Projecting the 2013 Big Ten Basketball Race: March 5

Last week, Indiana's grip on first place looked unassailable. A road loss at Minnesota briefly gave hope to the other contenders, but a tough loss at Michigan for MSU and surprising losses by Michigan (to Penn State) and Wisconsin (to Purdue) quickly gave Indiana back their two-game lead. With two to play, Indiana is now assured of a share of the title.

As always, ratings are here.

The Top Five

With seven games remaining that involve at least one of the top five, there are 128 different scenarios to explore. Here is a table that lists them all (click for full-size version):

The Tiebreakers

Indiana-MSU: Indiana wins on head-to-head.
Indiana-Michigan: Indiana wins (only top-5 opponent which they have different records against is MSU, assuming Indiana loses both and Michigan wins both).
Indiana-Wisconsin: Wisconsin on head-to-head.
Indiana-OSU: Indiana wins if MSU finishes at least even with Wisconsin; if Wisconsin finishes ahead of MSU, OSU wins.
MSU-Michigan: Michigan wins if they beat Indiana; MSU wins if they do not.
MSU-Wisconsin: Thursday's winner wins the tie (Wisconsin by superior record against Michigan and Indiana).
MSU-OSU: This is a moderately tricky one. If OSU beats Indiana, they win by superior record against Indiana. If not, MSU wins the tiebreaker if they beat Wisconsin (due to equal records against the rest of the top 5 and a better record against Wisconsin). If neither of those happens, the positions of teams further down will decide the tie: MSU wins if Illinois finishes at least tied with Minnesota; OSU wins if Minnesota finishes ahead of Illinois.
Michigan-Wisconsin: Wisconsin on head-to-head.
Michigan-OSU: Michigan only wins this if they beat Indiana and OSU does not. Otherwise, the only difference in their top-5 records will be against Wisconsin, which favors OSU.
Wisconsin-OSU: This is the really tricky one (at least, among two-team tiebreakers). If the other three teams are all tied (which involves MSU and Michigan each winning out, OSU beating Indiana and losing to Illinois, and Wisconsin beating Penn State), each will be .500 against the other three teams combined (Wisconsin's two 1-0 records against Indiana and Michigan balanced by their sweep at MSU's hands; OSU would split with all three), so the order further down would again determine it: for OSU to win, Minnesota would have to win both of their games and Illinois lose to Iowa. If Indiana and MSU are tied for first without Michigan, OSU has the advantage (2-2 instead of 1-2 against the top two). In any other case, Wisconsin wins.

Indiana-Michigan-MSU: Head-to-head puts it in that order.
Indiana-OSU-MSU: Same thing.
Indiana-Michigan-Wisconsin: Wisconsin is first on head-to-head, then Indiana second because they swept us.
Indiana-Michigan-OSU: Michigan is third either way; Indiana is first if MSU finishes ahead of or tied with Wisconsin, otherwise OSU is.
Indiana-Wisconsin-OSU: Wisconsin, OSU, Indiana on head-to-head.
MSU-Michigan-Wisconsin: The winner of Thursday's game is first, loser is second, Michigan third.
MSU-Michigan-OSU: This one is wild and depends very specifically on how it happens:
- Both Michigan and OSU beat Indiana: OSU first, Michigan second, MSU third
- OSU beats Indiana, Michigan doesn't: OSU first, MSU second, Michigan third
- Michigan beats Indiana, OSU doesn't: Michigan first, MSU is second if they beat Wisconsin or if Illinois finishes even with or ahead of Minnesota
- Both lose to Indiana: Michigan is third no matter what; MSU is first if they beat Wisconsin or if Illinois finishes even with or ahead of Minnesota
MSU-Wisconsin-OSU: If MSU wins on Thursday, the order is MSU-OSU-Wisconsin. If Wisconsin wins, they are first; OSU gets second if they beat Indiana or if Minnesota finishes ahead of Illinois.
Michigan-Wisconsin-OSU: Wisconsin first, OSU second, Michigan third.

Four-way tie without Wisconsin: Indiana, OSU, Michigan, MSU in that order (OSU-Michigan decided by their record against Wisconsin).
Four-way tie without MSU: Wisconsin, OSU, Indiana, Michigan in that order (Indiana ahead of Michigan on their record against MSU).
Four-way tie behind Indiana: If MSU wins on Thursday, the order is MSU-OSU-Wisconsin-Michigan. If not, Wisconsin is first and Michigan is still last; OSU gets second if they beat Indiana or if Minnesota finishes ahead of Illinois.

The Games

Ohio State @ Indiana: Indiana 78% basic / 86% (+10) margin-aware
Michigan @ Purdue: Michigan 78% / 81% (+8)
Wisconsin @ Michigan State: Michigan State 77% / 78% (+7)
Indiana @ Michigan: Michigan 61% / 56% (+1)
Northwestern @ Michigan State: Michigan State 93% / 96% (+16.5)
Wisconsin @ Penn State: Wisconsin 78% / 85% (+9.5)
Illinois @ Ohio State: Ohio State 72% / 84% (+9)

In addition, the relative positions of Illinois and Minnesota may affect some ties. If Illinois beats Ohio State, their chances of finishing at least tied with Minnesota are 78% / 64%; if they lose to Ohio State, their chances are 34% / 20%.

Based on the chart above and the game probabilities, here are each team's chances of finishing in each seed position (basic / margin-aware):

Team	#1	#2	#3	#4	#5
Indiana	97.56% / 98.48%	0.71% / 0.26%	1.72% / 1.27%	N/A	N/A
Michigan	N/A	33.20% / 32.38%	18.30% / 15.23%	14.14% / 10.71%	34.36% / 41.67%
Michigan State	N/A	33.66% / 37.41%	41.00% / 38.94%	16.62% / 14.58%	8.72% / 9.06%
Wisconsin	2.40% / 1.51%	17.97% / 18.90%	27.68% / 32.42%	33.62% / 33.30%	18.33% / 13.87%
Ohio State	0.04% / 1 in 10,300	14.45% / 11.04%	11.30% / 12.15%	35.62% / 41.40%	38.59% / 35.40%

Generalizing simple scenarios for the various seeds is ... not simple. A few things that stand out, however:

• If Michigan loses both games, they are #5 regardless of what happens with anyone else. No combination of midweek results can clinch a bye for Michigan.
  
• The MSU-Wisconsin winner cannot finish #5 and the loser cannot finish #2.
  
• OSU cannot finish #2 if they lose to Indiana but can if they lose to Illinois.
• OSU can beat Indiana and still finish 5th, though it is extremely unlikely.

The Middle Tier

Here there are 64 different scenarios to consider. The chart (click for full size):

The Tiebreakers

Minnesota-Iowa: Minnesota wins the tiebreaker with an equal or better record against all of the top 5.
Illinois-Iowa: Iowa has to win the head-to-head for this tie to occur.
Minnesota-Purdue: Purdue has to win the head-to-head for this tie to occur.
Illinois-Minnesota: This depends on the order of the highest-ranked teams. If Indiana is outright champion, tied with Ohio State only, or tied with Ohio State and one of Michigan and MSU, Illinois wins. If Wisconsin ties for the title or both Michigan and MSU do so, Minnesota wins. If Indiana is tied with MSU only or Michigan only, this group is even and it progresses to the remaining teams (Illinois has a better record against Ohio State, Minnesota against MSU and Wisconsin, neither beat Michigan but Illinois played them twice, which may affect things if Michigan is tied with someone else).
Illinois-Purdue: This also goes to the record against highest-ranked teams. Illinois wins it there unless the title is a Wisconsin-Indiana tie; if that happens, it goes to the order of the other three teams in the top 5. Purdue must beat Michigan to win any of these scenarios; they then have a better record against Michigan but worse against Ohio State, with two losses to MSU to Illinois's 0-1 record.
Iowa-Purdue: Again, record against highest-ranked teams decides it. If Indiana is tied with Wisconsin and possibly Ohio State (but not Michigan), Purdue wins this immediately. If Purdue beats Michigan, they win this no matter what; if not, they still win the tiebreaker if Wisconsin is not tied with anyone or is tied only with Ohio State, but lose if Wisconsin is tied with both Michigan and MSU (and possibly OSU). If Wisconsin is tied with one of Michigan and MSU and Purdue did not beat Michigan, the tiebreaker gets past the top 5 to look at Minnesota and Illinois.

Minnesota-Illinois-Iowa: Because Iowa must beat Illinois to make this happen, the order is Iowa, Minnesota, Illinois.
Minnesota-Illinois-Purdue: Purdue, Illinois, Minnesota (similar reason).
Minnesota-Iowa-Purdue: Purdue, Iowa, Minnesota.
Illinois-Iowa-Purdue: Iowa, Purdue, Illinois.

Four-way tie: Iowa and Purdue are the top two, with the order decided as specified in the two-way tie. Illinois and Minnesota are the bottom two, likewise with the order decided by the order of the top 5.

The Games

Illinois @ Iowa: Iowa 51% / 66% / +3.5
Michigan @ Purdue: Michigan 78% / 81% / +8
Minnesota @ Nebraska: Minnesota 67% / 79% / +7
Minnesota @ Purdue: Minnesota 65% / 69% / +4.5
Nebraska @ Iowa: Iowa 77% / 90% / +12
Illinois @ Ohio State: Ohio State 72% / 84% / +9

Based on the tiebreaker chart and game probabilities, seeding probabilities are:

Team	#6	#7	#8	#9
Illinois	11.31% / 4.06%	19.93% / 17.83%	35.48% / 52.38%	4.79% / 4.51%
Minnesota	52.01% / 70.57%	10.32% / 5.47%	6.73% / 4.55%	7.46% / 4.95%
Iowa	8.13% / 6.60%	38.01% / 57.99%	25.14% / 19.49%	14.72% / 7.39%
Purdue	5.37% / 5.01%	8.56% / 4.94%	13.34% / 7.59%	53.71% / 67.18%
Ill/Minn tie (unresolved)	21.46% / 13.10%		2.02% / 1.36%
Ill/Pur tie (unresolved)	0.98% / 0.36%		4.04% / 6.41%
Pur/Iowa tie (unresolved)	0.74% / 0.31%		13.26% / 8.21%

Interestingly, all the ties that are dependent on order of the top teams are either for 6th and 7th or 8th and 9th; no such ties for 7th and 8th exist.

Some points of interest in the scenarios:

• Illinois is guaranteed at least the 7th seed if they beat Iowa; Iowa will be locked into the 8/9 game.
  
• There is a scenario where Minnesota and Illinois will meet in the 8/9 game despite each winning a game; this happens if both Iowa and Purdue win twice.
• Similarly, Iowa and Purdue can get the 6 and 7 seeds with only one win each, if Minnesota and Illinois each lose twice.

Nebraska and Northwestern

Fortunately, here, the tiebreaker situation is simple: they played only once, and Nebraska won. Therefore, Nebraska gets the 10 seed if they win twice or Northwestern loses twice or both split.

The Games

Minnesota @ Nebraska: Minnesota 67% / 79% / +7
Penn State @ Northwestern: Northwestern 76% / 82% / +8.5
Nebraska @ Iowa: Iowa 77% / 90% / +12
Northwestern @ Michigan State: Michigan State 93% / 96% / +16.5

Nebraska is a favorite for the 10 seed according to the basic method (58.92%) despite not being a favorite in either game, since they only have to match Northwestern down the stretch. The margin-aware method favors Northwestern for the 10 seed instead, at 59.31%.

Penn State

They are the 12 seed, but you already knew that. At least they didn't go winless.