In the weirdest college basketball season, Colgate is one of the weirdest teams. Back in January after playing five games the Raiders ranked #1 in Strength, boasting three 40+ point blowout wins...and one loss against one of those teams. They've settled down a bit—they're down to #10 at 11-1—and have played only three teams, four times each. Only in 2021 will you likely see something like that.

So is our power rating right? Is Colgate a Sweet Sixteen team? Or maybe you'd rather go with the LRMC, which currently has Colgate at #4—a Final Four contender!

That's right, Colgate is #4 in the current LRMC rankings. The LRMC (Logical Regression Markov Chain, though it now uses a Bayesian method in place of the LR) has garnered a lot of respect in recent years for NCAA accuracy. But why are the Raiders ranked so high, when Pomeroy (#91), BPI (#57), and Sagarin (#63) have them well outside the top 50?

Sports-ratings.com's own Markov Chain system ranks Colgate at #59, and more interestingly, LRMC "Classic" only ranks them #91. Let's find out why.

First a look at how LRMC works, in a nutshell: A determination is made as to how likely a team is to win a given game; then, if they "win" a random trial of that game, the "ball" stays with them until they "lose." When they lose the ball goes to another team and the process repeats. The team that has the "ball" most often is ranked the highest.

In reality, math is done to compute the "steady state" of the "ball" moving around—the Markov Chain—but the simulation aspect works too, and that's what our Markov Chain ranking uses.

The important thing is in determining how likely a team is to win a given game. The LRMC papers get into a lot of mathematical symbols, but by looking at examples we can see some of the end result:

Above, Duke and North Carolina are compared over a variety of years. From the chart we can put together what the LRMC considers the basic odds of winning a game based on its outcome and location. Roughly speaking, after giving a 4 point home court advantage, we can divine the following:

Margin Game Odds 0 50% 1 52% 2 53% 3 55% 4 57% 5 59% 10 67% 12 70% 15 74% 21 82% 26 87% 33 93%

and we can fill in the blanks from there. Those are the odds of winning a given game, given a final victory margin. In a sense these games are "replayed" over and over, and close games can offer a different "result" than what actually happened. This way solid wins are rewarded, and if you do well against a tough schedule, you'll "get the ball back" a lot too.

Note that the Duke/UNC chart has two more columns; these are where the software determines whether team A actually "beats" team B. The LRMC doesn't go on a game-by-game basis, but aggregates the results of every game played between two opponents in the same year. The difference is in how it's done. The first column is a simple average of the odds for each game played. The 2nd column computes "joint odds" and uses that instead.

The "joint odds" are computed with more complicated math, but in the end a good estimate can be made by adding up all the victory margins, then treating that as a single game result. For example, 2000's Duke by 4 and 14 translate to winning by 8 and 10 on neutral court; the sum of 18 implies 78% aggregate odds, close to the 76% given in the chart. Likewise in 2006 the values 4 and -7 correct to 8 and -11, or -3 total, which matches the 45% in the 2nd column.

Perhaps the most relevant example is 2002, where the total margin is 66 and the Joint probability is 99%. That's the situation for Colgate for each opponent.

Colgate played 12 games with these results (sorted by opponent):

Adj Game LRMC LRMC Opponent Margin Loc Margin odds Classic New Army 44 home 40 99 71 99 Army -2 home -6 40 71 99 Army 10 road 14 73 71 99 Army 9 road 13 71 71 99 Boston 7 road 11 68 74 99 Boston 44 road 48 99 74 99 Boston 10 home 6 60 74 99 Boston 15 home 11 68 74 99 Holy Cross 40 home 36 95 73 99 Holy Cross 9 home 5 59 73 99 Holy Cross 0 road 4 57 73 99 Holy Cross 18 road 22 83 73 99

What stands out is the victory margin of 44 against Army, 44 against Boston U, and 40 vs. Holy Cross. These adjust to 40, 48, and 36 point wins roughly. You can see that the to-win odds for those games approaches 100%. In contrast, their loss to Army and the overtime win vs. Holy Cross are just 40% and 57%.

The LRMC Classic takes the game odds for each opponent and averages them, coming to remarkably similar conclusions around 71 to 74%. Based on that, it's not too hard to see Colgate ending up around #91—they hold onto the "ball" about 3/4 of the time, not bad, but against poor opponents, the ball probably won't come back to them that often.

The Bayesian LRMC ("LRMC New" column) shows what happens with Joint probabilities: the sums are 61, 76, and 67, all of which work out to near 100% odds of winning. Once Colgate gets the Markov "ball" they don't let go of it. Only a handful of teams with much tougher schedules have the ball more often in this scenario (undefeated Gonzaga, undefeated Baylor, and Iowa).

This situation could really only occur in a Covid-scarred season. Twelve games is a small sample, and that gets boiled down to three opponents by LRMC. Colgate is a black hole from which the Markov Chain rarely exits.

Will they hold their position until Selection Sunday? Only if they play only Army, Boston, and Holy Cross in the Patriot League tournament. If they play any other team, their rating is bound to suffer a hit—that is, unless they win another game by 40 points.

Note: Our own Markov Chain ranking puts Colgate at #59 because we don't aggregate the game results at all, though our probabilities are higher for assuming a win. For example, an 11-point win comes out to 84% rather than 68%. Thus Colgate does better most of the time, but they drop the ball a lot: if the software samples their loss to Army, they're probably giving up the ball.

**So how good is Colgate anyway?** The answer to that is: what day are we talking about? On some days they can beat an average team by 40 points, on other days they struggle with the very same opponent. They actually have a NET ranking of #12, which would imply a 3- or 4-seed, though the Bracket Matrix suggests a 13-seed is more likely.

Our Median Strength rating puts them at #30, which might be a good place for them. Using only their Median game rating, their 40 point wins are excluded from the equation completely, and they still rate fairly well. We can also make a modified Strength rating where the team's variance is subtracted from their rating; in that case, Colgate comes out at #38. That fits well with their #45 average in Ken Massey's rating comparisons page.

Those results might put them in the "others receiving votes" list in the AP poll. I do think they deserve some Top 25 votes; right now they have none.

**The final question is: Assuming they make it, how will they do in the tournament?** Is the Final Four a George-Mason-like possibility for the Raiders?

I'd say no. They are far too "random" to put together such a consistently great run. But they can definitely score a first-round upset as a projected 13-seed, and the Sweet Sixteen is not out of the question. That's probably the most we can ask of them. They did win back to back games against Boston and Holy Cross by 40+ points, but they also lost a 2-point game to Army a day after beating them by 44.

Bottom line, though, if I'm a 4-seed I'd rather not draw Colgate as a first-round opponent.

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