Ever since we remodeled the basement here at GK Central, we have had more room to work on advanced mathematics and take a look at some questions we’ve been meaning to address for a long time.

For example, our statistical model combs through historical data to find the traits common to the teams that pull off or succumb to big NCAA tournament upsets. But we’ve always wanted to find ways beyond citing the same old key metrics to get across how those teams play. And now, with help from our Giant Killer colleagues at Furman University, we have developed a new toy for doing just that: similarity. For any given team, our similarity method shows the five most comparable Giants or Killers from our historical database (which dates back to 2007), measured by what matters to Giants and Killers. Knowing a program’s most similar squads, you can get a better feel for its style -- and how it will fare.

The basic math behind this is pretty straightforward. (But feel free to skip this paragraph if you prefer to hide your vegetables under the mashed potatoes.) Suppose that on a graph, Point A is 3 inches away from Point B horizontally, and 4 inches away vertically. Using the Pythagorean theorem we all learned in high school, we can figure out pretty quickly that the distance from A to B along a straight line is 5 inches. In the same way, we can combine distances on any two metrics and see how “close” two teams are. For instance, Oklahoma plays at a quick tempo and has faced a tough schedule this season. If we look only at those two scales, the most similar teams to Oklahoma in 2016 -- other programs that have played at both a fast pace and against strong opponents -- would be UCLA, Wake Forest and Iowa State. Our similarity method extends this technique to measure the distance between teams while balancing all of the shooting, rebounding, turnover and pace statistics that define Giants and Killers. And then it looks for each team’s closest neighbors.

Now that the basic math lesson is out of the way, here’s what caught our eye once we crunched the numbers. First, to the Giants:

Of the 24 teams projected to be first-round Giants (i.e., No. 6 seeds and better in Joe Lunardi’s latest Bracketology), only three don’t generate a similarity to a previously slain Giant as a precursor. That’s good news for Oklahoma, Kentucky and Purdue. Oklahoma’s list of historical bracket brothers is particularly impressive: It includes the 2007 Ohio State team that reached the national championship game, another runner-up in 2012 Kansas and UCLA's Final Four team from 2007. (The two other squads most similar to this Oklahoma group were also previous Kansas teams. So much for a rivalry.) Meanwhile, Kentucky appears most similar to Georgetown’s 2007 Final Four team, and Purdue evokes echoes of North Carolina in 2012, when the Tar Heels reached the Elite Eight.

At the other end of the similarity spectrum, things look bleak for Wisconsin. The three squads most similar to this season’s Badgers were all slain Giants: Providence, 2015 (lost 66-53 to No. 11-seed Dayton); Wake Forest, 2009 (lost 84-69 to No. 13 seed Cleveland State); SMU, 2015 (lost 60-59 to No. 11-seed UCLA).

All three of those previously slain Giants faced a terrible differential in 3-point frequency: They hardly ever launched from deep and allowed their foes to go wild from beyond the arc. Wisconsin actually defends the arc extremely well this season (29.7 percent of opponents’ shots, 21st-fewest in Division I), but struggle from deep on offense. Our model doesn’t love the Badgers as a Giant anyway (77.4 rating); the similarity data makes them look even more vulnerable.

No team conjures a greater range of results than Indiana. The two teams most similar to the Hoosiers were the 2009 North Carolina Tar Heels and last season’s Duke Blue Devils. Both squads were national champions. But right after those bluebloods you’ll find Villanova in 2010 and Gonzaga in 2013, a No. 2 seed and a No. 1 seed, respectively, that each lost in the second round. The good news for Indiana fans is that the Hoosiers clearly profile as a top seed. The bad news is that if history is our guide, there’s no telling whether they are due for a long ride or a quick exit.

Finally, similarity scores provide another way to appreciate Michigan State. Our model spits out a host of powerful squads when it examines the Spartans. In decreasing order of similarity: Kentucky, 2012 (No. 1

seed, national champion); North Carolina, 2007 (No. 1 seed, lost in the Elite 8 to No. 2 Georgetown); UConn, 2009 (No. 1 seed, reached the Final Four); Kansas, 2011 (No. 1 seed, lost to 11th-seeded VCU in Elite 8); North Carolina, 2008 (No. 1 seed, reached the Final Four).

The Spartans are currently the Vegas favorite to win the national championship. Similarity scores don’t do anything to diminish that forecast.

How about the Killers? Glad you asked:

Usually, our similar teams method agrees with how our statistical model assesses Killers’ chances to pull off upsets. But similarity can go deeper, by suggesting a likely range of results. For example, the five teams most similar to Cincinnati (GK Rating: 50.6): Old Dominion, 2010 (upset sixth-seeded Notre Dame, 51-50); Wichita State, 2015 (upset No. 2 Kansas in the second round, 78-65); Wichita State, 2013 (reached the Final Four as a No. 9 seed, upsetting No. 1 Gonzaga and No. 2 Ohio State along the way); Clemson, 2011 (lost to fifth-seeded West Virginia, 84-76); San Diego State, 2010 (lost to sixth-seeded Tennessee, 62-59).

That’s a close-knit family of strong, slow-paced programs with superior offensive rebounding and excellent interior defense. And it’s a list that suggests Cincinnati will at least keep things close in tournament games, with a good chance to knock off a Giant, even if the Bearcats have to wait until the second round to do so.

Results are, um, similarly tight for Stephen F. Austin (GK Rating 32.4), whose best comparisons all achieved high efficiency through strong offensive rebounding and winning the turnover battle, including two Killers: Villanova in 2008 and VCU in 2007.

In contrast, the five teams most similar to UAB (GK Rating: 6.5) include one that pulled off a famous 14-3 upset of Duke, but also four forgotten squads that each went out in the first round by at least 14 points: Mercer, 2014; Oral Roberts, 2007; Coastal Carolina, 2015; Penn, 2007; Detroit, 2012.

That’s a wide variety of possibilities averaging out to “a puncher’s chance.”

Occasionally, similarity nails a set of comparisons, but offers cause for pessimism. The teams most similar to Chattanooga (GK Rating: 18.3): Albany, 2015 (lost 69-60 to No. 3-seed Oklahoma); Northern Colorado, 2011 (lost 68-50 to No. 2-seed San Diego State); Portland State, 2008 (lost 85-61 to No. 1-seed Kansas); Coastal Carolina, 2015 (lost 86-72 to No. 1-seed Wisconsin); Wofford, 2015 (lost 56-53 to No. 5-seed Arkansas).

Wofford’s strong showing last year offers a glimmer of hope. But basically, this is a collection of sharpshooting Killers that Giants handled rather easily.

In one case, similarity produces results so startling, it’s going to make us double-check our model, to make sure we’re not missing something. Only one projected double-digit seed has three Killers among its five most similar teams. And that’s the team we’ve hammered for the past month, Monmouth (GK Rating: 5.4): Ohio, 2010 (beat No. 3-seed Georgetown, 97-83); Lehigh, 2012 (beat No. 2-seed Duke, 75-70); Memphis, 2011 (lost to No. 5-seed Arizona, 77-75); BYU, 2012 (lost to No. 3-seed Marquette, 88-68); Florida Gulf Coast, 2013 (beat No. 2-seed Georgetown and No. 7-seed San Diego State).

Ohio, Lehigh and FGCU pulled off some of the tourney’s most memorable upsets, all from the 14- or 15-lines. All five of the teams above were run-and-gun squads whose speed got them good shots. They were a lot of fun, too. Those factors don’t help Killers in our model (not even the fun), so it’s possible we may have been underestimating the constellation of talents shared by these up-tempo Killers. Which is why we are excited to bring this method to you now -- and why, despite our gloomy evaluation of Monmouth last month, we’d like to see the Hawks test our latest theory in this year’s tourney.

Thanks to Liz Bouzarth, John Harris and Kevin Hutson of Furman University for research assistance.