1st ever SB Nation Power Rankings: 49ers in 9th place tie!
Everyone's a little down from the news of Manny Lawson's injury, so like any good entertainer, I'll try and distract you guys a little bit.
Since everybody else is doing it, the football sites here finally decided to debut the SB Nation Power Rankings. With some html help from The Sports Guru over at Mile High Report
I was able to compile league wide power rankings, which I present now for your viewing pleasure and debate. We received 18 total ballots and expect that number to rise in the coming weeks. I figure getting over half the sites is a pretty good turnout for this first week.
Basically, every team was ranked 1-32 and then there rank #'s were added up and divided by the total ballots (18) to get a rating. It's not the most scientific poll in the world, but it's fun and gives you an idea of things. For those curious, I voted the 49ers 13th. I love them and think they're going to be solid this year but based on the first two weeks I just couldn't rate them any higher.
So what do you think of the rankings? Who's too high and who's too low?
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7 comments
Comments
Good list
by rimrock101 on Sep 20, 2007 9:43 PM PDT reply actions 0 recs
Almost ranked even with Ravens
by Bob In Pacifica on Sep 21, 2007 5:56 AM PDT reply actions 0 recs
I can't believe...
by sfgfan on Sep 21, 2007 8:38 AM PDT reply actions 0 recs
much less two ties!
So unless I've forgotten how to do math, one person could submit any one of 2.6313083693369353016721801206e+35 (in windows calculator notation) possibilities. Ok, so that is way too much... I'll try to bring it down. I'll assume variance in groups of fours only (so the top four teams would be the same in each regardless of order, and so on down the line). Each group of four will have 24 possibilities (4x3x2x1), creating 8 groups of 24 possibilties that can be mixed and matched.
Man it's been a long time since I did anything resembling statistics or probability in a math class. Five years removed from math to begin with...
So that would work out as just 24 to the 8th power, no? Meaning one person could come up with 110,075,314,176 different combinations?
Well... it's less than before, anyway.
BUT the probability of averages levels it out! In this system there are 8 groups of 4 teams. Each team in the group of 4 is given to have an equal probability of being any spot 1-4. So the probability of a team averaging 1 (unanymous 1st place votes) is low, but the probability of a team averaging 2.5 (evenly distributed votes) is very high within an individual group. And rather than being dependent on huge numbers of combinations, it's dependednt on the tendency of those combinations to even out...
Anyway, I'm not nearly advanced enough in statistics or probability, nor am I close enough to the math experience I do have to work this out in numbers. What I will say is that I believe the rankings do GENERALLY fall into localized pockets of teams like my unfinished method uses (not as clean as groups of four, but general). Within these pockets there are further tendencies toward the top and the bottom of the order, but the probability for each team would still be to drift toward the mean of the group. I would imagine that because of this the probability of ties in the middle of each group is pretty high up to around 10 ballots (somewhat arbitrary estimation), and then of course continues to go down from there. Assuming there are like 8-10 "natural" groups in the NFL rankings (also kind of arbitrary), the fact that there are ties in only two of them (20-25%) would seem to show that by 18 ballots these chances are in fact thinning out pretty significantly...
But then again, a lot of this is semi-educated-ass-talking. If I had the capacity for these numbers I would have gladly cranked it out, but I can only go so far before I have to defer to "logic," which is significantly removed from hard fact.
Anyway, sorry for basically spending all this time coming up with very little that's worthwhile. It was fun for me, at least...
by howtheyscored on Sep 21, 2007 9:56 AM PDT up reply actions 0 recs
You went to Cal, right?
by sfgfan on Sep 21, 2007 10:39 AM PDT up reply actions 0 recs
To be honest
I probably could have worked this out five years ago in a snap. I just don't remember the relationships the numbers need to have to each other for these kinds of probabilities to work out. It looks like theres sine wave in there somewhere... maybe not a pretty one... trig was fun...
by howtheyscored on Sep 21, 2007 11:07 AM PDT up reply actions 0 recs
CS major
I seem to remember calculus somewhat, but linear algebra, stats, diff. EQs... they've all seemed (mostly) to escape me.
by sfgfan on Sep 21, 2007 11:21 AM PDT up reply actions 0 recs

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