couldn't apply parametric methods to analyze interval level data and that you needed to use non-parametric methods instead.

Hmm. I should stop rambling and start my stats homework.

This pedantry was brought to you by the number π and the letter Q

[dss28]

[Q]This pedantry was brought to you by the number n and the letter Q[/Q]

At least it wasn't brought to us by "n with property p."  I hated that little f*cker.

(edit: fixed quote)



Post Edited (02-12-04 23:10)

[jtwcornell91]

"Let X be a set Y we call Z ..."  (Just an example of what's wrong with mathematicians.)

[Ack]

Hayes...you're definitely not a facetimer, but maybe an outlier...

[dss28]

Now prove that Z, which somehow got property p, when combined with X-1, will mean that n-1 will have property p.  And as always, label your work.

(edit:  I realized I had capitalized that first property 'p,' and as we all know property 'P' is ENTIRELY different than property 'p.')



Post Edited (02-12-04 23:17)

[Ack]

Are we talking about obstruction penalty variability?

[jtwcornell91]

dss28 wrote:
Now prove that Z, which somehow got property p, when combined with X-1, will mean that n-1 will have property p.  And as always, label your work.

But can you prove it by induction?

(edit:  I realized I had capitalized that first property 'p,' and as we all know property 'P' is ENTIRELY different than property 'p.')

I have a colleague who once gave a lecture (with overhead transparencies) where p written in red ink was a different variable from p written in black ink, and they appeared in the same equation.

[dss28]

Did the students with blue pens try to shove them through their own eyes?  I'd have cried.

[Josh '99]

Most people would cry after shoving a pen through their own eyes.   ::twitch::

[dss28]

Gives a whole new meaning to that song "Black Eyes, Blue Tears," doesn't it....