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.
Illinois beats Iowa, putting Baylor ahead of Gonzaga
The college basketball season is finally getting interesting enough to write an article about. Here are some of the more offbeat things happening in our power ratings:
• Baylor finally passes Gonzaga at #1, and they can thank Illinois
Gonzaga and Baylor are clearly the best teams in the country, and are really the only two teams deserving of first-place votes. In our power ratings Gonzaga has held the edge at #1 for a long time. The teams have been nearly equal in Strength (winning-margin based power rating) but the Zags have been far ahead in Success (accomplishment-based rating).
When the rankings are combined, the Zags have been #1, Baylor #2. That's because Gonzaga's pre-conference schedule was tough as nails, and they hold wins over Kansas, Auburn, West Virginia, Iowa, and Virginia, all on neutral courts (home court counts a lot in Success). Baylor's lone non-conference skin was beating Illinois.
Lately though the tide has been turning; Gonzaga's West Coast Conference slate offers little advancement in Success, while Baylor has beaten Oklahoma, Texas Tech, Kansas, and Oklahoma State. They also beat Auburn in the Big 12-SEC challenge, giving them wins over two of Gonzaga's victims.
The game that gave Baylor the top spot this week was played on Friday, January 29, when Illinois beat Iowa 80-75. That diminished Iowa's value as a Gonzaga win, and elevated Baylor's win over Illinois. It was just enough to put Baylor on top. Had Iowa prevailed, Gonzaga would still be #1.
That's how close the two teams are: they're dependent on their opponents to decide the issue for them. If both teams remain undefeated, however, it's pretty clear that Baylor will start to pull ahead as their schedule going forward is a lot harder: Ken Pomeroy gives Gonzaga a 70% chance to win out while Baylor's odds are just 1 in 6.
• Drake tumbles in Markov Chain
The other undefeated team in the country is Drake. For those of you who don't know—probably the majority—the Bulldogs are located in the middle of the state of Iowa. Drake has ranked respectably in Strength, generally in the top 40 this year. The Bulldogs were winning games by an average of over 20 points per game against a weak schedule, and both aspects are taken into consideration.
But in our Markov Chain rankings, Drake was consistently in the top five. The Markov Chain formula is meant to cover both aspects, too: the "ball" moves from team to team based on win probability, and the better teams you beat, the more likely you are to "get the ball." In Drake's case, however, their weaker schedule should have prevented the ball from going to them. But their overpowering wins—as of January 4, they won every game but one by double digits—meant that once they got the ball, they pretty much never gave it up.
That changed on Sunday when they needed overtime to beat Illinois State. Suddenly there was a near 50/50 game on their schedule, so instead of being a black hole from which the Markov ball would rarely emerge, there was an out. Drake plunged from #5 to #19, still a respectable ranking but making it look far less likely that the Bulldogs are a stealth Final Four team.
In fact, Drake's last three winning margins have all been under 10 points. What changed? Well, the Bulldogs are coming back from a lengthy Covid layoff. After beating Southern Illinois 86-55 on January 4 they didn't play until the 26th. They beat Missouri State twice, by 7 points and 5 points, before the 2-point win at home vs. Illinois State.
Pomeroy gives Drake just a 2% chance of winning out, mainly because they face Loyola of Chicago twice. Loyola's Strength is a few points better than Drake's, and they also rank in the top 25 in the Markov Chain rankings.
• Winthrop loses and plummets in Success
The only other undefeated team for most of January was Winthrop, who started out 16-0 before losing to NC Asheville on the 29th. Unlike Drake, the Eagles didn't rank very well in the Markov rankings, floating somewhere in the 60s range. That's because while the Eagles won every game, they had a lot of close calls. This kept them pretty low on the Strength totem pole too, outside the top 100.
But in Success, where win margin doesn't matter? The Eagles were flying high at #7 before their fall, neck and neck with Drake who shared their undefeated record and poor strength of schedule, but beat teams much more convincingly.
After Winthrop's loss the bottom fell out of their high ranking and they plunged to #45. Why so far for one loss? Success takes into account who you lose to and where, and losing to 10-9 Asheville at home was a damaging hit.
• Colgate holds on in top ten of Strength
In addition to Drake, another team surprisingly high in some of our power ratings is Colgate, who at one point was #1 in Strength (though they had only played 4 games so they weren't included at the time). Colgate was #5 last week but falls this week to #10 after an overtime win at Holy Cross hurt their average.
Still, Colgate in the top ten? How did we get here? First off, our Strength rating uses no priors, meaning nothing from the last season or any pre-season "projections" affects the ratings. That means a small sample size makes a big difference. Normally these things go away by January, but this year is different, and Colgate had played only six games through mid-January, against three different opponents. They beat Army 101-57, then lost to Army by 2 points. They beat Boston U by 7 on the road, then won by 44 the next day. After beating Holy Cross by 40, and then 9, they ranked in the top five.
All of this incestuous scheduling was necessitated by Covid, and it meant that the Patriot League's ranking among the larger basketball conference was dependent on very few games: only Army and Navy played out of conference and they went 6-2 against Division I. One game that made a lot of difference was Army's 7 point loss to Florida (#19 Strength); Navy also beat Georgetown. This put the Patriot League in a better position than they normally are, and Colgate's three 40+ point wins inflated their rating.
The overtime win deflated their balloon a bit but their 8-game sample is still bloated. Or maybe Colgate's just that good? If so, they're pretty hot and cold, winning by 40+ one game, then losing to the same team the next day? Using standard deviation to rank team Strength by stability, the Raiders fall to #57, which is probably more of what they deserve. Our Median Strength ratings accomplish the same thing, pushing them down to #55 as all three of their huge wins are factored out, and their two "middle" performances are averaged to get the median performance.
The question for most people is, if they make the NCAA tournament, can they get a first-round upset? The answer is: if the team that wins by 40+ shows up, of course.
• All but five D-I teams present and accounted for
Most years we screen out non-division I teams by formula (number of games played being less than average). This year, many true D-I teams haven't played close to the average, while many non-D-I teams have played more. Also, there are 10 teams that aren't playing at all (the entire Ivy League, plus Maryland Eastern Shore and Bethune Cookman).
So we're having to make up the requirement as we go, trying to insure a reasonable number of games played while still letting in the vast majority of D-I teams. Currently the requirement is 6 games, which means out of 347 teams, 342 are listed. Right now American, Alabama A&M, NC Central, Loyola MD, and Howard are not ranked; that should change in about a week, Covid permitting.
It also means that there are currently 8 non-D-I teams counting as D-I. They are:
Interestingly most of these teams list their D-I games as "pre-season exhibitions" even if they were played in January. That's fair, since losses to D-I teams shouldn't really count on their record. The D-I winners aren't putting an asterisk by their wins though. So can a game be half exhibition, half real? Looks that way: the winners count their wins, the losers call them exhibitions.
What about when the non-D-I team gets an upset? Looks like Our Lady of the Lake's official record is 1-3, calling 3 losses exhibitions but their win over D-I Texas State is official. Flagler counts one of two losses to FIU official, while their wins over Central Michigan and North Florida both count, but not losses to Furman and South Alabama. Not surprisingly FIU counts both wins, but credit Central Michigan and North Florida for owning their losses. Flagler is the only non-D-I team that doesn't rank in the bottom 10 in Strength; in fact at #230 they're not in the bottom 100.
Assuming we are able to increase our requirement to 7 games, then 8, that means we will get rid of five of these interlopers. But we might be stuck with Saint Katherine and Bethesda. And Carver should be considered a D-I team this year anyway; if you play 20 D-I teams, you're D-I, even if you're losing by an average of over 50 points per game.
Posted on February 01, 2021 at 11:11 AM in analysis, commentary | Permalink | Comments (0)
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