Category Archives: Basketball
I saw a talk at JSM where I was introduced to a fun new (well, new to me) game to play during the NCAA tournament. First, teams are assigned a price based on their seed. This can be done in many ways, but it was set in the talk that the one seeds cost 25 cents, the two seeds cost 19 cents, all the way down to the 15 and 16 seeds which were a penny each. The goal is to choose a set of teams, that costs, in total, one dollar, that will win the most number of games in the NCAA tournament. So picking all the number one seeds, which will cost exactly one dollar, but the most wins they can earn is 19 (4 each to the final four and then one each for the two semifinals and one for the championship). So, according to the speaker, this usually won’t get you the win. First of all, this game is awesome. Once you can stop thinking about how awesome this game is, the next logical question is: How do you choose the optimal set of teams?
Douglas Noe and his student Geng Chen used an evolutionary algorithm to optimize the selection of teams, and they used Ken Pomeroy’s rankings as a guide to the probability that one team will beat another team in the tournament. Now, I don’t think I ever heard of evolutionary algorithms, and, if I have, I’ve totally forgotten about them. But they are wicked cool. Here is the wikipedia page for evolutionary algorithms, and it’s worth checking out. Does anyone have any suggestions as to a good resource for an introduction to evolutionary algorithms?
Rankings as of 2:18pm on 3/21/2012. Sagarin Ratings for games though 3/21/2012. AP rankings from 3/12/2012.
In case anyone is interested, here are my rankings after the first two rounds of the NCAA tournament. * indicates the team is in the Sweet Sixteen.
Three teams are in the Sweet Sixteen that are not in my rankings: NC State, Ohio, and Xavier.
Previous rankings are here.
Breakdown by conference: 2, 4, 5, 3,
0, 2, 2, 2, 5
ACC Big East Big Ten Big 12
Pac 12 SEC MWC MVC Other
26-35: New Mexico, Temple, Saint Louis, Purdue, San Diego St., Iowa State, UNLV, Notre Dame, Alabama, Virginia
BCS: My offer still stands…….if you want to contact me you can send me a tweet @StatsInTheWild.
My first round entry in the Stat Geek Idol contest was about using decision trees to predict teams that would make it to the Sweet Sixteen. Now that we are down to sixteen teams remaining in the tournament, let’s review how the model performed.
Let’s start out with what I consider to be the most impressive results. In the article, I stated, in the conclusion:
So the moral of the story is don’t get too excited about Florida State (even though they just won the ACC) or Michigan, and if you’re looking to pick an impressive upset, just about any of the fourteen seeds will do.
The second half of this sentence makes me look bad as I singled out the only seed other than 16 not to win a first round game. But I don’t think I was the only one to make this mistake. Plenty of people were really excited about Belmont. Alternatively, in the first half of the sentence I chose Florida State and Michigan as teams to not make it to the Sweet Sixteen based on the model results. Now, by itself, it’s not too impressive to pick a team to NOT make it to the Sweet Sixteen (just pick a 16 seed every year), but these were two teams that, if they only beat lower seeded teams were expected to make it to the Sweet Sixteen. Michigan lost in the Round of 64 and Florida State lost in the Round of 32 (after barely escaping the first round). This means that in the last six years no team with an overall RPI rating between 0.6169 and 0.643 with an opponent’s effective possession ratio greater than or equal to 0.9147 and an average second half scoring margin of less than 2.998 has ever made it to the Sweet Sixteen. These teams are 0 for 11. That’s kind of interesting.
Large RPI teams
In the article I said:
So what about this year teams? There are 6 teams in the tournament this year that fall into group R1. These teams are Kentucky (1), Michigan State (1), North Carolina (1), Syracuse (1), Kansas (2), and Duke (2). These are the high Overall RPI teams that almost always advance to the Sweet Sixteen.
Group R2 only contains one team this year, Ohio State (2). Recall that in the last five years, all nine of the teams from group R2 have advanced to the Sweet Sixteen.
Group R3, which has advanced 51.61% of the time over the past five years includes eight teams this year: Missouri (2), Marquette (3), Baylor (3), Georgetown (3), Louisville (4) [In the original article, I wrote eight teams and then only listed seven], Indiana (4), and Wichita State (5) and Memphis (8).
Group R4 consists of Florida State (3) and Michigan (4). No team from group R4 has advanced to the Sweet Sixteen in the last five years. We’ll see if either the Seminoles or the Wolverines can snap the losing streak for R4.
- Group R1 advanced 5 out of 6 (83.33%) teams this year with only Duke failing to make the Sweet Sixteen. Historically (previous five years), 91.17% of teams in this group advance to the Sweet Sixteen.
- Group R2 contained one team this year, Ohio State, and they did, in fact, advance to the Sweet Sixteen. Ohio State is now the tenth team to fall into this category over the last six years and all ten of these teams have qualified for the Sweet Sixteen.
- Group R3 had eight teams in it this year and historically 51.61% of teams in this group qualify for the Sweet Sixteen. This year 4 out of the 8 (50%) qualified. Marquette, Baylor, Louisville, and Indiana advanced while Missouri, Georgetown, Wichita State, and Memphis have been eliminated.
- Group R4, as previously mentioned, contained two teams this year and both failed to qualify for the Sweet Sixteen. In the last six years, no team from this group has ever made it to the Sweet Sixteen
Small RPI teams
In the article I said:
So what about the small RPI teams this year? The tournament this year features nine teams in the group L2. These teams include St. Mary’s (7), Florida (7), Notre Dame (7), Creighton (8), Purdue (10), California (12), South Dakota State (14), Belmont (14), and Iona (14).
The L3 group contains one team this year: BYU (14). 8 out of 12 teams in this group over the past five years have gone on to the Sweet Sixteen, however, BYU to the Sweet Sixteen this year seems unlikely as they are a 14 seed and have to win a play-in game just to get into the round of 64. I think it’s interesting that all these fourteen seeds fall into these categories with relatively high probabilities of advancing to the Sweet Sixteen.
All of the remaining teams fall into the L1 category, which has advanced a little over 5% of its teams to the Sweet Sixteen. Some of the notable teams that fall into this group include Wisconsin (4), New Mexico (5), Temple (5), Vanderbilt (5), Murray State (5), Cincinnati (6), UNLV (6), and San Diego State (6). Also, in this group are Gonzaga (7), Kansas State (8), Iowa State (8), Alabama (9), Saint Louis (9), UConn (9), and Southern Mississippi (9).
- Group L1 had 39 teams fall into this category (after the First Four had been played). Historically, 5.34% of these teams make it to the Sweet Sixteen. This year 5 out of 39 (12.82%) qualified. This is a little bit higher than usual and is reflected in just how crazy this tournament has been over the first two rounds. The teams that qualified from for the Sweet Sixteen from this group were Wisconsin, Cincinnati, Xavier, NC State, and Ohio.
- Group L2 had nine teams this year and historically 17.86% of these teams qualify for the Sweet Sixteen. Only one of these nine teams (11.11%), Florida, qualified for the Sweet Sixteen. Interestingly, two of these nine teams were knocked out in the First Four.
- Group L3 contained only one team, BYU. 8 of the 12 previous teams in the group qualified for the Sweet Sixteen, but with BYU’s loss, this group falls to 8 for 13 (61.5%)
The first round of this NCAA tournament was the craziest dating back to 1990, and through two round (I don’t acknowledge the First Four as a round) this is the second craziest tournament over the same time period behind only 1996. 1996 featured a 12 seed in the sweet sixteen as well as a 1 seed knocked out in the round of 32. 2012 might be crazy, but all four number 1 seeds are still around.
Note: Projected madness is based on higher seeds winning all remaining games.
An email from a friend of mine:
…they have a new “sliding scale” thing for their polls. One question was: “How many of the double digits seeds that won (on Thurs/Friday) will make the Sweet 16?” On one end of the scale was “none” on the other “5 or more”. Seems straightforward enough. Their sliding scale had 10 total partitions, the middle 8 all unlabeled. This is why people don’t trust “statisticians”…..
Here (Scroll to the end of the article) is a link to an example of one of these “polls”.