Not that free throw shooting is necessarily more fundamental than the others, but it is certainly the most noticeable. No one has ever said after a game-winning shot, “Man, the defender didn’t move his feet well enough there.”

Free throw shooting at the end of the game in particular is one of the most stressful moments in all of sports. Very rarely are all eyes on one player with the outcome of the game hanging in the balance and the rest of the team unable to do anything but watch. It is for that reason that free throws are so crucial. Memphis learned that lesson the hard way.

With the Tigers up four and under a minute and a half to play, Memphis proceeded to miss four out of five free throws at the end of regulation, leaving the door open for Mario Chalmers’ heroics. Was it a choke job? Probably. But, to be fair to Memphis, let’s look at this from a mathematical stand point.

The Law of Large Numbers says that, in the long run, things will act they way you expect them to. For example, if you fill a coin a million times, it will come up heads pretty close to 50% of the time. The general rule of thumb is that if you need 30 trials to use this theorem. On Monday night, we only needed 19.

Entering the NCAA Title game, Memphis had shot 61.4% from the free throw line as a team. In the final game, they shot about 63.2% – right at their average.

Before missing those four free throws down the stretch, they had been 9-12, 75%. But, when given enough attempts, the Law of Large Numbers says Memphis would end up shooting closer to 60%. And they did.

You could say Memphis choked, and you would probably be right. But I wouldn’t say that. I would say that the Tigers were always poor free throw shooters, but it just manifested itself at the worst possible time.

Looking back over the 23 previous tournaments, a #1 has won its regional championship game 41.3% of the time. When you think about it, that seems reasonable, as you would think by the time a team reaches the Elite Eight, they will have to play a pretty evenly matched opponent. So, given that probability, in order to calculate how likely it is that all four of the #1 seeds advance, you have to raise this number to the fourth power. When you do that, you get about a 2.9% chance that the Final Four is comprised of all #1 seeds, which translates to once every 34 years. This is the 24th year, so it is not too surprising it took as long as it did.

Perhaps a bit more interesting is if you look at the probability that no #1 seed advances to the Final Four. Here, we get that the probability a top seed does not advance to the Final Four is 58.7% (100% – 41.3%, see?). When raised to the fourth power, we get that the chances that no #1 seed is a Regional Champion is 11.9%, which means that about twice every 17 years, we should be without a #1 seed in the Final Four. However, this has only happened once in the 24 year history since the expansion, when #11 seed George Mason joined fourth seeded LSU, #3 seed Florida, and #2 seed UCLA.

What does this all mean? Perhaps our sample size is too small, but I have a feeling this is not the case – if anything it is getting tougher for #1 seeds to advance as the parity in college basketball grows. Instead, I think it is more of a sign that there is not much difference between a #1 seed and a #2 seed. Despite the fact that a #2 seed’s chances of reaching the Final Four is 21.7%, they match up very evenly with the top seeds. Coming into this year’s tournament, when the #1 seed has played the #2 seed with a place in the Final Four on the line, the record for the top seed is 16-16, exactly 50%.

Most years, there are somewhere between five to eight teams who go into Selection Sunday feeling they have a legitimate claim to a top seed. So it is not surprising that when they face off with each other, the rank becomes irrelevant. This year, however, was different. The top four teams were a class apart for most of the season, each team winning both their respective regular season title and conference tournaments, and have only nine losses combined. And considering the struggles that the second-seeded teams had, it made the road to San Antonio a little easier. Will it happen again that all four top seeds make it to the Final Four? Probably, but we might have to wait 34 more years.

The problem with most of these different criteria is that they are each flawed in some sense. Take, for example, the conference RPI. The ACC has the best overall conference RPI, but that is mostly due to the top two teams. Also, the difference between the top conference and the forth conference in terms of conference RPI is less than .01, hardly a distinguishing number.

It seems as if there is no good way to stay definitively that one conference is better than another other than just watching the teams play, which is too subjective to be used. For this reason, I am not going to partake in this particular debate today. What I will try to do is find the toughest conference.

What do I mean by toughest? Not the most physical or the one with the best defenders, I essentially mean the conference with the most teams you do not want to face in March. Now, granted, the Big East has the most teams, so they have an edge. Based on the way I took the numbers, though, I have tried to eliminate that advantage. Since I am not trying to find the best conference, I will only be looking at the top nine teams, but in some cases fewer. I chose nine since it would encompass all the bubble teams from the various conferences.

First, let’s compare the RPIs of the nine teams from each of the power conferences:

However, when you look at it that way, the top teams are being weighed down by the bottom ones. So, now, we will look at how the top four in each conference compare:

And how the 5-9 teams compare:

Finally, we want to look at just the top half of each conference, in an effort to account for the size difference of the conferences. In the case of an odd number, I rounded up.

The results are fairly conclusive. The Big East has the most competitive teams. Especially when you look at the teams in the middle of the conference, it becomes clear how deep the Big East is. People will say that it doesn’t mean the Big East is the best conference, but that is not my argument. My point is that when it comes to being battle-tested, the Big East teams will have an advantage over other conferences. And at a time when every game could be your last, you need every edge you can get.

In mathematics, sample size plays a large role in determining if a conclusion is reasonable. In order for a result to be statistically significant, the sample size needs to be large enough. For example, if I ask only one person to name his favorite basketball team, and then I attempt to generalize, I will try to claim that everyone’s favorite team is Georgetown. But, this is foolish. It is just as foolish to look at just one play and then make a claim about who should have won, or who was cheated.

If we look at the whole game, we will see that there were plenty of calls that went against Georgetown. Austin Freeman was called for a loose ball foul when he was in good position and got an offensive rebound. Patrick Ewing gained control of a loose ball and stood up and was whistled for a loose ball foul. There were plenty of calls that were wrong, and they hurt both teams. It is not only the last call of the game that decides the outcome of the game.

Were the referees bad? Absolutely. Was it goaltending? Perhaps. Did West Virginia get cheated? Definitely not. One play is not enough to make such a generalization. In order to come to a reasonable conclusion, one needs to look at the whole 40 minutes, not just the last 6.2 seconds. I know it’s easier to let one play define an outcome. But, if you want to get a true understanding of a game, you need to look at the Big Picture.

The assist-to-turnover ratio is one of the best methods we have for measuring the effectiveness of a point guard. In college, anything above 2:1 is considered good. I remember in the mid-90′s, the Heat’s Tim Hardaway would get a hefty bonus if he finished the season with a 3:1 ratio. During Steve Nash’s first MVP season, his assist-to-turnover ratio was 3.5:1. In Saturday’s game against Fairfield, Jeremiah Rivers assist-to-turnover ratio was infinity.

“What? Infinity? That’s impossible! What does that even mean?” Allow me to explain. Since a ratio is of the form x/y, sometimes y is zero. “Hey! In school, my teacher always told me never to divide by zero. It’s undefined.” Well, not exactly. When we have a positive number divided by zero, we sometimes call that infinity. Occasionally in baseball, you will see an ERA of infinity (ERA is another ratio – earned runs per 27 outs). The problem is, a pitcher who gives up one run and gets no outs has the same infinite ERA as a pitcher who gives up 20 runs and doesn’t get any one out. You run into the same problem with the assist-to-turnover ratio. So, we should look closer at River’s performance.

Rivers’ ratio was 5:0. Five assists is good for the Hoyas’ offensive system, and especially so for a backup point guard. Factor in the zero turnovers in 27 minutes, and that is a phenomenal performance, much more impressive than a one assist, zero turnover night in 5 minutes of garbage time. Further, Rivers has nine assists and only one turnover for the season. While it is unlikely that this trend will continue, if Rivers can even keep doing a third as well, he will provide immense support for this team. If Rivers can replace Wallace or Sapp without a noticeable drop-off in quality, and, with his defense already recognized as superior, Rivers will be a key bench performer for this team.

If he can keep it up, Georgetown’s win-to-loss ratio will stay at infinity for a while.

In Georgetown’s 69-59 win over the Hartford Hawks, Jeff Green led all scorers with 17. But, Tyler Crawford had eight, Marc Egerson seven, and freshman DaJuan Summers was held scoreless. So, perhaps this gives us an idea that the season opener is not necessarily the best indicator of a team’s scoring options. As the season progresses, the new players will get more accustomed to the system and to the other Hoyas, and as the team forms its identity and each player becomes comfortable with his role, the scoring will take care of itself. That being said, the Hoyas have a tough home game coming up against Michigan and would like to find another player to add some points.

Jeff Green contributed a little over 20% of Georgetown’s offense last year, which is not too large of a number, a testament to the offense Coach Thompson runs. However, the Hoyas still need to make that 20% up. Obviously Hibbert will take over some of that load, as will Wallace, Sapp, and Summers, but the Hoyas will need an extra weapon. Despite his starting roll, I don’t think Patrick Ewing Jr. is the answer. His role is to provide energy on the defensive end and to make hustle plays. While he does have the ability to score, (he has a career high of 15 against Notre Dame in last year’s Big East Tournament), I think the Hoyas are better off using Ewing Jr. as a rebounder rather than a scorer. Jeremiah Rivers is much better at defending than at putting up points, so the Hoyas won’t be looking to him for the missing offense. Vernon Macklin might help to some degree, taking some of the pressure off of Hibbert, but we’ll have to see if he becomes more aggressive after attempting only one field goal on Saturday. For me, though, the player I would like to see get a few more shots is Austin Freeman. He had some good looks in the opener that didn’t fall, but he certainly has the potential to score some points and relieve some of the pressure on Sapp and Wallace outside. Also, with his size, he creates match-up problems for the opponents, which will help his teammates get open looks or create space inside for penetration.

The season is young, so the Hoyas still have time to find the extra scorer, whoever it will be. But, when over 95% of your scoring is coming from four players, it puts a lot of pressure on those guys to perform every night. If one of those should get into foul trouble in an upcoming game, or have an off shooting night, one of the other players will be forced to step up. When that happens, maybe people will stop writing articles about missing Jeff Green.

For our purposes, I will only consider the top five teams in the preseason AP Polls, but the ESPN/Coaches Polls have only differed by at most one team in any given year. Let’s begin by looking at the first games of the year. Over the past six seasons, at least one of the teams in the top five has lost a game in its first week of play. Four of those times, the top five team was defeated in its season opener, and in the 2001-02 season, two of the five lost their first game (Maryland and Kentucky). But, Georgetown fans know that early season bumps in the road don’t always translate to a poor season, so let’s look at how the preseason top five faired in March.

Again, looking at the past six years, two times one of the preseason top five failed to even make the NCAA Tournament. In two other years, one of the teams failed to win a tournament game. Not very good stats for a preseason frontrunner. But, the news isn’t all bleak. In four of the six years, the AP Poll had the future NCAA Tournament Champion ranked in top five, and in a fifth year they ranked a finalist. It appears that there is hope for Georgetown after all.

While we know the past does not predict the future, we can use it as a guide, or rather an omen. This particular omen says something along the lines of “Beware of a Preseason Top 5 Ranking!” And like any good warning, it can have two meanings. The first is that a top five ranking does not translate into a successful season. But, the second interpretation is that a high ranking can indicate a great deal of Championship potential. So, as we move towards the start of another season, we must remember one thing. Preseason polls mean nothing. While it’s nice to be recognized as an early favorite, teams still have to go out and win games. Let’s hope the “Beware!” is a warning to Georgetown’s opponents and not to its players.

Here’s an example: Georgetown was in the midst of a slugfest with the Univeristy of Virginia at University Hall in the 2000 NIT. With the end of the third overtime nearing, the score was deadlocked at 109. Georgetown had the ball with less than a minute left, and someone had to take a shot. Kevin Braswell was having an MVP night, with 39 points shooting 44% from the field on the night. Gharun Hester, on the other hand, was a walk-on to the Georgetown Basketball squad. He had played in 8 games in the 1999-2000 season, and was averaging .375 going into that game. That was not field goal percentage. That was points per game. So, based on the numbers, you might think that letting Hester, instead of Braswell, attempt a three pointer with the game on the line might not be the best way to win the game. But, you would be wrong. Hester made the jumper to put Georgetown up 112-109, and the Hoyas went on to defeat the Cavaliers in one of the most exciting games in recent history.

My point is this: Sometimes, statistics don’t matter. I am not saying statistics never matter. For the most part, the numbers give us insight into a matchup. They help us see what we need to improve on, which of our opponents we need to watch out for, or how to play to our strengths. And some of the Hoya Hoops Team, including myself, will be referencing these numbers as if they are the be-all-end-all. And, while they might be good indicators most of the time, we have to try not to get carried away by them. Think of it like this: It’s highly unlikely, almost impossible, to flip a coin and have it land on heads one thousand times in a row. But, if you have already flipped the coin 999 times, and it has come up heads every time, what are the chances of it coming up heads again? 50%. So, while in general, statistics help us understand the game, in a specific game at a specific time in a specific scenario, you can toss the numbers (and your coin) out the window. Just ask Gharun Hester.