I concur that 8 teams is a good guess for number of B1G teams invited to the Big Dance this season. Both for the reasons cited (strong Big Ten, but some teams may have injuries, and other teams may struggle in B1G play), but also for an additional reason: the mathematics of RPI is self-limiting to the Big Ten, especially in a season (like probably this one) with a very strong Big Ten.

Let me try to simplify the explanation of the latter via quoting parts of the longer explanation in the Monday NCAA RPI thread. First, let’s update the projected end-of-season RPI data to as of today (Thursday, 12/12/2019) from the Warren Nolan projections.

Projected End of Season RPIs and Charlie Creme Bracketology

RPI Team W-L (Conf W-L) SoS Charlie

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#5 Maryland 27-2 (18-0) 21 #13-16

#7 Indiana 27-3 (16-2) 13 #9-12

#20 Rutgers 25-4 (15-3) 66 #25-28

**#24 Minnesota 23-6 (13-5) 37 #21-24**

#25 Northwestern 23-6 (13-5) 41 #37-40

#34 Michigan State 21-8 (12-6) 48 #25-28

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#56 Michigan 19-10 (10-8) 38 #21-24

#69 Iowa 16-13 (7-11) 19 #33-36

#72 Ohio State 13-16 (6-12) 6 #41-44

#97 Nebraska 17-12 (7-11) 52 #45-48

#98 Purdue 15-15 (6-12) 22 #29-32

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#184 Wisconsin 10-19 (2-16) 35 out

#217 Illinois 9-20 (1-17) 54 out

#220 Penn State 7-22 (1-17) 46 out

Creme’s bracketology is as of last Monday, where (as noted) he picks 11 Big Ten teams (and not Notre Dame) for the Big Dance. The Creme numbers are a range from 4*N-3 to 4*N where N represents his ranking of the team within its regional (so that the above-listed rank ranges represent the partial ordering induced by Charlie’s bracketology).

I split the listing by projected end-of-season RPI into three segments of B1G teams: you could call them Very Good, Good and Bad.

First let’s look at the Gophers. Subsequent to our crushing of GW, our projected end-of-season RPI got bumped from a (Good) #47 to a (Very Good) #24. In other words, Nolan was impressed enough to cut our expected RPI ranking number in half. This also puts the expected Gopher season result in complete alignment with Charlie’s opinion of #21-24. Why did we make such an RPI leap? Because (in the view of the Nolan projection model), we went from a projected 10-8 Big-Ten season to a projected 13-5 record. That actually informs us of what our B1G target should be if we want to stay completely off-bubble - namely, 13-5.

Now note that Charlie’s list of 11 favored teams is comprised of the Good and Very Good groups. Per Warren Nolan, we expect the Very Good group to end the season with a better-than-bubble RPI, where we consider the bubble to be RPI = 45 (and the Gophers just moved off-bubble in Nolan’s view with that win). But the Good teams (that Charlie, at least, thinks are deserving of the Big Dance) all have a projected end-of-season RPI that is greater than bubble-level of about 45. Specifically, 56, 69, 72, 97 and 98.

Now let’s fast forward to the end of the season, and for sake of argument make the following assumptions:

(a) No outcome-influencing injuries in the B1G.

(b) Teams play as expected in the B1G season.

(c) In fact, let’s assume that the Warren Nolan projection model is very accurate, so that at end of season the RPIs as projected in the above table hold true (to within some small epsilon).

(d) Also assume that Charlie has not changed his mind, and still supports the same list of 11 Good and Very Good Big-Ten teams for the Big Dance.

In that case, we potentially have a huge argument brewing between Charlie and (the rest of) the Committee (I’m guessing that perhaps Charlie sits on the Committee).

We understand that they consider other things besides RPI, such as Team Sheets, good wins, bad losses, etc. - but fundamentally, the Committee drinks their own RPI Kool-Aid.

If Charlie is promoting Nebraska and Purdue at #97 and #98, that’s gonna raise some eyebrows. Did the Committee let the Gophers in last year at RPI #102? Nope.

“But those are Good teams!” Charlie exclaims. “But the RPI numbers don’t lie,” the Committee says.

What about the case for Iowa (RPI #69) and Ohio State (RPI #72)? Both of those have losing records in the Big Ten. In fact, both teams would have had an even worse RPI (certainly over #100) if it weren’t for the fact that both teams were wise in not scheduling many non-conf opponents with really bad RPIs - such that they didn’t tank their SoS. Ohio State even achieved (under our for-sake-of-argument assumptions) the 6th best Strength of Schedule in the NCAA. Thus, in spite of (hypothetically) losing 2/3 of their Big-Ten games, they still get an end-of-season RPI of #72, since RPI is 3/4 a measure of SoS and only 1/4 a measure of won-loss record. Shrewd scheduling on the part of Ohio State. Yet, despite the losing record, Charlie (perhaps legitimately) still argues that Ohio State is a Good team that deserves an invite to the Big Dance.

When we get down to Michigan at RPI #56, with its (hypothetical) 10-8 winning record in the (admittedly) strong Big Ten, now we have a true bubble team, and Charlie has a good argument (against the Committee).

Let’s say Michigan is in (just for sake of argument). Along with the 6 Very Good teams (including Minnesota, who ends up 4th best RPI within the Big Ten, by our assumptions), we now have a count of 7 teams in so far.

In order to get the Big-Ten Big-Dance count to 8, Charlie has to successfully argue in favor of one of {Iowa, Ohio State, Nebraska, Purdue} with RPIs of {69, 72, 97, 98}. Fat chance of the latter two getting in. Perhaps one of {Iowa, Ohio State} gets in, bringing the count to 8.

So the Big Ten is self-limited to about 8 NCAA tournament contestants exactly because the Big Ten is so good this season (and in spite of Charlie arguing that 11 Big-Ten teams deserve to Dance).

That hard cap at 8 exists regardless of any unexpected injury situation. If we remove assumption (a), and significant injuries were to affect Big-Ten game outcomes, then that might only serve to reduce the Big-Ten Tournament invites from 8 to 7 or fewer.

The reason is that the very goodness of the Big Ten concentrates most of the B1G losses in just 3 Bad teams. In the B1G season, there must be 50% Wins and 50% Losses (by the definition of the word “game”). Most of those Losses get absorbed by the Bad teams, but there’s still some left over to be absorbed by the Good teams, and a few Losses befall the Very Good teams too.

But because of the high quality of the Big Ten, that extremely skews the probability distribution of where the 50% Losses go. That results in extremely bad RPI ranks for the Bad teams (#184, #217 and #220) plus lower-than-deserved RPIs for the Good teams and Very Good teams. Because they all have to play the Bad teams, which acts like a boat anchor on their SoS, but since RPI is mostly a measure of SoS (and not basketball quality of a team), that SoS boat anchor ruins the RPI for every Big-Ten team. Even the Very Good teams experience this boat-anchor effect, but their pre-boat-anchor RPI is high enough so as not to put them in jeopardy. It’s the Good teams that are in danger. Merely because the Big Ten is so good, some otherwise-certainly-in Good teams are pushed to on-the-bubble; and some otherwise on-the-bubble teams are pushed to “out.”

So, quality of the Big Ten is mathematically self-limiting in the sense that the better the Big Ten is, the worse of an SoS penalty is imposed on it (for playing themselves), and the more of a hard cap (at about 8 teams) is imposed on the B1G for admission to the Big Dance. This effect is purely due to the mathematics of the definition of RPI and SoS. In essence, it’s directly due to the horribleness of RPI. Add to that the fact that each seat at the Big Dance table comes at the expense of some other team that can’t go, plus the automatic bids, and we see that (as long as RPI is in play) it is extremely unlikely that the Big Ten will ever get more than 8 NCAA Big Dance invitations. No matter what Charlie says about 11 Big-Ten teams deserving to Dance.