Big Ten Bradley-Terry Projections

by SpartanDan on Sep 27, 2010 10:38 AM CDT

[Bumped. With no clear #2 team in the Big Ten--based on non-conference results, at least--not playing OSU looking like an even bigger advantage for MSU. -KJ]

Based on the current Bradley-Terry ratings, I thought it would be interesting to see what the system predicts for Big Ten season. A few caveats, obviously: Four games, mostly against mediocre competition, is not a huge sample size (and a couple teams haven't even played that many; future non-conference games by these teams are not included in the predictions), so ratings may be skewed. Also, home field is not factored into either the basic or the margin-aware system. I first calculated win probability for each game from the ratings, then added them up to get average number of wins and ran 1000 simulations of the season to check for outright and shared Big Ten titles (the program I used for this was not aware of tiebreakers, so I don't know who would go to the Rose Bowl in shared-title situations). Results below the jump.

Basic (W-L only) Method

Team	BT WPct	Average wins	Unbeaten	Winless	Outright title	Shared title
Northwestern	0.8575	5.98	8.32%	1 in 775,000	177	243
Ohio State	0.8339	5.72	5.54%	1 in 264,000	129	232
MSU	0.8312	5.40	3.23%	1 in 113,000	98	177
Michigan	0.8360	5.28	3.02%	1 in 15,600	83	143
Wisconsin	0.8145	5.07	1.77%	1 in 43,000	59	135
Penn State	0.7645	4.39	0.52%	0.03%	25	64
Iowa	0.7009	3.52	0.07%	0.21%	4	26
Illinois	0.6132	3.44	0.03%	0.21%	3	18
Indiana	0.6370	3.14	0.03%	1.04%	1	11
Purdue	0.2970	1.54	1 in 12,000,000	10.47%	0	0
Minnesota	0.1212	0.53	1 in 45,100,000,000	56.38%	0	0

The five teams that are 4-0 thus far have a pretty sizable gap on everyone else; they're between 13th and 21st nationally. Michigan's numbers are worse than ours despite having a better rating because they don't play Minnesota. Really, I'm not sure how useful it is at this point - four games is a pretty tiny sample size to make predictions on, especially when all you know is wins and losses.

Margin-Aware Method

I'm using parameters calculated based on last year's data for the win ratio exponent and the victory point scale. There isn't enough data this year to test if that's reasonable or not.

Team	BT WPct	Average wins	Unbeaten	Winless	Outright title	Shared title
Ohio State	0.9756	7.46	56.74%	1 in 302,000,000,000	707	202
MSU	0.8558	5.57	4.09%	1 in 554,000	24	97
Northwestern	0.8185	5.26	2.26%	1 in 159,000	14	63
Iowa	0.8913	5.19	1.51%	1 in 93,400	26	50
Michigan	0.8257	4.46	0.28%	0.02%	8	31
Wisconsin	0.7689	4.03	0.07%	0.01%	3	6
Penn State	0.7815	3.93	0.07%	0.04%	2	10
Indiana	0.7167	3.41	0.02%	0.26%	2	4
Illinois	0.5861	3.03	1 in 49,300	0.32%	0	3
Purdue	0.2068	1.22	1 in 1,560,000,000	15.97%	0	0
Minnesota	0.0867	0.44	1 in 8,820,000,000,000	61.56%	0	0

This looks a bit more realistic. Iowa isn't dinged as heavily for a close loss out in the desert, Wisconsin's win over Arizona State looks less impressive, Ohio State looks like a juggernaut thanks to a moderately comfortable win over a good team and three annihilations of MACrifices, and Minnesota looks even more hapless. Our not playing Ohio State, and Iowa and Michigan not getting the near auto-wins over Purdue and Minnesota, respectively, give us a very good shot at finishing up high in the Big Ten standings.

It will be interesting to see how accurate these turn out to be. I intend to revisit this at the halfway point of the Big Ten season with updated projections for the rest of the season.

This is a FanPost, written by a member of the TOC community. It does not represent the official positions of The Only Colors, Inc.--largely because we have no official positions.

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Comments

Remind me again

These ratings don’t take into account any info from last season? If that’s true, the top of the margin-aware standings look remarkably reasonable.

Fight for The Only Colors: Green and White!

by KJ@theonlycolors on Sep 27, 2010 10:39 AM CDT reply actions

That's right

No carryover at all. Partly for that reason, I wouldn’t pay a whole lot of attention to the basic system until midway through the conference season when there’s a lot more BCS-on-BCS data and not just BCS-on-cupcake games. I am a little surprised at how quickly the margin-aware system settled into something reasonable-looking, though there are still some things I would consider outliers at this point (Nevada at #4 in particular).

Just for reference, here’s what this system predicts the spread (again, neglecting home/away) to be for MSU against all Big Ten opponents (including OSU and Indiana):

OSU -12 (about 13% to win)
Iowa -2 (42%)
Michigan +1.5 (56%)
NW +1.5 (56%)
PSU +3 (62%)
Wisconsin +3.5 (64%)
Indiana +5.5 (71%)
Illinois +9.5 (82%)
Purdue +19.5 (96%)
Minnesota +25.5 (98%)

The ugly part of that is that all four of the toughest games we play are road games, and they’re all plenty close enough for home field to swing things. So our projection is probably a little optimistic. (Assuming that home field is worth a fixed number of points on the spread, it has the biggest impact on winning percentage when the home team would be a small underdog at a neutral site. That describes three of our road games very well according to this formula.)

by SpartanDan on Sep 27, 2010 8:20 PM CDT up reply actions