So, as it turns out, no fancy probabilities were required. I'm writing this because I said that I would give an update, not because any of us needed it. With the Wisconsin game still to come, since my last update, everything has, stunningly, gone perfectly for the Wolverines. Based on the pre-game numbers, KenPom suggested that if Illinois were to play 100 games in East Lansing, Sparty would win 85. Maybe the lack of injuries affected their psyche, or maybe they got unlucky -- or maybe you can't really predict sports. :-) Luckily for Illinois, and for us, they didn't have to win 100 times at Breslin -- just once.
The Fighting Illini's improbable win, coupled with Michigan's defeat of a plucky Golden Gopher squad, assures Michigan of a Big Ten title. Their regular season record histogram, according to the KenPom update:
To earn a title share, either Staee or Wisconsin would have to win out; per KenPom, Sparty has a 17% chance, and Wisconsin has a 42% chance.
Putting this all together, the Wolverines have a 97% chance of an outright title.
Let's not kid ourselves, though. Winning at Illinois is going to be tough, and Indiana is always a challenge. None of us is going to feel completely confident until the outright title is clinched, but chances have never looked so good.
BTW, Michigan has also clinched no worse than a #2 seed in the Big Ten tournament. Michigan wins a three-way tie or a head-to-head tie with Sparty. The winner of a Wisconsin/Michigan tie that did not include the Spartans would depend upon who finishes #4. However, none of us wants to be concerned with tiebreakers or who beat whom further down the standings. The team has two bites at the apple and just needs one of them to count. Win one, and we'll all party like it's 1986. ;-)
OK, so that happened. The great thing about the Big Ten standings is that they don't take 19-point first-half deficits into account. :-) Unsurprisingly, the performance in West Lafayette reduced KenPom's probabilities of Michigan victory in each of the next three games; combined with an Illinois victory over Nebraska, the remaining schedule looks a couple of percentage points harder than it did a few days ago.
Having said that, GRIII's layup turned a 74% (pregame) probability of victory into 100%, which more than makes up for the slightly smaller future percentages. Here's an updated chart of Michigan's expected final record, again to two signficant figures:
Staee hasn't played; their chart is nearly unchanged:
Wisky, now alone in third place:
|11-7 or worse||13%|
Ohio, still up half a game on Iowa:
|11-7 or worse||67%|
|11-7 or worse||79%|
(Nebraska, unsuprisingly, has been eliminated from title contention).
Combining the various scenarios, we get the following chance of winning the title with the given record (i.e., the rows add up to 100% and represent the probability of each outcome if Michigan achieves the record listed).
|Record||Outright Title||Shared Title||No Title|
Multiplying by the data in the first table -- the chance that Michigan achieves each of these records -- gives us an 83% chance of an outright title (up from 75% on Sunday) and a 15% chance of a shared title, for a whopping 98% chance of hanging a Big Ten championship banner for 2014.
With the victory over the Boilermakers, Michigan has also locked up a first-round bye in the Big Ten tournament. (I'll spare you the details, but suffice it to say that even if they lose out, Michigan's worst possible finish is a tie for fourth, and the winning record against the top teams in the B1G standings would pay dividends in any tiebreaker).
Clinching/eliminatation scenarios for the remainder of the week and weekend:
- Michigan cannot clinch the outright title this weekend. However, Michigan can clinch a share of the title with a win and a loss by Staee.
- Iowa plays @Indiana and vs. Purdue and is eliminated with any loss or Michigan victory.
- Ohio plays @PSU and @Indiana and is eliminated with any loss or Michigan victory.
- Wisconsin plays @PSU. A loss or Michigan victory means that they can do no better than a share of the title; a loss and a Michigan victory would eliminate them entirely.
- Staee plays at home against Illinois; if they lose and Michigan wins, they can do no better than a share of the title.
As always, Go Blue!
(Edit: corrected a typo - "play dividends" -> "pay dividends")
(Apologies if this belongs elsewhere, but I haven't seen this analysis done yet).
At 11-3, with a half-game lead on Staee and four games remaining, Michigan is obviously in the driver's seat for the B1G basketball title. Using the game predictions from KenPom's site, I've done a quick probability analysis to see what the odds are that there's a banner to be hung.
First, Michigan's expected record, along with a percent chance:
(I used two significant figures, since there were two in the KenPom data; obviously, they won't add to exactly 100%).
Here's Staee's expected record:
|10-8 or worse||12%|
|10-8 or worse||2.4%|
|10-8 or worse||23%|
|10-8 or worse||68%|
Put it all together, and you get the following possibilities (all chances here are conditional -- e.g., each line should add up to 100% within the limits of rounding and significant figures):
|Record||Outright Title||Shared Title||No Title|
|11-7||< 0.01%||0.20%||> 99%|
When you factor in the chances that Michigan achieves each of these records (from the first table), and add it all up, and there is a 75% chance of an outright title, a 19% chance of a shared title, and a 6% chance of being bannerless. (Coincidentally, I coded up a simulation using the same KenPom percentages, ran it 100 times, and got at least a share of the title exactly 94 times).
Long story short, even with a single loss, the odds are still in our favor to win the title outright, since KenPom doesn't think Staee is likely to run the table, and 2-2 down the stretch is likely to be enough to secure a share of the title. Like many of you, I never would have predicted this in December.