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Sports by the Numbers

Category: NCAA Men’s Basketball

Shot Clock Effects Redux

Posted on January 24, 2017January 24, 2017 by Peter Lemieux

Last year I posted two items concerning the effects of the change to a thirty-second shot clock in NCAA mens’ college basketball.  I found that total scoring had increased by nearly twelve points per game between the 2014-2015 season and the 2015-2016 season after the shot-clock rule was changed.  However the margin of victory was unaffected.  An equally dramatic effect was seen for three-point shooting.  Teams were hoisting nearly two more three-point shots per game, probably because the shorter clock meant more “desperation” threes were being taken.  However I found no change in the accuracy of three-point shooting after the clock was shortened.

Scoring in the current 2016-2017 season differs hardly at all from last season.  All three measures show insignificant gains compared to last year.

This table extends the results for three-point shooting to include all games played though January 20th of this year.

Three-point attempts have continued to rise in the 2016-2017 season, but we also see an improvement in three-point accuracy.  Teams are shooting three more three-pointers every four games than they did last season, and their accuracy has improved by about half a percentage point.

This change might represent improvements in players’ abilities over time, or a conscious decision by coaches to recruit better three-point shooters out of high schools.  However it may also simply be random fluctuation.  If we go back to the data for 2008-2009, the earliest year available at the NCAA’s site, accuracy was 34.7 percent, hardly different from this year’s figure.  Attempts in 2008-2009 were still significantly lower at 18.9 per game.

Posted in NCAA Men's Basketball

Bracketology 2016: Predicted Seedings

Posted on February 24, 2016February 24, 2016 by Peter Lemieux

Last year I published a simple model of NCAA Men’s Tournament seedings based on RPI and conference membership.  To recap, higher RPI teams received better seedings, and teams representing major and “mid-major” conferences got better seeds than teams from the other conferences even if they had identical RPI scores.  In principle we should see no differences between conferences once RPI is taken into account because the measure relies heavily of a team’s strength of schedule.  Teams in stronger conferences should have higher RPI scores because they face a more difficult schedule.

In practice, though, the NCAA Selection Committee clearly prefers teams from major and mid-major conferences and fails to give teams from other conferences a fair shake when it comes to seedings as this chart shows:

seedings

A team with an RPI of 0.600 from a “single-bid” conference like the Colonial or the Ivy League is predicted to be seeded tenth or eleventh, while schools with identical RPI figures from the mid-major and major conferences would receive a six or a seven seed.  The advantage for both those conferences over single-bid schools grows as RPI increases, as does the advantage for major-conference teams over mid-majors.

We can use the model I estimated that underpins this chart to estimate how teams will be seeded in 2016 based on their current RPI scores.  Using RPI figures from CBS Sports through Sunday, February 21st, gives us the following predictions for the 36 teams that will make up the at-large field in this year’s Tournament:seeding-model-simulationBoth Louisville and SMU are ineligible for Tournament play in 2016, so Seton Hall and Wisconsin have a chance to slip in at the bottom of the rankings.

Posted in NCAA Men's Basketball

Effects of the Shot-Clock Change on Three-Point Shooting

Posted on January 26, 2016February 23, 2016 by Peter Lemieux

The newly-accelerated speed of play in NCAA Men’s College Basketball may have had some side effects other than a simple increase in tempo and higher scores.  The faster pace may make teams change the way the play the game itself.  One place we might see such a change is in three-point shooting.  Teams often resort to hoisting a “desperation three” if their half-court offense has bogged down and the horn on the shot clock is about to sound.

I’ve compiled the statistics for three-point attempts and three-point shooting percentage for the complete 2013-2014 and 2014-2015 seasons from the NCAA’s archive. This season’s figures represent those same data through games of January 25, 2016.  Including 2013-2014 enables us to compare any change this season to “normal” seasonal change before the shot clock was shortened. Here are the results for three-point attempts:

shot-clock-3pt-multi

With the shorter clock, teams have been averaging a smidgen over twenty three-point attempts per game this season, about one and a half more than in 2014-2015.  Three-point attempts grew between 2015 and 2014 as well, but the rise in 2016 is some 3.5 times greater than the increase between 2015 and 2014.  Even if we deduct the 0.42 growth in attempts between 2014 and 2015 from this year’s total, that still leaves an additional 1.5 three-point attempts per game since the clock was shortened.  “Desperation” three-point shots probably account for a lot of this growth.

shot-clock-3ptpc

All these extra three-point shots have not affected accuracy. Teams shot 34.3 percent from outside the arc in 2014-15 and are shooting a statistically identical 34.6 percent now.  More striking is the sharp decline from the rate of 36.1 percent in 2013-2014.  While three-point accuracy rebounded slightly this season, it still remains statistically below 2013-2014.

 

 

 

 

Posted in NCAA Men's Basketball

Effects of the Shot-Clock Change in Men’s College Basketball

Posted on January 25, 2016February 23, 2016 by Peter Lemieux

Most basketball teams play with a “shot clock” that limits the amount of time that either team can spend holding the ball.  In professional men’s basketball the clock runs for 24 seconds.  Both professional and collegiate women use a 30-second clock.

Until this season collegiate men had the luxury of a 35-second clock, considerably longer than that used in the professional ranks to which many of these players aspire.  Now the men have joined their female peers and play on a 30-second clock.  Has the faster pace of play affected scoring and, if so, how?

shot-clock-scoring

These figures come from games played during two equivalent weekends in 2016 and 2015.  Most teams were playing conference opponents so the level of competition is roughly the same. This year’s large snowfall in the Mid-Atlantic states produced a few cancellations so the number of games is slightly smaller for 2016.

Scoring has increased nearly twelve points per game this year.  Winners score about 6.5 points more per game in 2016, while losers score an additional 5.0 points. All of these differences are well beyond standard criteria for “statistical significance.”

The margin of victory also grew by 1.5 points, but that difference doesn’t pass statistical muster. There is no statistical evidence that the faster clock has increased the margin of victory.

Reducing the clock from 35 to 30 seconds constitutes a 14 percent reduction (5/35) in time of possession.  Scoring, on the other hand, has increased by only 8.6 percent in response (11.5/133.8).

The shorter shot clock has increased the pace of play as well.  Using the enormous archives of collegiate basketball statistics available to subscribers at Ken Pomeroy’s kenpom.com, I averaged his measures of “tempo” and “efficiency” for the 351 Division I teams in his database.  These figures are based on his estimates of the number of possessions per game using a formula explained here.  I compared the entire season figure for 2015 with those for games played through Sunday, January 24th of 2016.

shot-clock-pomeroy

“Tempo,” the number of possessions per forty-minute game, has increased drastically since 2015, rising well over four per game.  That alone might account for the increase in scoring, but it is not the only factor.  Teams are also scoring about one point more per hundred possessions this year than last.  So not only do teams have more possessions with a shorter clock, the faster pace appears to make those possessions slightly more productive as well.

Obviously this change will wreak havoc on historical comparisons to the 35-second era.  Identically-skilled players in 2016 should be scoring on average about nine percent more compared to the men who played in years past.

 

 

Posted in NCAA Men's Basketball

Them That’s Got Shall Get: Seedings for March Madness

Posted on March 10, 2015March 13, 2015 by Peter Lemieux

In just a few weeks time the Selection Committee for the 2015 Division I Men’s Basketball Tournament, better known as “March Madness,” will be inviting sixty-eight teams to fill a field of sixty-four.  (Eight of the teams play off for four of the sixty-four seedings.)  These seedings matter greatly over the three weeks of the Tournament.  Top seeds win on average four out of five games they play.  Teams seeded seventh win half their games, while teams seeded twelfth win about two out of every five.

Most college basketball fans know that the NCAA considers something called the “RPI,” or “Ratings Performance Index,” as a measure of each team’s strength.  The Selection Committee uses RPI to help decide on at-large bids and seedings.

The RPI adjusts each team’s won-loss record by its “strength of schedule,” the won-loss record of its opponents.  The NCAA also adjusts for the won-loss record of those opponents’ opponents.  The team’s own performance gets only a 25% weight in the RPI.  Its opponents’ record counts 50%, and their opponents records count 25%. These weightings make strength of schedule the primary determinant of RPI.

In principle these adjustments should make RPI a neutral measure of team strength and remove the effects of conference affiliations. Teams playing in “major” conferences like the ACC or Big 12 have higher RPI scores because they play a tougher schedule.  In a world where seedings depended only a team’s innate abilities, it shouldn’t matter which conference that team plays in. The historical data summarized in this chart says otherwise.

seedings

The Selection Committee awards better seedings to teams playing in the major conferences than it awards to schools with identical RPI scores from weaker conferences. In the chart I’ve shown the relationship between seeding and RPI for teams grouped by their type of conference.  At the top are the six “major” conferences — the ACC, Big East, Big 10, Big 12, Pac 12, and SEC.  Next come the eight so-called “mid-major” conferences — Atlantic 10, Colonial Athletic, Conference USA, Horizon League, Missouri Valley, Mountain West, Western Athletic, and West Coast conferences.  The Selection Committee routinely grants multiple Tournament bids to members of both these types of conferences.

The eighteen remaining conferences receive only a single Tournament invitation, the one extended to each conference’s champion.  This policy forever limits teams in these conferences to also-ran status.  Take a team with an RPI of 0.600.  If that school plays for a team in a single-bid conference, the Committee is likely to seed that team eleventh (10.7 according to the model).  Put that same team in a mid-major conference, and it would be awarded an eight seed (7.8).  Playing in a major conference would earn that team a seven (7.1). Both the advantage the majors have over the mid-majors, and the advantage they both have over single-bid schools, widens with RPI.

 

Posted in NCAA Men's Basketball

Technical Appendix: Estimating Seedings from RPI

Posted on February 26, 2015September 9, 2015 by Peter Lemieux

Method using program averages for teams with at least two appearances
seeding-model-estimates

Ordinary Least Squares applied to 832 team appearances (64 teams x 13 years):

Model 6: OLS, Appearances, 2002-2014 (832 observations)
Dependent variable: seed

             coefficient   std. error   t-ratio   p-value 
  --------------------------------------------------------
  const        36.7650      1.86680      19.69    4.38e-71 ***
  midmaj       29.1555      2.97857       9.788   1.76e-21 ***
  power        29.6810      2.63332      11.27    1.65e-27 ***
  rpi         −42.1049      3.45923     −12.17    1.82e-31 ***
  rpimid      −53.8989      5.23069     −10.30    1.66e-23 ***
  rpipower    −57.5874      4.60477     −12.51    5.46e-33 ***

Mean dependent var   8.500000   S.D. dependent var   4.612545
Sum squared resid    2389.298   S.E. of regression   1.700768
R-squared            0.864859   Adjusted R-squared   0.864041
F(5, 826)            1057.224   P-value(F)           0.000000
Log-likelihood      −1619.405   Akaike criterion     3250.809
Schwarz criterion    3279.152   Hannan-Quinn         3261.677

 

OLS does not have any special methods to handle “censored” information like seedings.  The coefficients above predict seeds below one and above sixteen.  A better alternative is Tobit with censors at one and sixteen.  This model (with some minor adjustments to the intercept differences) generates the graph in the article.

Tobit, 2002-2014 (n = 831)
Dependent variable: seed

             coefficient   std. error      z      p-value 
  --------------------------------------------------------
  const        49.1581      2.54088      19.35    2.16e-83 ***
  midmaj       18.8101      3.59081       5.238   1.62e-07 ***
  power        25.0724      3.32994       7.529   5.10e-14 ***
  rpi         −64.1098      4.64080     −13.81    2.09e-43 ***
  rpimid      −35.3690      6.31863      −5.598   2.17e-08 ***
  rpipower    −48.6491      5.83366      −8.339   7.47e-17 ***

Chi-square(5)        4401.971   p-value              0.000000
Log-likelihood      −1517.352   Akaike criterion     3048.703
Schwarz criterion    3081.762   Hannan-Quinn         3061.380

sigma = 1.79472 (0.0469158)
Left-censored observations: 52 (seed <= 1) 
Right-censored observations: 51 (seed >= 16)

Estimates from this model show a greater difference between the majors and mid-majors than do the OLS estimates.

 

 

Posted in NCAA Men's Basketball, Technical Notes

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