On Fri, 26 Mar 2004 13:46:56 -0500, Wayne T Smith wrote:

>John T Whelan wrote, in part:
>> There is a straightforward extension which adds the effects of
>> home-ice advantage to the Bradley-Terry method used in KRACH.  The
>> resulting rating system is one I've taken to calling KASA (KRACH
>> Adjusted for Site Advantage).  It's not being published anywhere yet,
>> but I've got some code to calculate it.
>
>Interesting.  Can you tell us how this extension works, or give us a
>reference, please?

Reference: Davidson, R and Beaver, RJ (1977) "On extending the
Bradley-Terry model to incorporate within-pair order effects", Biometrics
vol. 33 p. 693-702.

The basic idea is that, as well as figuring out ratings for each team in
the usual way, you also figure out a rating for "home team", which might be
a number like 1.3. This figure applies to all teams. Then you scale up the
home team's rating by this figure, which reflects the advantage it has by
playing at home.

Example, using John's figures (and my 1.3):
Minn-Duluth rated 484, Notre Dame rated 191.
If Minn-Duluth at home, odds of winning are 1.3*484/191 = 3.29:1 (77%-23%)
If Notre Dame at home, odds of winning are 1.3*191/484 = 0.51:1 (34%-66%)

Notice how each team's chances of winning are slightly better at home than
on the road, as you'd expect. (77% vs. 66% for Minn-Duluth, 34% vs. 23% for
Notre Dame.)

(To estimate the "home team" rating, you find the team ratings that make
observed and predicted wins equal for each team, as usual, and also make
observed and predicted home wins equal, totalled up over all games with a
home team.)

>I've always figured "home ice advantage" varied with
>each team and what big parties might be on campus the day before each
>game. ;-)

Well, naturally :-)

It would be possible to estimate a home ice advantage separately for each
team, too. I expect John has code for this also :-)

>Next, we need a system to measure how a team has changed over the course
>of the season (wrt a specific or average team?).  Then KASA could be
>adjusted to measure the teams as they are now, not (so much) as they
>have been over the whole season.

One way to do this would be to give each game a "weight" according to how
recent it is. The difficulty here is that most of the inter-conference
games happen early in the season, and it's these games that are most needed
to establish how the conferences stack up against each other.

>Leaving seriousness behind ... then we could add factors for attendance,
>throw in a couple of polls, injury reports plus what Bob Norton thinks,
>and we'd have something better than the BCS!

Oh yeah!

Cheers,
Ken, not staking his statistical credentials on that.

--
Ken Butler
Brampton, Ontario, Canada