Sagarin says

[Bison bison]

They pretty much do, though. There's just a little bumpiness to the distribution because of the way points are scored, as Audit pointed out.

ORLY.

When's the last time a team scored negative points?

[bisonaudit]

ORLY.

When's the last time a team scored negative points?

Since the model is designed to predict the margin of victory I'm not sure that's relevant.

[cbline]

ORLY.

When's the last time a team scored negative points?

A neighbor of ours attended NDSU in the early 1970's. Said his Organic Chem tests were all true and false. +3 points for a correct answer, -6 for an incorrect, and +1 if you wrote "I don't know." He actually received a negative score on his first test. Ouch.

[VirginiaBison]

NDSU may have scored negative points against UN_ in a cold, windy day, overcast day game at Dakotah Field in 1973(?). Worst game I ever saw the Bison play.

[56BISON73]

NDSU may have scored negative points against UN_ in a cold, windy day, overcast day game at Dakotah Field in 1973(?). Worst game I ever saw the Bison play.

May be 75.

[JDZ]

Since the model is designed to predict the margin of victory I'm not sure that's relevant.

Right, but the entire bell curve cannot be achieved, since anything to the left of a certain point, that represents zero points for the loser, is chopped off. Or am I all wet?

[bisonaudit]

Right, but the entire bell curve cannot be achieved, since anything to the left of a certain point, that represents zero points for the loser, is chopped off. Or am I all wet?

Not entirely all wet, no, the bell curve doesn't technically ever reach the zero bound so it runs out to infinity in both directions yielding absurdly large margins at either end that would imply not impossibly low scores for the losing team but impossibly high ones for the winning team, but those results also typically come with absurdly low probability.

Again, we're not modeling team scores here we're modeling the margin of victory, so a three standard deviation event that's not a 42 point win, it's a win or loss by 42 points more or less than expected. Lots and lots of teams win by 42 points during the course of a season but we'd only expect three or four events a year where the margin of victory was 42 points different from the model's expectation.

Additionally, we know that we're using a continuous function to model results that can only occur in integers, but the normal distribution has some very nice features, like the central limit theorem, so when it's a good fit for the data, and it is in this case, you can use it.

In any event, it's a model, a mere approximation of reality, and some may say that given the relatively large standard deviation, it's not even a particularly good approximation of reality. The challenge then is to design a better one.

[bisonboone11]

Right, but the entire bell curve cannot be achieved, since anything to the left of a certain point, that represents zero points for the loser, is chopped off. Or am I all wet?

You might be right that the entire bell curve cannot be achieved, but I don't think the zero is the limiting factor in this situation. I think the limiting factor would be the maximum number of points a team could theoretically score in a game. I'm not sure what that maximum theoretical number is though, if there even is one. If there is a way for a team to score back to back without any time running off the clock, then I suppose the maximum margin of victory would be infinity. Then maybe the entire bell curve would be achieved? I'm not sure how that works.

[IzzyFlexion]

A neighbor of ours attended NDSU in the early 1970's. Said his Organic Chem tests were all true and false. +3 points for a correct answer, -6 for an incorrect, and +1 if you wrote "I don't know." He actually received a negative score on his first test. Ouch.

Blutarsky laughs in your neighbor's general direction.

[thebootfitter]

I'm not sure if Hammersmith is still on hiatus, as I think I've seen him still on here a bit, but I figured I'd post this just in case. I altered the format slightly, but I believe I am still showing all the same information that he had been showing, plus a few extra bits that I thought would be interesting. I created some formulas in Excel to extract the information, and this format was easier to produce. I'm open to any feedback anyone may have, including reverting to the familiar way that Hammersmith had been posting.

Not unexpectedly, we dropped a few points due to underperforming against Sagarin's prediction. UNI jumped up a few points as well. Surprisingly, Western Illinois just made the top 25.

Sagarin's Week 12 Predictions

Rank	Team                Sagarin	Predict	Result	Diff
38	North Dakota State  	76.40			
80	Iowa State          	66.19	+7.06	+20.00	+12.94
206	Weber State         	41.16	+32.09	+17.00	-15.09
232	Incarnate Word      	29.11	+50.44	+58.00	+7.56
135	Montana             	55.24	+24.31	+12.00	-12.31
127	Western Illinois    	56.04	+17.21	+7.00	-10.21
95	Southern Illinois   	62.75	+16.80	+28.00	+11.20
104	Indiana State       	61.12	+18.43	+17.00	-1.43
174	South Dakota        	47.62	+25.63	+40.00	+14.37
81	South Dakota State  	66.11	+13.44	+20.00	+6.56
66	Northern Iowa       	69.56	+3.69	-20.00	-23.69
120	Missouri State      	58.29	+14.96		
102	Youngstown State    	61.63	+17.92		
	                    				
62	Illinois State      	70.13			

				Total Diff:	      -10.10
	Home Field	3.15			

Note that I added the strength of schedule (SOS) rating and rank, as well as conference affiliation below. It is kind of fun to see all those MVFC teams in the top 25.

Sagarin FCS Top-25

Rank	SagRank	RATING	Team               	SOS	SOSRank	Conference
1	38	76.40	North Dakota State  	56.50	133	Missouri Valley
2	58	71.46	Jacksonville State  	50.26	175	Ohio Valley
3	62	70.13	Illinois State      	55.41	136	Missouri Valley
4	66	69.56	Northern Iowa       	59.75	116	Missouri Valley
5	77	66.49	New Hampshire       	47.89	188	Colonial
6	81	66.11	South Dakota State  	64.98	79	Missouri Valley
7	84	65.86	Chattanooga         	52.83	156	Southern
8	85	65.68	Harvard             	40.35	226	Ivy League
9	86	65.49	Coastal Carolina    	44.57	204	Big South
10	88	64.90	Villanova           	48.71	182	Colonial
11	95	62.75	Southern Illinois   	59.14	122	Missouri Valley
12	99	62.24	SE Louisiana        	46.81	195	Southland
13	100	62.18	Eastern Washington  	50.77	168	Big Sky
14	102	61.63	Youngstown State    	54.47	141	Missouri Valley
15	104	61.12	Indiana State       	62.89	93	Missouri Valley
16	106	60.68	Fordham             	41.86	219	Patriot
17	107	60.56	Sam Houston State   	53.08	153	Southland
18	110	60.38	Liberty             	51.31	165	Big South
19	111	60.37	Samford             	50.69	170	Southern
20	115	59.44	Richmond            	48.68	183	Colonial
21	117	58.62	McNeese State       	47.38	192	Southland
22	120	58.29	Missouri State      	60.04	110	Missouri Valley
23	121	58.12	Idaho State         	54.21	143	Big Sky
24	124	57.47	Eastern Illinois    	52.45	159	Ohio Valley
25	127	56.04	Western Illinois    	63.14	91	Missouri Valley

I'm showing the conference rankings in one table, sorted by the conference rating (CentralMean). I am also showing the rating for the highest ranked team in each conference (ConfMax) and finally where NDSU would fall in each conference.

Conference Rankings

ConfCat	Conference	CentralMean	ConfMax	NDSU Rank
P5	SEC                 	85.64	98.84	13
P5	BIG 12              	78.98	93.20	6
P5	PAC-12              	78.11	91.29	8
P5	BIG TEN             	74.10	89.44	5
P5	ACC                 	74.07	87.43	7
NA	I-A INDEPENDENTS    	69.66	83.85	2
G5	AMERICAN ATHLETIC   	63.99	74.05	1
G5	MWC                 	63.29	77.70	2
FCS	MISSOURI VALLEY     	63.02	76.40	1
G5	CONFERENCE USA      	58.84	78.97	2
G5	MAC                 	57.29	67.43	1
G5	SUN BELT            	55.38	70.37	1
FCS	BIG SOUTH           	50.13	65.49	1
FCS	COLONIAL            	49.60	66.49	1
FCS	SOUTHERN            	49.44	65.86	1
FCS	SOUTHLAND           	48.93	62.24	1
FCS	BIG SKY             	47.76	62.18	1
FCS	OHIO VALLEY         	47.47	71.46	1
FCS	PATRIOT             	45.03	60.68	1
FCS	IVY LEAGUE          	43.99	65.68	1
FCS	NORTHEAST           	42.92	54.39	1
FCS	I-AA INDEPENDENTS   	42.37	42.37	1
FCS	MID-EASTERN         	35.52	51.36	1
FCS	SWAC                	32.07	51.65	1
FCS	PIONEER             	28.58	45.97	1