friedcheese.org

Sep 29, 2021
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)
Apr 9, 2021
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.
Jan 12, 2021
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
Jan 3, 2021
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)
Dec 20, 2020
college football poll - week 16

Not many changes after conference championships.

1 - Coastal Carolina (11-0) (24.75)
2 - BYU (10-1) (22.34375)
3 - Cincinnati (9-0) (20.609375)
4 - Louisiana (9-1) (20.1552734375)
5 - Notre Dame (10-1) (17.1912841796875)
6 - Clemson (10-1) (16.3787841796875)
7 - San José State (7-0) (12.20703125)
8 - Miami (8-2) (12.1214599609375)
9 - Alabama (11-0) (12.0)
10 - Army (9-2) (10.8701171875)
11 - Liberty (9-1) (10.71697998046875)
12 - Tulsa (6-2) (10.623046875)
13 - Ohio State (6-0) (9.25)
14 - Oklahoma State (7-3) (9.1953125)
15 - UCF (6-3) (9.1123046875)
16 - Texas A&M (8-1) (9.0)
17 - Boise State (5-2) (7.95703125)
18 - NC State (8-3) (7.79144287109375)
19 - Appalachian State (8-3) (7.7646484375)
20 - Indiana (6-1) (7.5)
21 - Ball State (6-1) (7.0)
22 - North Carolina (8-3) (6.9578857421875)
23 - Tulane (6-5) (6.849609375)
24 - Colorado (4-1) (6.8125)
25 - SMU (7-3) (6.69140625)
Dec 13, 2020
college football poll - week 15

Not many changes this week.

1 - Coastal Carolina (11-0) (24.625)
2 - BYU (10-1) (22.125)
3 - Louisiana (9-1) (19.8125)
4 - Cincinnati (8-0) (18.125)
5 - Notre Dame (10-0) (18.0703125)
6 - Clemson (9-1) (14.6328125)
7 - Miami (8-2) (11.53173828125)
8 - Alabama (10-0) (11.5)
9 - San José State (6-0) (11.203125)
10 - Tulsa (6-1) (10.833984375)
11 - Liberty (9-1) (10.703369140625)
12 - Boise State (5-1) (8.953125)
13 - Oklahoma State (7-3) (8.82421875)
14 - Appalachian State (8-3) (8.640625)
15 - Texas A&M (7-1) (8.5)
16 - UCF (6-3) (8.3544921875)
17 - Ohio State (5-0) (8.25)
18 - USC (5-0) (8.125)
19 - Army (8-2) (7.8857421875)
20 - NC State (8-3) (7.77783203125)
21 - Air Force (3-2) (7.59375)
22 - Indiana (6-1) (7.5)
23 - Iowa State (8-2) (7.396484375)
24 - Colorado (4-1) (7.0625)
25 - Buffalo (5-0) (6.875)
Dec 7, 2020
college football poll - week 14

Coastal Carolina moves to the front of the pack after its win over BYU, who stays in the #2 spot.

1 - Coastal Carolina (10-0) (22.927734375)
2 - BYU (9-1) (20.35546875)
3 - Louisiana (9-1) (19.208984375)
4 - Notre Dame (10-0) (17.97265625)
5 - Cincinnati (8-0) (17.96875)
6 - Miami (8-1) (15.31640625)
7 - Clemson (9-1) (14.26953125)
8 - Alabama (9-0) (11.0)
9 - San José State (5-0) (10.599609375)
10 - Tulsa (6-1) (10.427734375)
11 - Liberty (9-1) (9.455078125)
12 - Colorado (4-0) (9.375)
13 - Texas A&M (7-1) (8.5)
14 - Ohio State (5-0) (8.25)
15 - Boise State (4-1) (8.099609375)
16 - UCF (6-3) (8.0341796875)
17 - Florida (8-1) (8.0)
18 - Oklahoma State (6-3) (7.90234375)
19 - Marshall (7-1) (7.8544921875)
20 - Appalachian State (7-3) (7.787109375)
21 - Indiana (6-1) (7.5)
22 - NC State (8-3) (7.064453125)
23 - Air Force (3-2) (6.82421875)
24 - Buffalo (4-0) (6.375)
25 - Memphis (6-3) (5.740234375)
Dec 1, 2020
college football poll - week 13

Thanks to COVID, a last-minute Colorado v. SDSU game was played on Saturday, merging the Pac-12 component of the graph in with the mega-component occupied the ACC, Big 12, and friends. The Buffs’ win was good enough for them to become the first Pac-12 team to break into the Top 25, to boot.

Not much change at the top, as #1 - 8 remain the same as last week.

1 - BYU (9-0) (20.060546875)
2 - Cincinnati (8-0) (17.53125)
3 - Notre Dame (9-0) (17.34765625)
4 - Coastal Carolina (9-0) (17.083984375)
5 - Louisiana (8-1) (16.904296875)
6 - Marshall (7-0) (14.7607421875)
7 - Miami (7-1) (14.19140625)
8 - Clemson (8-1) (13.69140625)
9 - Appalachian State (7-2) (11.583984375)
10 - Alabama (8-0) (10.5)
11 - Tulsa (5-1) (10.076171875)
12 - Florida Atlantic (5-1) (9.330810546875)
13 - UCF (6-3) (8.6787109375)
14 - Liberty (9-1) (8.64935302734375)
15 - San José State (4-0) (8.6083984375)
16 - Oklahoma State (6-2) (8.41796875)
17 - Boise State (4-1) (8.3583984375)
18 - Texas A&M (6-1) (8.0)
19 - Florida (7-1) (7.5)
20 - Memphis (6-2) (7.466796875)
21 - Ohio State (4-0) (7.125)
22 - Colorado (3-0) (6.5)
- Indiana (5-1) (6.5)
24 - Buffalo (4-0) (5.75)
25 - NC State (7-3) (5.7281494140625)
Nov 22, 2020
college football poll - week 12

The Bearcats are closing in on the Cougars after their win over UCF yesterday.

The Pac-12 finally occupies a single connected component of the graph (we’re down to 5 total now!), with Oregon leading the pack at #32.

1 - BYU (9-0) (18.9404296875)
2 - Cincinnati (8-0) (17.25)
3 - Notre Dame (8-0) (16.2294921875)
4 - Coastal Carolina (8-0) (15.7705078125)
5 - Louisiana (7-1) (15.66796875)
6 - Marshall (7-0) (14.17041015625)
7 - Miami (7-1) (13.16162109375)
8 - Clemson (7-1) (12.9482421875)
9 - SMU (7-2) (10.8896484375)
10 - Tulsa (5-1) (10.044921875)
11 - Alabama (7-0) (10.0)
12 - Appalachian State (6-2) (9.2373046875)
13 - Florida Atlantic (5-1) (9.210205078125)
14 - Memphis (5-2) (8.94482421875)
15 - Oklahoma State (5-2) (7.90234375)
16 - San José State (4-0) (7.89129638671875)
17 - Northwestern (5-0) (7.75)
18 - Liberty (8-1) (7.74456787109375)
19 - UCF (5-3) (7.4150390625)
20 - Texas A&M (5-1) (7.25)
21 - Boise State (4-1) (7.20379638671875)
22 - Florida (6-1) (7.0)
23 - Nevada (5-0) (5.875)
24 - Ohio State (4-0) (5.5625)
25 - Texas (5-2) (5.21484375)
Nov 15, 2020
college football poll - week 11
I don’t think anyone is going to touch BYU as long as they keep winning, at least until bowl season.

I did a little analyzing of the data, and there are currently six different components of our graph:
- ACC, Big 12, and non-MAC G5 conferences. This component has 75 teams, which is why the poll is currently so skewed toward this group.
- SEC
- Big Ten
- MAC
- There are two Pac-12 groups! So far, the Arizona schools and USC have only played each other, so they’re still separated from the rest of the conference.
1 - BYU (8-0) (17.563232421875)
2 - Louisiana (7-1) (14.8857421875)
3 - Cincinnati (7-0) (14.859375)
4 - Notre Dame (8-0) (14.5625)
5 - Coastal Carolina (7-0) (13.69287109375)
6 - Marshall (7-0) (13.67431640625)
7 - Miami (7-1) (11.875)
8 - Liberty (8-0) (11.5)
- Clemson (7-1) (11.5)
10 - SMU (7-2) (10.671875)
11 - Alabama (6-0) (9.5)
12 - Oklahoma State (5-1) (9.484375)
13 - Tulsa (4-1) (9.1484375)
14 - Appalachian State (6-1) (8.92041015625)
15 - Memphis (4-2) (8.8359375)
16 - San José State (4-0) (7.6484375)
17 - UCF (5-2) (7.390625)
18 - Texas A&M (5-1) (7.25)
19 - Florida Atlantic (4-1) (6.875)
20 - Georgia Southern (6-2) (6.77099609375)
21 - Northwestern (4-0) (6.5)
- Florida (5-1) (6.5)
23 - Texas (5-2) (5.625)
24 - Boise State (3-1) (5.2734375)
25 - Nevada (4-0) (4.875)

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