A quality win over Notre Dame pushed Stanford up a few notches, while OSU falls a notch on a bye week.

At this point BCSRank would put LSU vs Houston in the BCS Championship game — a scenario that is incredibly unlikely. Also, while Bama sits on nearly all ranking systems at a solid #2, according the BCSRank they are down at #7. Again, I suspect there is bias against teams in good conferences and need a way to address this. I would like to do this without sacrificing the generality of the method.

RANK                     TEAM LOSSES      SCORE
  1                       LSU      0      0.01554
  2                   Houston      0      0.01212
  3              Oklahoma St.      1      0.01153
  4                 Boise St.      1      0.01118
  5                  Stanford      1      0.01097
  6             Virginia Tech      1      0.01094
  7                   Alabama      1      0.01086
  8                       TCU      2      0.01059
  9                  Oklahoma      2      0.01054
 10       Southern California      2      0.01047
 11                    Oregon      2      0.01042
 12                  Michigan      2      0.01041
 13              Michigan St.      2      0.01029
 14            South Carolina      2      0.01012
 15                   Clemson      3      0.01007
 16                  Nebraska      3      0.01000
 17                 Wisconsin      2      0.00999
 18                    Baylor      3      0.00986
 19                  Arkansas      2      0.00973
 20                Kansas St.      2      0.00957
 21            Southern Miss.      2      0.00935
 22                   Georgia      2      0.00932
 23                Notre Dame      4      0.00916
 24                  Iowa St.      5      0.00901
 25              Arkansas St.      2      0.00899

As a student of statistics/computer science and a fan of college football — I got pretty interested in just how these computer rankings work. This pages lists the different algorithms that are used, but the sites don’t really describe how the teams are ranked (probably trade secrets or something).

It occurred to me that Larry Page and Sergey Brin invented a this little algorithm to rank web pages on the internet based on their credibility. The idea behind their ranking algorithm is that more credible pages will have more links to them AND that links from more credible pages are worth more. Well, this is quite similar to college football. Teams that win lots of games are better teams (i.e. more credible). So instead of links between pages we have links between teams. A link is established between each team that has completed a game. The link is directional and goes from the team that lost to the team that won.

This is quite intuitive in that if you beat a team that loses to a lot of teams (e.g. a webpage that promiscuously links to all other pages) you are going to get less credit than if you beat a team that has never lost (e.g. a page that all other pages point to, but where it only points to you). Unless two teams play twice in a year (which typically won’t happen in the regular season) then there will at most one link between each team.

My implementation is far from finished and there are definitely some limitations, but I figure the internet may be able to help me improve the method so here it is.

As an example, lets say we have three teams (A, B, and C), we define our link matrix according the results of those teams playing each other.

L = ((0, 0, 0),

     (1, 0, 0),

     (1, 1, 0))

We call the matrix L for links for losses, you pick. When we try to invert this matrix according to the algorithm we cannot so to make the matrix non-singular I set the diagonal equal to 1.

L = ((1, 0, 0),

     (1, 1, 0),

     (1, 1, 1))

This makes the matrix invertible and we can implement the algorithm as described on Wikipedia. This means that team A has never lost, team B lost only to team A, and team C lost to both A and B.

The other parameter we need is the dampening factor — which for the PageRank algorithm is the probability that a random surfer goes to a random page on the internet rather than using the links. When this value is set to 1 that means the surfer always uses the links and will end up on a terminally linked page. For our football ranking this means that the value will congregate in the top one or two teams (analogous to the surfer ending up at a terminally linked page). We want to spread out the scores a bit more than that so we will set this dampening factor quite low (~0.3).

So, in week 13 of the 2011 season, what does PageRank say about the way the teams should be ranked? Here are the top 25.

Rank                     Team  Losses  RankScore
------------------------------------------------
  1                       LSU   0      0.01474
  2              Oklahoma St.   1      0.01192
  3                   Houston   0      0.01179
  4                   Alabama   1      0.01141
  5                 Boise St.   1      0.01094
  6             Virginia Tech   1      0.01082
  7                       TCU   2      0.01070
  8                  Stanford   1      0.01055
  9                   Clemson   2      0.01046
 10                  Oklahoma   2      0.01040
 11       Southern California   2      0.01039
 12                  Michigan   2      0.01037
 13                  Arkansas   1      0.01036
 14                    Oregon   2      0.01029
 15              Michigan St.   2      0.01009
 16                  Nebraska   3      0.01004
 17                Kansas St.   2      0.00979
 18                    Baylor   3      0.00972
 19            South Carolina   2      0.00952
 20                  Penn St.   2      0.00951
 21                 Wisconsin   2      0.00950
 22            Southern Miss.   2      0.00941
 23                Notre Dame   3      0.00937
 24                  Iowa St.   4      0.00927
 25                   Rutgers   3      0.00917

Now this is pretty good for a first pass at ranking. LSU is clearly the best team going into week 13 and indeed they do come out on top of our rankings. One interesting feature of our rankings is that Houston is right there at #3 above Alabama. This is the result of our algorithm assuming all teams are equal at the start.  It’s a little disappointing that Stanford is sitting at #8 behind a two-loss TCU, but TCU has beat “higher quality” opponents (i.e. Boise State) and that’s contributing their score.

Another interesting/curious ranking is Arkansas sitting very low at #13. This makes me wonder about biases against conferences that are filled with good teams (i.e. SEC West). Because a team has to play the teams in their own conference more than from other conferences this may bias against teams in good conferences. I have not figured out a way to visualize or estimate this bias yet. Once we can understand it we can invent methods for removing it.

If you have ideas for improving this method please feel free to comment. This may ultimately prove a futile effort and will not perform as well as those established ranking systems — but at least it’s an open solution based on some sound CS models.

I’m only posting this for prosterity sake, you should really go to the original blog post (link above) for more detailed information.

Close down iTerm and run this bash script from Terminal. Open up iTerm and you’ll see the changes.

http://twitter.com/caddymob

I think I’m waiting now.

UPDATE:
Jason posted details describing his troubles and how he worked around it here:
http://corneveaux.com/blog/installing-snow-leopard-a-big-fail-and-a-work-around

My Trekkie heart has melted! I am in love and I won’t deny it.  I am ready to stand up on the roof tops and proclaim my love for the series that, up until last night, I believed was forever destined for re-run nostalgia.  Too much?

Too bad!  I am thrilled with the new movie.  I am head over heals for the young, sexy, talented new cast and am delighted that the writers tackled the new/old story line with a splash of nostalgia and a heap of creativity.

It’s a whole new game now, we can again visualize a Star Trek story line that isn’t confined to the plot devices that were relevant 10, 20, 30, or even 40 years ago.  I love that I don’t have to worry about how what happened in this story might affect my beloved Picard (le sigh Jean Luc).  I don’t have to worry about plot lines that no longer make sense (with the major exception of Spock Prime living out his life in a parallel universe as opposed to the universe we all know and love).  In all honesty, this is a huge relief.

Besides, this new cast brought the “sex” back to the series.  Never had I thought to think of what a restrained yet sensual kiss from a Vulcan might be like.  Thank you Zachary Quinto for making it abundantly clear that T’Pol was not the only sexy Vulcan in existence.   I am doing my best not to sound like an obsessed fan-girl, but I don’t think I am succeeding.  Forgive me men if you do not share my good opinion in the lusciousness of the Spock-Uhura kiss.

More to that point, as a woman, I always had a hard time relating to Kirk.  In TOS he was the John Wayne of the Federation.  No rules, lots of sex, and your mans-man!  But after Chris Pine’s performance, I feel like I understand Kirk better.  All of the above still holds true, but it just makes sense now.  Don’t bash me for not “getting it” sooner, I am just a little late to arrive on the Captain Kirk bandwagon.   Oh, I almost forgot to mention, the young Kirk is super sexy too.

I know that I am a minority in the Trek Universe (being young and female), so perhaps my male counter-parts won’t share the same passion that I do for this new/old series.  I know there are things to complain about when a favorite story attempts to expand in a new direction (don’t get me started on the Harry Potter movie franchise), but I think that this deserves an “A” for effort!  Keep ‘em comin’ boys.

What I have found most dissapointing is the interface for Copy and Paste. I loaded up the CNN front page and tried to copy a few phrases. It didn’t go so well. It keeps trying to copy the entire text. Then it displays little crop buttons, but don’t even think of trying to use them. If you drag toward the edge of the screen (like when you’d want to scroll down) they switch modes and become completely unusable.

Perhaps with some more time I would be able to figure out how to use it nicely, but this is way outside of “it just works” right now. Hopefully the Apple designers will be improving this feature before 3.0 is released to the public. Otherwise there are going to be a lot of very frustrated people out there.

Oh, and not having to enter my username/password every time I need to log into a website. Priceless.

I don’t want to give too much away, but it’s loads of fun and it’s free. Download it now and have some fun with your friends!

Free Download here.

-Spicy

Visit Mophilia now to sign up!

-Spicy

Stay tuned!