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college football poll - week 10
Shockingly, Notre Dame’s win over 2-7 Navy is enough to vault them over the Georgia Bulldogs. I think one disadvantage of the coefficient of relationship algorithm the poll uses is that it rewards independents who play teams from lots of different conferences and thus have shorter “win” paths to more teams than teams that have only a small non-conference schedule.
Meanwhile, still-unbeaten Cincinnati and UTSA bump Michigan down to #5, but the Wolverines are still ahead of also-unbeaten Oklahoma.
1 - Notre Dame (8-1) (36.03125)
2 - Georgia (9-0) (34.1796875)
3 - Cincinnati (9-0) (31.53125)
4 - UT San Antonio (9-0) (28.6015625)
5 - Michigan (8-1) (27.9786376953125)
6 - Oklahoma (9-0) (27.8203125)
7 - Ohio State (8-1) (24.971710205078125)
8 - Oklahoma State (8-1) (23.87994384765625)
9 - Alabama (8-1) (23.5255126953125)
10 - Wisconsin (6-3) (22.80322265625)
11 - Michigan State (8-1) (22.129150390625)
12 - Ole Miss (7-2) (22.062744140625)
13 - Iowa (7-2) (21.707275390625)
14 - Texas A&M (7-2) (20.769775390625)
15 - Oregon (8-1) (19.92779541015625)
16 - Arkansas (6-3) (19.515869140625)
17 - Baylor (7-2) (19.1524658203125)
18 - Wake Forest (8-1) (18.79345703125)
19 - BYU (8-2) (16.35205078125)
20 - Kansas State (6-3) (16.07525634765625)
21 - Purdue (6-3) (15.57080078125)
22 - Penn State (6-3) (15.3408203125)
23 - Auburn (6-3) (14.14892578125)
24 - San Diego State (8-1) (13.547119140625)
25 - Louisiana (8-1) (13.27642822265625) -
college football poll - week 9
Michigan State’s comeback win against their in-state rivals isn’t quite enough to rank them higher than the Wolverines, but it is enough to vault them from #17 last week to #5 this week. Also the loss drops Michigan a spot, making way for Notre Dame to move in to #2. UGA still leads the field after its commanding victory in the World’s Largest Outdoor Cocktail Party.
1 - Georgia (8-0) (31.35546875)
2 - Notre Dame (7-1) (30.265625)
3 - Michigan (7-1) (29.578125)
4 - Cincinnati (8-0) (28.6953125)
5 - Michigan State (8-0) (28.4921875)
6 - Wake Forest (8-0) (26.41796875)
7 - Oklahoma (9-0) (26.265625)
8 - Baylor (7-1) (23.816436767578125)
9 - UT San Antonio (8-0) (23.43359375)
10 - Ohio State (7-1) (23.187042236328125)
11 - Oklahoma State (7-1) (21.16412353515625)
12 - Alabama (7-1) (20.1578369140625)
13 - Oregon (7-1) (18.94439697265625)
14 - Iowa (6-2) (17.972900390625)
15 - BYU (7-2) (17.61767578125)
16 - Ole Miss (6-2) (17.115478515625)
17 - Auburn (6-2) (16.68212890625)
18 - Wisconsin (5-3) (15.64697265625)
19 - Air Force (6-2) (14.676025390625)
20 - Texas A&M (6-2) (14.577392578125)
21 - Arkansas (5-3) (14.307861328125)
22 - San Diego State (7-1) (13.8262939453125)
23 - Kansas State (5-3) (13.49224853515625)
24 - SMU (7-1) (13.060562133789062)
25 - Fresno State (7-2) (11.777587890625) -
college football poll - week 8
The Wolverines move up a notch after Iowa State knocks Oklahoma State out of the #2 spot.
1 - Georgia (7-0) (28.6484375)
2 - Michigan (7-0) (27.28125)
3 - Notre Dame (6-1) (25.3515625)
4 - Cincinnati (7-0) (25.015625)
5 - Wake Forest (7-0) (23.953125)
6 - UT San Antonio (8-0) (22.20703125)
7 - Oklahoma (8-0) (22.150390625)
8 - Oklahoma State (6-1) (21.061279296875)
9 - Ole Miss (6-1) (20.365966796875)
10 - Baylor (6-1) (19.3040771484375)
11 - San Diego State (7-0) (19.2744140625)
12 - Iowa (6-1) (19.1669921875)
13 - Ohio State (6-1) (18.745849609375)
14 - Kentucky (6-1) (18.337890625)
15 - Alabama (7-1) (18.17333984375)
16 - Oregon (6-1) (16.79638671875)
17 - Michigan State (7-0) (16.7353515625)
18 - Auburn (5-2) (15.111572265625)
19 - Air Force (6-2) (14.5)
20 - SMU (7-0) (13.953125)
21 - Texas A&M (6-2) (13.8603515625)
22 - Arkansas (5-3) (13.801025390625)
23 - Wisconsin (4-3) (13.535400390625)
24 - Kansas State (4-3) (12.871826171875)
25 - Penn State (5-2) (12.57861328125) -
college football poll - week 7
Oklahoma States moves in to #2 after taking out Texas, and Iowa drops from the top three after losing to the Boilermakers.
1 - Georgia (7-0) (27.828125)
2 - Oklahoma State (6-0) (23.859375)
3 - Michigan (6-0) (22.5654296875)
4 - Cincinnati (6-0) (22.28515625)
5 - Notre Dame (5-1) (20.3125)
6 - Oklahoma (7-0) (19.970703125)
7 - Iowa (6-1) (17.3515625)
8 - Baylor (6-1) (16.90966796875)
9 - Kentucky (6-1) (16.90625)
10 - Auburn (5-2) (16.12890625)
11 - UT San Antonio (7-0) (15.7919921875)
12 - Ohio State (5-1) (15.4375)
13 - Ole Miss (5-1) (15.3662109375)
14 - Penn State (5-1) (15.068359375)
15 - Wake Forest (6-0) (15.001708984375)
16 - Alabama (6-1) (14.974609375)
17 - Air Force (6-1) (13.939453125)
18 - Michigan State (7-0) (13.41552734375)
19 - Arkansas (4-3) (11.929443359375)
20 - Oregon (5-1) (11.349609375)
21 - San Diego State (6-0) (11.158203125)
22 - SMU (6-0) (10.7703857421875)
23 - Coastal Carolina (6-0) (10.5211181640625)
24 - Purdue (4-2) (10.234375)
25 - UCLA (5-2) (10.021484375) -
college football poll - week 6
Iowa moves into #3 after its comeback win against Penn State, and Alabama drops down to #14 after its shocking loss to Texas A&M.
1 - Georgia (6-0) (23.74951171875)
2 - Michigan (6-0) (19.46875)
3 - Iowa (6-0) (18.91845703125)
4 - Oklahoma State (5-0) (18.513671875)
5 - Oklahoma (6-0) (17.775390625)
6 - Notre Dame (5-1) (16.3406982421875)
7 - Cincinnati (5-0) (16.2666015625)
8 - Kentucky (6-0) (15.55224609375)
9 - Wake Forest (6-0) (13.91351318359375)
10 - Penn State (5-1) (13.90771484375)
11 - Ohio State (5-1) (13.1221923828125)
12 - UT San Antonio (6-0) (12.58984375)
13 - Michigan State (6-0) (11.88037109375)
14 - Alabama (5-1) (11.342041015625)
15 - Arkansas (4-2) (11.32281494140625)
16 - Ole Miss (4-1) (10.5645751953125)
17 - SMU (6-0) (10.44287109375)
18 - Kansas State (3-2) (9.728271484375)
19 - BYU (5-1) (9.56646728515625)
20 - Arizona State (5-1) (9.080535888671875)
21 - Air Force (5-1) (9.031219482421875)
22 - Oregon (4-1) (8.99066162109375)
23 - Auburn (4-2) (8.652099609375)
24 - Texas (4-2) (8.269073486328125)
25 - Baylor (5-1) (7.874320983886719) -
college football poll - week 5
The Dawgs leap over Michigan into the top spot after their shutout of Arkansas.
1 - Georgia (5-0) (17.612518310546875)
2 - Michigan (5-0) (15.0433349609375)
3 - Oklahoma State (5-0) (12.84661865234375)
4 - Oklahoma (5-0) (12.1279296875)
5 - Iowa (5-0) (12.031768798828125)
6 - Notre Dame (4-1) (11.88616943359375)
7 - BYU (5-0) (11.61376953125)
8 - Alabama (5-0) (11.2305908203125)
9 - Cincinnati (4-0) (10.474334716796875)
10 - Arkansas (4-1) (10.458831787109375)
11 - Penn State (5-0) (10.407045364379883)
12 - UT San Antonio (5-0) (10.279476165771484)
13 - Wake Forest (5-0) (9.6640625)
14 - Texas (4-1) (9.531829833984375)
15 - Kentucky (5-0) (9.483055114746094)
16 - Ohio State (4-1) (8.579238891601562)
17 - Western Michigan (4-1) (8.2679443359375)
18 - Oregon (4-1) (7.813140869140625)
19 - Arizona State (4-1) (7.7374114990234375)
20 - Kansas State (3-2) (7.7283935546875)
21 - Michigan State (5-0) (7.4501953125)
22 - Maryland (4-1) (7.386932373046875)
23 - Wyoming (4-0) (7.1614990234375)
24 - Auburn (4-1) (6.868831634521484)
25 - UCLA (3-2) (6.694671630859375) -
college football poll - week 4
A little delay this season as I had to make some tweaks to the code. In particular, https://collegefootballdata.com/ switched to requiring a (free) API key, which broke CFBScrapy. So I switched to the official Python interface, cfbd.
But it’s working now, so a-polling we will go!
1 - Michigan (4-0) (10.453125)
2 - Oregon (4-0) (8.6806640625)
3 - Notre Dame (4-0) (8.4375)
4 - Georgia (4-0) (8.03125)
5 - Oklahoma State (4-0) (7.96875)
6 - Arkansas (4-0) (7.625)
7 - Alabama (4-0) (6.375)
8 - UCLA (3-1) (6.22265625)
9 - UT San Antonio (4-0) (5.8916015625)
10 - Fresno State (4-1) (5.861328125)
11 - Penn State (4-0) (5.78125)
12 - Iowa (4-0) (5.75)
13 - BYU (4-0) (5.5)
14 - Kentucky (4-0) (5.375)
- Michigan State (4-0) (5.375)
16 - Army (4-0) (5.3125)
17 - Maryland (4-0) (5.2578125)
18 - Oklahoma (4-0) (5.1953125)
19 - Purdue (3-1) (4.625)
20 - Wyoming (4-0) (4.28125)
21 - Boston College (4-0) (4.25)
- Texas (3-1) (4.25)
23 - Baylor (4-0) (4.0)
24 - Wake Forest (4-0) (3.875)
25 - Ole Miss (3-0) (3.828125) -
strange adventures in algebra
I’ve been catching up on my comic book reading recently, and saw a fun little math problem at the bottom of the first page of Tom King’s Strange Adventures #2. Mr. Terrific’s T-spheres are quizzing him on a little math problem:
In the equation \(x^2 + mx + n = 0\), \(m\) and \(n\) are integers. The only possible value of of \(x\) is \(-3\). What is the value of \(m\)?
Mr. Terrific correctly guesses, “six”, apparently nearly instantly. Why is this the answer?
This is a quadratic equation, and so it has either zero, one, or two real solutions. Recall the quadratic formula, i.e., a quadratic equation of the form \(a x^2 + bx + c = 0\) has solution(s):
\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]In particular, we have a unique solution when \(b^2 - 4ac = 0\), and in this case, this solution is
\[x = -\frac{b}{2a}\]In Mr. Terrific’s equation, we have \(a = 1\), \(b = m\), and \(c = n\), so the unique solution is:
\[x = -\frac{m}{2\cdot 1} = -\frac{m}{2}\]Since the T-sphere says that \(x = -3\), we have
\[-3 = -\frac{m}{2}\] \[m = 6\]The T-sphere doesn’t ask Mr. Terrific the value of \(n\), but we can figure it out. Recall that \(b^2 - 4ac = 0\), or in this case:
\[m^2 - 4\cdot 1\cdot n = 0\] \[6^2 - 4n = 0\] \[4n = 36\] \[n = 9\]Also, the T-sphere didn’t really need to specify that \(m\) and \(n\) were integers. Indeed, these are the only complex numbers that work.
Geometrically, we’re looking for a parabola with an \(x\)-intercept of \(-3\), and so it must have equation
\(y = a(x + 3)^2 = a(x^2 + 6x + 9) = ax^2 + 6ax + 9a\),
but we know that \(a = 1\), and so we obtain the same result.
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college football poll - championship edition
After trouncing the Buckeyes last night, Alabama pulls into a commanding lead to finish with its fourth friedcheese.org national championship. They previously won in 2009 (the first year of the poll!), 2015, and 2016, although the latter two are retroactive (i.e., I wasn’t actively updating the poll during those seasons.)
Not surprisingly, 32.3203125 “wins” is the lowest total for a champion yet, given that so few games were played this year in comparison to a season not taking place during a global pandemic… The next closest is Florida State’s 39.34375 “wins” in 2014.
1 - Alabama (13-0) (32.3203125)
2 - Louisiana (10-1) (24.53650665283203)
3 - Coastal Carolina (11-1) (22.807388305664062)
4 - BYU (11-1) (22.77869415283203)
5 - Texas A&M (9-1) (22.6640625)
6 - Ohio State (7-1) (21.255859375)
7 - Oklahoma State (8-3) (21.0865478515625)
8 - Ball State (7-1) (18.4404296875)
9 - Oklahoma (9-2) (18.063720703125)
10 - Texas (7-3) (17.0460205078125)
11 - Iowa State (9-3) (17.0196533203125)
12 - Cincinnati (9-1) (16.833526611328125)
13 - Liberty (10-1) (16.540557861328125)
14 - Notre Dame (10-2) (16.498046875)
15 - Georgia (8-2) (16.21002197265625)
16 - Buffalo (6-1) (15.919921875)
17 - Clemson (10-2) (15.685546875)
18 - San José State (7-1) (13.0771484375)
19 - West Virginia (6-4) (12.0069580078125)
20 - Northwestern (7-2) (11.595100402832031)
21 - TCU (6-4) (10.821533203125)
22 - Miami (OH) (2-1) (10.22021484375)
23 - Nevada (7-2) (9.81689453125)
24 - Florida (8-4) (8.2169189453125)
25 - Appalachian State (9-3) (8.1641845703125)Anyway, just so I have it written down somewhere, here is a list of all the friedcheese.org national champions to date, based on the current algorithm:
2009 - Alabama
2010 - Auburn
2011 - LSU
2012 - Notre Dame
2013 - Florida State
2014 - Florida State
2015 - Alabama
2016 - Alabama
2017 - UCF
2018 - Clemson
2019 - LSU
2020 - Alabama -
college football poll - bowl edition
Things are finally (kind of) looking normal after bowl season. Our graph is finally connected! The Crimson Tide vault to a commanding lead before next week’s champsionship game, and their scarlet and gray opponents jump to #6. (If the Buckeyes can pull of a win, will they end up in #1? I think there’s a decent chance – they’d inherit a bunch of SEC “wins” from ‘Bama.)
1 - Alabama (12-0) (29.3203125)
2 - Louisiana (10-1) (24.53650665283203)
3 - Coastal Carolina (11-1) (22.807388305664062)
4 - BYU (11-1) (22.77869415283203)
5 - Texas A&M (9-1) (22.6640625)
6 - Ohio State (7-0) (22.255859375)
7 - Oklahoma State (8-3) (21.0865478515625)
8 - Ball State (7-1) (18.4404296875)
9 - Oklahoma (9-2) (18.063720703125)
10 - Texas (7-3) (17.0460205078125)
11 - Iowa State (9-3) (17.0196533203125)
12 - Cincinnati (9-1) (16.833526611328125)
13 - Liberty (10-1) (16.540557861328125)
14 - Notre Dame (10-2) (16.498046875)
15 - Georgia (8-2) (16.21002197265625)
16 - Buffalo (6-1) (15.919921875)
17 - Clemson (10-2) (15.685546875)
18 - San José State (7-1) (13.0771484375)
19 - West Virginia (6-4) (12.0069580078125)
20 - Northwestern (7-2) (11.970100402832031)
21 - TCU (6-4) (10.821533203125)
22 - Miami (OH) (2-1) (10.22021484375)
23 - Nevada (7-2) (9.81689453125)
24 - Florida (8-4) (8.2169189453125)
25 - Appalachian State (9-3) (8.1641845703125)
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