You Are Here > Basketball-Reference.com > BBR Blog > NBA and College Basketball Analysis

SITE NEWS: We are moving all of our site and company news into a single blog for Sports-Reference.com. We'll tag all Basketball-Reference content, so you can quickly and easily find the content you want.

Also, our existing Basketball-Reference blog rss feed will be redirected to the new site's feed.

Basketball-Reference.com // Sports Reference

For more from Neil, check out his new work at BasketballProspectus.com.

March Madness, By the Numbers

Posted by Neil Paine on March 16, 2009

It's time for the NCAA Tournament again, and if you're anything like me, that means filling out your brackets, crossing your fingers, and just hoping for the best. I mean, I'd like to think I'm some kind of great prognosticator on the basis of my correctly picking the two title-game participants in 6 of the last 10 years (1999, 2001, 2003, 2005, 2007, 2008), but I always neglect to remind myself that I correctly picked the winner only twice in that span (2001, 2008). In the early days of my braket career, I strictly picked from the gut (this was before I knew about APBRmetrics -- or SABRmetrics, for that matter), and in 2001 my intuition was spot-on... but it has also led me astray more times than I care to recall.  So in recent years, I've gone with a more scientific approach to filling out my bracket, with decent results (I have to say that the amazing kenpom.com has really aided me in that venture).

Now, I have to confess that I've taken to filling out 2 brackets -- one from a no-stats, strictly "from the heart" perspective, and one from a cold, hard statistical viewpoint -- for each of the past 3 Tournaments, but I can imagine that you're probably not interested in my gut-reaction picks. Instead, I'll drop some picks on you using the "scientific" method:

Like most NCAA number-junkies, I start with Ken Pomeroy's famous tempo-free ratings: overall stats, offensive 4 factors, & defensive 4 factors (this year I also had to use his FT% data to calculate FTM/FGA). I then dump the data into Excel and get to work. For each team, Ken lists unadjusted offensive and defensive ratings, eFG%, TO%, Reb%, & FT rate, plus offensive and defensive ratings that have been adjusted for strength of schedule. For my purposes, I want to adjust the 4 factors that make up ORtg & DRtg for SOS as well, so I jack up (or down) a team's component stats based on how much of a bump their rating recieved with the SOS adjustment. I also make sure the national averages are equal for team & opponent factors.

With that out of the way, I use the factors to predict each matchup. Say I've got this matchup:

Team Conf Region Seed aPace eFG% TO% OR% FTr oeFG% oTO% oOR% oFTr
Pittsburgh BE East 1 66.4 55.1 17.2 43.9 22.8 45.7 20.1 28.2 20.5
ETSU ASun East 16 71.0 50.0 19.4 32.0 27.7 49.5 21.6 33.2 23.0

...and I want to predict what the teams' 4 factors will be when they play. At first glance it might seem that all I need to do is average the offensive and defensive factors like this:

eFG%_Pitt = (55.1 + 49.5) / 2

Unfortunately, this doesn't really work because it penalizes good teams and boosts poor ones. Pitt's eFG% is well above average and ETSU's eFG% defense is below-average, so why would we want to drag the Panthers' eFG% down to 52.3, which is below their season average? Instead, we should use the national averages:

eFG%_Pitt = 49.5 * (55.1 / 49.1)

That gives us an expectation of 55.6, which makes much more sense. Do that for every category (plus pace), and you've got expected factors for every team. Then use a regression to predict efficiency from the 4 factors, multiply by the expected pace, and you've got expected scores, like this:

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Pittsburgh BE East 1 71.0 55.6 18.1 44.5 20.7 121.2 86.1
ETSU ASun East 16 71.0 46.6 19.0 27.5 22.5 95.5 67.8

So this system calls for an 86-68 Pittsburgh win over ETSU. I know it's a lot of prep work, but I've found that this method works pretty well over the past few seasons. Here's the rest of the bracket, if picked this way:
Play-in game

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Alabama St. SWAC Midwest 16 64.2 48.6 18.0 28.8 23.6 101.1 64.9
Morehead St. OVC Midwest 16 64.2 45.3 19.3 42.9 29.2 103.5 66.4

Midwest

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Louisville BE Midwest 1 68.1 52.9 16.8 31.7 23.4 111.4 75.8
Morehead St. OVC Midwest 16 68.1 41.4 27.6 34.5 24.5 80.2 54.6
Ohio St. B10 Midwest 8 68.6 57.1 21.7 32.4 19.4 111.4 76.5
Siena MAAC Midwest 9 68.6 50.0 18.3 34.1 16.2 104.7 71.9
Utah MWC Midwest 5 64.5 53.9 18.7 27.7 21.6 107.8 69.5
Arizona P10 Midwest 12 64.5 48.9 15.1 28.1 26.5 105.4 68.0
Wake Forest ACC Midwest 4 71.4 50.3 24.0 38.3 31.9 103.2 73.7
Cleveland St. Horz Midwest 13 71.4 43.8 19.9 31.1 23.3 92.2 65.9
West Virginia BE Midwest 6 64.3 47.9 18.6 39.1 25.7 105.7 68.0
Dayton A10 Midwest 11 64.3 43.9 24.9 34.8 25.0 88.2 56.7
Kansas B12 Midwest 3 70.8 55.3 18.9 33.0 24.7 113.6 80.4
NDSU Sum Midwest 14 70.8 47.0 17.2 27.7 26.2 99.3 70.3
Boston College ACC Midwest 7 64.7 46.4 19.4 37.0 23.1 100.6 65.1
USC P10 Midwest 10 64.7 49.5 18.9 41.7 26.8 109.8 71.0
Michigan St. B10 Midwest 2 68.0 51.7 22.8 41.1 32.2 109.0 74.1
Robert Morris NEC Midwest 15 68.0 47.4 24.5 25.0 23.1 88.1 59.9
Louisville BE Midwest 1 65.3 51.2 19.2 35.3 14.3 105.8 69.1
Ohio St. B10 Midwest 8 65.3 49.8 23.8 28.0 23.1 94.8 61.9
Utah MWC Midwest 5 72.3 49.8 21.2 25.9 27.6 97.8 70.7
Wake Forest ACC Midwest 4 72.3 47.3 16.5 27.6 29.6 101.3 73.2
West Virginia BE Midwest 6 67.2 45.2 17.1 36.4 24.7 101.5 68.2
Kansas B12 Midwest 3 67.2 50.0 25.3 35.0 29.7 98.6 66.2
USC P10 Midwest 10 65.9 48.8 21.6 30.5 26.6 98.2 64.7
Michigan St. B10 Midwest 2 65.9 46.6 20.8 37.2 24.4 99.4 65.5
Louisville BE Midwest 1 75.6 48.5 19.8 32.3 19.0 99.6 75.3
Wake Forest ACC Midwest 4 75.6 46.6 24.3 33.4 26.1 92.9 70.2
West Virginia BE Midwest 6 66.4 46.9 18.4 33.2 23.6 100.4 66.6
Michigan St. B10 Midwest 2 66.4 47.0 24.5 38.5 29.1 96.9 64.3
Louisville BE Midwest 1 67.1 48.9 22.9 32.6 21.5 97.0 65.1
West Virginia BE Midwest 6 67.1 44.4 20.9 38.2 21.2 95.6 64.1

West

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Connecticut BE West 1 71.4 55.5 16.6 40.0 26.2 121.4 86.6
Chattanooga SC West 16 71.4 42.5 18.7 29.9 15.9 89.4 63.8
BYU MWC West 8 68.6 53.2 15.4 26.5 20.8 110.0 75.5
Texas A&M B12 West 9 68.6 47.6 18.7 29.6 32.6 100.6 69.0
Purdue B10 West 5 62.4 51.0 14.5 25.8 20.7 107.2 66.8
Northern Iowa MVC West 12 62.4 46.5 20.7 28.1 26.9 94.4 58.9
Washington P10 West 4 76.3 46.0 18.5 43.6 25.8 105.6 80.6
Mississippi St. SEC West 13 76.3 47.1 20.1 28.5 25.5 96.0 73.3
Marquette BE West 6 63.4 52.0 13.4 31.6 27.8 115.1 73.0
Utah St. WAC West 11 63.4 54.0 20.3 33.3 22.8 109.4 69.3
Missouri B12 West 3 71.6 52.5 16.0 34.2 24.2 113.5 81.3
Cornell Ivy West 14 71.6 48.6 26.0 32.0 24.7 92.8 66.5
California P10 West 7 68.1 51.7 19.8 35.2 21.2 107.3 73.1
Maryland ACC West 10 68.1 47.1 16.2 32.8 19.4 102.5 69.8
Memphis CUSA West 2 73.0 48.5 21.3 36.7 31.8 103.1 75.3
CS Northridge BW West 15 73.0 42.0 27.6 31.8 21.1 79.1 57.7
Connecticut BE West 1 71.1 47.7 18.1 31.8 30.0 102.6 72.9
BYU MWC West 8 71.1 46.9 14.3 26.6 13.9 99.9 71.0
Purdue B10 West 5 74.8 47.8 17.9 27.7 20.9 98.7 73.8
Washington P10 West 4 74.8 45.2 22.1 39.9 26.9 97.5 72.9
Marquette BE West 6 73.8 49.2 21.2 35.7 34.3 104.1 76.8
Missouri B12 West 3 73.8 53.1 18.5 32.6 20.3 109.3 80.6
California P10 West 7 67.3 45.9 19.8 29.6 24.3 94.9 63.9
Memphis CUSA West 2 67.3 48.3 16.8 34.9 24.4 106.0 71.3
Connecticut BE West 1 67.9 46.3 20.4 38.2 25.8 100.4 68.2
Purdue B10 West 5 67.9 44.5 14.6 28.0 12.9 96.3 65.4
Missouri B12 West 3 71.3 44.4 19.1 31.6 22.6 94.2 67.2
Memphis CUSA West 2 71.3 46.6 23.3 38.2 29.0 97.8 69.7
Connecticut BE West 1 67.5 43.0 20.5 36.0 28.0 93.8 63.3
Memphis CUSA West 2 67.5 42.7 15.4 34.2 14.9 96.3 65.0

East

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Pittsburgh BE East 1 71.0 55.6 18.1 44.5 20.7 121.2 86.1
ETSU ASun East 16 71.0 46.6 19.0 27.5 22.5 95.5 67.8
Oklahoma St. B12 East 8 73.2 53.1 17.8 26.0 29.6 108.1 79.1
Tennessee SEC East 9 73.2 51.2 18.8 34.2 27.6 108.3 79.2
Florida St. ACC East 5 60.4 49.5 21.1 29.5 26.0 99.4 60.1
Wisconsin B10 East 12 60.4 46.2 18.5 34.5 24.8 100.2 60.6
Xavier A10 East 4 66.5 55.8 22.0 39.2 29.8 115.1 76.5
Portland St. BSky East 13 66.5 46.9 19.0 28.8 17.9 95.9 63.8
UCLA P10 East 6 67.3 52.1 18.3 38.5 23.2 112.2 75.5
VCU CAA East 11 67.3 50.2 23.5 28.9 23.3 96.4 64.9
Villanova BE East 3 63.1 50.8 17.4 34.6 32.6 110.7 69.9
American Pat East 14 63.1 49.4 23.6 28.8 21.0 94.6 59.7
Texas B12 East 7 65.1 45.8 21.1 38.5 25.1 98.6 64.2
Minnesota B10 East 10 65.1 46.4 21.6 35.3 24.1 96.7 63.0
Duke ACC East 2 69.5 51.6 17.3 42.9 35.7 117.9 82.0
Binghamton AE East 15 69.5 45.0 23.5 30.2 22.8 88.7 61.6
Pittsburgh BE East 1 69.0 53.7 18.4 39.0 21.9 114.7 79.1
Tennessee SEC East 9 69.0 49.3 17.4 33.6 21.2 105.4 72.7
Wisconsin B10 East 12 60.3 47.4 15.0 29.2 23.9 103.3 62.3
Xavier A10 East 4 60.3 51.8 20.7 30.7 28.6 104.7 63.2
UCLA P10 East 6 68.7 52.8 19.6 34.4 22.6 109.0 74.9
Villanova BE East 3 68.7 51.2 22.9 33.3 29.7 102.7 70.6
Texas B12 East 7 67.2 46.7 21.3 38.4 21.9 99.0 66.5
Duke ACC East 2 67.2 48.5 17.3 38.0 29.4 108.6 72.9
Pittsburgh BE East 1 66.9 49.7 16.3 37.4 20.3 109.7 73.4
Xavier A10 East 4 66.9 50.2 20.7 33.2 26.6 103.4 69.2
UCLA P10 East 6 67.7 52.8 20.9 36.6 18.7 107.8 73.0
Duke ACC East 2 67.7 51.7 20.9 35.7 28.4 107.4 72.7
Pittsburgh BE East 1 66.6 53.6 21.4 39.4 20.7 110.6 73.6
UCLA P10 East 6 66.6 52.6 17.1 32.8 18.6 110.1 73.3

South

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
North Carolina ACC South 1 78.0 53.2 13.4 37.8 26.7 120.6 94.1
Radford BSth South 16 78.0 46.4 23.6 32.6 19.7 91.7 71.5
LSU SEC South 8 63.9 46.2 17.4 33.9 24.4 101.2 64.7
Butler Horz South 9 63.9 48.5 18.3 30.4 30.0 102.7 65.6
Illinois B10 South 5 63.1 52.3 17.9 30.8 15.2 106.8 67.4
W. Kentucky SB South 12 63.1 45.1 21.9 34.9 16.9 92.7 58.5
Gonzaga WCC South 4 68.0 52.7 20.4 36.7 31.0 110.9 75.4
Akron MAC South 13 68.0 43.3 22.2 32.7 21.0 88.7 60.3
Arizona St. P10 South 6 58.3 52.3 16.7 28.3 23.0 108.3 63.1
Temple A10 South 11 58.3 47.5 18.8 30.3 16.4 97.8 57.0
Syracuse BE South 3 66.8 51.1 19.9 34.2 29.2 107.0 71.5
S.F. Austin Slnd South 14 66.8 43.8 18.1 27.4 13.6 90.3 60.3
Clemson ACC South 7 66.7 52.8 20.8 38.6 17.8 109.0 72.7
Michigan B10 South 10 66.7 51.0 20.1 32.8 20.2 104.0 69.3
Oklahoma B12 South 2 68.0 53.0 20.2 39.5 37.8 114.7 78.0
Morgan St. MEAC South 15 68.0 42.5 18.3 34.7 17.3 93.0 63.2
North Carolina ACC South 1 70.7 50.4 16.4 38.2 29.2 112.9 79.9
Butler Horz South 9 70.7 49.2 20.4 31.0 21.6 99.8 70.6
Illinois B10 South 5 65.5 46.6 19.8 29.8 13.8 94.0 61.6
Gonzaga WCC South 4 65.5 49.0 17.6 31.0 17.8 102.3 67.0
Arizona St. P10 South 6 63.8 52.5 17.9 32.8 20.2 109.2 69.7
Syracuse BE South 3 63.8 52.1 19.2 33.6 21.9 107.7 68.7
Clemson ACC South 7 71.0 50.2 17.6 37.4 18.2 108.2 76.8
Oklahoma B12 South 2 71.0 53.9 22.9 40.4 28.7 111.3 79.0
North Carolina ACC South 1 76.3 48.5 17.8 39.6 25.2 108.0 82.4
Gonzaga WCC South 4 76.3 52.0 16.9 30.7 17.1 107.9 82.4
Arizona St. P10 South 6 61.7 52.4 16.7 29.7 23.2 109.5 67.6
Oklahoma B12 South 2 61.7 50.8 19.2 33.3 26.0 106.2 65.6
North Carolina ACC South 1 67.1 49.8 16.7 37.2 25.1 110.1 73.8
Arizona St. P10 South 6 67.1 53.7 18.9 29.7 19.8 108.0 72.4

Final Four

Team Conf Region Seed Pace eFG% TO% OR% FTr Rtg Points
Louisville BE Final4 1 68.5 44.4 21.4 31.5 19.7 90.6 62.1
Memphis CUSA Final4 2 68.5 44.0 21.6 34.6 23.1 92.3 63.2
North Carolina ACC Final4 1 74.1 50.8 16.2 36.1 25.6 111.9 82.9
Pittsburgh BE Final4 1 74.1 51.7 17.9 40.7 15.4 111.7 82.8
Memphis CUSA Nat'l Title 2 74.2 47.2 18.6 35.6 19.2 101.2 75.1
North Carolina ACC Nat'l Title 1 74.2 45.2 18.9 37.1 28.3 100.2 74.3

So, according to this system, Memphis avenges their National Title Game collapse last season by returning to the big Monday-night matchup and defeating UNC for the championship. Now, I know you'll say "there aren't that many upsets", especially in earlier rounds, but remember that this is what's most probable to happen, not what's certain to happen. For the most part, though, I could see this happening. Of course, they call it "March Madness" for a reason -- so I guess we'll see in exactly three weeks whether these picks were clairvoyant or clueless.

ShareThis

13 Responses to “March Madness, By the Numbers”

  1. antone Says:

    How did last years look compared to what actually happened? I used kenpom stats to and predicted 7 of 8 Elite 8, 3 of 4 Final 4, and had Kansas over Memphis. I'm going to use the stats again this year, but I don't like Louisville and have a hard time not picking UConn over Memphis, so I'm starting to doubt myself.

  2. mrparker Says:

    The thing about the Pomeroy Ratings is that they work great when there are alot of dominant teams like 07 and 08. However, in years like 06 when there are alot of teams that aren't as good as their records/seedings you get chaotic outcomes like George Mason going to the final four.

    I won't be surprised to see alot of dbl digit seeds in the sweet 16, and some lower seeded teams in the final 8 after you get away from the five number 1s(I'm calling Memphis 1e).

  3. antone Says:

    George Mason actually finished that season 23rd in Pomroy ratings though, so they were actually underseeded. I noticed if a team is underseeded according to Pomroy ratings, they usually pull an upset or two and sometimes more. Likewise, if you have a 2 seed who is overseeded based on Pomroy(Oklahoma) then they usually bow out early.

  4. antone Says:

    This season is very similar to 2006 though...even the depth of teams is similar...usually there are 40+ teams with overall pomroy rating of .900 or higher...this year there are only 27 and in 2006 there were only 25. This season is a little stronger at the top, but unless Memphis is legit there is no clear cut team right now. The chances of a team like George Mason making a run to the Final 4 is probably not likely though...I think it's more likely that a team rated in the 'teens or twenties like Syracuse, Arizona State, Villanova, Wake Forest, Clemson, USC, Marquette makes an unexpected run to the Final 4. Also, the committee gave us some nice Final 4 high seed sleepers with West Virginia, UCLA, Arizona State all being 6 seeds but ranking in the Top 15 in Pomroy ratings. Also, Gonzaga as a 4 seed is ranked 5th in the ratings. I would love to see them matchup with UNC.

  5. mrparker Says:

    Yes, George Mason was under seeded but they were not a top 4 team by Pomeroy rankings. I think they are the only non top 10 team to make the final four going back to 04. IMO that those top teams were weak. This year is a little different because the 1 seeds all do something(off or def) very well. That wasn't the case in 06.

    I think the Pomeroy rankings would prove true in a round robin, double elimination type tournament. The ratings are great but they don't explain "streakiness" of teams. I've been going back and looking at how teams played after a win and vs a team coming off of a win and some teams fall down the ratings when I adjust for that.

  6. antone Says:

    Yes, George Mason was under seeded but they were not a top 4 team by Pomeroy rankings. I think they are the only non top 10 team to make the final four going back to 04.
    --------------------
    Yeah, they are the only non Top 10 team since '04....but still not as big of a long shot as some people who don't look at Pomroy ratings might think. They are definitely an outlier though...even LSU was an outlier that season based on their offensive efficiency. LSU was 50 and G Mason was 49, the next highest offensive efficiency since '04 was also in 2006 and it was UCLA at 28. There aren't any mid-majors that are as good this year as George Mason was that year. I do think a lower rated big conference team could make a run to the Final 4 though.

  7. mrparker Says:

    Agree with every thing you just said. We do have Xavier and Utah ranked in the mid 20s but they are a 4 and a 5 seed respectively which means they would have to beat a 1 to make noise and I just don't see that happening. Looking at 6,7,10,and 11 seeds we could hear some noise from Clemson, southern cal, or Texas. I can't decide if Clemson's going to lose in the first road or make a run. Gotta love this week.

  8. antone Says:

    I think Clemson will get things done against Michigan and then knock off Oklahoma. I don't think Texas is that good and they would have to get by some combination of Duke, Villanova/UCLA, and then possibly Pitt. I don't see that happening. Utah and Xavier could both possibly lose in the 1st round and I agree that neither one can probably knock off a 1 seed. I think BYU and Oklahoma State could be dangerous 8 seeds that present matchup problems. I think BYU, UCLA, Arizona State, West Virginia, and Clemson got screwed on their seeds the most.

  9. mrparker Says:

    Yep, IMO that UCLA got screwed worse than anyone. I think they were a final four team if they were on the other side of the bracket. Instead, they'll have to take solace in having the chance to knock off dick U. Something about having a bunch of teams in your conference in the tourney meant screwing around with the seeds to meet the rules. Im pretty sure this is why the seeds seem so funky.

  10. antone Says:

    I still think UCLA can make the Elite 8, but that second round matchup against Villanova in Philly scares me. I'm not as worried about VCU as everyone else is. I think they got screwed just as much having to play UCLA as a 6 seed.

  11. Eddy Says:

    I was like you, Neil.

    Years ago, I just used to fill out my bracket strictly with my gut and intuition. But now for the past couple years, I've sworn to fill out my bracket strictly via a scientific and statistical approach. Obviously kenpom is a great resource to use, but surprisingly ESPN Insider has a number of stat heads that punch out probabilities and trends (using advanced metrics), with regards to the history of the NCAA Tournament since the field expanded to 64 teams in 1985. I have a few spread sheets, which track nothing but "prerequisites" and trends by how a seed (and the type of team that is a certain seed) fair. It's real fascinating actually.

    For example, some people have been touting VCU as possibly upsetting UCLA, but looking closer into the numbers, VCU has, literally, almost no chance of beating UCLA. This statement is made with the data and historical trends I have accumulated the past year or two.

  12. Duff Soviet Union Says:

    Did anyone else notice that UNC vs Gonzaga is projected to be a dead heat?

  13. mrparker Says:

    I noticed it because Im a UNC fan. That game reminds me of the sweet 16 matchup UNC had with Nova in 05' on their way to their last championship.