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A More Objective College Football Rankings System

College football playoff season is upon us and since I am a USC fan I was curious how our résumé actually stacks up against those SEC/Big Ten schools statistically.

Back in college I was pretty obsessed with this problem and was really inspired by this paper which describes a ranking system that is both simple and powerful. To me, it is the most attractive of the many ways to rank teams when all the teams have played different schedules and have limited sample sizes.

This method takes into account your body of work plus your opponent's body of work plus your oponnent's opponent's ad infinitum. It discounts these indirect result by a tunable parameter. The author's also do the math so that the solution is solved using algebra. The authors use only wins/losses in their rankings but here I have extended it so that margin of victory also matters. Essentially when team a plays team b, team a accumulates points in its favor against team b and team b does the same each according to the outcome of the game. You end up with a network of results (represented as as matrix) and then do some math to figure out how many total points each team ends up with when factoring in all the other teams results.

The nice thing about this problem is there are tunable parameters. Here I have parameterized the ratings using the following parameters:

• alpha - this is the original parameter from the paper linked above. It represents how much emphasis to place on strength of schedule vs direct results
• beta - this is gets multiplied by the adjusted margin of victory, determining relative importance of margin of victory
• zeta - this the amount of points a team gets for actually winning the game and the amount a team loses when they lose the game
• hfa - this is the amount the adjusted margin of victory get adjusted to account for home field advantage

If team i plays team j and wins, the paper says that $A_{ji}$ = 1 asumming they've just played once. The paper also says that $A_{ij} = 0$ meaning that team j gets no points for this matchup no matter how close the game actually was. In my formulation, if team i plays team j and wins by a score of $p_{i}$ to $p_{j}$, then $A_{ij} = 1 + \zeta + \beta\cdot adjmargin$ and $A_{ji} = 1 - \zeta - \beta\cdot adjmargin$. I reversed the indexes since it makes more sense to me. To compute adjusted margin I take $p_{i}$ subtracted $p_{j}$ subtracted the $hfa$ parameter times an indicator if either team a or team b played at home. Let's call that $ham$ for home field adjust margin. To compute the adjusted margin in the end I do this $adjmargin = \log(|ham| + 1)\cdot sign(ham)$. The reason for the log is intuitive - the impressiveness of a win is no proportional to the marign of victory but closer to the log of it.

The nice this about this rating/ranking system is that it has parameters that you can fit to data. In my mind ratings are as good as they can predict the future. So here I download a bunch of game reuslt data from the massey rating website and implement the rating system and then use them to predict a future week of games using the ratings for each team from the games up to that week (using logistic regression). I use logloss of the predictions to measure the success of the ratings - the better the ratings the lower the logloss of the regression is. I kept the seeds the same between runs so that each parameter combination had the same games to predict. Before setting up the final parameterized verison I implemented the original formulation from the paper and predicting the same games it had a logloss of . I iterated a bit on the ratings to come up with this formulation and below is the final tuning process where I run a grid search for the best combination of parameters and output the final ratings.

Ultimately what it shows that even though the humans favor USC over Alabama, Tennessee and Ohio State, the cold hard numbers say that those teams' body of work is more impressive. Not saying that this is necessarily the way the CFB should be determined, but sometimes it's useful and neat to check our human biases with objective numbers.

import pandas as pd
pd.options.display.max_rows = 999
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import log_loss
import requests
from bs4 import BeautifulSoup
import datetime
import json
import itertools

downloading the data and parsing it to a dataframe:

games = []
url = 'https://masseyratings.com/scores.php?s=cf%s&sub=ncaa-d1&all=1&sch=on'
id_mappings = {}
for year in range(1995, 2023):
    r = requests.get(url % (year,))
    soup = BeautifulSoup(r.text)
    lines = soup.find('pre').text.splitlines()
    sep1 = datetime.date(year, 9, 1).weekday()
    week1_cutoff = datetime.date(year, 9, 4 + -1 * ((sep1 - 5) % -7))
    team_to_id = {}
    for line in lines:
        game = [year]
        pieces = line.split()
        if len(pieces) < 5:
            continue
        date = datetime.date(*map(int, pieces.pop(0).split('-')))
        if date >= datetime.date.today():
            continue
        week = max(1, ((date - week1_cutoff).days - 1) // 7 + 2)
        game.extend([week, date])
        for _ in range(2):
            team, is_home = '', False
            while True:
                new_piece = pieces.pop(0)
                try:
                    score = int(new_piece)
                    break
                except ValueError:
                    team = team + (' ' if team else '') + new_piece
            if team.startswith('@'):
                is_home = True
                team = team[1:]
            if team not in team_to_id:
                team_to_id[team] = len(team_to_id)
            game.extend([team_to_id[team], is_home, score])
        games.append(game)
    id_mappings[year] = {val: key for key, val in team_to_id.items()}

columns = [
    'year', 'week', 'date',
    'team_a', 'team_a_home', 'team_a_score',
    'team_b', 'team_b_home', 'team_b_score'
]
df = pd.DataFrame(games, columns=columns).sort_values('date', ascending=True)
df.to_csv('df.csv', index=False)
with open('id_mappings.json', 'w') as f:
    json.dump(id_mappings, f, indent=4)

df = pd.read_csv('df.csv')
with open('id_mappings.json', 'r') as f:  
    id_mappings = {int(year): {
        int(id_): name for id_, name in map_.items()
    } for year, map_ in json.load(f).items()} #cause keys cant be int in json
    school_lookup = {year: {
        name: id_ for id_, name in map_.items()
    } for year, map_ in id_mappings.items()}

the parsed games:

df.tail(15)

	year	week	date	team_a	team_a_home	team_a_score	team_b	team_b_home	team_b_score
40876	2022	13	2022-11-26	14	True	21	205	False	17
40877	2022	13	2022-11-26	125	True	26	145	False	13
40878	2022	13	2022-11-26	127	True	28	141	False	23
40879	2022	13	2022-11-26	129	True	37	110	False	0
40880	2022	13	2022-11-26	113	False	44	182	True	7
40881	2022	13	2022-11-26	32	False	42	131	True	16
40882	2022	13	2022-11-26	133	False	45	138	True	23
40883	2022	13	2022-11-26	34	True	35	97	False	16
40884	2022	13	2022-11-26	36	False	46	143	True	39
40885	2022	13	2022-11-26	116	False	49	93	True	46
40886	2022	13	2022-11-26	148	True	49	153	False	27
40887	2022	13	2022-11-26	170	False	48	151	True	19
40888	2022	13	2022-11-26	192	False	37	183	True	30
40889	2022	13	2022-11-26	160	True	47	103	False	27
40890	2022	13	2022-11-26	13	False	49	173	True	14

functions for computing the ratings and scoring the parameter combinations:

def get_ratings(year, week, alpha, beta, zeta, hfa):
    sub = df.loc[(df.year == year) & (df.week < week)]
    hfa_adjustment = np.zeros((sub.shape[0],))
    hfa_adjustment[np.where(sub.team_a_home)] = hfa
    hfa_adjustment[np.where(sub.team_b_home)] = -hfa
    teams = pd.concat([sub.team_a, sub.team_b]).unique()
    n_teams = teams.shape[0]
    assert teams.min() == 0 and teams.max() == n_teams - 1
    assert (sub.team_a_score >= sub.team_b_score).mean() == 1
    A = np.zeros((n_teams, n_teams))
    team_a_won_mask = sub.team_a_score > sub.team_b_score
    team_a_won = sub[team_a_won_mask]
    margin = team_a_won.team_a_score - team_a_won.team_b_score - hfa_adjustment[team_a_won_mask]
    adj_margin = np.log(np.abs(margin) + 1) * np.sign(margin)
    np.add.at(A, (team_a_won.team_a, team_a_won.team_b), 1 + zeta + beta * adj_margin)
    np.add.at(A, (team_a_won.team_b, team_a_won.team_a), 1 - zeta - beta * adj_margin)
    tie_mask = sub.team_a_score == sub.team_b_score
    ties = sub[tie_mask]
    margin = ties.team_a_score - ties.team_b_score - hfa_adjustment[tie_mask]
    adj_margin = np.log(np.abs(margin) + 1) * np.sign(margin)
    np.add.at(A, (ties.team_a, ties.team_b), .5 + beta * adj_margin)
    np.add.at(A, (ties.team_b, ties.team_a), .5 - beta * adj_margin)
    game_counts = pd.concat([sub.team_a, sub.team_b]).value_counts().sort_index()
    A = A/game_counts.values[:, None] #normalize by num. of games
    max_alpha = 1 / np.linalg.eigvals(A).max().real
    alpha_ = alpha * max_alpha
    ratings_w = np.linalg.inv(np.eye(n_teams) - alpha_ * A) @ A.sum(1)
    ratings_l = np.linalg.inv(np.eye(n_teams) - alpha_ * A.T) @ A.sum(0)
    return ratings_w - ratings_l

def get_score(alpha, beta, zeta, hfa, folds=50):
    all_years = list(range(1995, 2023))
    scores = []
    for fold in range(folds):
        np.random.seed(fold)
        train_years = set(np.random.choice(all_years, size=int(len(all_years) * .8), replace=False))
        test_years = set(year for year in all_years if year not in train_years)
        X_trains, y_trains = [], []
        X_tests, y_tests = [], []
        for year in all_years:
            np.random.seed(year * (fold + 1))
            week = np.random.randint(8, df.loc[df.year == year, 'week'].max() + 1) #week to predict
            ratings = get_ratings(year, week, alpha, beta, zeta, hfa)
            n_teams = ratings.shape[0]
            games = df.loc[(
                (df.year == year) & (df.week == week) & 
                (df.team_a < n_teams) & (df.team_b < n_teams) &
                (df.team_a_score > df.team_b_score)
            )]
            ratings_diff = ratings[games.team_a] - ratings[games.team_b]
            home_indicator = games.team_a_home.astype(float) - games.team_b_home.astype(float)
            outcomes = np.random.choice([0., 1.], size=len(games))
            ratings_diff[outcomes == 0] = -1 * ratings_diff[outcomes == 0]
            home_indicator[outcomes == 0] = -1 * home_indicator[outcomes == 0]
            if year in train_years:
                X_trains.append(np.column_stack([ratings_diff, home_indicator]))
                y_trains.append(outcomes)
            else:
                X_tests.append(np.column_stack([ratings_diff, home_indicator]))
                y_tests.append(outcomes)
        
        X_train, y_train = np.vstack(X_trains), np.concatenate(y_trains)
        X_test, y_test = np.vstack(X_tests), np.concatenate(y_tests)
        model = LogisticRegression(fit_intercept=False, C=10.)
        model.fit(X_train, y_train)
        score = log_loss(y_test, model.predict_proba(X_test)[:, 1])
        scores.append(score)
    return np.mean(scores)

running the grid search:

alphas = np.arange(.75, .97, .03)
betas = np.arange(.0, .5, .1)
zetas = np.arange(.05, .2, .05)
hcas = np.arange(0., 3., 1.)

results = {}
combos = list(itertools.product(alphas, betas, zetas, hcas))
combos = [(a, b, z, h) for a, b, z, h in combos if not (h > 0 and b == 0)]
print(f"{len(combos)} combos")
for i, (alpha, beta, zeta, hca) in enumerate(combos):
    result = get_score(alpha, beta, zeta, hca)
    if i % 25 == 0:
        print(i)
    if results and result < min(results.values()):
        print('found new best', alpha, beta, zeta, hca, result)
    results[(alpha, beta, zeta, hca)] = result

416 combos
0
found new best 0.75 0.0 0.1 0.0 0.6480628244501047
found new best 0.75 0.0 0.15000000000000002 0.0 0.624640445530048
found new best 0.75 0.0 0.2 0.0 0.6070883832458315
found new best 0.75 0.1 0.05 0.0 0.567147865349118
found new best 0.75 0.1 0.1 0.0 0.5636435437019677
found new best 0.75 0.1 0.15000000000000002 0.0 0.5614045930804463
found new best 0.75 0.1 0.2 0.0 0.5599827410962219
found new best 0.75 0.2 0.05 0.0 0.5512674855040569
25
50
found new best 0.78 0.2 0.05 0.0 0.550735725869885
75
100
found new best 0.81 0.2 0.05 0.0 0.5503019307166305
125
150
found new best 0.8400000000000001 0.2 0.05 0.0 0.5499931069504221
175
200
found new best 0.8700000000000001 0.2 0.05 0.0 0.5498550794207714
225
250
275
300
325
350
375
400

best combination:

alpha, beta, zeta, hca = min(results, key=results.get)
alpha, beta, zeta, hca

(0.8700000000000001, 0.2, 0.05, 0.0)

computing the ratings using the best parameters:

year, week = 2022, 14
ratings = get_ratings(year, week, alpha, beta, zeta, hca)

assembling the rankings into a dataframe:

current_cfp_rankings = {
    'Georgia': 1,
    'Michigan': 2,
    'TCU': 3,
    'USC': 4,
    'Ohio St': 5,
    'Alabama': 6,
    'Tennessee': 7,
    'Penn St': 8,
    'Clemson': 9,
    'Kansas St': 10,
    'Utah': 11,
    'Washington': 12,
    'Florida St': 13,
    'LSU': 14,
    'Oregon St': 15,
    'Oregon': 16,
    'UCLA': 17,
    'Tulane': 18,
    'South Carolina': 19,
    'Texas': 20,
    'Notre Dame': 21,
    'UCF': 22,
    'North Carolina': 23,
    'Mississippi St': 24,
    'NC State': 25
}

final_rankings = pd.DataFrame(zip(
    range(1, len(ratings) + 1),
    pd.Series(np.argsort(ratings)[::-1]).map(id_mappings[year]),
    np.sort(ratings)[::-1]
), columns=['ranking', 'school', 'rating'], )
final_rankings['cfp_ranking'] = final_rankings.school.map(current_cfp_rankings)

here are the final rankings alongside what the committee is currently saying. Mostly there is a lot of agreement. Noteable exceptions where the committee disagrees with these rankings are USC (committee higher), Texas (committee lower) and NC State (committee higher). In general the committee seems to be being kind to the Pac-12 this year, which I am not complaining about :).

final_rankings

	ranking	school	rating	cfp_ranking
0	1	Georgia	19.951193	1.0
1	2	TCU	16.667676	3.0
2	3	Alabama	15.589647	6.0
3	4	Michigan	15.536973	2.0
4	5	Tennessee	15.206362	7.0
5	6	Ohio St	14.788169	5.0
6	7	Texas	13.739468	20.0
7	8	Kansas St	13.520607	10.0
8	9	USC	13.283809	4.0
9	10	Clemson	13.227090	9.0
10	11	Penn St	12.205245	8.0
11	12	LSU	12.076505	14.0
12	13	Florida St	11.492409	13.0
13	14	Utah	10.940231	11.0
14	15	Oregon	10.656330	16.0
15	16	Tulane	10.634370	18.0
16	17	Oregon St	10.149833	15.0
17	18	Notre Dame	9.948450	21.0
18	19	Mississippi St	9.910323	24.0
19	20	Mississippi	9.817282	NaN
20	21	Washington	9.739654	12.0
21	22	UCLA	9.434639	17.0
22	23	Louisville	8.798316	NaN
23	24	South Carolina	8.650026	19.0
24	25	UCF	8.552051	22.0
25	26	Illinois	8.468478	NaN
26	27	Kentucky	8.417337	NaN
27	28	Arkansas	8.087891	NaN
28	29	CS Sacramento	7.898523	NaN
29	30	Troy	7.660884	NaN
30	31	North Carolina	7.653496	23.0
31	32	Pittsburgh	7.526987	NaN
32	33	UT San Antonio	7.488730	NaN
33	34	Cincinnati	7.451187	NaN
34	35	Texas Tech	7.417065	NaN
35	36	South Alabama	7.400338	NaN
36	37	Baylor	7.301112	NaN
37	38	Oklahoma	7.243573	NaN
38	39	Oklahoma St	7.147379	NaN
39	40	Holy Cross	7.062713	NaN
40	41	Wake Forest	7.056135	NaN
41	42	S Dakota St	7.042007	NaN
42	43	Florida	6.903087	NaN
43	44	William & Mary	6.856718	NaN
44	45	NC State	6.843997	25.0
45	46	Jackson St	6.822085	NaN
46	47	Delta St	6.713427	NaN
47	48	James Madison	6.691507	NaN
48	49	Coastal Car	6.537978	NaN
49	50	Washington St	6.454943	NaN
50	51	Missouri S&T	6.192580	NaN
51	52	Missouri	6.116855	NaN
52	53	Iowa	6.099140	NaN
53	54	Purdue	6.097954	NaN
54	55	Kansas	6.081273	NaN
55	56	Duke	6.069801	NaN
56	57	Maryland	6.054920	NaN
57	58	Syracuse	5.921051	NaN
58	59	N Dakota St	5.852531	NaN
59	60	Boise St	5.847480	NaN
60	61	Minnesota	5.844059	NaN
61	62	Marshall	5.834362	NaN
62	63	Princeton	5.738110	NaN
63	64	SMU	5.591731	NaN
64	65	Samford	5.564950	NaN
65	66	Yale	5.501422	NaN
66	67	Air Force	5.314200	NaN
67	68	Weber St	5.170600	NaN
68	69	Montana St	5.065328	NaN
69	70	Iowa St	5.039742	NaN
70	71	Ohio	4.949886	NaN
71	72	Incarnate Word	4.920613	NaN
72	73	Auburn	4.857711	NaN
73	74	East Carolina	4.802734	NaN
74	75	Texas A&M	4.664974	NaN
75	76	Houston	4.648101	NaN
76	77	Memphis	4.403205	NaN
77	78	Wisconsin	4.317273	NaN
78	79	Fresno St	4.238352	NaN
79	80	BYU	4.202426	NaN
80	81	Furman	4.043615	NaN
81	82	Richmond	3.919282	NaN
82	83	Delaware	3.890215	NaN
83	84	Penn	3.760171	NaN
84	85	Jacksonville St	3.533387	NaN
85	86	West Virginia	3.467647	NaN
86	87	Liberty	3.319831	NaN
87	88	WKU	3.315355	NaN
88	89	Harvard	3.220894	NaN
89	90	Elon	3.177852	NaN
90	91	Montana	2.957866	NaN
91	92	Michigan St	2.935823	NaN
92	93	Louisiana	2.924911	NaN
93	94	UC Davis	2.829245	NaN
94	95	San Jose St	2.788468	NaN
95	96	Albany GA	2.784256	NaN
96	97	Vanderbilt	2.726908	NaN
97	98	St Thomas FL	2.552671	NaN
98	99	North Texas	2.534444	NaN
99	100	Appalachian St	2.509055	NaN
100	101	Mercer	2.504366	NaN
101	102	UAB	2.482240	NaN
102	103	Arizona	2.476542	NaN
103	104	Navy	2.434591	NaN
104	105	Army	2.130146	NaN
105	106	IN Wesleyan	2.097075	NaN
106	107	Miles	2.093753	NaN
107	108	Rhode Island	1.980268	NaN
108	109	Lane	1.898907	NaN
109	110	California	1.664304	NaN
110	111	Bloomsburg	1.638954	NaN
111	112	SE Missouri St	1.607124	NaN
112	113	W Oregon	1.602201	NaN
113	114	New Hampshire	1.576071	NaN
114	115	Northern Iowa	1.541436	NaN
115	116	Chattanooga	1.418259	NaN
116	117	Idaho	1.414201	NaN
117	118	Toledo	1.403216	NaN
118	119	Fordham	1.336145	NaN
119	120	Virginia	1.284026	NaN
120	121	Buffalo	1.269730	NaN
121	122	Michigan Tech	1.224092	NaN
122	123	San Diego St	1.049207	NaN
123	124	W New Mexico	1.036203	NaN
124	125	SW Baptist	0.992975	NaN
125	126	Georgia Tech	0.987648	NaN
126	127	Southern Miss	0.961807	NaN
127	128	NC Central	0.952596	NaN
128	129	Ga Southern	0.895373	NaN
129	130	St Thomas MN	0.828540	NaN
130	131	Limestone	0.784220	NaN
131	132	Barton	0.745723	NaN
132	133	Indiana	0.744868	NaN
133	134	North Greenville	0.637388	NaN
134	135	FL Atlantic	0.605553	NaN
135	136	Assumption	0.505991	NaN
136	137	W Salem St	0.493514	NaN
137	138	S Illinois	0.489719	NaN
138	139	Nebraska	0.450837	NaN
139	140	Florida A&M	0.399019	NaN
140	141	Miami FL	0.353584	NaN
141	142	Wyoming	0.328557	NaN
142	143	SE Louisiana	0.269483	NaN
143	144	MTSU	0.268041	NaN
144	145	Tulsa	0.208043	NaN
145	146	Concordia MI	0.179353	NaN
146	147	Youngstown St	0.141287	NaN
147	148	Gardner Webb	0.135672	NaN
148	149	Faulkner	0.117002	NaN
149	150	E Michigan	0.101655	NaN
150	151	Mississippi Col	0.099512	NaN
151	152	Edward Waters	0.084357	NaN
152	153	Austin Peay	0.035151	NaN
153	154	Columbia	0.034064	NaN
154	155	North Dakota	0.008890	NaN
155	156	McKendree	-0.031140	NaN
156	157	Thomas More	-0.110327	NaN
157	158	Georgia St	-0.150441	NaN
158	159	St Francis PA	-0.152542	NaN
159	160	Taylor IN	-0.181927	NaN
160	161	Morehouse	-0.189213	NaN
161	162	Stanford	-0.269110	NaN
162	163	E New Mexico	-0.289517	NaN
163	164	Keiser	-0.290639	NaN
164	165	Abilene Chr	-0.419643	NaN
165	166	Utah St	-0.436331	NaN
166	167	Kent	-0.462956	NaN
167	168	Kentucky St	-0.500371	NaN
168	169	Mars Hill	-0.511493	NaN
169	170	Arizona St	-0.515764	NaN
170	171	Wm Jewell	-0.542231	NaN
171	172	St Andrew's	-0.545712	NaN
172	173	Tuskegee	-0.581151	NaN
173	174	Chadron St	-0.672004	NaN
174	175	S Connecticut	-0.856804	NaN
175	176	FL Memorial	-0.985127	NaN
176	177	Sam Houston St	-0.991370	NaN
177	178	Lincoln PA	-0.995064	NaN
178	179	Southern Univ	-1.012459	NaN
179	180	La Verne	-1.074068	NaN
180	181	TN Martin	-1.095462	NaN
181	182	Louisiana Chr	-1.103126	NaN
182	183	Connecticut	-1.137986	NaN
183	184	Bowling Green	-1.143575	NaN
184	185	UVA-Wise	-1.219923	NaN
185	186	Warner	-1.637233	NaN
186	187	Illinois St	-1.657703	NaN
187	188	Missouri St	-1.710604	NaN
188	189	Virginia Tech	-1.737634	NaN
189	190	UNLV	-1.791550	NaN
190	191	Kentucky Chr	-1.802591	NaN
191	192	E Kentucky	-1.826442	NaN
192	193	NC A&T	-1.831648	NaN
193	194	Rutgers	-1.859322	NaN
194	195	Rice	-1.972408	NaN
195	196	Cent Arkansas	-1.995411	NaN
196	197	Villanova	-2.038528	NaN
197	198	Campbell	-2.060742	NaN
198	199	Post	-2.313419	NaN
199	200	Merrimack	-2.330931	NaN
200	201	W Michigan	-2.378867	NaN
201	202	W Carolina	-2.471476	NaN
202	203	Miami OH	-2.496056	NaN
203	204	Dartmouth	-2.632242	NaN
204	205	Southern Utah	-2.709928	NaN
205	206	UTEP	-2.720737	NaN
206	207	Ball St	-2.752110	NaN
207	208	Towson	-2.758605	NaN
208	209	Boston College	-2.902685	NaN
209	210	New Mexico St	-3.006257	NaN
210	211	SF Austin	-3.013434	NaN
211	212	Monmouth NJ	-3.159396	NaN
212	213	Cornell	-3.194413	NaN
213	214	ULM	-3.274284	NaN
214	215	C Michigan	-3.366400	NaN
215	216	Texas St	-3.519217	NaN
216	217	Prairie View	-3.611589	NaN
217	218	Old Dominion	-3.651485	NaN
218	219	South Dakota	-3.678128	NaN
219	220	Lindenwood	-3.806438	NaN
220	221	Kennesaw	-3.843476	NaN
221	222	Alabama St	-3.914791	NaN
222	223	TX Southern	-3.917119	NaN
223	224	Northwestern	-3.965733	NaN
224	225	Temple	-3.966318	NaN
225	226	North American	-3.978959	NaN
226	227	E Washington	-3.998206	NaN
227	228	Davidson	-4.053414	NaN
228	229	San Diego	-4.152413	NaN
229	230	Butler	-4.186960	NaN
230	231	Dayton	-4.189590	NaN
231	232	Portland St	-4.217445	NaN
232	233	Louisiana Tech	-4.341291	NaN
233	234	Colorado St	-4.397055	NaN
234	235	Arkansas St	-4.446804	NaN
235	236	Utah Tech	-4.654362	NaN
236	237	Northern Arizona	-4.710085	NaN
237	238	Tarleton St	-4.715637	NaN
238	239	Alcorn St	-4.754446	NaN
239	240	Colorado	-4.823167	NaN
240	241	Brown	-4.959002	NaN
241	242	Howard	-5.129221	NaN
242	243	ETSU	-5.154704	NaN
243	244	Akron	-5.163017	NaN
244	245	SUNY Albany	-5.475824	NaN
245	246	Citadel	-5.484321	NaN
246	247	South Florida	-5.501069	NaN
247	248	Wofford	-5.770905	NaN
248	249	Bryant	-5.785882	NaN
249	250	N Illinois	-5.867416	NaN
250	251	Lafayette	-5.926783	NaN
251	252	TX A&M Commerce	-5.962650	NaN
252	253	Nevada	-6.085639	NaN
253	254	Tennessee Tech	-6.266275	NaN
254	255	Charlotte	-6.517040	NaN
255	256	Indiana St	-6.598354	NaN
256	257	Lincoln CA	-6.729517	NaN
257	258	Hawaii	-6.976316	NaN
258	259	Tennessee St	-6.996346	NaN
259	260	Hampton	-7.047185	NaN
260	261	Alabama A&M	-7.104948	NaN
261	262	New Mexico	-7.113931	NaN
262	263	Charleston So	-7.231389	NaN
263	264	Florida Intl	-7.372671	NaN
264	265	Colgate	-7.640828	NaN
265	266	Stonehill	-7.681304	NaN
266	267	Duquesne	-7.757698	NaN
267	268	Sacred Heart	-7.799025	NaN
268	269	Morgan St	-7.862250	NaN
269	270	Cal Poly	-7.965747	NaN
270	271	Northwestern LA	-8.044503	NaN
271	272	Maine	-8.154745	NaN
272	273	McNeese St	-8.250213	NaN
273	274	N Colorado	-8.390109	NaN
274	275	Valparaiso	-8.496765	NaN
275	276	Grambling	-8.606401	NaN
276	277	Stetson	-8.637578	NaN
277	278	Delaware St	-8.668998	NaN
278	279	S Carolina St	-8.783732	NaN
279	280	Lehigh	-9.206290	NaN
280	281	Nicholls St	-9.247364	NaN
281	282	LIU Post	-9.332291	NaN
282	283	Drake	-9.399163	NaN
283	284	Idaho St	-9.560482	NaN
284	285	VMI	-9.702658	NaN
285	286	Bucknell	-9.769923	NaN
286	287	Georgetown	-9.800058	NaN
287	288	W Illinois	-9.905696	NaN
288	289	E Illinois	-9.987174	NaN
289	290	Stony Brook	-10.008251	NaN
290	291	North Alabama	-10.255156	NaN
291	292	Ark Pine Bluff	-10.278144	NaN
292	293	Murray St	-10.286789	NaN
293	294	Massachusetts	-10.553665	NaN
294	295	Marist	-10.985417	NaN
295	296	MS Valley St	-11.096806	NaN
296	297	Bethune-Cookman	-11.204950	NaN
297	298	Central Conn	-11.793550	NaN
298	299	VA-Lynchburg	-12.028063	NaN
299	300	Norfolk St	-12.241488	NaN
300	301	Lamar	-12.368052	NaN
301	302	Houston Chr	-12.569194	NaN
302	303	Morehead St	-13.010842	NaN
303	304	Wagner	-14.829867	NaN
304	305	Robert Morris	-15.232463	NaN
305	306	Presbyterian	-16.884224	NaN

Written on December 2, 2022