## How Virginia Tech Got to the ACC Finals

With the ACC Tournament coming up, I thought an interesting way to preview March 3-March 6th in Greensboro, NC would be to try to simulate the outcomes of the tournament.

We have enough information to do this - or at least, I think we do.  We really need two things:

1.  A way to measure the various strengths of each team, and
2.  A way to measure how random chance affects game performance.

There are multiple ways to measure team strengths, and one of my favorite ways is the Sagarin RPI rating.  Not only does the Sagarin RPI assign a single numerical ranking value to teams, but this ranking value can be explicitly translated into a number of points.  However, the number to look for is not in the left-most column of the rankings, but the right-most one.  This is the "Predictor" value which is used to predict the outcomes of games and the explanation indicates that it can be used as a substitution for points.

Here are the various Sagarin values for ACC teams:

 Duke 98.26 Maryland 90.81 North Carolina 90.8 Miami 90.67 Georgia Tech 87.31 Florida State 86.84 Boston College 83.77 NC State 81.53 Virginia 79.34 Wake Forest 75.46 Virginia Tech 69.43 Clemson 67.04

Sagarin predicts that on a neutral court, Duke should beat Maryland by 98.26 - 90.81 = 7.45 points.  All of the ACC matches will be considered to be neutral court matches regardless of Greensboro's proximity to Wake Forest.

But in real life, Duke doesn't always beat Maryland by 7.45 points.  Sometimes, Duke wins by 20, and once this year, Duke lost to Maryland.  The 8.21 points is an average value.  We need some way to model random spread, or to answer some questions about margin of victory.

This is a little tougher.  What is the average margin of victory among teams in Division I women's basketball?  If you think about it, the answer should be zero.  Let's assume two teams play in Divison I, Team A and Team B.  To make it easier, let's assume they play one game.  Team A beats Team B 90-70.  So what is the average margin of victory?

It should be twenty, right?  Well, no, because you have to count each individual team's margin of victory into the mix.  We have to count the +20 margin for Team A and the -20 margin for Team B.

Points scored by all teams (A and B):  160
Points scored against all teams (A and B)
:  160

Average margin of victory among teams:  (160 - 160) / 1 = 0.

It turns out that the NCAA keeps these statistics - unfortunately, they only provide average points for and average points against, so we're taking an average of averages and introducing an error factor.  However, the average margin of victory among teams is close to zero : 0.568.  Undoubtedly this 0.568 factor comes from the average of averages problem and the fact that Division I teams don't always play division I opponents.

As for random spread, we'll model that by generating a random z-score (for those statheads, it's a random probability based location on the normal distribution curve).  We'll assign a standard deviation of 8.806 points, which is the standard deviation of all of the various margins of victory - the claim is that about 67 percent of all teams in Division I women's basketball have an average margin of victory between 8.806 points and -8.806 points.

This allows us to generate some movement away from the mean in both directions.  It gives a chance, figuratively speaking, for Jimmy Olsen to punch Superman in the face and knock him out cold.  Granted, Jimmy Olsen needs to be having the best day of his life and Superman needs to be dead tired from eating stars all day, but now we can have that sucker-punch factor.

All that's left is to master the simulation itself.  The first column is the count of ACC Championships in 10,000 simulations.  The second column is the count of ACC Finals appearances in 10,000 simulations - one expects the values in the second column to always be greater than or equal to the first.

 Duke 5495 7212 Miami 1380 4012 North Carolina 1169 3447 Maryland 1007 1911 Florida State 455 1729 Georgia Tech 341 784 Boston College 99 541 NC State 39 270 Virginia 13 74 Wake Forest 2 18 Clemson 0 1 Virginia Tech 0 1

If our assumptions are correct, we can conclude that 54.95 percent of the time or thereabouts, Duke will walk away with the ACC championships.  There is a 72.12 percent chance that it's worthwhile for a Blue Devils fan to get a hotel room and some tickets for the ACC final.

A big question:  if Maryland is ranked second out of all the teams in the ACC according to the Sagarin poll, how come their finals percentage is actually smaller than that of Miami?  The reason is path dependency.  Frankly, Miami has an easier path to the tournament than Maryland does.  Maryland will probably have to take on both Duke and Georgia Tech, whereas Miami might take on Boston College and Florida State - and almost every team in the ACC would prefer the second set of opponents over the first.  Maryland has a greater chance of being knocked out than Miami does.

Even lowly Virginia Tech has a 1 in 20,000 (0.005 percent) chance of making it to the ACC Finals.  (Hey, we know stranger things have happened.)  As for Clemson, they might just want to wait until next year.  I suspect the odds will be better then.

So how did Virginia Tech end up in the finals?  They beat Georgia Tech by 11 points in the opener on Thursday, then beat Maryland by seven points and then beat in-state rival Virginia by five (which beat Duke in a buzzer-beater in their opening round game).  It was a great story until North Carolina walloped them by 32 points in the final.  And hey, it only took 20,000 tries to get there!