Monday, February 14, 2011

Is "Best" Always The Best?

With just about two weeks to the tip of the first conference tournament, the Ivy League will once again have its run as a popular footnote, since the Ivies are the only Division I conference not to hold the event.

Instead of giving the automatic bid to the NCAA Tournament to the conference tourney winner, the league hands it to the team that survives the 14 game round robin Ivy schedule. There are a variety of reasons for this, including but not limited to: logistics and class, necessity as it relates to the Ivy athletic mission and a sense of merit.

In a previous post, I raised the point that while 14 is a larger sample size than three, it is hardly sizeable enough to guarantee that the best team wins the league. In fact, the odds of the 14-Game Tournament selecting the best team versus a simple 1-8 seeded conference tournament were only about 9 to 20 percentage points better depending on the amount of parity and whether the games were staged at the higher seed's gym or on a neutral floor. When you consider that quite often the Ivy champion would at least be in the discussion for an at large bid, especially as the tournament continues to expand, some of those unlucky teams in that 9 to 20 percentage point delta might wind up getting picked for the Big Dance anyway.

There is an important logical extension of that post that I would like to address now, as the analysis made one latent, but very fundamental assumption, so ride along with me on a quick thought experiment.

The newly formed Omega Conference boasts two and only two teams, playing each other ten times and jockeying for an automatic bid in the Big Deal Tournament. The first squad, Team Steady, is the 75th best team in the country. As its name might indicate, it is quite consistent. It plays like the 65th to 85th ranked team in the nation every night without fail.

Team Steady is joined in Omega Conference by Team Enigma. Team Enigma is truly all over the place. It settles in as the 90th best team in Division I, but some nights it can't shoot, other nights it can't hold onto the ball and still other nights it opts out of defense altogether. Other nights, it just runs opponents off the floor, scoring in bunches, creating turnovers defensively and sticking 15-0 runs on teams like it's nothing. Team Enigma is likely to play like the 25th to 155th best team in the country on any given night and believe me, it liberally explores that range.

Omega Conference has a problem. It needs money. Specifically it needs to play as many games in the Big Deal Tournament as possible to get as many shares of the overall Massive TV Revenue pie as possible.

Omega Conference decides that it has to structure its automatic bid rules to send its best team to the Big Deal Tournament in order to maximize its odds of winning one or more games. It decides that whichever of Steady or Enigma wins the most of the ten games between them will be the team most qualified to pull down an improbable victory.

Under the above scenario, Omega Conference would send Steady to the Big Deal Tournament about 2/3 of the time, while Enigma would go 1/3 of the time. Every time they face Team State, which is about 15th to 20th nationally and is of average variance.

Many of you have probably seen where this was going long ago, but in this rough construct, Team Enigma would have about a 15 percent chance of beating Team State while Team Steady's chances would hover around 5 percent.

How is that possible? Team Steady is legitimately the better team - it should be the most likely to win a game in the Big Deal Tournament.

The answer lies in that variance number.


The ideal outcome for Omega Conference or any mid-major league is to have its best team be incredibly high variance and far enough ahead of the rest of the league to avoid that variance tripping it up during the short regular season slate.

Last year's Ivy champion Cornell finished the season just outside the Top 50 in the Pomeroy rankings. It's March run has been well chronicled and involved knocking off the No. 22 and No. 9 teams in those rankings. There have been better Ivy champions in the past and ones with easier matchups than playing an "about right" five-seed and a true three seed to get to the Sweet 16.

The Big Red, however, was an incredibly high variance team, boasting 2010's highest variance offense and defense by a wide margin in each category. When you take a very good Ivy champion with incredibly high variance and have it post two straight tournament games with offensive ratings north of its already expansive 95 percent confidence interval, it's almost impossible to lose. An adjusted 150 offensive rating against Temple and 161 against Wisconsin were followed by an 83 against Kentucky - the type of lucky ordering that one wishes for at a craps table in Vegas.

Those years are easy though. The best team truly does provide the best chance to win an NCAA game and it's far enough ahead of the field to win the league relatively comfortably.

Fast forward one year, and one can see where the problems arise. The two remaining contenders in the Ivy race, Harvard and Princeton, are about even in almost every ranking system. In attempting to apply the comparative in this case, it's hard to use the term better in any statistically significant sense.

Yet, at present, the Tigers are the clear favorite to win the league and the Crimson would be a huge favorite to win a first-round NCAA game. There are two reasons for this and both stem from variance.

First, Princeton has the lowest variance offense and sixth lowest variance defense in the league. As discussed before, this means that the Tigers will have fewer brilliant games on both sides of the ball, but also fewer absolute stinkers - an important quality for a team seeking to win a 14 game round robin. Harvard's variance falls in the middle of the league pack on both sides of the ball, leaving its offensive and defensive efficiency floors below those of the Tigers.

When you get into a knockout game against a Top 75 opponent, however, the floor no longer matters. Losing by 10 or 30 produces substantially the same result. The Crimson's offensive rating ceiling is 127.9, while the Tigers' is 119.6, meaning that while Harvard is more likely to lose by more than Princeton, it's also more likely to pull off the stunning upset.

The second effect of variance has already happened. In its biggest games, Princeton played right at about expectations, taking No. 75 Rutgers to OT and winning at home, while losing close games on the road at No. 91 James Madison and No. 97 UCF and getting destroyed at No. 3 Duke.

Meanwhile, Harvard has been all over the place against quality opponents. The Crimson got shellacked at No. 21 UConn, 81-52, met expectations at No. 22 George Mason, lost close at No. 55 Michigan, killed No. 57 Colorado at home and won by nine at No. 68 Boston College. Harvard has also lucked out in its "bottom of the confidence interval games," slipping past Dartmouth, Monmouth and Bryant in forgettable showings.

Thus, the high variance Crimson have, as expected, posted some odd quality wins - enough to push its profile a seed line or two higher than the Tigers. That's particularly important in the Ivies' case, since at the 12, 13 and 14 seed level, one line can seriously jump a team's odds of winning an NCAA game, all else equal.


The point of this argument is not to promote without reservation a conference tournament over the regular season as the means for selecting the league's automatic bid. Neither system can come remotely close to guaranteeing the selection of the team most apt to pull at tournament upset.

A neutral floor tournament does favor variance more than the mean, but it is still a blunt instrument in terms of identifying the league team with the best chance of pulling the tournament upset, because one of every ten to 20 tries, it produces a team with absolutely no chance of succeeding on the national stage.

Ultimately, if the league truly wanted to give itself the best chance to win a tournament game, it would convene after the regular season ended and go through a selection process, much like the NCAA's, in which it considers potential seed and variance of the top Ivy League team and selects the one with the best possible chance of success. (Also, it could easily game the system by selecting the second-best choice in a year when the league's best team would clearly be an at-large.)

Since both players and fans prefer to see their titles and distinctions settled on the court and not in a conference room, obviously we're left with the choice of the automatic bid going to the regular season or conference tournament winner.

Given that neither explicitly attempts to find the team with the highest ceiling, but rather the one with the most consistency, neither system can boast the universal ability to choose which team gives the league the best chance to win an NCAA tournament game.

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