# LRMC Information Page

## What is LRMC?

LRMC is a college basketball ranking system designed to use only basic scoreboard data (which two teams played, whose court they played on, and (in the "pure" version) what the margin of victory was). LRMC was created by Dr. Joel Sokol and Dr. Paul Kvam, and is now maintained, updated, and improved by Dr. Joel Sokol, Dr. George Nemhauser, and Dr. Mark Brown. Drs. Sokol, Kvam, and Nemhauser are all professors in Georgia Tech's H. Milton Stewart School of Industrial and Systems Engineering, and Dr. Brown is a professor in the Department of Mathematics of City College, City University of New York.

## How good is LRMC?

The original research paper on LRMC (Kvam, P. and J.S. Sokol, "A logistic regression/Markov chain model for NCAA basketball", Naval Research Logistics 53, pp. 788-803) gives a mathematical description of the method, and reports statistical testing showing that LRMC is better than other standard methods at predicting NCAA tournament outcomes. A followup paper on Bayesian LRMC by Drs. Sokol and Brown is currently in revision.

A more-recent non-mathematical summary of LRMC and its powerpoint-style equivalent points out three important highlights:

• LRMC is right more often: When LRMC and other NCAA tournament ranking methods disagree, the team LRMC ranks higher wins significantly more often than the other method's team.
• LRMC is particularly effective at sorting out the top teams, as measured by the last three rounds of the NCAA tournament, and it is more successful at identifying "surprise" Final Four teams. (We're not perfect, though--LRMC didn't expect George Mason's run in 2006!)
• LRMC is more effective at picking potential bubble teams; the teams it ranks in the "last-teams-in" bubble range tend to win more games than the teams that other methods rank in that area.

## How is LRMC different from other methods?

In non-mathematical terms, LRMC differs from many other ranking systems most clearly in its treatment of home court advantage and win/loss outcomes.

• When determining the value of home court advantage, LRMC considers how much playing at home helps a team win, rather than how many "points" playing on a home court is worth.
• Our research shows that very close games are often "toss-ups"; the better team barely wins more than half the time. So, winning a close game shouldn't be worth as much as winning easily, and losing a close game shouldn't hurt a team's ranking as much as losing badly. In fact, a close loss to a top-tier team often shows more about a team's quality than a blowout win over a weak team; LRMC's ranking methodology takes this into account.

## What does LRMC have in common with other methods?

LRMC is composed of the same two basic components that most ranking methods use:

• the quality of each team's results, and
• the strength of each team's schedule.

## What rankings are available on this web site?

We currently calculate three different versions of LRMC:

• Pure LRMC is our original predictor of NCAA tournament results, and uses exact margin of victory in its calculations.
• Bayesian LRMC is a modification of our original LRMC method, and seems so far to be a slightly (but statistically-significantly) better predictor of NCAA tournament results. It also uses exact margin of victory in its calculations. Bayesian LRMC has not been tested as thoroughly as Pure LRMC, so at the moment we report the two on the same page rather than giving the Bayesian LRMC its own page.
• LRMC(0) does not use margin of victory data at all in its calculations. It is somewhat less accurate than Pure LRMC, but is still competitive with many other methods, even ones that do use margin of victory.
These charts show how Pure LRMC, LRMC(0), and a variety of Capped LRMC models fare against some competing ranking methods.

## Acknowledgements

In addition to Drs. Sokol, Kvam, Nemhauser, and Brown, Georgia Tech undergraduate students Kristine Johnson, Harold Rivner, Blaine Deluca, Pete Kriengsiri, Dara Thach, Holly Matera, Jared Norton, Katie Whitehead, and Blake Pierce all assisted in various stages of data collection, analysis, and validation.