MICH-again #1 in B1G (acc to sagarin poll predictions)

MICH-again #1 in B1G (acc to sagarin poll predictions)

Submitted by michelin on November 4th, 2012 at 11:57 AM

Michigan again is the top team in the B1G according to the Sagarin poll PREDICTOR ratings--which are the best in actually predicting game outcomes.  Here are the ratings and overall national rank:


1. Michigan  (#23 overall, rating 82.42)

2. Ohio (#24 overall, rating 82.40) INELIGIBLE for postseason

3. Neb (#25, rating 82.01)

4. PSU (#28, 79.44) INELIGIBLE for postseason

5. Wisconsin (#32, rating 78.73)

6. NU (#39. 77.2)


So, what are the chances UM will get to the championship game in INDY?  Based on the Sagarin ratings (and a few heroic assumptions given below), NEB has a better than 50-50 chance of losing at least one more game.  The chances of UM actually getting to INDY are about one in five.

UM’s chances are not higher than this largely because we play at Ohio.  But, if  Ohio were not ineligible and Michigan played them in INDY, UM would be a narrow favorite.   Likewise, on a neutral field, UM would be favored over NEB (-0.5 points). 

In any case, if we get a bit lucky and do get to INDY, we would be nearly a 2-1 favorite over WISC (or -3.5 points which translates into a greater than 60% chance of winning).




One predicts the outcome of future games by subtracting the two Sagarin PREDICTOR ratings (with +3 for home field advantage)  That gives us the estimated point spread for each matchup.  We can convert the point spreads into odds based on a conversion chart (see bovada).  Then, we can convert the odds (O) into win probabilities (p) as p=O/(1+O).   For example,

PtSprdOdds   win prob

-2         1.2       0.54

-3         1.45     0.59

-4         1.85     0.65

5          2.15     0.68

-6         2.4       0.71

-7         2.9       0.74

-8         3.2       0.76

-9         3.35     0.77

-10       3.875   0.79




NEB would be a

-5.5 favorite vs PSU (win probability of .68)

- 14.5 vs MIN which has a 67.75 rating (win probability of .9)

-8.5 at IA which has a 70.71 rating (win probability of .76).

Assuming independence of game outcomes (discussed below), the chances of NEB winning out would be

= .68*.9*.76 = .46.  The chance of not winning out would be 1-.46 =.54.


In Ann Arbor, UM would be

-8 pts vs NU (5+3 for home field, equivalent to a win probability of .76),

-15 Pts vs IA (or win probability of about .90)

In Columbus, UM would be not quite +3 underdogs (equivalent to a win probability of .4). 

So, the chances of UM winning out would be = .76*.9*.4 = .27.



Thus, the chances of UM winning out and NEB not would be = .54*.27 = .15.  I would guess that the chances might be as high as 0.20, since other outcomes could also lead to UM winning one more game than NEB (eg one loss by UM and two by NEB or two losses by UM and three for NEB),  

One factor that might increase UM’s chances a bit further is that game outcomes are not likely to be independent but positively correlated (due to injuries and other factors that would make runs of wins or losses more likely).   Since UM’s chances of winning all games will depend more heavily on Denard’s injury situation, the chances of a run of wins (with a healthy Denard) would seem to increase the chances of UM winning out over NEB’s chances (for which game outcomes would be more nearly independent). 

On the other hand, if Denard is not healthy the chances of UM winning out would be lower than the Sagarin ratings predict. But given the usual course of recovery from his condition and the encouraging performance of DG, I think that 20% is still a reasonable estimate for UM’s chances of getting to INDY.




Sagarin Ratings Rigged?

Sagarin Ratings Rigged?

Submitted by NOLA Blue on December 7th, 2010 at 7:42 PM


No, I don't believe Sagarin rigged his schedule ratings to help Oregon and prevent TCU from miraculously slipping by Oregon.  But it is interesting to note that while I have heard plenty of talk about TCU and Boise St. lacking schedule strength, I hadn't really heard much regarding Oregon's.

Step in unnamed MGoBlogger* (**edit** named Drakeep) who pointed out that the Big Ten teams' schedules included an average of 7 winning opponents (while each SEC team faced an average of 5.8, and the PAC-10 something like 4...)  This savvy blogger also pointed out that Oregon had only faced 3 teams with a winning record.  I could barely believe it, and checked the stats myself.  Such is true.

So I head over to Sagarin to see where exactly a schedule against 3 winning teams and a very much non-winning FCS school would rank.  20th.  What was U of M's against 7 winning teams and a winning FCS school? 40th.  Hmmm....

Next, I give Sagarin the benefit of the doubt and assume that although Oregon's opponents didn't all win a lot of games, the games they did win must have been meaningful.  (In other words, Oregon's opponents must have combined to beat a lot of winning teams... as beating crappy teams and losing to good ones should not build a team's own strength.)

Oregon - Played 3 teams with winning records (out of 11, plus one losing FCS team.)  The 12 teams Oreg played, combined to achieve 12 victories over "winning FBS opponents" and 7 victories over "winning FCS opponents."  That equates to Oregon's opponents each beating ONE winning team.

Mich - Played 7 teams with winning records (out of 11, plus one winning FCS team.)  The 12 teams Mich played, combined to achieve 32 victories over "winning FBS opponents" and 7 victories over "winning FCS opponents."  That equates to Michigan's opponents each beating 2.67 winning teams.

These statistics are not even close, on either the primary or secondary level.  Yet, there it is:  Oregon's SOS at 20 and Michigan's SOS at 40.

For another reference point:  Mich St. played 5 teams with a winning record, and MSU's opponents combined to haul in 19 wins against "winning FBS opponents."  They lie between Michigan and Oregon on both the primary and secondary levels, and have a SOS rated 65th.

In conclusion, based on the ranking of Michigan and MSU schedules, Oregon's schedule should probably rate somewhere between 70 and 80.  This has placed me in the odd position of questioning the legitimacy of Sagarin's rankings... if any mathematician out there can point out how strength of schedule might use something more meaningful and direct than opponent's wins and opponents' wins against winning teams to rank schedules, let me know.  Until then, I'm going to have to believe that Sagarin is off his rocker.

*Unnamed MGoBlogger - my apologies, but I went in search of your forum and could no longer find it.  If you (or anyone else) would care to link to your post, I will gladly edit the above content to include your name and a link.  

UM back into the top 25 next year?.

UM back into the top 25 next year?.

Submitted by michelin on December 7th, 2009 at 12:38 PM
To determine how realistic it would be for UM to get back in the top 25, I reanalyzed the changes in the Sagarin ratings from last year to this year.

The conclusion (see analysis below): The task of getting back into the top 25 in the national rankings is daunting, since to do so, we must change and improve our Sagarin ratings more than any other B10 team did from last year to this year. 

The good news: Only one B10 team improved last year more than UM did (Indiana).

Also, I would guess that we had as many key Freshmen playing in 2009 as in 2008.  That won’t be the case next year.  Thus, in 2011 and 2012, there should be a lot more upperclassmen added to the UM lineup, compared with other teams.  So, things are definitely looking up.  But the progress may not be as fast we’d like.


Summary of details (based on the Sagarin Predictor ratings--which unlike the ones used in the BCS that ignore point spreads--are the best predictors of actual game results).


UM gained about 3-3.5 points in the Sagarin ratings from last year.  

Just improving by 3-3.5 points again next year (from 2009-10) would move us clearly above Purdue into 6th place alone in the B10 (assuming that, for each B10 team that improves next year, there is one that declines equally),

But improving by only 3.5 points next year would move us up no further, since there was a big gap this year between the 1-5 teams and the 6-11 ones in the B10.  In fact, to move into the top 4 in the B10 and the top 25 teams in the nation, we would need to improve by about 10-11 points—at least three times the improvement made from 2008-9.


Is that doable?  I think so but it would be the biggest jump either way in the past 2 years for a B10 team.  To put it into perspective, note that from 2008-9

PSU lost 10 points

NW lost 8.5 points.

Iowa and Illinois lost 7 points (surprising since Iowa’s now in a BCS bowl). 

MSU lost 2.5 points

OSU, Minn and Purdue and were unchanged.

(OSU did not improve, despite Pryor going from being a Fresh to Soph probably because they lost Wells).

Wisc was only one of two teams to gain as much as UM did:  3.5 points.

Only one team, Indiana, gained more than us: 8 points.

So, to gain 10-11 points next year in the Sagarin ratins, we must gain more than any B10 team did this year.  We must change slightly more than any other team changed in either direction (PSU made the biggest change by losing 10 points).


2009 sagarin




Why the collapse? A tougher second half of the season?

Why the collapse? A tougher second half of the season?

Submitted by michelin on November 16th, 2009 at 2:59 PM

There’s been a debate on this board whether UM had a tougher schedule during the second part of the season.
No, based on the Sagarin PREDICTOR ratings for B10 plus ND games only. Our strength of schedule (SOS) has NOT been tougher in the second part of the season, even when the games are corrected for 3-point home-road advantage-disadvantate.* Our schedule during the second half of the season was about 2 points easier on average.

However. If we include ALL of the games, the second half of the season WAS tougher overall. They were only mildly tougher. However, statisticians often seek to improve the reliability of the data by throwing out the highest and lowest ratings (here, IA and DSU). If you do that, there is a significant trend toward tougher games throughout the season (r-.47) —making each successive game almost 2 points tougher than the next, on average.

See link

When we add OSU (87.1) next week, our second-half season ratings will seem even tougher.

*Summary (for comparison purposes, note that UM’s current ratings is 69.0).
IA 80.8 80.2 with Home-Road (+3,-3)
ND 79.8 > WI 77.7 actually 76.9 Purdue 69.0 actually even more so 79.6>66.0 (+3,-3)
Ind 64.9 > IL 63.9 actually 61.9293.8 actually with the same corrected ratings (H-R balances out)

WMU 59.3 actually 56.3
EMU 56.5 actually 53.5
DSU 38.6 actually 35.6

**** Based on the current rating, UM should have lost to ND, beaten Purdue and Il. We beat ND , lost to Purdue and Il. The other five major games (Ind, IA, PSU, WI,MSU) went as expected, when you make adjustments for H-A. Note that to really make a fair test, however, we should recomputed the sagarin rating for all the games except the one we are considering (ie to determine whether we should have won or lost it). I don’t have the software to make those corrections, however.