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Bradley-Terry Projections Recap: Who Was Who We Thought They Were?


Throughout Big Ten season I've been projecting the Big Ten race based on the Bradley-Terry method and a modified version I created that focuses on margin of victory but with extra weight on points scored or allowed in close games. Time to look back and see how those projections turned out, and where the turning points were. Naturally, most of the big swings will be early in the season when the ratings are more volatile and have more games to influence down the road. Teams will be presented in alphabetical order.

Illinois

Final Big Ten record: 4-4
Pre-conference projected wins, basic system: 3.44 (error: -0.56)
Pre-conference projected wins, margin-aware system: 3.03 (error: -0.97)

Fb2010ill_medium

Point of maximum optimism: after Week 5 of conference play (Pur 44-10, 3-2 record, projected finish 5.36/5.68 wins in BT/MABT systems)
Point of maximum pessimism: pre-conference (3.44/3.03), after Week 1 (OSU 13-24, 0-1, 3.03/3.45)
Biggest positive swing: PSU 33-13 (+1.55/+1.83)
Biggest negative swing: Minn 34-38 (-1.19/-1.10)

A reasonably good start to conference play (one win in the gauntlet of OSU-PSU-MSU, followed by two comfortable pastings of the Indiana schools) quickly raised expectations for Illinois, to the point where there was legitimate hope for a share of a Big Ten title as late as Halloween (though it would have required a few upsets along the way). But the basketball game at the Big House put an end to that hope, and losing to Minnesota added further insult to injury.

Indiana

Final Big Ten record: 1-7
Pre-conference projected wins, basic system: 3.14 (error: +2.14)
Pre-conference projected wins, margin-aware system: 3.41 (error: +2.41)

Fb2010ind_medium

Point of maximum optimism: pre-conference (3.14/3.41)
Point of maximum pessimism: after Week 8 (PSU 24-41, 0-7, 0.37/0.48)
Biggest positive swing: Pur 34-31 (+0.63/+0.52)
Biggest negative swing: OSU 10-38 (-0.54/-0.66), NW 17-20 (-0.73/-0.52)

Indiana's weak non-conference schedule left them unbeaten coming in. While the ratings weren't too impressed due to the horrid competition, they still thought highly enough of Indiana to expect 7 wins and a bowl trip. A narrow escape against Arkansas State sandwiched between beatdowns by OSU and Illinois quickly snapped Indiana's projections back to reality, and the Northwestern game sealed Purdue as Indiana's last, best chance to get off the schneid, which they eventually did.

Iowa

Final conference record: 4-4
Pre-conference projected wins, basic system: 3.52 (error: -0.48)
Pre-conference projected wins, margin-aware system: 5.19 (error: +1.19)

Fb2010iowa_medium

Point of maximum optimism: after Week 6 (Ind 18-13, 4-1, 6.41/6.45), after Week 1 (PSU 24-3, 1-0, 5.22/6.66)
Point of maximum pessimism: pre-conference (3.52/5.19), end of season (4-4)
Biggest positive swing: PSU 24-3 (+1.70/+1.47)
Biggest negative swing: NW 17-21 (-1.13/-1.22)

Iowa's early projections were wildly different between the basic and margin-aware ratings; the narrow loss to Arizona in pre-conference play hurt badly in the basic system but not as much in the margin-aware ratings. Gradually the basic projections caught up (fueled especially by the wins over Michigan and MSU) until it appeared Iowa was 50-50 to beat Ohio State and virtually certain to win their other three remaining games. It appeared Iowa would have an excellent shot at sharing in the Big Ten title. Then, suddenly, the bottom fell out. With three weeks to go, you could have gotten odds of 1 in 2000 or 1 in 41,000 that Iowa would wind up 4-4 in conference, based on the ratings at the time, but three late TD drives later, here we are.

Michigan

Final conference record: 3-5
Pre-conference projected wins, basic system: 5.28 (error: +2.28)
Pre-conference projected wins, margin-aware system: 4.46 (error: +1.46)

Fb2010mich_medium

Point of maximum optimism: after Week 1 (Ind 42-35, 1-0, 6.10/5.21)
Point of maximum pessimism: after Week 5 (PSU 31-41, 1-3, 2.38/2.22)
Biggest positive swing: Ill 67-65 (+0.88/+0.88)
Biggest negative swing: MSU 17-34 (-1.23/-1.28)

Michigan romped through its non-conference schedule (though with a close shave against 1-AA UMass) and escaped Indiana as well, starting the season 5-0. Then, moving into the meat of the schedule, Michigan's fortunes quickly turned south. After the Illinois win, there was little doubt how the last three games would go, and unlike Iowa's finish these three played out exactly to form, resulting in the flattest segment of these curves so far.

Michigan State

Final conference record: 7-1
Pre-conference projected wins, basic system: 5.40 (error: -1.60)
Pre-conference projected wins, margin-aware system: 5.57 (error: -1.43)

Fb2010msu_medium

Point of maximum optimism: after Week 4 (NW 35-27, 4-0, 7.85/7.61), after Week 3 (7.74/7.66)
Point of maximum pessimism: pre-conference (5.40/5.57)
Biggest positive swing: Mich 34-17 (+1.27/+1.10)
Biggest negative swing: Iowa 6-37 (-1.06/-0.73)

Back-to-back wins over unbeaten-at-the-time Wisconsin and Michigan shot MSU's projection into the stratosphere after two weeks of conference play; beyond this point none of the games other than Iowa cause much swing since MSU was projected as prohibitive favorites to win them all and did. The Minn-BYE-Pur stretch is as dull as one of these graphs can get.

Minnesota

Final conference record: 2-6
Pre-conference projected wins, basic system: 0.53 (error: -1.47)
Pre-conference projected wins, margin-aware system: 0.44 (error: -1.56)

Fb2010minn_medium

Point of maximum optimism: end of season (2-6)
Point of maximum pessimism: after Week 6 (MSU 8-31, 0-6, 0.05/0.02)
Biggest positive swing: Ill 38-34 (+1.00/+0.99), Iowa 27-24 (+0.95/+0.99)
Biggest negative swing: Wisc 23-41 (-0.17/-0.18), Pur 17-28 (-0.13/-0.21)

When you lose to a 1-AA and only manage to beat Middle Tennessee State in non-conference play, your projection isn't going to look good to start. The near miss with Northwestern raised Minnesota's hopes according to the margin-aware system, but otherwise it was a steady decline through the firing of Brewster and beatings by two of the three co-champions; two unexpected wins finished the season on a high note.

Northwestern

Final conference record: 3-5
Pre-conference projected wins, basic system: 5.98 (error: +2.98)
Pre-conference projected wins, margin-aware system: 5.26 (error: +2.26)

Fb2010nw_medium

Point of maximum optimism: pre-conference (5.98/5.26)
Point of maximum pessimism: after Week 6 (PSU 21-35, 2-3, 2.48/2.15)
Biggest positive swing: Iowa 21-17 (+1.18/+1.10)
Biggest negative swing: Pur 17-20 (-2.44/-1.31), Minn 29-28 (-0.41/-1.64)

Beating an awful Minnesota team by 1 in the first week of conference play is not good for your margin-aware numbers, nor is ending your unbeaten season in week 2 against a not-much-better Purdue team good for either set of numbers. At this point, NW is 5-1 against an awful schedule (and not a particularly pretty 5-1 given the opponents, either), and the projections reflect that. The only real expectation of a win beyond that point is Indiana, and Iowa is the only game that defied said expectations.

Ohio State

Final conference record: 7-1
Pre-conference projected wins, basic system: 5.72 (error: -1.28)
Pre-conference projected wins, margin-aware system: 7.46 (error: +0.46)

Fb2010osu_medium

Point of maximum optimism: after Week 2 (Ind 38-10, 2-0, 7.07/7.71)
Point of maximum pessimism: pre-conference (5.72/7.46), after Week 3 (Wisc 18-31, 2-1, 5.84/6.31)
Biggest positive swing: Ill 24-13 (+0.82/-0.08), Ind 38-10 (+0.53/+0.33), PSU 38-14 (+0.49/+0.33)
Biggest negative swing: Wisc 18-31 (-1.23/-1.40)

The close win against an Illinois team that wasn't thought to be good at that point actually dropped OSU's margin-aware projection as it gave them their biggest jump in the basic system. After the loss to Wisconsin, a handful of semi-serious challengers to close out the season saw a gradual but significant rise in OSU's projection after a steady section consisting of Purdue, Minnesota, and BYE.

Penn State

Final conference record: 4-4
Pre-conference projected wins, basic system: 4.39 (error: +0.39)
Pre-conference projected wins, margin-aware system: 3.93 (error: -0.07)

Fb2010psu_medium

Point of maximum optimism: pre-conference (4.39/3.93), after Week 8 (Ind 41-24, 4-3, 4.16/4.15)
Point of maximum pessimism: after Week 2 (Ill 13-33, 0-2, 2.22/2.15)
Biggest positive swing: Mich 41-31 (+1.22/+1.06)
Biggest negative swing: Iowa 3-24 (-1.18/-0.56), Ill 13-33 (-0.99/-1.22)

This is the closest any projection came to nailing down the final record; two beatdowns at the hands of Iowa and Illinois put a big dent in any optimism, but a win over Michigan put Penn State back on course for 4-4. With everything holding to form in the final four weeks, that's exactly where they landed.

Purdue

Final conference record: 2-6
Pre-conference projected wins, basic system: 1.54 (error: -0.46)
Pre-conference projected wins, margin-aware system: 1.22 (error: -0.78)

Fb2010pur_medium

Point of maximum optimism: after Week 3 (Minn 28-17, 2-0, 3.37/2.91)
Point of maximum pessimism: pre-conference (1.54/1.22)
Biggest positive swing: NW 20-17 (+1.43/+0.93)
Biggest negative swing: Ind 31-34 (-0.63/-0.52)

Purdue opened conference play with a bye, an upset of Northwestern, and a win over Minnesota. It was all downhill from there. Even at that point, the margin-aware ratings projected less than one win on average in the remaining six games. They were right (although the Indiana loss was a mild upset).

Wisconsin

Final conference record: 7-1
Pre-conference projected wins, basic system: 5.07 (error: -1.93)
Pre-conference projected wins, margin-aware system: 4.03 (error: -2.97)

Fb2010wisc_medium

Point of maximum optimism: end of season (7-1)
Point of maximum pessimism: after Week 1 (MSU 24-34, 0-1, 3.33/3.20)
Biggest positive swing: OSU 31-18 (+1.54/+1.71)
Biggest negative swing:MSU 24-34 (-1.74/-0.83)

A loss in the opener plus an awful non-conference schedule and some close wins in said schedule had Wisconsin marked as a Texas Bowl contender instead of a Rose Bowl contender in early October. Then MSU beat Michigan (making Wisconsin's loss look less bad), Wisconsin beat OSU and Iowa, and suddenly Wisconsin was favored in every remaining game by a wide margin. And they delivered those wide margins.

Average absolute error of pre-conference play projections: 1.42 for both systems. Not bad for just four weeks of data to project eight more, particularly in a year as unusually stratified as this one.

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