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How Often Does the Nation’s Best Team Win the National Championship?

Posted by Neil Paine on March 30, 2010

In a variation on a running theme (one that’s especially pertinent given the early departures of Syracuse, Kansas, & Kentucky from this year’s tourney), I wanted to know how often the “best” (i.e., most talented, most dominant over the entire season, etc.) team wins the NCAA Tournament. We know that the NFL’s best team wins the Super Bowl about 24% of the time, that the best team in baseball wins the World Series about 29% of the team (or at least, they did back in the 1980s when Bill James studied the issue), and that the NBA’s best team wins the Finals almost half of the time… So what’s your guess for college basketball?

On the one hand, the NCAA tourney seems to have more in common with football, since it’s a string of single-elimination games (made even more random by the games being played at neutral sites); however, on the other hand it’s still basketball, and the structure of the game itself is set up such that the better team wins more often than in other sports (in no small part due to the massive number of possessions per game — unlike football — as well as the ability to have your best player carry a disproportionate share of the team’s offensive chances — unlike baseball).

But rather than just make a guess, I once again set up a Monte Carlo simulator and ran a series of “test seasons”. To do this, I used the 2009-10 D-I basketball schedule, excluding postseason & conference tournament games, as well as games involving non-D-I schools. For each school, I assigned them a random “strength rating” from a normal distribution based on the average SRS scores of their conference members since 1980:

Conf avgSRS stdvSRS
A10 2.96 7.01
ACC 12.18 7.08
AMEA -8.87 5.70
ASUN -7.79 7.02
BG10 11.54 7.09
BG12 9.23 7.37
BIGE 10.06 6.52
BSKY -4.49 6.63
BIGS -11.15 5.62
BIGW -1.93 6.35
CAA -3.43 6.81
CUSA 3.01 7.43
GWC -9.58 7.28
HRZN -2.21 6.44
IND -19.09 9.72
IVY -7.93 6.62
MAAC -5.15 6.03
MAC -0.93 6.24
MEAC -14.77 6.41
MVC 2.53 5.90
MOUW 5.08 6.93
NEAS -10.69 5.65
OVC -6.94 5.91
PC10 9.22 6.87
PATR -8.36 6.52
SUNB -2.83 6.86
SOUC -6.14 6.26
SEC 10.76 5.91
STHL -8.13 6.34
SUML -5.73 5.57
SWAC -13.93 7.51
WAC 1.48 6.01
WCC 0.26 6.70

So for instance, you might end up with an ACC that looks like this:

Team Conf Strength
North Carolina St ACC 21.61
Virginia Tech ACC 21.36
Wake Forest ACC 19.58
Duke ACC 16.01
Maryland ACC 12.81
Boston College ACC 11.65
Florida St ACC 7.82
Miami FL ACC 7.80
Georgia Tech ACC 4.18
Virginia ACC 3.39
North Carolina ACC 3.21
Clemson ACC -1.13

…And a Patriot League that looks like this:

Team Conf Strength
Holy Cross MA Pat 0.07
Colgate Pat -5.19
Lehigh Pat -5.54
Bucknell Pat -6.11
Navy Pat -7.10
Army Pat -7.14
Lafayette Pat -9.75
American U Pat -12.34

Do this for every team in the country, and estimate the chances of one team beating another at home using this equation:

p(homeWin) = 1 / (1 + EXP(-0.7390072 – 0.179593 * SRSdiff))

(Note: For neutral games, I averaged p(homeWin) and p(roadWin) in a given matchup.)

From this, you can generate standings for the 2010 regular season, like these:

Team Conf W L W% confW confL confW%
California P10 28 2 0.933 16 2 0.889
Washington St P10 23 6 0.793 12 6 0.667
Washington P10 23 7 0.767 12 6 0.667
Oregon St P10 20 10 0.667 11 7 0.611
Oregon P10 20 10 0.667 9 9 0.500
Stanford P10 17 13 0.567 8 10 0.444
UCLA P10 17 13 0.567 8 10 0.444
Arizona St P10 15 16 0.484 7 11 0.389
Arizona P10 8 22 0.267 5 13 0.278
Southern Cal P10 6 24 0.200 2 16 0.111

You can also use these simulated W-L results to calculate RPI, the Ratings Percentage Index that the selection committee uses to inform their picks. The formula is 25% team winning pct., 50% opponents’ winning pct., and 25% opponents’ opponents’ winning pct:

Team Conf W% Opp% Opp^2% RPI
Arkansas SEC 0.968 0.542 0.538 0.648
Kentucky SEC 0.871 0.554 0.544 0.631
LSU SEC 0.767 0.568 0.546 0.612
Mississippi SEC 0.800 0.528 0.548 0.601
South Carolina SEC 0.700 0.550 0.543 0.586
Vanderbilt SEC 0.690 0.547 0.544 0.582
Florida SEC 0.548 0.567 0.539 0.555
Georgia SEC 0.517 0.575 0.545 0.553
Alabama SEC 0.467 0.593 0.535 0.547
Tennessee SEC 0.467 0.589 0.539 0.546
Mississippi St SEC 0.419 0.559 0.530 0.517
Auburn SEC 0.367 0.580 0.525 0.513

Now we have all the components in place to put together the field for a simulated NCAA Tournament. The selections go like this: the 32 conference regular-season champions get automatic bids (ties are broken by RPI); the remaining 32 at-large slots are filled by the 32 best non-conference champs by RPI. Overall seedings are then made, ranking all tourney selections by RPI, and the regions are seeded according to an S-curve.

As you can see, I tracked the global “talent ranking” of the eventual champion for each simulated season; in this case, it was Kentucky, who ranked 9th in team talent (in case you’re wondering, NC State was #1, but they were toppled by Arkansas in the Round of 32). Repeat this process 1,000 times, and how often does a team of each talent ranking win it all?

Ranking Championships
1 336
2 165
3 103
4 79
5 62
6 35
7 37
8 27
9 34
10 18
11 15
12 16
13 13
14 9
15 6
16 9
17 6
18 2
19 2
20 4
21 1
22 2
23 5
24 2
25 1
26 1
27 0
28 4
29 0
30 1
31 2
32 0
33 1
34 0
35 1
36 0
37 0
38 1

The nation’s most talented team wins the National Championship approximately one-third of the time in this simulation, which is slightly higher than we observed for football and baseball, but much lower than the results of a similar simulation of NBA results. Going back to our original hypotheses, it was clear that a single-elimination tournament of 6 rounds creates many opportunities for favored teams to slip up along the way to a title, in much the same way that the NFL playoffs’ one-and-done format encourages parity. At the same time, though, the better team wins a basketball game more often than it wins a football or baseball game simply because the random variance of luck is reduced with higher-scoring games and more possessions.

In the end, we saw basically what we should have predicted before the experiment — by mixing high-variance elements of other playoffs, including a single-elimination format, the NCAA Tournament will never see the best team prevail as often as we see in the NBA Playoffs, but the nature of basketball offsets these elements to a certain degree, resulting in a winning percentage for the best team that falls between those of the NBA and the NFL/MLB.

And a less abstract take-home message? Well, when the 2010 NCAA champs are crowned on Monday night, they’ll be the most deserving team, having outlasted 64 others over the past few weeks… But will they be the nation’s best college basketball team? The odds have spoken — and they say probably not.

14 Responses to “How Often Does the Nation’s Best Team Win the National Championship?”

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  2. Bryan Says:

    How do the results from your simulation compare to the observed frequency of the best regular season team winning the championship? Also, it might be interesting to see whether some measure of the “dominance” of the best team has an effect. Maybe only 30% of your simulations produce a dominant #1 team, and in the rest of the simulations, the #1 team is closer to the rest of pack.

  3. Jesse Says:

    I want to know the answers to Bryan’s questions, as well.

    Also, I note that nearly 75% of the time, one of the best five teams won the simulated championship. I don’t know that the format – the six-round, 64-team tournament – needs any kind of validation, but I think if the eventual champion is in the 98th percentile or higher that often, the format “works”.

    And maybe it’s just me, but I was far more interested in the sample tournament you showed than I probably should have been.

  4. David Hess Says:

    What I thought was fascinating was that the most talented team in your example simulation only received an 8 seed. I’d be interested to see a distribution of the NCAA seed received by the most talented team. I would have never guessed that the best team could be as low as an 8.

  5. Neil Paine Says:

    OK, I can actually run this quickly, at least the first question… Here are the champs from 1980-2009 and their SRS rankings:

    year_id school_id conf_id region seed rk_srs
    2009 UNC ACC South 1 1
    2008 KAN BG12 Midwest 1 1
    2005 UNC ACC Syracuse 1 1
    2001 DUKE ACC East 1 1
    1996 KEN SEC Midwest 1 1
    1994 ARKA SEC Midwest 1 1
    1993 UNC ACC East 1 1
    1981 IND BG10 Mideast 3 1
    2007 FLA SEC Midwest 1 2
    2004 CONN BIGE Phoenix 2 2
    1995 UCLA PC10 West 1 2
    1989 MICH BG10 Southeast 3 2
    1982 UNC ACC East 1 2
    2000 MICS BG10 Midwest 1 3
    1999 CONN BIGE West 1 3
    1992 DUKE ACC East 1 3
    1990 UNLV BIGW West 1 3
    1987 IND BG10 Midwest 1 3
    2006 FLA SEC Minneapolis 3 4
    2002 MARY ACC East 1 4
    1998 KEN SEC South 2 4
    1991 DUKE ACC Midwest 2 4
    1997 ARIZ PC10 Southeast 4 6
    1986 LOU MECA West 2 8
    2003 SYRA BIGE East 3 9
    1980 LOU MECA Midwest 2 11
    1988 KAN BIG8 Midwest 6 19
    1983 GTWN BIGE West 1 22
    1985 VILL BIGE Southeast 8 23
    1984 NCST ACC West 6 32

    So the observed rate is about 27%, a bit lower than in the simulation, but certainly not outside the realm of possibility in a 30-season sample.

    As for the SRS of the top team, I’ll have to run some sims again and see how they compare to the top scores of the real-life teams. I’m pretty sure they’ll both top out around 24-ish on avg.

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  7. Matt Says:

    How did you come up with the equation you used to predict each game?

    p(homeWin) = 1 / (1 + EXP(-0.7390072 – 0.179593 * SRSdiff))

  8. Neil Paine Says:

    Logistic regression.

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