Big Ten Basketball Bradley-Terry Projections: 7 Games In

by SpartanDan on Jan 24, 2011 8:43 PM CST

Our last look showed Ohio State solidly at the top, Illinois-Wisconsin-Purdue as the second tier, and us at the head of a close pack fighting for fifth (and the only one of the pack with a realistic shot at moving up). Two weeks later ...

	Pom Rank	Pom WPct	BT Rank	BT WPct	MABT Rank	MABT WPct
Ohio St	1	0.9823	1	0.9928	3	0.9855
Purdue	9	0.9669	14	0.9428	12	0.9693
Wisconsin	8	0.9682	16	0.9362	14	0.9665
Minnesota	42	0.8821	19	0.9289	31	0.9198
Michigan St	26	0.9251	23	0.9178	28	0.9236
Illinois	14	0.9444	25	0.9142	18	0.9545
Northwestern	48	0.8578	54	0.8365	37	0.9011
Penn St	53	0.8518	67	0.8073	63	0.8461
Michigan	66	0.8091	73	0.7939	62	0.8476
Indiana	69	0.8019	119	0.6245	97	0.7234
Iowa	81	0.7652	140	0.5718	108	0.6896

Relative to last time: Penn State has shot up the rankings (especially under Pomeroy's system), Minnesota (aided by a 3-0 record including a win over Purdue) has actually managed to jump us in one system (although that one also has us leapfrogging Illinois), and Michigan has slid back.

After the jump: Projections (ignoring home court, as always) and our win probabilities for every remaining game. Conference title projections are based on 10,000 simulations of the remainder of the season.

Basic Bradley-Terry (W-L Only)

Team	WPct	Current	Average wins	18-0	15-3 or better	12-6 or better	9-9 or better	6-12 or worse	3-15 or worse	Outright title	Share of title
Ohio St	0.9928	7-0	17.26	45.99%	99.58%	1 - (1 in 1.08M)	1 - (1 in 238B)	N/A	N/A	98.80%	99.74%
Purdue	0.9428	6-1	12.38	N/A	5.47%	74.37%	99.79%	1 in 326k	N/A	0.22%	0.85%
Wisconsin	0.9362	5-2	11.61	N/A	0.82%	54.35%	98.88%	1 in 11,900	N/A	0.04%	0.30%
Minnesota	0.9289	4-3	11.14	N/A	0.21%	41.07%	96.75%	0.07%	N/A	0.00%	0.06%
Michigan St	0.9178	4-3	10.75	N/A	0.09%	30.07%	94.69%	0.12%	N/A	0.00%	0.03%
Illinois	0.9142	4-3	10.54	N/A	0.06%	25.03%	92.64%	0.21%	N/A	0.00%	0.02%
Northwestern	0.8365	3-5	7.40	N/A	N/A	0.10%	21.22%	25.93%	0.11%	0.00%	0.00%
Penn St	0.8073	3-4	6.69	N/A	N/A	0.05%	10.54%	45.87%	0.62%	0.00%	0.00%
Michigan	0.7939	1-6	5.33	N/A	N/A	1 in 561k	1.31%	79.73%	9.38%	0.00%	0.00%
Iowa	0.5718	1-6	2.98	N/A	N/A	1 in 919M	1 in 20,900	99.52%	68.58%	0.00%	0.00%
Indiana	0.6245	1-6	2.91	N/A	N/A	1 in 8.96B	1 in 51,400	99.71%	71.43%	0.00%	0.00%

Ohio State's jumped out to a commanding lead (being unbeaten gives an enormous lead in these rankings unless there's a major difference in strength of schedule, and there isn't enough to overcome 3 losses for Purdue or more for everyone else). It appears to be a five-way battle for second place, with Purdue having about 3/4 of a game advantage over Wisconsin and all five in good shape to make the tournament (Illinois should be safe from a repeat of last year's fate - 10-8 and out - with a better non-conference schedule and better record against it). Northwestern and Penn State remain fringe bubble candidates at best, but if either can get to .500 they have a shot (Northwestern's non-conference schedule has little to recommend it but does include a win over Georgia Tech; Penn State's win over Duquesne is surprisingly valuable but losing to Maine may prove to be their doom). Michigan could fight their way into an NIT bid but it appears odds-against at this point.

Margin-Aware Bradley-Terry

Team	WPct	Current	Average wins	18-0	15-3 or better	12-6 or better	9-9 or better	6-12 or worse	3-15 or worse	Outright title	Share of title
Ohio St	0.9855	7-0	15.93	9.26%	87.27%	99.92%	1 - (1 in 10.6M)	N/A	N/A	81.51%	92.06%
Purdue	0.9693	6-1	13.12	N/A	16.36%	87.45%	99.95%	1 in 2.08M	N/A	5.24%	12.78%
Wisconsin	0.9665	5-2	12.38	N/A	5.12%	74.81%	99.73%	1 in 87,100	N/A	1.94%	6.00%
Illinois	0.9545	4-3	11.28	N/A	0.48%	44.72%	97.52%	1 in 43,500	N/A	0.17%	1.07%
Michigan St	0.9236	4-3	10.17	N/A	0.04%	17.55%	87.94%	0.50%	N/A	0.03%	0.24%
Minnesota	0.9198	4-3	10.04	N/A	0.04%	16.33%	85.07%	0.83%	N/A	0.03%	0.21%
Northwestern	0.9011	3-5	8.00	N/A	N/A	0.48%	36.22%	14.46%	0.03%	0.00%	0.00%
Penn St	0.8461	3-4	6.53	N/A	N/A	0.04%	8.73%	50.71%	0.91%	0.00%	0.00%
Michigan	0.8476	1-6	5.39	N/A	N/A	1 in 182k	1.67%	77.90%	9.24%	0.00%	0.00%
Iowa	0.6896	1-6	3.22	N/A	N/A	1 in 269M	0.01%	99.11%	61.18%	0.00%	0.00%
Indiana	0.7234	1-6	2.94	N/A	N/A	1 in 3.54B	1 in 41,600	99.67%	70.36%	0.00%	0.00%

Here Ohio State's lead is somewhat less formidable, with Purdue, Wisconsin, and Illinois all at a higher rating (in terms of win percentage against an average opponent) than in the basic system. Even so, it's Ohio State's to lose. We're in 5th in both methods, but here it's much closer ahead of Minnesota and a full game behind Illinois. Again, six teams look solidly in, and Northwestern's chances actually look better here (though still not especially good).

Upcoming MSU Games

	Pomeroy	Basic	Margin-Aware
Mich	85%, -10	74.4%	68.5%, -4.5
Ind	85%, -11	87.0%	82.2%, -8.5
@Iowa	67%, -4	89.3%	84.5%, -9.5
@Wisc	18%, +8	43.2%	29.5%, +5
PSU	80%, -8	72.7%	68.7%, -4.5
@OSU	10%, +12	7.5%	15.1%, +10
Ill	58%, -2	51.2%	36.6%, +3
@Minn	46%, +1	46.1%	51.3%, -0.5
Pur	45%, +1	40.4%	27.7%, +5.5
Iowa	88%, -11	89.3%	84.5%, -9.5
@Mich	60%, -2	74.4%	68.5%, -4.5

Keep in mind that Pomeroy's projections include home court but the other two do not.

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Comments

Pomeroy has us finishing 7-4

So would be 19-11 (11-5), with our best wins being Wisc at home, Minny on the road & (projected) Minny at home. Not sure what to say about that. Let’s just win some games guys!!!!

by MSUDersh on Jan 24, 2011 9:31 PM CST reply actions

make that 11-7 B10, obivously

by MSUDersh on Jan 24, 2011 9:32 PM CST up reply actions

If there's anything that this season's taught us

it’s that the projections and expectations are poor predictors. Let’s hope that the boys break the system yet again, this time in a more positive way

by Chunkydonut on Jan 24, 2011 10:34 PM CST reply actions

Any thoughts to adding home court?

I don’t know what would be a good number or not, so arbitrarily adding a number probably isn’t the best idea. I’d guess that it’s likely around 55/45 in favor of a home team given two nearly equal teams.

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by Mike Rogers on Jan 25, 2011 12:21 AM CST reply actions

According to Pomeroy

Home teams win 62% of the time in D-I conference play.

by Con-T on Jan 25, 2011 12:28 AM CST up reply actions

It's on the offseason docket

My instinct is that the way to do it will be that for some factor H (empirically determined, probably by figuring out the best fit for some assumed value, then checking to see that the fit holds with that value and if not, repeating the adjustment iteratively):

for purposes of calculating strength of schedule, opponents in road games will be rated at H times their neutral-court rating and opponents in home games will be rated at 1/H times their neutral-court rating (semi-home and semi-away get sqrt(H) instead);
for purposes of predicting games, multiply the home team’s rating by H (sqrt(H) for semi-home) before calculating the win ratio.

Unfortunately, at the moment I don’t have time to do the code tweaks and check everything (not to mention making sure this is the sanest way to do it; I think it probably is but something else might occur to me later).

I've got this terrible pain in all the diodes down my left-hand side.
Bradley-Terry rankings for college football and basketball: because there aren't enough computer rankings already.

by SpartanDan on Jan 25, 2011 11:53 PM CST up reply actions