This paper uses the difference in seeding ranks to predict the outcome of March Madness games. It updates the Boulier-Stekler method by predicting the outcomes by rounds. We also use the consensus rankings obtained from individuals, systems and poll. We conclude that the consensus rankings were slightly better predictors in the early rounds but had the same limitations as the seedings in the later rounds.Sports forecasts, March Madness, Ranking methods, Expert forecasts, Consensus forecasts

Andrew Klein

H.O. Stekler

English

Research Papers in Economics

Research Program on Forecasting (RPF)  Working Papers represent preliminary work circulated for 
comment and discussion.  Please contact the author(s) before citing this paper in any publications.  The 
views expressed in RPF Working Papers are solely those of the author(s) and do not necessarily represent 
the views of RPF or George Washington University.   
 
 
 
 
Predicting the Outcomes of NCAA Basketball 
Championship Game 
 
 
 
H.O. Stekler and Andrew Klein 
 
Department of Economics 
George Washington University 
Washington DC 20052 
Phone: 202-994-1261 
Fax: 202-994-1947 
 
 
 
 
RPF Working Paper No. 2011-003 
http://www.gwu.edu/~forcpgm/2011-003.pdf 
 
 
 
 
 
July 7, 2011 
 
 
 
 
 
RESEARCH PROGRAM ON FORECASTING 
Center of Economic Research  
Department of Economics 
The George Washington University 
Washington, DC 20052 
http://www.gwu.edu/~forcpgm 
  
Predicting the Outcomes of NCAA Basketball Championship Games 
H.O. Stekler
* 
hstekler@gwu.edu 
 
Andrew Klein 
aeklein88@gmail.com 
 
Department of Economics 
George Washington University 
Washington DC 20052 
Phone: 202-994-1261 
Fax: 202-994-1947 
 
* corresponding author  
 
Predicting the Outcomes of NCAA Basketball Championship Games 
 
Abstract 
 
This paper uses the difference in seeding ranks to predict the outcome of March 
Madness games. It updates the Boulier-Stekler method by predicting the outcomes 
by rounds. We also use the consensus rankings obtained from individuals, systems 
and poll. We conclude that the consensus rankings were slightly better predictors 
in the early rounds but had the same limitations as the seedings in the later rounds. 
 
Key words: Sports forecasts, March Madness, Ranking methods, Expert forecasts, 
Consensus forecasts  Predicting the Outcomes of NCAA Basketball Championship Games 
 
Every year college basketball fans participate in March Madness. They enter office pools 
or bet on the outcome of the 63 games that constitute the National Collegiate Athletic 
Association’s (NCAA) basketball championship tournament.  One web site indicated that 
billions of dollars are bet on the outcomes of games during this tournament. Moreover, Google 
Scholar found over 18,000 references to the term “March Madness Betting”. Not all of these 
references are relevant to economics, but at least some include optimal betting strategies, e.g. 
Metrick, 1995; Kaplan and Garstka, 2001; Clair and Letscher, (2007). So it is no surprise that 
there has been interest in methods for forecasting the outcomes of these games. 
A variety of statistical methods have been used to forecast which team should win each 
game. Although there are many other approaches, one forecasting procedure is to use rankings 
based on the seeds of the teams as determined by the NCAA committee and to always select the 
team that has the better seeding. Boulier and Stekler (1999) showed that between 1985 and 1995 
the higher-ranked men’s basketball team beat lower-ranked opponents 73.5% of the time. There 
are three reasons to explore this approach further. 
First, as we explain below, this method has limitations. Given the nature of the NCAA 
tournament (which will be explained below), this methodology can only be used to predict the 
outcomes of the first four (of six) rounds of the tournament. It can not be used in forecasting 
winners among the Final Four teams. Second, this method may be successful in some rounds of 
the tournament but not in others. Thus we explore the forecasting accuracy of this method by the 
rounds of the tournament. Finally, an entirely new data set that yields a different set of rankings 
is available to make forecasts about the outcomes of these games. These data are obtained from an average of the teams’ rankings of 29-45 (depending upon the year) individuals, systems, and 
polls. Predictions that could be obtained from these data have never previously been analyzed. 
Moreover, this approach can be applied to all six rounds of the tournament.  In addition to being 
available for all six rounds, these consensus rankings may have a valuable forecasting 
characteristic. The macroeconomic forecasting literature has shown that the mean of a set of 
predictions is usually more accurate than any one given estimate. Thus, the difference in the 
consensus rankings may be more accurate than the difference in seeds, which is the ranking 
established by the NCAA committee.
i 
This paper updates the procedures of Boulier and Stekler to the period 2003-2010, 
including an analysis of the results by round, and determines whether the consensus rankings 
contain any information that is not already embodied in the seedings. The next section describes 
the structure of the NCAA tournament and is followed by a data and methodology section. This 
is followed by a discussion of the results and conclusions. 
I. The Structure of the NCAA Tournament 
Since 1985 the NCAA tournament has consisted of 64 teams.
ii These teams are divided 
into four groups (regions) of 16 teams each. Within each region the teams are ranked 1 through 
16, and in the first round the best team (ranked 1) plays the lowest-ranked team. The Number 2 
plays Number 15, etc. Since this is a single elimination tournament, the winner plays in the 
second round; the loser goes home. If the difference in seedings yielded perfect forecasts, in the 
second round Number 1 would play Number 8 etc.
iii It is thus possible to determine whether the 
difference in rankings has predictive value. 
This process continues through two more rounds, yielding four regional winners (the 
Final Four) who then play two more rounds to determine the Nation Champion. The seedings in the regional rounds cannot be used in making predictions for these final two rounds because they 
only refer to the team rankings in each region and do not measure the overall difference in the 
abilities of these teams. Thus the Boulier-Stekler method of using the difference in ranks as a 
forecast of the winner cannot be used in these rounds, but the consensus rankings do provide this 
information. 
II. Literature Review 
A number of different methods for predicting the winner of a game in the NCAA 
tournament have been proposed. These predictors include a variety of information about the 
teams’ performance during the regular season and various ratings systems. (See Carlin, 1996; 
Harville, 2001; Caudill, 2003; Kvam and Sokol, 2006). Currently, a frequently used 
methodology has been to use the difference in seeds either as a predictor by itself or in models 
which predict the probability that the better seeded team will win (Schwertmann et al., 1991; 
Schwertmann et al., 1996; Boulier and Stekler, 1999; Jacobson and King, 2009). 
Boulier and Stekler presented two sets of results. The first was descriptive and provided 
information about the winning percentage by rank and the overall result that higher-ranked teams 
defeated lower-ranked opponents 73.5% of the time. These results were obtained by aggregating 
the results over the first four rounds of the tournament. The statistical method was a probit 
function, in which the outcome of a discrete event, (winning or losing), was related to the 
difference in the seeds of the two teams. This approach was applied in pseudo real time by 
recursively estimating the probits and evaluating the forecasts using the Brier Score.  
 
 
 III. Data and Methodology 
A. Data 
The data cover the NCAA tournaments of 2003-2010
iv. The seedings and the outcomes of 
the games were obtained from the NCAA Web site. The second set of data is the consensus 
(average) rankings of each Division I team obtained from 29-45 individuals, systems, and polls. 
These rankings are gathered by Kenneth Massey and are archived on his web site, 
www.masseyratings.com. The rankings that are used in this analysis were those that were 
available just before each NCAA tournament began. 
B. Methodology 
The methodology used in this analysis is similar to that of Boulier and Stekler. We first 
calculated the percentage of times when the better rated team won. This was done for both the 
seedings and the consensus rankings, yielding the descriptive statistics. A variation of the earlier 
procedure was to calculate these percentages for each round not just for the entire tournament as 
was done by Boulier and Stekler.  
In order to establish the relationship between the difference in seedings (consensus 
rankings) and the probability that the better ranked team wins, we use probit models. These 
probits were calculated for the entire tournament and for each of the rounds.
v A probit model 
relates the probability that a discrete event (winning or losing) is explained by either the 
difference in tournament seedings or the difference in consensus rankings. 
Formally, the probit model is written as: Pr(y=1|x) = Φ(xb), 
 
where Φ is the standard cumulative normal probability distribution; y =1 is a win; the xis are the 
explanatory variables, the difference in seedings and consensus rankings; and  a one unit change 
in x increases the probability of a win by  b units. IV. Results 
There were 504 games in the eight tournaments between 2003 and 2010, with 480 
occurring in the first four rounds.  The seedings and consensus rankings data were both available 
for only the 480 games in these rounds. In all but 21 of these 480 games, both rankings agreed on 
which team was considered better. These differences primarily occurred in the first round and 
involved the teams seeded eighth (seventh) playing the ninth (tenth) seed.  
In the first four rounds, forecasts based on the difference in the consensus rankings were 
slightly more accurate but not significantly different than those based on the difference of the 
seeds, 73.8% versus 72.3% (Table 1). In Rounds 1-3, both measures provide predictions that are 
significantly different from chance but in Round 4, the Regional Championship, neither measure 
was significantly better than chance.  
Only the consensus rankings were available for Rounds 5 and 6, the Final Four and 
Tournament Championship games. Those results are mixed. The results for Round 5, when 12 of 
the favored 16 favored teams won, are significantly different from zero; those for Round 6 are no 
better than chance, i.e. 5 of 8. If the results for those two rounds are combined, the better ranked 
team won 17 of the 24 games which is significantly better than chance. However, if the results 
based on the difference in consensus rankings for Rounds 4-6 are combined, the results, once 
again are not significant.
vi  
One explanation for the difference in the results for Rounds1-3 and those for Rounds 4-6 
is that the teams in the later rounds are more comparable in quality, thus making forecasting 
more difficult. The difference in rankings based on either set of rankings is much smaller in the 
later rounds. (Table 2).
vii  The probits (presented in Table 3) related the outcomes of the game to the differences in 
the two types of rankings. The results are similar to the descriptive findings. Using the difference 
in either ranking, the relationship is significant and has the appropriate sign in each of the first 
three rounds. The relationship does not hold in the later rounds. Moreover, the availability of the 
consensus rankings does not contribute substantially to the information in the seedings and vice 
versa.
viii However, it should be noted that the consensus rankings were slightly more accurate 
and were available for the later rounds. 
V. Conclusion 
Using data for 2003-2010, this paper evaluated the Boulier-Stekler methodology, derived 
from another set of tournaments, for predicting the winners in the NCAA Tournaments. We 
showed that this approach was successful in predicting the overall winners and those of the first 
three rounds. Its record was no better than chance in the fourth Round.  
Because these data were not available for the Final Four and Championship games, we 
also evaluated another set of data that was available for all six rounds. These data consisted of 
the average rankings of analysts, etc. We showed that the consensus rankings were slightly more 
accurate than the seedings in the early games, but had the same limitations as the seedings in the 
later rounds. We also showed that the quality of the teams, as measured by the consensus 
rankings, were more similar in those later games, thus making predictions more difficult. 
  
Table 1: Percentage of Time Better Ranked Team Won; 
By Seed and Consensus Rankings, By Round 
    Seed  Consensus
 
Overall  Number of Games  480  504 
%  72.3  73.6
a 
Round 1  Number of Games  256  256 
%  75.8  77.7 
Round 2  Number of Games  128  128 
%  68.8  71.1 
Round 3  Number of Games  64  64 
%  75.0  75.0 
Round 4  Number of Games  32  32 
%  53.1  50.0 
Round 5  Number of Games  N/A  16 
%  N/A  75.0 
Round 6  Number of Games  N/A    8 
%  N/A  62.5 
 
    a. The winning percentage for the 480 Round 1-4 games was 73.8%.  
Table 2 
Magnitude of Difference in Seedings and 
Consensus Rankings by Round 
  Seedings  Consensus 
Rankings 
Round 1  8  62 
Round 2  5.6  25 
Round 3  4.2  16 
Round 4  2.7  11 
Round 5  N/A  7.6 
Round 6  N/A  4.8 
  
Table 3: Probit 
Estimates
a 
  Overall 
Diff 
seed 
-0.14 
(8.40) 
  -0.05 
(1.62) 
Diff 
consensus 
  -0.02 
(6.4) 
-0.01 
(3.09) 
 
  Round 1  Round 2  Round 3 
Diff 
seed 
-.015 
(7.64) 
  -0.06 
(1.23) 
-0.12 
(2.63) 
  0.009 
(0.166) 
-0.21 
(2.37) 
  -0.14 
(0.96) 
Diff 
consensus 
  -0.02 
(6.40) 
-0.01 
(2.25) 
  -0.04 
(4.53) 
-0.04 
(3.72) 
  -0.05 
(2.80) 
-0.02 
(0.73) 
 
  Round 4  Round 5   Round 6 
Diff 
seed 
-0.1 
(0.88) 
  0.062 
(0.030) 
NA    NA  NA    NA 
Diff 
consensus 
  -0.03 
(1.01) 
-0.04 
(0.86) 
  -0.03 
(0.93) 
    0.04 
(0.38) 
 
 
a. The number in parentheses is the t-ratio.Bibliography 
 
Boulier, B. and Stekler, H. O., (1999). Are Sports Seedings Good Predictors?: An Evaluation, 
International Journal of Forecasting, 15, 83-91. 
Carlin, B. P., (1996). Improved NCAA Basketball Tournamant Modeling via Point Spread and 
Team Strength Information, The American Statistician, 50, 39-43. 
Caudill, S. B., (2003). Predicting Discrete Outcomes with the Maximum Score Estimator: The 
Case of the NCAA Men’s Basketball Tournament, International Journal of Forecasting, 19, 
313-317. 
Clair, B. and Letscher, D., (2007). Optimal Strategies for Sports Betting Pools, Operations 
Research, 55, 1163-1177. 
Harville, D. A., (2003). The Selection or Seeding of College Basketball or Football Teams for 
Postseason Competition, Journal of the American Statistical Association, 98,17-27. 
Jacobson, S. H. and King, D.M., (2009). Seeding in the NCAA Men’s Basketball Tournament: 
When is a Higher Seed Better?,The Journal of Gambling Business and Economics, 3, 63-87.  
Kaplan, E. H. and Garska, S. J., (2001). March Madness and the Office Pool, Management 
Science, 47, 369-382.  
Kvam, P. and Sokol, S. J., (2006). A Logisitic Regression/Markov Chain Model for NCAA 
Basketball, Naval Research Logistics, 53,788-803. 
Metrick, A., (2001). March Madness? Strategic Behavior in NCAA Basketball Tournament 
Betting Pools, Journal of Economic Behavior and Organization, 30, 159-172. 
Schwertman, N. C., McCready, T. A. and Howard, L., (1991). Probability Models for the NCAA 
Regional Basketball Tournaments, The American Statistician, 45, 35-38. Schwertman, N. C., Schenk, K. L. and Holbrook, B. C., (1996). More Probability Models for the 
NCAA Regional Basketball Tournaments, The American Statistician, 50, 34-38. 
 
 
                                                 
 
End Notes 
 
i Of course, the NCAA committee is aware of the rankings of the various analysts. 
ii The actual tournament consists of only 64 teams, but a 65
th team is selected and there is a play-in game that 
eliminates one of the lower-ranked teams. 
iii The sum of the rankings of the two teams is 17 in the first round; with perfect results, the sum would be 9 in the 
next round. 
iv The consensus data were not available prior to 2003. That factor determined the years that were selected for this 
study. 
v These probits are estimated for the four rounds for which the seedings data are available and the six rounds for 
which the consensus data are available. There is an additional difference from the Boulier-Stekler procedure. They 
recursively estimated the probit models for each year while this paper calculates only a single ex post set of 
equations. 
vi The coefficients of the probits that were estimated combining the data for rounds 4-6 were not significant. 
vii As further evidence about the difficulty of forecasting the outcomes of games when the teams are similar in 
quality, we examined the first round games between teams ranked 7 and 10 and 8 and 9. The better ranked team won 
only 53% of the time. 
viii This result is not surprising because the correlation between the two variables is .85. 

A Logisitic Regression/Markov Chain Model for NCAA Basketball,

Are Sports Seedings Good Predictors?: An Evaluation,

Improved NCAA Basketball Tournamant Modeling via Point Spread and Team Strength Information,

Madness and the Office Pool,

Madness? Strategic Behavior in NCAA Basketball Tournament Betting Pools,

Optimal Strategies for Sports Betting Pools,

Predicting Discrete Outcomes with the Maximum Score Estimator: The Case of the NCAA Men’s Basketball Tournament,

Probability Models for the NCAA Regional Basketball Tournaments,

Seeding in the NCAA Men’s Basketball Tournament: When is a Higher Seed Better?,The

The Selection or Seeding of College Basketball or Football Teams for Postseason Competition,

Predicting the Outcomes of NCAA Basketball Championship Games

Predicting the Outcomes of NCAA Basketball Championship Games

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics