March Madness! Wanna Win?

March 14, 2012
By

(This article was first published on Graph of the Week, and kindly contributed to R-bloggers)




Description:
Winning percentage of all NCAA Men's Basketball Tournament Champions.


Analysis:
Down by one, the ball spins in his hand as he dribbles up the floor. With tennis shoes squeaking, he feints left, then right. Glancing up at the clock, he sees only five seconds left. Out of the corner of his eye, he spies a teammate break towards the basket. With a knowing glance he lobs the ball upward. The crowd, already standing, goes silent and everybody's eyes follow "the dime."  His teammate crouches like a panther and lurches upward. The ball floats into his hands while he twists his upper body, slamming it through the metal hoop with authority. Hanging onto the rim, his own roar is drowned out by the crowd. The buzzer blares and the game is over. They win!


There is nothing quite like the NCAA Basketball Tournament. The fans love it so much that they become somewhat mad, hence the name "March Madness." Their brackets marred with eraser shavings, enthusiasts the world over fret over who they think will win. In every office pool, there is 'the guy' who has 'a theory' that will guarantee him a winner.

If only that were true...

That being said, the above graph shows an interesting trend: the teams that are winning the tournament lately have lower season winning percentages than in years past. In fact, no team with fewer than three - count 'em, three - losses have won the tournament for the last eleven years:


Take a close look at the above graph. The colors which denote the decades 2000-2010 and 2010-2019 can only be seen in the bars showing three or more losses. Assuming this trend continues, then neither Syracuse (31-2) nor Kentucky (32-2) will win the 2012 tournament, as they are 'too' good. Missouri, sitting at 30-4 seems to be a strong bet, if you go along with the data presented here.

The tournament started in 1939 with only eight teams, expanding between 22 and 25 teams up through 1978. It was during this time that we saw a few undefeated teams win the title. After that, the tournament expanded greatly, taking 40 teams in 1978, 48 from 1980-1982 and finally settling on 64 since 1985 (although later editions featured 'play-in' games).

Since the expansion to 64 teams, it seems that the larger number of entrants (and thus games) has given the 'good, but not *too* good' teams a real shot to win it all with some regularity. It would be an interesting exercise to review this particular aspect (perhaps it has already been done). At any rate, March Madness is upon us. To all of those participating in some way: good luck!

Questions:
1) Will Kentucky or Syracuse break the trend (both have only 2 losses)?
2) Will the NCAA expand the tournament further?
3) Based on this story's angle, the author thinks Missouri will win - will they?


Data:
http://www.hoopstournamement.net/


Code:
This graph was generated using the 'ggplot2' package within the R programming language:
ggplot(hoops.champions.frame, aes(x=Year, y=(Season.Wins/(Season.Wins+Season.Losses)), xmin=Year, xmax=Year+0.5, ymin = 0, ymax=(Season.Wins/(Season.Wins+Season.Losses)))) +
  
 geom_rect(aes(NULL, NULL, xmin=2010, xmax=2019, fill="2010-2019"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=2000, xmax=2009, fill="2000-2009"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1990, xmax=1999, fill="1990-1999"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1980, xmax=1989, fill="1980-1989"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1970, xmax=1979, fill="1970-1979"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1960, xmax=1969, fill="1960-1969"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1950, xmax=1959, fill="1950-1959"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1940, xmax=1949, fill="1940-1949"), alpha=.01) +
 geom_rect(aes(NULL, NULL, xmin=1930, xmax=1939, fill="1930-1939"), alpha=.01) +
  
 geom_rect(fill="black") +
 geom_smooth(size=1.1, method="lm", na.rm=FALSE) +
  
 ylab("Regular Season Winning Percentage") +
 xlab("Year") +
  
 opts(title="Wanna win March Madness?  Be Good, But Not *Too* Good",
   legend.title = theme_blank(),
   panel.background = theme_blank(),
   panel.grid.minor=theme_blank(),
   panel.grid.major=theme_blank())

Further Reading (the following all have at least 3 stars or are unrated):

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