Follow me on twitter

Most recent entries

  • Your 2014 kPOY: Russ Smith
  • Tourney scoring up; pace down
  • Who’s the best in-game coach?
  • This was the best year in history for free-throw shooting
  • Sweet 16 log5
  • Draw trumps seeding
  • 2014 NCAA tournament log5
  • Big West log5
  • WAC log5
  • Sun Belt log5
  • Favorites


    Hoops
  • Murray State and variance
  • Play-by-play Theater: earliest disqualification
  • Predicting John Henson's free throw percentage
  • Can Derrick Williams set the three-point accuracy record?
  • Why I won't give up on Washington (or Kentucky)
  • On overvaluing road play (again)
  • One shining e-mail
  • A treatise on plus-minus
  • The preseason AP poll is great
  • Non-hoops
  • Just how crazy was the Pacquiao/Bradley decision?
  • You have no skill at betting on NFL games
  • The case for Tiger Woods
  • Replaying Isner/Mahut a million times
  • The Majerus Files
  • Rick Majerus: awesome coach
  • Majerus does the unthinkable...again
  • Let's play four
  • One day at a time
  • Monthly Archives

  • April 2014
  • March 2014
  • February 2014
  • January 2014
  • December 2013
  • November 2013
  • October 2013
  • September 2013
  • August 2013
  • July 2013
  • June 2013
  • May 2013
  • April 2013
  • March 2013
  • February 2013
  • January 2013
  • December 2012
  • November 2012
  • October 2012
  • September 2012
  • August 2012
  • July 2012
  • June 2012
  • May 2012
  • April 2012
  • March 2012
  • February 2012
  • January 2012
  • December 2011
  • November 2011
  • October 2011
  • September 2011
  • August 2011
  • July 2011
  • June 2011
  • April 2011
  • March 2011
  • February 2011
  • January 2011
  • December 2010
  • November 2010
  • October 2010
  • August 2010
  • July 2010
  • June 2010
  • May 2010
  • April 2010
  • March 2010
  • February 2010
  • January 2010
  • December 2009
  • November 2009
  • October 2009
  • July 2009
  • February 2009
  • January 2009
  • December 2008
  • November 2008
  • October 2007
  • September 2007
  • July 2007
  • June 2007
  • May 2007
  • April 2007
  • March 2007
  • February 2007
  • January 2007
  • December 2006
  • November 2006
  • October 2006
  • September 2006
  • August 2006
  • July 2006
  • June 2006
  • May 2006
  • April 2006
  • March 2006
  • February 2006
  • January 2006
  • December 2005
  • November 2005
  • October 2005
  • September 2005
  • August 2005
  • July 2005
  • June 2005
  • May 2005
  • April 2005
  • March 2005
  • February 2005
  • January 2005
  • December 2004
  • November 2004
  • October 2004
  • September 2004
  • August 2004
  • July 2004
  • June 2004
  • May 2004
  • April 2004
  • March 2004
  • February 2004
  • January 2004
  • December 2003
  • November 2003

  • RSS feed

    The missing 1-point games

    by Ken Pomeroy on Wednesday, September 25, 2013


    Here’s a histogram of the home team’s scoring margin in all conference games over the past ten seasons.

    For the most part it has the look of a normal distribution. But it’s not exactly normal. Most noticeably, there’s the lack of data at the values of 1, 0, and -1. There are many fewer one-point games than Carl Friedrich Gauss would expect (as indicated by the red line depicting the normal distribution), and there are no zero-point games. I have a theory on the lack of zero-point games, and it goes like this: There are no ties in basketball. I think that’s airtight. The lack of one-point games is slightly less-obvious, but it too is an artifact of how the game is played. There are fewer one-point games than two-point games (or three, four, five and seven-point games, for that matter).

    We can solve the problem of the missing zero-point games by looking at scoring margin at the end of regulation.

    C.F. Gauss is rolling over in his grave. Zero-point games happen a lot, at least relative to other close games. It makes some sense that zero is a popular number. If you have the ball with 30 seconds to go and the game is tied, you’ll hold for the very last shot, which if unsuccessful will result in overtime. Whereas if you trail by a small amount, you won’t take the very last shot and if you lead by a small amount, you’ll get fouled. A tie score late in the game has a high chance of going to overtime, while being up by three late in the game has a much lower probability of ending in a three-point win. There’s a lot more stuff that goes on late in a game that’s not tied.

    It’s also possible that coaches are a little too willing to settle for overtime. I’m not the only one that has wondered why there aren’t occasions where the defensive team fouls in a situation where the game is tied and the shot clock is off. I mean, by not fouling your options are getting beat on a last-second shot or going to overtime where your chances of winning are around 50 percent. There certainly have to be cases where fouling improves your chance of winning. It would be interesting to see a similar plot of data from Euroleague games, where apparently the practice of fouling in a tied game is common.

    The tie-game scenario also helps to explain the relative scarcity of one-point outcomes. The offensive team is either going to miss which lead to overtime, or they will score and the game will end. And in those cases, the possibility of a one-point possession is very low. Likewise, last-possession scenarios where a team trails by two or three are not going to feature strategies where a team will get within one point.

    There’s more interesting stuff here, too. Notice that there are many more 7-15 point wins for the home team than a normal distribution would suggest. These appear to come at the expense of 16-30 point wins for the home team. Are home teams more likely to coast at the end games than visitors? I have no evidence to support that, but there is something different about the home team’s behavior.

    Finally, here’s a plot of scoring margin in single-overtime games over the past ten seasons…

    You still see the spike of tie games and the lack of one-point games, too. The other thing is that the home team wins by an average of .35 points. Now, that’s not the best way to compute home-court advantage, but it’s not a bad estimate either. It happens to be one-tenth of the value for regulation games. Overtime is one-eighth the length of regulation games. I wouldn’t sweat the difference in those two numbers. Perhaps home-court advantage is not as big of a deal at the end of close games as conventional wisdom would have us believe.

    That concludes this episode of “Fun with Histograms”. Next time you observe a one-point game, appreciate its significance. It’s way more rare than an overtime game.