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Octonion Power Rankings

Re: Octonion Power Rankings

To make my previous point concrete, let's take your statement: "That's why KRACH has rated Minnesota over Quinnipiac." But the question is: which one is better, and by how much? KRACH currently has ratings of 162.619 for QPac and 153.051 for Minny. This means that the probability of a Quinnipiac win over Minnesota on neutral ice is 162.619/(153.051+162.619) or 51.5 percent. I'm not sure exactly how your Poisson model works, of course, but if works like a typical Poisson model with offensive factors of 1.536 and 1.916 for QPac and Minny, with defensive factors of .398 and .453, then on neutral ice we get a Poisson score of 1.536-.453= 1.083 for QPac's goals and 1.916-.398 = 1.518 for Minny, then we get a probability of a QPac victory of 37.7 percent (I have taken the liberty of breaking ties proportional to net strength, but that should be relatively robust.) OK. So that's a pretty big difference between two methods right? One has QPac with a 37.7 percent chance of winning head to head and the other method has 51.5 percent. But it's really hard to separate those two probabilties even if they played 10 times. using a likelihood ratio of 8 to signify strong evidence, 0 wins would be evidence that you had the better argument and 9 or 10 wins would suggest KRACH did, the remainder of the cases would not be very strong evidence one way or the other. Even using a weak evidence standard of a likelihood ratio of 4, 3-6 QPac wins would be inconclusive. And that's playing 10 times!
 
Re: Octonion Power Rankings

octonion said:
It predicted 11/15 (73.3%) of the NCAA D1 tournament outcomes correctly last year, fitting on only non-tournament games. Is that good or bad?
Click to expand...


So, is this just something you are doing for fun this season, or is this something you are taking seriously? Can I expect to look up where my team ranks in the Octonion Ratings week to week next season and into the future?!
 
Re: Octonion Power Rankings

Hah - no, there's a time to respond to more substantial issues. Usually that's the weekends.
 
Re: Octonion Power Rankings

Hockey tends to be more weakly predictive than other sports, but you can pool the predictions and results over a large number of teams and years to compare the relative accuracy of different methods. You can still be wrong, of course, as team strengths aren't even constant within the same game. But is it a useful approximation?
 
Re: Octonion Power Rankings

I'm a professional sports analyst, but I'm an amateur at ice hockey analytics (so just for fun). I need to enhance it with some type of informative prior distribution to handle early-season games to make it more useful.
 
Re: Octonion Power Rankings

I like your rating system better than the PWR and RPI for sure. And from what I can tell it seems better than the KRACH as well. But for now I still favor Massey's Rating system. Your's mirrors his in many ways, but there are still some notable differences.


Your system seems to really not like MA-Lowell, Yale & BU. But really likes AFA, Ferris St, Mich Tech and Union?

Be interesting to figure out why that is?!


Massey's biggest differences with your system is where he has Miami(#7) & Union(#20).
 
Re: Octonion Power Rankings

octonion said:
I'm a professional sports analyst, but I'm an amateur at ice hockey analytics (so just for fun). I need to enhance it with some type of informative prior distribution to handle early-season games to make it more useful.
Click to expand...


So how do you get a job as a professional sports analyst?! lol Do you need a degree from MIT or something like that?
 
Re: Octonion Power Rankings

octonion said:
Poisson model, pooled NCAA divisions, home/away/neutral factors.

div = NCAA division
str = team strength
ofs = offensive strength
dfs = defensive strength
sos = strength of schedule

Code: 
  rk |             school              | div |  str  |  ofs  |  dfs  |  sos  
-----+---------------------------------+-----+-------+-------+-------+-------
   1 | minnesota                       |   1 | 4.230 | 1.916 | 0.453 | 1.489
   2 | quinnipiac                      |   1 | 3.858 | 1.536 | 0.398 | 1.460
   3 | miami                           |   1 | 3.469 | 1.402 | 0.404 | 1.458
   4 | minnesota-state                 |   1 | 3.443 | 1.753 | 0.509 | 1.502
   5 | north-dakota                    |   1 | 3.321 | 1.727 | 0.520 | 1.526
   6 | denver                          |   1 | 3.259 | 1.837 | 0.564 | 1.548
   7 | st-cloud-state                  |   1 | 3.216 | 1.720 | 0.535 | 1.499
   8 | new-hampshire                   |   1 | 3.173 | 1.687 | 0.532 | 1.470
   9 | umass-lowell                    |   1 | 3.113 | 1.565 | 0.503 | 1.428
  10 | notre-dame                      |   1 | 3.084 | 1.605 | 0.521 | 1.482
  11 | union                           |   1 | 3.012 | 1.570 | 0.521 | 1.448
  12 | rensselaer                      |   1 | 2.931 | 1.551 | 0.529 | 1.496
  13 | wisconsin                       |   1 | 2.868 | 1.369 | 0.477 | 1.496
  14 | providence                      |   1 | 2.863 | 1.544 | 0.539 | 1.482
  15 | boston-college                  |   1 | 2.808 | 1.761 | 0.627 | 1.437
  16 | western-michigan                |   1 | 2.786 | 1.295 | 0.465 | 1.459
  17 | nebraska-omaha                  |   1 | 2.679 | 1.760 | 0.657 | 1.495
  18 | air-force                       |   1 | 2.673 | 1.534 | 0.574 | 1.349
  19 | ferris-state                    |   1 | 2.625 | 1.463 | 0.558 | 1.475
  20 | dartmouth                       |   1 | 2.618 | 1.526 | 0.583 | 1.462
  21 | cornell                         |   1 | 2.541 | 1.377 | 0.542 | 1.502
  22 | yale                            |   1 | 2.527 | 1.576 | 0.624 | 1.486
  23 | niagara                         |   1 | 2.508 | 1.494 | 0.596 | 1.354
  24 | colorado-college                |   1 | 2.507 | 1.798 | 0.717 | 1.567
  25 | michigan-tech                   |   1 | 2.493 | 1.611 | 0.646 | 1.516
Click to expand...




When do you update your standings?
 
Re: Octonion Power Rankings

I'd be interested in an update as well, just to see how much a single 10-0 game improves Quinnipiac's numbers.
 
Re: Octonion Power Rankings

I have three graduate degrees, one of which was in biostatistics. I had studied gene microarrays and quantitative genetics and wasn't planning on working in baseball at all.
 
Octonion Power Rankings (updated 3/18)

Octonion Power Rankings (updated 3/18)

Including games from 3/17/2013.

Code: 
 rk  |             school              | div |  str  |  ofs  |  dfs  |  sos  
-----+---------------------------------+-----+-------+-------+-------+-------
   1 | minnesota                       |   1 | 4.133 | 1.898 | 0.459 | 1.489
   2 | quinnipiac                      |   1 | 4.031 | 1.611 | 0.400 | 1.457
   3 | miami                           |   1 | 3.431 | 1.400 | 0.408 | 1.456
   4 | minnesota-state                 |   1 | 3.416 | 1.718 | 0.503 | 1.504
   5 | north-dakota                    |   1 | 3.409 | 1.747 | 0.512 | 1.524
   6 | st-cloud-state                  |   1 | 3.322 | 1.757 | 0.529 | 1.498
   7 | new-hampshire                   |   1 | 3.209 | 1.690 | 0.527 | 1.473
   8 | denver                          |   1 | 3.181 | 1.794 | 0.564 | 1.550
   9 | union                           |   1 | 3.125 | 1.601 | 0.512 | 1.447
  10 | umass-lowell                    |   1 | 3.120 | 1.568 | 0.503 | 1.432
  11 | notre-dame                      |   1 | 3.096 | 1.593 | 0.515 | 1.481
  12 | wisconsin                       |   1 | 2.949 | 1.387 | 0.470 | 1.497
  13 | rensselaer                      |   1 | 2.903 | 1.560 | 0.537 | 1.498
  14 | boston-college                  |   1 | 2.855 | 1.767 | 0.619 | 1.437
  15 | providence                      |   1 | 2.838 | 1.533 | 0.540 | 1.491
  16 | nebraska-omaha                  |   1 | 2.710 | 1.743 | 0.643 | 1.500
  17 | yale                            |   1 | 2.686 | 1.603 | 0.597 | 1.486
  18 | ferris-state                    |   1 | 2.612 | 1.462 | 0.560 | 1.473
  19 | western-michigan                |   1 | 2.606 | 1.268 | 0.486 | 1.463
  20 | air-force                       |   1 | 2.580 | 1.547 | 0.600 | 1.351
  21 | colorado-college                |   1 | 2.571 | 1.800 | 0.700 | 1.570
  22 | boston-university               |   1 | 2.522 | 1.619 | 0.642 | 1.464
  23 | dartmouth                       |   1 | 2.521 | 1.505 | 0.597 | 1.464
  24 | niagara                         |   1 | 2.518 | 1.471 | 0.584 | 1.356
  25 | ohio-state                      |   1 | 2.493 | 1.389 | 0.557 | 1.494
 
Re: Octonion Power Rankings (updated 3/18)

Re: Octonion Power Rankings (updated 3/18)

Interesting... Big offensive jump for QPac, as you'd expect. The question is whether or not it's meaningful....
 
Re: Octonion Power Rankings

I'm sure it's flawed - hockey is a difficult sport to model. We'll see how it does in the tournament.
 
Re: Octonion Power Rankings

octonion said:
I'm sure it's flawed - hockey is a difficult sport to model. We'll see how it does in the tournament.
Click to expand...


Every system has its flaws, but compared to the VERY flawed PWR system NCAA hockey uses now, omg, its ridiculous that they still use that dinosaur of a rating system.

But thanks for posting your updated ratings. Will be looking forward to seeing the final standings after the conf tourney's are over.
 
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