It's time to bid farewell to the 2011 edition of our Giant Killers project, where we hope you've had as much fun as we did trying to pick big NCAA upsets over the past month. Before we close up our spreadsheets for good, here's some final accounting and a few lessons.

How did we do overall?

In the games we called "Best Bets," in which our statistical model said underdogs had more than a 30 percent chance of winning, potential Giant Killers went 2-2.

In games we said were "Worth a Long Look" (20 to 29.9 percent odds), Killers went 1-2.

In games we claimed were "Not Completely Crazy" (10 to 19.9 percent odds), Killers went 3-6. This category includes VCU's big wins over Purdue and Kansas.

In games where we told you to "Stay Away" (odds of less than 10 percent), Killers went 0-10, losing by an average margin of 26 points.

We can be happy that the game we called the single best chance for an upset, Richmond versus Vanderbilt, did indeed result in a Giant slaying, and that our statistical model liked VCU (especially against Georgetown and Florida State). But what the overall shape of these numbers says more loudly than anything is that a down year for dominant hoops teams made for a lot of mild-to-moderate surprises in this year's tournament, but just a few opportunities for huge shockers. Compared with the 1- and (especially) 2-seeds, the 3- and 4-seeds were unusually strong this March, and so were the mid-major 8- and 9-seeds. That left Belmont facing Wisconsin, Oakland playing Texas, UNLV squaring off against Illinois and Old Dominion taking on Butler. Ugh. Our model estimates that in the entire tournament, there were just seven games in which a Giant Killer had a more than 16 percent chance of pulling off an upset. Just six Giants fell in the tournament, but given this year's seedings and matchups, our model predicted even fewer, a total of four.

That we got to see as much carnage as we did is thanks, of course, to VCU's amazing run. Every good model adapts to changing circumstances, and the Rams' success has us thinking about three factors we're looking to tinker with when we ramp up for next year.

Momentum: We never want to assume too much from a small sample size, like one or two tournament wins. But by the time VCU crushed Purdue for its third impressive tournament victory in a row, clearly the Rams were playing at the top of their game, or even better than their earlier stats suggested they could. We wrote about this, but our model really couldn't account for it on the fly. So it looks like we need better rolling measures of team performance.

Strength of schedule: To all of you who wrote in to tell us that we shouldn't have liked Belmont because it played in a weak conference, duh. The Bruins' stats were extremely impressive even after adjusting for their opponents, which our statistical model does. (Even now, Ken Pomeroy has Belmont ranked No. 19 in the country.) But given the toughness of the schedule VCU played, maybe it doesn't do it enough, or in the right way. This seems like another balancing act: we want to credit teams for playing in the toughest mid-major or small conferences (which means counting conference or overall SOS) but also for scheduling tough teams (which means counting nonconference SOS). So maybe we need to count both. This year, 19 teams ranked among the top 75 in both overall strength of schedule and nonconference SOS (as measured by opponents' expected winning percentage given their offensive and defensive efficiency): 17 Giants (including Connecticut, Butler and Kentucky), one team that didn't make the NCAA tournament (Cal) and VCU. Hmmmm.

Assists: By themselves, why should assists tell us anything about a team's chance to pull an upset? You can pass the ball all you want but possessions have to end sometime, and it's in how they terminate -- shots, rebounds and turnovers -- that we expect to measure performance. But the numbers indicate assists do have independent significance when it comes to Giant Killing. VCU moves the ball around a lot, and so does Richmond (and so does George Mason, though we couldn't count it as a Killer until its meeting with Ohio State this year). All three squads had assists on 27 percent or more of possessions this year, and historically, about one of every three teams meeting that threshold pulls off big NCAA upsets. In fact, five of the nine potential Killers since 2004 who have posted assists on more than 30 percent of possessions went on to slay Giants. A high level of assists may indicate the ability to both play effectively on the perimeter and penetrate inside. It did for VCU, which had 100 assists in the tournament. Its opponents had just 61.

Finally, here's a statistical bonus for all of you who have made it this far. You'll recall that for a while around here, it's been a core concept that in order to boost their chances of winning, deep underdogs need to increase the variability of their performance. That's why Giant Killers tend to employ high-risk/high-reward strategies like taking a lot of 3s on offense and pressing on defense. We have written about this, among other places, in our methodology for 2011 and in this Mag piece, where you can scroll to the bottom and check out colorful overlapping Bell curves to see graphically how greater unpredictability helps Davids against Goliaths.

So you can imagine our reaction when we were strolling through the MIT/Sloan Sports Analytics Conference last month and came upon a presentation entitled "Scoring Strategies for the Underdog: Using Risk as an Ally in Determining Optimal Sports Strategies" -- complete with colorful overlapping Bell curves! In this research, Brian Skinner of the University of Minnesota's Fine Theoretical Physics Institute not only writes, "An underdog should be willing to sacrifice from its expected final score in order to increase the variance" in its scoring, he goes on to mathematically derive how high-risk/high-reward strategies affect a team's chance of winning. And then he gives concrete examples with respect to basketball strategy.

Let us tell you, we have had the pleasure of meeting Jennifer Love Hewitt in person, and the sensation from seeing this in print was not dissimilar.

We'll spare you all the math, but the short of it is this: If a team, on average, is outscored by an opponent, it will maximize its chances of winning by increasing the variation in the value of its (and opponents') scoring plays. Suppose your favorite team shoots 50 percent on 2-point attempts and 30 percent on 3s, and is playing an opponent that shoots 55 percent on 2-pointers. By hoisting 3s, it will score fewer points overall but can still boost its chances of winning, especially if it trails and time is running out.

This is direct mathematical confirmation of Giant Killers.

Unfortunately, it doesn't translate into a formula our statistical model can use, because teams good enough to make the NCAA tournament don't always play as underdogs over the course of a season. Teams like Belmont, Richmond and VCU don't have to employ giant-killing strategies all the time, because usually they're crushing weaker teams from their conferences. We don't need to find teams with the greatest variation in scoring, we need to find teams with the greatest capacity to vary their scoring when they need to, which is much trickier prey to hunt.

But we're getting better. We'll stay in touch with Skinner to see how his work might apply to ours. And in the meantime, we're sure a few of you will sleep better knowing just how the fundamental laws of statistics explain the theory behind Giant Killers.