# NCAA Tournament Scores and Rules/Format Changes

Application Project Proposal
Natalie Larson, Ryan Steier, Scott Yeskie
Math 216
3-24-2012

NCAA Tournament Scores and Rules/Format Changes

In the 1985-1986 season the NCAA introduced the shot clock, a timer designed to increase the pace of the game. The rules of the shot clock work like this: before the time on the clock expires the ball must leave the hands of a player on the offensive team, and must either make a basket or hit the rim, otherwise possession will be turned over to the defensive team.  If the ball hits the rim, the shot clock resets and the offensive team has another 35 seconds before having to shoot again.  The shot clock will also reset if the team scores a basket, in which case possession of the ball is turned over to the other team.  If the clock runs out, the game is stopped and possession is given to the defensive team.  The shot clock was originally implemented in the men’s NCAA tournament with a 45-second time limit, but changed to 35 seconds in the 1993-1994 season.

We hypothesize that NCAA tournament scores increased as a result of the introduction of the shot clock, since teams can no longer hold the ball for more than the allotted time without attempting to score points.  Our null hypothesis is that the shot clock did not change NCAA tournament scores, and our alternative hypothesis is that the shot clock increased tournament scores.  After examining the data if we observe that scores increased by a certain percentage after the addition of the shot clock we might also test a secondary hypothesis based on the specific amount of score increase and determine a 95% confidence interval for that increase.  We plan to create at least one infographic displaying winning scores and losing scores over time (before and after the introduction of the shot clock).

In addition to the above study, we would like to undertake an examination of the effect that increasing the number of teams playing in the NCAA tournament has had on NCAA tournament scores.  From 1939 to 2011 the number of teams in the NCAA tournament increased from 8 to 68.  We hypothesize that as more teams were added to the tournament the winning margin became more variable.  Our null hypothesis is that the addition of more teams to the tournament did not change the variability of the winning margin, and our alternative hypothesis is that the addition of teams to the tournament increased the variability of of the winning margin.  We plan to create a linear regression of variance in winning score margin from 1939 to 1995, the span of our dataset, but will also look at variance over the specific time intervals over which teams were incrementally added.  A simple infographic for this data would be a plot showing score variance over time, with markers indicating the number of teams in the tournament at various points in the timeline.

Our initial dataset comes from the American Statistical Association website and is easily imported into R (we have already done this).  It contains the year, winning score, losing score, and school names in each game for all NCAA tournament games over the years 1939-1995.  Since this data ends at 1995, we might try to find other sources that could extend the data by several years or into the present.  This would be particularly useful for examining the effect that the change from a 45 to 35 second shot clock, made in the 1993-1994 season, had on tournament scores.

References:

Journal of Statistics Education, American Statistical Association.  Larry Winner, Department of Statistics, University of Florida. (1998). Basketball.dat [Data file].  Retrieved from http://www.amstat.org/publications/jse/datasets/basketball.dat .

Journal of Statistics Education.  Larry Winner, Department of Statistics, University of Florida. (1998). Basketball.txt [Description].  Retrieved from