A collection of answers to questions about the NEW college hockey
computer ranking.
 
>From: Matthew Merzbacher <[log in to unmask]>
 
>I assume you'd get the same results by putting the NCAA champions at 100 and
>working down instead of selecting a bad team and working up.
 
You get the same results no matter what team you select as the
reference team. (Before normalizing) if you pick MSU at the ref team,
then they will get a rating of zero and everyone else will be negative.
If you pick Kent, then everyone else will be positive. I tried it with
several ref teams and always got the exact same ratings. That is one
reason I normalized:  then you can't tell which team I picked. Since it
doesn't matter in the end, why bother even knowing it?
 
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>From: "Steve M. Kapetanakis" <[log in to unmask]>
 
>>If the winners were on the road, add 1;if home subtract 1; if neutral, 0.
>
>>If the teams tied, then start with zero, call the visiting team the winner,
>>and apply the home/road rule from above.
>
> Do I understand this correctly, for a tie game on non-neutral ice the
> visiting team gets 20 points, 20 for the win + 1 for road - 1 for OT.
> And the home team gets nothing!
 
Nope. First rule: if one team gets +20, the other MUST get -20. (This
is inherent in the mathematical formulas and there is little I can do
about it.)
 
Second: for ties, apply the home/road rule ONLY, not the "winner gets 20
rule" or the overtime rule.
For example,
>>If A and B had tied, then B would get +1 and A -1.
 
That's it, 1 lousy point for a tie.
 
I experimented with ties early on in my research with Leake's system.
(He never mentioned ties in his paper, so I was worried about the large
numbers of ties in hockey compared to football.) I had 4 teams, 1
clearly the top team and 1 clearly the last. I applied the ranking
(without home/away stuff) and the numbers supported this. Then I added
1 more game: the top team tying the last place team (I used a GOM = 0).
The top team went down and the bottom team went up. Neither team went
up/down as much as if they had won/lost. I thought this made sense.
This supported what I thought SHOULD happen. I felt warm inside. (^;
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>From: [log in to unmask]
>
>    This doesn't help poor teams who gain ties with good teams, among
>    others.  If Michigan State goes to Kent and the game ends up a tie,
>    MSU gets +1 and Kent gets -1 (if I understand correctly).  Conversely,
>    a Kent one-goal win at Notre Dame or Huntsville is worth 22 points.
 
Yes, you got the points correct. But, fortunately, we do not just look
at how many points a team earned. With the schedule graph, we know who
everybody played and beat. From Kent's perspective, that -1 branch to
MSU will probably raise its rating more than the +22 against Notre Dame
because MSU is a better team. How do we know it is better? The MSU node
has LOTS of positive branches coming out of it and ND has a lot of
negative branches.
 
Think of it this way: if you win, you get +20; if you lose, -20; if you tie,
then you accomplished a feat somewhere between winning and losing and
zero is a nice middle ground.
 
Bad teams *are* rewarded by tying better teams with this system. It
works like this: when two nodes (teams) are connected by a branch of
zero value, their ratings will tend to be the same. Thus if Kent and
MSU tie, the math will try to push these two ratings together to be
equal. This is not always possible because of other constraints
(branches), but we try.
 
If Kent were to *beat* MSU, their +20 would tend to raise Kent's rating
above MSU's. Kent's +22 vs. ND will push Kent's rating above ND's. But when
ND's rating is already the pits, it won't do Kent much good.
 
Inconsistencies will arise, however. Say if Kent beats MSU, MSU beats
Brown and Brown beats Kent, then what? That is where the least squares
approximation comes in. We pick the ratings that give us the smallest
error from the "perfect" rating.
 
Remember, the Game Outcome Measure is only an indication of how you did
for that game, independent of who you played. It is the system of equations,
based on the schedule graph AND the GOMs, that determines your rating.
 
>    Why 20?  This overshadows the "subtract one for winning in OT" so
>    that OT is hardly a factor, along with road/home/neutral.
 
Exactly, the OT/home stuff isn't very important. I planned it that way.
 
Here is how I got at the number 20.
 
I started with getting 1 point per margin of victory. I put a cap of 5
to discourage running up the score. Then I included the home-away at +/- 1.
Home ice is worth about 1 goal (0.7, actually), so that meshes with the
margin of victory number. The overtime minus is to give you credit for
winning in OT, but to take away that extra goal that you scored in it.
Then selecting a victory bonus of 20 gave a good balance (IMO) with the
other numbers. Margin of victory is at most 20% as important as winning.
The site of the game isn't very important, only 5%. Going into OT is also
not too important, only 5%.
 
I am certainly open to arguments about why 100 or 5.65 points should be awarded
for winning.
 
Thanks for the input. Keep the comments & questions coming.
 
Keith